Chemical engineering education

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Title:
Chemical engineering education
Alternate Title:
CEE
Abbreviated Title:
Chem. eng. educ.
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v. : ill. ; 22-28 cm.
Language:
English
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American Society for Engineering Education -- Chemical Engineering Division
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Chemical Engineering Division, American Society for Engineering Education
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Frequency:
quarterly[1962-]
annual[ former 1960-1961]

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Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )

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Chemical abstracts
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Also issued online.
Dates or Sequential Designation:
1960-June 1964 ; v. 1, no. 1 (Oct. 1965)-
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Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
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Title from cover.
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Place of publication varies: Rochester, N.Y., 1965-1967; Gainesville, Fla., 1968-

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issn - 0009-2479
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ddc - 660/.2/071
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Full Text











Chemical engineering education




VOLUME 36 NUMBER 4 FALL 2002





t GRADUATE EDUCATION...

A Novel Approach for
Describing Micromixing Effects in Homogeneous Reactors (pg. 250)
V'emuri Balakotatah, Saikat Chakrabortv

SIntroducing Moleculr Biology to Environmental Engineers
t Through Development of a New Course Ipg. 258)
o Daniel B. Oerther


Articles of General Interest...

SChem-E-Car Downunder (pg. 288)
Rhodes
On Improving "Thought with Hands," ipg.292)
S. Sureshkunuar, Khilar
( h Making Phase Equilibrium More User-Friendly (pg. 284)
"So Misovich
W Random Thoughts: Speaking of Education-llI (pg. 282)
|Felder
E No\el Concepts for Teaching Particle Technology Ipg. 272.)
Peukeri, Schmid
Portfolio Assessment in Introductory ChE Courses (pg. 310)
A Baliai
l New Approach to Teaching Turbulent Thermal Convection tpg. 2641
SChurchill
,, Determining the Flow Characteristics of a Power Law Liquid (pg. 304)
S a Hillier, Ting. Kopplin, Koch, Gupta
The Earth's Carbon Cycle: Chemical Engineering Course Material (pg. 296)
5 Schmitz
Aspects of Engineering Practice: Examining Value and Behaviors in Organizations (pg.316)
Espino
Gas Station Pricing Game: A Lesson in Engineering Economics and Business Strategies (pg. 278)
Sin, Cenier
















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Chemical Engineering Education


Volume 36


Number 4


Fall 2002


GRADUATE EDUCATION
250 A Novel Approach for Describing Micromixing Effects in Homoge-
neous Reactors,
Vemuri Balakotaiah, Saikat Chakraborty
258 Introducing Moleculr Biology to Environmental Engineers Through
Development of a New Course,
Daniel B. Oerther

> CLASSROOM
264 A New Approach to Teaching Turbulent Thermal Convection,
Stuart W Churchill
278 Gas Station Pricing Game: A Lesson in Engineering Economics and
Business Strategies,
Aaron Sin, Alfred M. Center
284 Making Phase Equilibrium More User-Friendly,
Michael J. Misovich

> CURRICULUM
272 Novel Concepts for Teaching Particle Technology,
Wolfgang Peukert, Hans-Joachim Schmid
296 The Earth's Carbon Cycle: Chemical Engineering Course Material,
Roger A. Schmitz
316 Aspects of Engineering Practice: Examining Value and Behaviors in
Organizations,
Ramon L. Espino

RANDOM THOUGHTS
282 Speaking of Education-III,
Richard M. Felder

> LABORATORY
288 Chem-E-Car Downunder,
Martin Rhodes
292 On Improving "Thought with Hands,"
G.K. Sureshkumar K.C. Khilar
304 Determining the Flow Characteristics of a Power Law Liquid,
James R. Hillier, Dale Ting, Lisa L. Kopplin, Margaret Koch,
Santosh K. Gupta

> ASSESSMENT
310 Portfolio Assessment in Introductory ChE Courses, Surita R. Bhatia

257, 263, 270 Letter to the Editor
281 Announcements
320 Index for Graduate Education Advertisements

CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the Chemical Engineering
Division, American Society for Engineering Education, and is edited at the University of Florida. Correspondence
regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical Engineering Department,
University of Florida, Gainesville, FL 32611-6005. Copyright 2002 by the Chemical Engineering Division, American
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necessarily those of the ChE Division, ASEE, which body assumes no responsibility for them. Defective copies replaced if
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POSTMASTER: Send address changes to Chemical Engineering Education, Chemical Engineering Department., University
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Fall 2002










SGraduate Education


A Novel Approach for Describing

MICROMIXING EFFECTS IN

HOMOGENEOUS REACTORS



VEMURI BALAKOTAIAH, SAIKAT CHAKRABORTY
University of Houston Houston, TX 77204-4004


Reacting flow systems are hierarchical in nature, i.e.,
they are characterized by multiple length (or time)
scales. Scale separation exists in most reactors, how-
ever, and these disparate scales are typically characterized
by three representative ones, namely, micro (molecular), meso
(catalyst particle or tube diameter), and macro (reactor or pro-
cess) scales. In most cases of practical interest, a strong non-
linear coupling exists between reaction and transport at micro
and meso scales, and the reactor performance at the macro scale.
As a result, transport limitations at the smaller scales signifi-
cantly influence the reactor and hence the process performance.
Such effects could be quantified by numerically solving
the convection-diffusion-reaction (CDR) equation from the
macro down to the micro scale. But the solution of the CDR
equation from the reactor (macro) scale down to the local
diffusional (micro) scale, using computational fluid dynam-
ics (CFD), is prohibitive in terms of numerical effort and im-
practical for the purpose of reactor control and optimization.
Moreover, even with today's computational power, it is im-
practical to explore the different types of bifurcation features
and spatio-temporal behaviors that exist in the multidimen-
sional parameter space, using CFD codes. In such cases, low
dimensional models are a natural alternative.
Historically, chemical engineers have derived low dimen-
sional models for reactors using a top-down approach, which
is based on a priori assumptions on the length and time scales
of convection, diffusion, and reaction. The classical ideal re-
actor (CSTR and PFR) models are examples of such low-
dimensional models obtained on the basis of simplified (or
oversimplified) assumptions. These assumptions are usually
not justified since justification requires comparison of the
solution obtained from the simplified models with that ob-
tained from the CDR model.
In order to account for experimental observations that could
not be explained by these ideal reactor models, the latter have
been modified by introducing the concepts of dispersion co-


efficientsE"5] and residence time distribution3,6'71 to account
for macro- and micro-mixing effects. Several other reactive
mixing models followed in the next forty years: the two- and
three-environment model,[89' the coalescence-redispersion
model,"101 interaction by exchange with mean model,["" en-
gulfment-deformation-diffusion model,'12' and CFD models
using probability density functions (PDF) and direct numeri-
cal simulation (DNS).
This article presents an alternative (bottom-up) approach
and an elementary treatment of mixing effects on reactor per-
formance. We will present a brief historical review of homo-
geneous reactor models before discussing this new approach.

BRIEF HISTORY OF
HOMOGENEOUS REACTOR MODELS
The most widely used homogeneous reactor models are
the three classical ideal reactor models: the plug-flow reactor
(PFR) model, the continuous stirred tank reactor (CSTR)
model, and the batch reactor (BR) model. While the BR model
and the PFR model (which are identical for constant density
systems with time replaced by space time or dimensionless
distance along the tube) have existed since the late eighteenth
century. A conceptual leap came in the form of the CSTR
model through the work of Bodenstein and Wohlgast in
1908.[131 Unlike the PFR model, which assumes no gradients
in the radial direction and no mixing in the axial direction,

Vemuri Balakotaiah is Professor of Chemical Engineering at the Uni-
versity of Houston. He received his BTech from the Indian Institute of
Technology (Madras) in 1978 and his PhD from the University of Hous-
ton in 1982, both in chemical engineering. His teaching and research
interests are in the areas of chemical reaction engineering, multiphase
flows, and applied mathematics.
Saikat Chakraborty is a PhD candidate in the Department of Chemical
Engineering at the University of Houston. He received his BTech from
Jadavpur University in 1997 and his MS from the Indian Institute of Sci-
ence (Bangalore) in 1999, both in chemical engineering. His research
interests are in the areas of chemical reaction engineering and granular
materials.
Copyright ChE Division of ASEE 2002


Chemical Engineering Education










Graduate Education ]


the CSTR model assumes complete mixing at all scales. For
constant density systems, the three classical reactor models
are described by
PFR

(u)C) -R((C)) with (C) = Ci @ x = 0 (1)
dx
BR

d(C)
d = -R((C)) with (C)= Cin @ t = 0 (2)
dt
CSTR

(C) -R((C)) (3)
Tc
where (C) is the spatially (or cross-sectional) averaged reac-
tant concentration, Cln is the mean inlet concentration of the
reactant, R((C)) is the sink term due to the presence of ho-
mogeneous reaction, x is the coordinate along the length of
the PFR, (u) is the mean fluid velocity in the reactor, t is the
time, and Tc is the total residence time in the reactor.
Irving Langmuirt" first replaced the assumption of no axial
mixing of the PFR model with finite axial mixing and the
accompanying Dirichlet boundary condition ((C) = Cn @ x
= 0) by a flux-type boundary condition

Dm d( =(u)(C)-Cin] @ x=0 (4)
dx
where Dm is the molecular diffusivity of the species. The above
boundary condition was rediscovered several times in the
years that followed: first by Forster and Geibl61, which was
quoted and applied by Damk6hler,[12 and then, later, by
Danckwerts.13] Since then it has been known as the
"Danckwerts" boundary condition. In his paper, Langmuir
dealt with both the limiting cases of "mixing nearly com-
plete" and "only slight mixing."
Thirty years later, Gerhard Damk6hler in his historic pa-
per, summarized various reactor models and formulated the
two-dimensional CDR model for tubular reactors in complete
generality, allowing for finite mixing both in the radial and
the axial directions. In his paper, Damk6hler used the flux-
type boundary condition at the inlet and also replaced the
assumption of plug flow with parabolic velocity profile, which
is typical of laminar flow in tubes.
Forster and Geib first introduced the concept of residence
time distribution (RTD) to study the case of longitudinal dis-
persion in tubes. Twenty years later, Danckwerts, in his much
celebrated paper,131 devised a generalized treatment of RTD
and introduced the concepts of holdbackk" and "segregation."
Following this, it was Zweitering,[7' who quantified the de-
grees of mixing with the ideas of "complete segregation" and


"maximum mixedness" and brought forth the concept of
micromixing, or mixing at the molecular scale in homoge-
neous reactions.
In the last forty years, a wide range of micromixing mod-
els for homogeneous reactors have been formulated. While
most of these low-dimensional mixing models are phenom-
enological in nature, the rigorously derived CFD models are
high-dimensional and therefore numerically very expensive,
especially for the case of multiple reactions with fast/non-
isothermal kinetics. As a result, in spite of the simplifying
assumptions present, the century-old ideal classical reactor
models (Eqs. 1-3) are still the most popular choices among
chemical engineering practitioners (and teachers). The clas-
sical ideal reactor models, which are easy-to-solve ordinary
differential or algebraic equations with no adjustable param-
eter, are particularly preferred over the full CDR models
(which are partial differential equations in more than one di-
mension) in case of multiple reactions with complex kinetics.

SPATIAL AVERAGING OF
CONVECTION-DIFFUSION-REACTION
EQUATION
The main goal of this article is to illustrate a new approach
for deriving low-dimensional homogeneous reactor models,
capable of predicting mixing effects. These models are de-
rived through rigorous spatial averaging of the three-dimen-
sional CDR equations over local length scales by using the
Liapunov-Schmidt (L-S) technique of classical bifurcation
theory. We illustrate this spatial averaging technique using
the simple case of laminar flow in a tube with homogeneous
reaction. The scalar concentration C(r, 0, x,t') in a tubular
reactor is assumed to obey the CDR equation

oC /C
C + u(r)- C=
I t DxC I +-BC- D1
SD D r -+ l D D + D -R(C) (5)
r Lr ar r 2- ae d9 ) ax ( ax)

with accompanying initial and boundary conditions, given by

aC
C(r,6,x,t'=0)=Co =0 @ r=a
Dr
C(r,0, x,t')= C(r,0 + 27,x,t')
Dc
Dx-C =u(r)[C(r,9,x,t')-Cin @ x=0
ax


-=0 @ x=L
ax


where D and Dx are the transverse and axial diffusivities,
respectively; r,O,x are the radial, azimuthal, and axial coor-


Fall 2002










Graduate Education


dinates, respectively; and u(r) is the fluid velocity profile.
We take a (radius of the pipe) and L (length of the pipe) to be
the characteristic lengths in the radial and axial directions,
respectively; (u) is the cross-sectional average velocity; and
CR is a reference concentration. Then, we obtain four time-
scales in the system associated with convection ( C), radial
diffusion (tD), axial diffusion (t), and reaction (tR)


a2 L2
tD tx =
Dl Dx


SL CR
tC=- tR-(CR)
(u)' R(CR)


(7)


and the ratios of these time scales give rise to the dimension-
less parameters: p (transverse Peclet number), Pe (axial Peclet
number), Da (Damk6hler number), and 02 (local Damkohler
number), given by


a2(u) tD
LD TC


P(u)L tx
Pe= c
Dx TC


Da LR(CR) tC
(u)CR tR


a2R(CR) tDpDa
DxCR tR
In dimensionless form, Eq. (5) for the case of constant spe-
cies diffusivities, can be rearranged as

V2c aC c 1 (a2c)


p 2 +u()C-+Da^(c) pg(c) (8)
Pt Pe az2 az =
1 -^ ^( w-r\ ~+

^-^^-(^ "M^*'


sion time is small but finite compared to convection, reac-
tion, and axial diffusion time, local (transverse) gradients re-
main small and we can write
c( e,0,z,t)= (c)(z,t)+ c'(,O,z,t) (11)
where (c) is the transverse averaged concentration and c' is
the fluctuation about this average, and c' ---> 0 as p -> 0.
(Also, by definition (c')= 0.) Multiplying Eq. (11) by the
local velocity profile, u(4) = (u) + u', and averaging over the
cross-section gives
c = (c) + (u'c') (12)
where cm is the mixing-cup (velocity weighted) concentra-
tion. Similarly, transverse averaging of Eq. (8) over the cross-
section gives
/=1 \=27t
a(c) 1 a2(c) ac 8
(C) 1 +Da 1 (c)dJd4=0 (13)
at Pe az2 z
5=0 9=0
For the case of a tubular reactor, the spatial (transverse) aver-
age and mixing-cup concentrations are defined by


=1 0=2n
f I c(,6,x,t)d0d
S() =0 =0
S =1 0=2n
S0f d6d=
=0 0=0


with initial and boundary conditions being

c(,0,z,t=0)=co =0 @ i=1
ac(,zt)=c(
c(4,0,z,t)= c(,0 + 2t, z,t)


1 ac
Sa u(4)[c Cin] @z=0
Pe az


0@ z=l
az


where

t' r x u
t=- t = z=- u=
TC a L (u)
C R(C)
c= C (c) = (10)
CR R(CR)
The form of the CDR equation (Eq. 8) clearly illustrates that
a scale separation exists in the system, with p being the ratio
of the local to the global scale (when Pe and Da are of order
unity), and spatial averaging over the local scales is possible.
It can be seen from Eqs. (8) and (9) that in the limit of
p-> 0, V2c 0 and transverse (or small scale) concentra-
tion gradients vanish, in which case the equations simplify to
the classical one-mode axial dispersion model. If local diffu-


t=1 0=27n
f f i u(i)c(4,0,x,t)d6d(
cm- =1 0=2 (15)
f f u(i)dOd4
=0 0=0
It may be noted that in all flow reactors, cm is the experimen-
tally measured variable. We refer to (c) and cm as the two
modes of the system and our spatially averaged reactor mod-
els as Two-Mode Models (TMMs). Equation 13 is called the
global equation, while Eq. (12) is called the local equation.
The local equation shows that the difference between cm and
(c) depends on the local velocity gradients (u') and the local
concentration gradients (c') caused by molecular diffusion
and reaction at the local scales. Micromixing is captured by
the local equation as an exchange between the two modes
(scales), cm and (c).
In order to determine c' (and hence the term (u'c') or the
difference between cm and (c)), we substitute Eq. (11) in Eq
(8) to obtain
Vic'=pg((c)+c') (16)


Chemical Engineering Education










Graduate Education


The L-S technique solves Eq. (16) for c' by expanding it in
the parameter p as

c,'= pici (17)
i=1
and by using the Fredholm Alternative (i.e., the fact c' lies
in the function space orthogonal to which (c) resides). Such
an expansion (Eq. 17) is possible, since for p = 0, the trans-
verse diffusion operator in Eq. (8) has a zero eigenvalue with
a constant eigenfunction. Thus, (u'c') could be determined
to any order in p, i.e., closure of the local equation could be
accomplished to any desired accuracy. In practice, the lead-
ing term (that is of order p) is sufficient to retain all the quali-
tative features of the full CDR equation. For example, for the
case of azimuthally symmetric feeding, we have

eC -p -(c)L + +02) (18)
ac z L12 4 8 ]Op (18)
Substituting Eq. (18) into Eqs. (12) and (13) gives the two-
mode model to O(p) as

a(c) +acm a2(c) O
a + a) + Da r((c)) + O(2) 0 (19)
at az Pe az2

(c)- Cm = P + 0(p2)

= ,pip m + o(p2) (20)
az
with boundary and initial conditions given by

1 atc)
= cm Cmin @ z= 0 (21)
Pe az m
am 0 @ z=1 (22)
az
(c)= (c) @ t=0 (23)

where 1 / pi is called the exchange coefficient, which depends
on the local shear rates. For the case of fully developed lami-
nar flows, DL = Dx = Dm (molecular diffusivity of the spe-
cies), and P3 =1/48. We refer to this model as the two-mode
axial dispersion model. (Further details of the spatial averag-
ing procedure using the L-S technique can be found in
Chakraborty and Balakotaiah.l'4.'5')
It should be noted that the spatially averaged CDR equa-
tion (Eqs. 19 and 20) retains all the parameters (p, Pe, Da) of
the three-dimensional CDR equation (Eq. 8) and hence all
the qualitative features of the latter. It should also be men-
tioned that this model is capable of capturing macromixing
effects through the axial Peclet number Pe in the global equa-
tion (Eq. 19), as well as micromixing effects through the ex-
change coefficient Pi1 and transverse Peclet number p in the


local equation (Eq. 20). In fact, the L-S technique guarantees
that the solution of the averaged model (Eqs. 19-23) agrees
with the exact solution of the three-dimensional CDR equation
to O(p). [Three decimal accuracy is obtained for a second-or-
der reaction for the case of Pe -o if 02 < 1 (see ref. 14).]
Using the spatial averaging technique illustrated above,
accurate low-dimensional models could be obtained for dif-
ferent types of reactors and flow profiles. For example, the
two-mode model for a tubular reactor with fully developed
turbulent flow is the same as Eqs (19) through (23), where
D_ is the effective turbulent diffusivity and PI is a function
of Reynolds number (Re) and friction factor f. This model is
obtained by starting with the time-smoothed (Reynolds aver-
aged) CDR equation, where the reaction rate R(C) in Eq. (5)
is replaced by the Reynolds averaged reaction rate (after clo-
sure) R,(C). Spatial averaging by the L-S technique is then
performed on the time-averaged CDR equation (i.e., spatial
averaging follows time averaging) to obtain the two-mode model
(see ref. 15 for details). In the next section, we will present the
two-mode models for other types of homogeneous reactors.

TWO-MODE MODELS
FOR HOMOGENEOUS REACTORS

Tubular Reactors

The steady-state two-mode model for a tubular reactor for
the case of Pe o (i.e., no macromixing present) may be
obtained from Eqs. (19) through (21). In dimensional form,
it is given by

(u) d -R((C)) with Cm(x = 0)= C,in (24)
dx

Cm (C) = -tix (u) dC = txR((C)) (25)

where the local mixing time tmix (in the local Eq. 25 describ-
ing micromixing effects) is given by
2
tmix = Pi a (26)
D
where a is the local diffusional length scale over which spa-
tial averaging is performed, DI is the local diffusion coeffi-
cient, and P1l is the exchange coefficient. In the limit of com-
plete micromixing (i.e., tmix -- 0), the two-mode convection
model reduces to the ideal one-mode zero-parameter PFR model.

Loop and Recycle Reactors
In a loop reactor of length L, a flow rate of q,, and with an
average velocity of (Uin), enters and leaves the reactor at
points x = 0 and x = /, respectively (where x is the length
coordinate along the loop). The total flow rate in the loop is
Q + q between points x = 0 and x = 1, and is Q between


Fall 2002










Gmdwate Edke~gagion


points x = 1 and x = L, due to a recycle rate of Q. The recycle
ratio A is the ratio of the volume of fluid returned to the
reactor entrance per unit time to the volume of fluid leaving
the system per unit time, and is given by A = Q/qin. The two-
mode model for such a loop reactor can be obtained as


x I- R((C))
dx R((C))


0
l~xL


Cm -(C) = tmiR((C)) 0 x
with boundary conditions

Cm(x = 0)= Cmin+ACm(=L)
I+A

(C)(x = = (C)(x=/+) (29)

For the special case when no reaction occurs between x = 1
and x = L, i.e., Cm(x=l) = Cm(x=L), the loop reactor reduces
to a recycle reactor of length 1, the two-mode model for which
is given by


(uin)dCm 1 R((C))
dx 1+A

with Cm(x0)=Cmin +A (x (30)
I+A

Cm -(C)= tmixR((C)) 0
The two-mode loop and recycle reactor models, like the
two-mode axial dispersion model, are two-parameter two-
mode models. Here, the two parameters are the recycle ratio
A, and the local mixing time tmix, which describe macro- and
micro-mixing effects in the system, respectively.
Tank Reactors (CSTRs)
It is well known that as the recycle ratio A of a recycle
reactor is increased, the behavior shifts from a PFR at A = 0
(no macromixing) to a CSTR as A = o (perfect
macromixing). We use this idea to obtain the two-mode model
for a perfectly macromixed CSTR, by integrating Eq. (30)
along the length of the reactor x and simplifying the resulting
equation for A > > 1. This gives the two-mode model for a
perfectly macromixed CSTR as

Cm (C) C min- C (32)
tmix "C
Cm (C)= tmixR((C)) (33)

where c(=V/qin) is the total residence time in the reactor,
and tmx is the characteristic local mixing time, which cap-


tures micromixing effects. In the limit of complete
micromixing (i.e., tmix 0), the TMM for a CSTR reduces
to the ideal one-mode zero-parameter CSTR model.
It should be pointed out that the local equation (eqs. 25,
28, 31, 33) is the same for all reactor types. This is an impor-
tant observation, which shows that scale separation exists in
all types of homogeneous reactors.

PHYSICAL INTERPRETATION OF
TWO-MODE MODELS
Using the example of a tank reactor, we present a physical
interpretation of the two-mode models. The physical system
equivalent to the two-mode model of a CSTR is a tank reac-
tor consisting of two zones, each of size V, namely, a non-
reacting convection zone (A), represented by Cm, and a reac-
tion zone (B), represented by (C). Thus, Cm is representative
of the convection scale of the system and (C) is representa-
tive of the reaction scale of the system. The interaction be-
tween the two scales (or the two zones A and B) is quantified
by an exchange of materials at a rate of qE. This exchange
occurs only through local diffusion, and tmi(=V/qE), which is
the characteristic time scale for this exchange, therefore de-
pends on the local shear rate and diffusion coefficient. Equa-
tions (32) and (33) represent the steady-state material bal-
ances for zone B and zone A, respectively.
In general, any infinitesimal volume dV inside the tank
could be so imagined to consist of two zones/scales, and a
corresponding two-mode model could be written (Eqs. 32-
33) for the volume dV. If macromixing in the tank is com-
plete, the two-mode model for any control volume dV could
be integrated over the entire volume of the tank to generate a
single two-mode model (Eqs. 32-33) for the whole tank.
Macromixing effects are often not negligible in real tanks,
however, and are influenced by several factors including the
type and speed of impellers (turbines) and the manner of feed
distribution. Several macromixing models are available in
the literature, e.g., the two-compartment model, recycle
model, tanks-in-series model, exchange-with-stagnant-zone
model, any of which could be suitably coupled with the TMM
to describe both macro- and micro-mixing in tanks. How-
ever, if micromixing effects are dominant compared to
macromixing ones (as in well-stirred tanks), it could be shown
by using L-S reduction in finite dimensions, that these mod-
els (i.e., the two-mode n-compartment model, etc.) could be
reduced to Eqs. (32) and (33), where the local mixing time
tmix is replaced by an effective mixing time tM, which cap-
tures both macro- and micro-mixing effects. This effective
mixing time tM now not only depends on the local diffusion
time and local shear rates, but also intricately on the tank
geometry, type and number of impellers, baffle positions, and
power dissipation in the system.


Chemical Engineering Education











Graduate Education ]


SIMILARITY BETWEEN TWO-MODE MODELS
OF HOMOGENEOUS REACTORS AND
TWO-PHASE MODELS OF
CATALYTIC REACTORS

A striking structural similarity between the two-mode mod-
els for homogeneous reactors and two-phase models for het-
erogeneous catalytic reactors exists. This could be seen more
clearly when Eqs. (24) and (25) are rewritten as


(ux) dCm Cm -(C) -R((C))
dx tmix

with Cm =Cm.in @x=0 (34)

The two-phase model for a heterogeneous wall-catalyzed re-
action in a tubular reactor is given by

uxdCm Cm Cs -R(Cs)
dx tTp

with Cm = C,in @x = 0 (35)

It may be noticed that the spatially averaged concentration
(C) of the TMM (in Eq. 34) is replaced by the surface (wall)
concentration Cs in the two-phase model (Eq. 35), while the
local mixing time tmix of the TMM is replaced in the two-
phase model by a characteristic mass transfer time between
the two phases t,,, which is given by
1 2
tTP = PTptD -- (36)
Sh-,T Dm

where tD is the transverse diffusion time scale and Sh (=l/
PTP) is the two-phase dimensionlesss mass) transfer coeffi-
cient (asymptotic Sherwood number) that depends on the
velocity profile and tube geometry. For the case of fully de-
veloped laminar flow in a circular tube, ShT = 48/11 = 4.36,
while its analogue in the TMM (comparing Eqs. 26 and 36)
is Sh,E = 1/ P = 48 (the dimensionless mass exchange coef-
ficient in the TMMs).
As illustrated in the next section, just as the two-phase
models can capture the mass-transfer limited asymptote in
heterogeneous reactions (which is missed by the pseudo-
homogeneous models), so can the two-mode models capture
the mixing-limited asymptote in homogeneous reactions,
which is rendered inaccessible by the traditional one-mode
models. Thus, there exists the following one-to-one corre-
spondence between two-phase models of catalytic reactors
and two-mode models of homogeneous reactors: two-phase
transfer time (tr) -> local mixing time (tmix), two-phase trans-
fer coefficient (Sh_,) -> two-mode exchange coefficient
(ShE), surface (wall) concentration Cs -> spatially averaged
concentration (C), and mass-transfer limited reaction -> mix-
ing-limited reaction.

Fall 2002


APPLICATIONS OF TWO-MODE MODELS

Bimolecular Second-Order Reactions

Second-order reactions provide the simplest example of
nonlinear kinetics, where micromixing limitations have sig-
nificant effects on reactant conversion. We use the TMM to
determine micromixing effects on conversion of a typical
bimolecular second-order reaction of the type

A + B P with rate = kCACB
occurring in a CSTR, where k is the reaction rate constant.
For the case of stoichiometric feeding (i.e., CAi=C=B,in=Cin)
the conversion (X) obtained by using the TMM is given by

1 4 Da(l+1)+ 1 (37)
1+11 2 Da(l + T)2

where 1 (=t.i / c) is the dimensionless local mixing time,
and Da(=kC,, Tc) is the Damkohler number. Figure 1 shows
the variation of conversion X with Da for different values of
the dimensionless local mixing time 1. The case of rl = 0
corresponds to the ideal CSTR. For 11 > 0 and Da -> -, the
local concentrations (Ci)(i=A,B) approach zero, while the
mixing-cup concentrations approach a mixing limited asymp-
tote, given by


(CA)=(CB)=O CAm =CB,m-
1+11


1
X-
l+r|


As mentioned in the previous section, this mixing-limited


Figure 1. Variation of exit conversion with Damk6hler
number, Da, for a second order reaction in a CSTR, for
different values of dimensionless local mixing time, 1l.


100-









40



20
0 -
6 0 -
o








e.el


1 10 100
Da










Graduate Education

asymptote for homogeneous reactions is analogous to the
mass-transfer limited asymptotefor wall-catalyzed reactions.
Just as the wall (surface) concentrations approach zero for
the case of infinitely fast surface reactions (while the bulk/
mixing-cup concentrations remain finite), so do the local con-
centrations (Ci) for infinitely fast homogeneous reactions
(i=A,B). Unlike in catalytic reactions, where exchange be-
tween the phases occurs at the solid-fluid boundary, the ex-
change between modes (scales) in homogeneous reactors
occurs over the entire domain.


Competitive-Consecutive Reactions
Competitive-consecutive reactions of the type

A+B "C and B+C---D
are prototype of many multistep reactions such as nitration
of benzene and toluene, diazo coupling, bromination reac-
tions, etc. Experimental observations'61 show that if the first
reaction is infinitely fast as compared to the second one (i.e.,
k,/k -> oo), under perfectly mixed conditions B is completely
consumed by the first reaction and the yield of D is zero (if A
and B are fed in stoichiometric amounts). But it was observed
that if the mixing of A and B is not attained down to the mo-
lecular scale, the first reaction is not complete and there re-
mains a local excess of B, which can then react with C to
produce D. The yield of D increases monotonically as the
rate of the second reaction increases, finally attaining a mix-
ing-limited asymptote. We use the TMM for a CSTR to verify
this observation. Figure 2 shows the increase in the yield of
D, YD with Damk6hler number of the second reaction, Da2,
where YD = 2CDm/(Cm+2CDm), and Da2 = kCin Tc. The figure
corresponds to the case when the first reaction is infinitely
fast (i.e., k,/k, --> o), and A and B are fed in stoichiometric
amounts (i.e., CBin = CAi=Ci, and Cc,in = Cin= 0). While no
D is formed for the case of Tr = 0 (ideal CSTR), a significant
increase in yield of D is obtained if finite micromixing limi-
tations are present in the system. The maximum yield of D,
obtained when the mixing limited asymptote is attained also
for the second reaction, is

S2T1 for 1 < 1
YD1,mx = (39)
2 for n >1
1+21

Thus, in this case, an optimal yield of D is obtained for rl = 1.

CONCLUSIONS

In the hierarchy of homogeneous reactor models, the clas-
sical ideal reactor models stand at one end as the simplest,
while the generalized convective-diffusion-reaction (CDR)


model stands at the other end as the most detailed one. While
the former cannot capture the mixing effects due to local ve-
locity gradients, molecular diffusion and reaction, the latter
requires extensive computations, especially for large Schmidt
and/or Damkihler numbers, and for multiple reactions with
large number of species. The Two-Mode Models (TMMs)
proposed here bridge the gap between the two extreme cases
of reactor models and provide a practical approach for de-
scribing mixing effects on reactor performance. They retain
all the parameters present in the full CDR model and there-
fore all the qualitative features of the latter, and yet their so-
lution requires a numerical effort comparable to that of the
classical ideal reactor models.
The analogy between the two-mode models of homoge-
neous reactors and two-phase models of catalytic reactors
could be carried further by noting that for all cases of well-
defined flow-fields, where two-phase mass-transfer coeffi-
cients (Sh ) can be estimated theoretically, the exchange co-
efficient (ShE) or the local mixing time (tmix) of the TMMs
could also be estimated. For more complex flow-fields (e.g.,
packed beds), the local mixing time, like the mass-transfer
coefficient, could be correlated to Re, Sc, and the geometri-
cal characteristics of the system. Thus, the two-mode models
of homogeneous reactors are as general as the two-phase
models of catalytic reactors and have a similar range of ap-
plicability. (In fact, the classical two-phase models are also
two-mode models, the modes being the cup-mixing and the
surface (or solid-phase) concentrations. Thus, the two-mode/


Figure 2. Variation of the yield ofD with Damk6hler num-
ber for a competitive-consecutive reaction scheme
A+B- C, B+C- D, when the first reaction is infinitely
fast, for different values of the dimensionless local mixing
time, 1.


Chemical Engineering Education


10 100 1000
Da











Graduate Education ]


two-scale approach may be used to present a unified theory
of homogeneous and heterogeneous reactors!)
To summarize, the two-mode models are the minimal mod-
els that provide a low-dimensional description of mixing, by
coupling the interaction between chemical reaction, diffusion,
and velocity gradients at the local scales to the macro-scale
reactor variables. Due to their simplicity and generality, it is
hoped that they will find applications in the preliminary de-
sign and optimization of homogeneous chemical reactors, as
well as provide an alternative method for teaching
micromixing effects in homogeneous reactors.

ACKNOWLEDGMENTS
This work was supported by grants from the Robert A.
Welch Foundation, the Texas Advanced Technology Program,
and the Dow Chemical Company. We thank David West of
Dow Chemical, Dr. Grigorios Kolios of the University of
Stuttgart and Prof. Dan Luss of the University of Houston
for their help in locating and translation of the articles by
Bodenstein and Wolgast and Forster and Geib.

REFERENCES
1. Langmuir, I., "The Velocity of Reactions in Gases Moving Through
Heated Vessels and the Effect of Convection and Diffusion." J. Am.
Ceram. Soc., 30, 656 (1908)
2. Damk6hler, G., "Einflusse der StrOmung, Diffusion und
Wdrmeiiberganges auf die Leistung von Reaktions6fen. II Die
Isotherme, Raumbestindige, Homogene Reaktion Ester Ordnung," Z.
Elektrochem., 43, 1 (1937)
3. Danckwerts, P.V., "Continuous Flow Systems: Distribution of Resi-
dence Times," Chem. Eng. Sci., 2, 1 (1953)
4. Taylor, G.I., "Dispersion of Soluble Matter in Solvent Flowing Slowly
Through a Tube," Proc. Roy. Soc. Lond. A, 219, 186 (1953)
5. Aris, R., "On the Dispersion of a Solute in a Fluid Flowing Through a
Tube," Proc. Roy. Soc. Lond. A, 235, 67 (1956)
6. Forster, V.T., and K.H. Geib, "Die Theorietische Behandlung
Chemischer Reaktionen in Strbmenden Systemen," Annalen. der
Physik, 5, 250 (1934)
7. Zwietering, T.N., "The Degree of Mixing in Continuous Flow Sys-
tems," Chem. Eng. Sci., 11, 1 (1959)
8. Ng, D.Y.C., and D.W. T. Rippin, "The Effect of Incomplete Mixing on
Conversion in Homogeneous Reactions," Chem. Eng. Sci., 22, 65
(1965)
9. Miyawaki, O., H. Tsujikawa, and Y. Uraguchi, "Chemical Reactions
Under Incomplete Mixing," J. Chem. Eng. Japan, 8, 63 (1975)
10. Harada, M., "Micromixing in a Continuous Flow Reactor (Coales-
cence and Redispersion Models)," The Memoirs of the Faculty of En-
gineering, Kyoto Univ., 24, 431 (1962)
11. Villermaux, J., and J.C. Devillon, "Reprdsentation de la Coalescence
et de la Redispersion des Domaines de S6grdgation dans un Fluide per
Moddle d'Interaction Ph6nomdnologique," Proc. 2ndlnd. Symp. Chem.
React. Eng., Amsterdam, BI (1972)
12. Baldyga, J., and J.R. Bourne, "Mixing and Fast Chemical Reaction-
VIII. Initial Deformation of Material Elements in Isotropic Homoge-
neous Turbulence," Chem. Eng. Sci., 39, 329 (1984)
13. Bodenstein, M., and K. Wolgast, "Reaktionsgeschwindigkeit in
Str6menden Gasen," Ztschr Phys. Chem., 61, 422 (1908)
14. Chakraborty, S., and V. Balakotaiah, "Low Dimensional Models for
Describing Mixing Effects in Laminar Flow Tubular Reactors," Chem.


Eng. Sci., 57, 2545 (2002)
15. Chakrabory, S., and V Balakotaiah, "Two-Mode Models for Describ-
ing Mixing Effects in Homogeneous Reactors," AIChE J., in review
(2002)
16. Li, K.T., and H.L. Toor, "Turbulent Reactive Mixing with a Series-
Parallel Reaction-Effect of Mixing on Yield," AIChEJ., 32, 1312 (1986)


Ms letter to the editor


Dear Editor:

I recently used the illustration below to explain the ben-
efits of countercurrent flow to students in a separation pro-
cesses subject that I teach. I've never heard this illustration
used before and it seems to be a good one, so I thought it
would be good to put it in the public domain for the benefit
of other lecturers. However, it is very short and does not war-
rant being a "peer-reviewed" paper.

Explaining Why Counter-Current is
More Efficient than Co-Current

While washing the dishes one night, I realized that this ac-
tivity provides a useful everyday illustration of why counter-
current mass and heat transfer processes are more efficient
than co-current ones.
I asked the students in my class what would be the best
way to clean a pile of dirty dishes if they had at their disposal
one basin of dirty wash water and one basin of clean wash
water. The class quickly reached the consensus that it would
be best to first use the dirty water to clean off as much of the
dirt as possible and then use the clean water to perform a
second-stage clean. The dirty water would remove the bulk
of the dirt, minimizing the contamination of the clean water
and leaving it in better condition to clean off any remaining
stubborn dirt. Putting the dirty dishes straight into the clean
water would quickly dilute and waste its cleaning ability.
This is equivalent to having the countercurrent flow of
streams in a liquid-liquid extraction or gas-liquid absorption
column. The clean solvent is best used to perform the final
stage of cleaning, while the used solvent is still able to perform
some cleaning of the raw feed stream as it enters the column.
Students seemed to intuitively understand this illustration,
and it provides a non-graphical complement to the usual
method of explaining the benefits of countercurrent flow,
which involves showing how the average concentration (or
temperature) difference driving force differs between co- and
countercurrent flows.
Simon Iveson
University ofNewcastle
Callaghan NSW 2308, Australia
cgsmi @ cc. newcastle. edu. au


Fall 2002










Graduate Education


INTRODUCING MOLECULAR BIOLOGY

TO ENVIRONMENTAL ENGINEERS

Through Development of a New Course


DANIEL B. OERTHER
University of Cincinnati Cincinnati, OH 45221-0071
Historically, applications of biology in chemical and
environmental engineering have been approached
from different perspectives with different goals. For
example, chemical engineering optimizes biochemical reac-
tions of pure cultures of microorganisms in highly controlled
bioreactors used for manufacturing (e.g., fermentation),
whereas environmental engineering employs mixed micro-
bial communities with minimum controls as least-cost pro-
cesses for meeting regulatory requirements (e.g., sewage treat-
ment). Although chemical and environmental engineering
education often incorporates formal training in biology, the
motivation for course selection can be very different. Incre-
mental advances in biological knowledge that can be used to
increase manufacturing capability or improve efficiency are
useful in chemical engineering practice, and their integration
into chemical engineering education is justified.
The same principle does not hold for environmental engi-
neering, however. Once minimum regulatory requirements
are met, incremental advances in biological knowledge do
not offer the significant cost savings for environmental bio-
logical unit operations that are needed to encourage the adop-
tion and integration of the new knowledge into environmen-
tal engineering education.
Recently, development of 16S ribosomal ribonucleic acid
(16S rRNA)-targeted technology provided researchers in en-
vironmental engineering with new tools to identify
microorganisms and to study microorganisms in bioreactor
environments. As compared to classical techniques for iden-
tification and enumeration, 16S rRNA-targeted technology
allows in situ examination of the structure (i.e., who is
present?) and function (i.e., what are they doing?) of micro-
bial communities without a prerequisite for isolating pure cul-
tures.1E' For researchers in environmental engineering, 16S
rRNA-targeted technology has been extensively tested, and
current research activities have moved beyond the "proof-
of-concept" state to widespread applications.12'3 In contrast,
integration of 16S rRNA-targeted technology within the en-
vironmental engineering curriculum remains to be fully de-


veloped. At the University of Cincinnati, the author has de-
veloped and pilot tested a "proof-of-concept" course titled
"Molecular Methods in Environmental Engineering."
The course was designed to teach limited fundamentals of
molecular biology in the context of quantitative engineering
design and practice. During its first offering, fifteen graduate
students in environmental engineering were exposed to "state-
of-the-art" technology, including hands-on laboratory exer-
cises following the "full-cycle 16S rRNA approach."111 Stu-
dents learned the importance of detailed understanding of
microbial communities and microbial-mediated biochemical
networks in biological unit operations, natural biological sys-
tems, and the global biosphere. The format of the course in-
cluded a weekly lecture as well as a semester-long series of
hands-on laboratory exercises designed to teach students to
develop scientific questions, learn appropriate methodology,
conduct careful experimentation, analyze data, and draw con-
clusions worthy of presentation to peers. Thus the final out-
come of the course included preparation of peer-review quality
manuscripts by each team of students as well as one-on-one
interviews with the instructor.

FULL-CYCLE 16S rRNA APPROACH
Traditionally, the identification of microorganisms in en-
vironmental samples has relied upon semi-selective cultur-
ing or direct microscopic examination. These techniques have
led to a rudimentary understanding of the role of microor-
ganisms in the global biosphere as well as the importance of
microorganisms in public health and biocatalysis. Recently,
the techniques for determinative microbiology have been dra-
matically expanded to include cultivation-and-morphologic-
independent identification and enumeration of microorgan-
Daniel B. Oerther joined the Department of Civil and Environmental Engi-
neering at the University of Cincinnati in 2000. For ten years, he has been
adapting methods from molecular biology to identify, enumerate, and mea-
sure the physiology of microorganisms in biotechnology processes includ-
ing wastewater treatment and bioremediation. His research links the re-
sults of novel molecular biology assays with mechanistic modeling of
bioreactor performance.
Copyright ChE Division of ASEE 2002


Chemical Engineering Education


258










Graduate Education


Collect Sample Extract Genomc DNA











Polymerase Chain Reaction
Denature, Anneal, Extend for Exponential Growth









Cloning
Ligation, Transformation, Isolate Recombinants










FISH and Microscopic Examination









Figure 1. Schematic of the principal steps in the "full-cycle
16S rRNA approach." Genetic material is isolated directly
from an environmental sample and the 16S rDNA genes
are amplified in a PCR. The product of the PCR is cloned,
and recombinants are isolated for extraction of plasmid
DNA. Automated sequencing is used to provide the primary
nucleotide structure of the clones, and probe design is ac-
complished using semi-automated procedures and readily
available software. Finally, individual microbial cells are
visualized through fluorescence in situ hybridization (FISH)
with fluorescently labeled 16S rRNA-targeted oligonucle-
otide probes.


isms in environmental samples. Arguably, one of the most
widespread families of new techniques for determinative
microbiology targets rRNA. Comparative studies of rRNA
nucleotide sequences collected from a variety of microorgan-
isms led to the development of a universal phylogenetic frame-
work for understanding the evolutionary history of microor-
ganisms."- Subsequently, these comparative approaches were
coupled with oligonucleotide probe hybridizations to study
microorganisms in situ without prerequisite culturing." 6'
The "full-cycle 16S rRNA approach" refers to the process
of obtaining genomic information directly from an environ-
mental sample and then employing molecular methods to
assay the abundance of nucleotide sequences directly within
an environmental sample. The steps of the cycle, as applied
in my course, are briefly described and outlined in Figure 1.
Genomic deoxyribonucleic acid (DNA) is extracted from an
environmental sample using chemical and physical disrup-
tion of the microorganisms. Subsequently, a polymerase chain
reaction (PCR) is used to selectively "grow-up" target genes
from the heterogeneous pool of genetic material. In our case,
the target genes are 16S rRNA. The target genes, amplified
in the PCR, are cloned into bacterial vectors and transformed
into competent cells of Escherichia coli. The recombinant
clones are cultured and plasmid DNA is extracted. The re-
sults from commercial dideoxy terminal sequencing are used
to design an oligonucleotide hybridization probe purchased
from a commercial vendor. The fluorescently labeled probe
is hybridized to a "fixed" sample, and individual microbial
cells are identified using an epifluorescence microscope.
For my class, commercially available kits were used to the
extent possible to minimize the time spent by students and
the teaching assistant in preparing reagents. Genomic DNA
was extracted using an UltraClean Soil DNA Isolation Kit.r7'
PCR was conducted using a model 2400 thermal cycler'8' and
the Takara Ex Taq kit.'11 Cloning of the PCR products was
accomplished with the TOPO TA Cloning kit version K2,1"01
and plasmid DNA was prepared using PerfectPrep Plasmid
Mini preps."" Throughout the exercises a variety of equip-
ment was used including an ultra low temperature freezer,"2'
a Mini Beadbeater-8,"I a system for agarose gel electrophore-
sis,1"4 a Genesys 10uv,l'" a constant-temperature rotary
shaker,"6' and an epifluorescence microscope.["7

FORMAT FOR LABORATORY EXERCISES
Step 1 Students arranged themselves into teams of three.
The selection of teammates was based both on a common
interest in one environmental sample and on an effort to spread
previous experience and expertise in molecular biology
among the groups.
Ste 2 Teams identified, evaluated, and proposed an ap-
propriate environmental system for study. Each system se-


Fall 2002










_Graduate-Education


... we plan to expand the enrollment [in this course] to include undergraduate envi-
ronmental engineering students as well as graduate and undergraduate students from
related disciplines, including chemical engineering and biomedical engineering.


elected for the course was novel for the field of environmental
engineering and possessed the capacity to stimulate a more
extensive research question (e.g., supplemented a research
question in an existing/developing MS or PhD degree, or pro-
moted a novel research direction generally underexplored.)
A sample was obtained from the selected system. In all cases,
preference was placed on samples that were a part of a devel-
oping/ongoing research project with significant supplemen-
tary information generated from advanced process engineer-
ing and chemical/physical analyses (e.g., samples) from a
novel bioreactor configuration or a bioreactor treating a novel
waste stream).

Ste 3 Each team generated 16S rDNA sequence infor-
mation from their sampless. Genomic DNA was extracted
using an UltraClean Soil DNA Isolation Kit"' according to
the manufacturer's instructions. Mechanical lysis of the
samples was performed for one minute at the maximum set-
ting of a Mini Beadbeater-8.[13] Genomic DNA was quanti-
fied using a Genesys 10uv'115 spectrophotometer assuming
that an absorbance reading of 1.0 at a wavelength of 260 nm
corresponded to a concentration of 50 mg DNA/1.
The 16S rDNA genes of bacteria present in the sample were
amplified by PCR using primer set S-D-Bact-0011-a-S-17
(5' to 3' sequence = gTT TgA TCC Tgg CTC Ag) and S-D-
Bact-1492-a-A-21 (5' to 3' sequence = ACg gYTACC TTg
TTA CgA CTT).[8' The conditions for PCR included: 5 min.
at 94C; 30 cycles of 0.5 min. at 940C, 0.5 min. at 550C, and
0.5 min. at 720C; 7 min at 720C; and hold at 40C. Each reac-
tion tube contained: 1.25 U Takara Ex Taq polymerase,E9' lx
Takara Ex Taq reaction buffer, 200 M of each deoxy ribo-
nucleotide triphosphate (dNTP), 0.2 gM of each primer, and
500 ng of genomic DNA. PCR was conducted using a model
2400 thermal cycler.J81
Agarose gel electrophoresis was used to check the quality
of the PCR product. A 1% (wt./vol.) agarose gel was pre-
pared in 1 x tris buffered EDTA (1 x TBE is 90mM tris borate
and 2 mM ethylenediamine-tetraacetic acid [EDTA]) accord-
ing to the manufacturer's instructions.E191 Electrophoresis was
conducted for two hours using a setting of 100 V for the power
supply. DNA fragments were visualized with a hand-held UV
lamp after staining the agarose gel for ten minutes at room
temperature with 50 mg/1 of ethidium bromide.
The PCR products were cloned into component cells of E.
coli using the TOPO TA cloning kit, version K2110 according


to the manufacturer's instructions. The blue/white screen with
x-gal was used to detect the presence of insert in each plas-
mid, and the antibiotic ampicillin was used to screen for the
presence of plasmids in colony-forming units of competent
cells. Ten clones were selected for each team of students, and
plasmid DNA was prepared using Perfectprep Plasmid Mini
prepsi"' according to the manufacturer's instructions. Puri-
fied plasmid DNA was subjected to endonuclease restriction
analysis using EcoRI.120' Digested plasmid DNA was electro-
phoresed on 2% (wt./vol.) agarose gels and visualized using
ethidium bromide staining and a hand-held UV lamp as de-
scribed above.
Two clones from each team were selected for commercial,
automated dideoxy terminal sequencing by the DNA Core
Facility at the University of Cincinnati. Sequencing primers
included M13(-20) forward and M13 reversel1 as well as S-
*-Bact-0343-a-A-15 (5' TAC ggg Agg CAg CAg 3'), S-*-
0519-a-S-18 (5'gTATTACCg Cgg CTg CTg 3'), S-*-Bact-
0907-a-A-20 (5' AAA CTC AAA TgA ATT gAC gg 3'), and
S-*-Bact-a-S-16 (5' Agg gTT gCg CTC gTT g 3').Y'8

Step 4 An initial phylogenetic analysis was conducted,
and the results were used to design oligonucleotide hybrid-
ization probes for fluorescence in situ hybridization (FISH).
Assembled sequences were compared to the Ribosome Da-
tabase Project (RDP) (available at rdp.cme.msu.edu) using
Chimera Check and Probe Match. Preliminary phylogenetic
affiliation was confirmed using a BLAST (Basic Local Align-
ment Search Tool) search of GenBank (available at
www.ncbi.nlm.nih.gov, follow the links to BLAST). The
fluorescently labeled oligonucleotide probes were ordered
from a commercial vendor.
Ste 5 Each team conducted fluorescence in situ hybrid-
ization (FISH) analysis of their original samples. Aliquots of
the original sample were chemically "fixed" for one hour at
room temperature with 4% (wt./vol.) paraformaldehyde pre-
pared in 1 x phosphate buffered saline (1 x PBS is 130 mM
NaCl and 10 mM sodium phosphate buffer). The samples
were subsequently stored at -200C in a 50% (vol./vol.) mix-
ture of ethanol and 1 x PBS. The fixed samples were applied
in a sample well on a Heavy Teflon Coated microscope slide1[2
and air-dried. FISH was performed as previously described.1221
Briefly, each microscope slide was dehydrated in an increas-
ing ethanol series (50, 80, and 95% [vol./vol.] ethanol, one
minute each), each sample well was covered with 9 pl of


Chemical Engineering Education













hybridization buffer (20% [vol./vol.] formamide, 0.9 M NaCI, >
100 mM Tris HCI [pH 7.0], 0.1% SDS), and fluorescently
labeled oligonucleotide probe, 1 [il (50 ng), was added to
each sample well. Hybridizations were conducted in a mois-
ture chamber for two hours, in the dark, at 460C. The slides
were washed for 30 minutes at 480C with 50 ml of prewarmed >
wash solution (215 mM NaCI, 20 mM Tris HCI [pH 7.0], >
0.1% SDS, and 5 mM EDTA). Fixed, hybridized cells were
mounted with Cargille immersion oil2-31 and a cover slip. >
Probe-conferred fluorescence was visualized with a model
E600 upright epifluorescence microscope,124] and digital im-
ages were captured using
a Spot-2 charge coupled
device (CCD) cam- Sex N=13 Age N=13
era.[25] The results of the Male 5 <23 0
Female 8 23-26 4
FISH analysis included 27-30 5
30+ 4
determining the abun-
dance and spatial orga- Current Degree N=13 Current Degree Field N=13
nization of phylo- B.A. 1 EnvEng 5
B.S. 4 Env. Scil 1
genetically defined mi- M.S 7 Engineering 2
Ph.D. 1 Other 5
crobial populations Highest Degree N=13 Highest Degree Field N=13
identified by unique M.S. 4 Env. Env. 8
oligonucleotide hybrid- Ph.D. 9 Env. Si.
ization probes.


figure z. uemograpnlc o
The students learned
he students learned course as determined by
the procedures for the
laboratory exercises through
a video series produced specifically for this course. They were
given a laboratory manual at the start of the class, and videos
of the laboratory exercises were distributed biweekly in VHS
format. The manual outlined all of the procedures for the labo-
ratory and provided step-by-step instructions to complete each
exercise. The videos gave the students an opportunity to
view the instructor completing all of the steps of each
exercise. The laboratory exercises were completed inde-
pendently by the three-student teams according to a sched-
ule arranged at the start of the class. Approximately the
first fifteen minutes of the weekly lectures were dedicated
to reviewing the progress of each team toward meeting
the schedule for completion of the laboratory exercises.

TOPICS FOR THE LECTURES
Each week, approximately two hours were spent in a lec-
ture discussion format with the entire class. The nine topics
that were covered in the pilot course included:
> Overview of methods including the value of differ-
ent methods and an answer to the question, "Why do
Environmental Engineers need to learn molecular bi-
ology?"
> Measuring microbial community structure
> Measuring microbial community function


Graduate Education

Quantitative molecular biology for Environmental
Engineering versus qualitative molecular biology for
Environmental Science
Troubleshooting the laboratory exercises to improve
the course for the subsequent year
What is this "phylogeny stuff' anyway?
Historical development of molecular tools in Envi-
ronmental Science and Engineering
Success stories for molecular tools in Environmen-
tal Science and Engineering
Principles of microscopic examination


STUDENT
FEEDBACK
Figure 2 summarizes
the results of students'
responses to a demo-
graphic survey. Thirteen
of the fifteen students
enrolled in the course re-
sponded to the survey.
The class was divided
almost equally between
male and female stu-
dents with a median age
of 27-30 years old. Five of


the students had received significant formal training in biol-
ogy, previously participating in more than ten biology courses.
The majority of the students had already completed their MS
degree (eight out of thirteen), but more than 50% of the stu-
dents had received their degree outside of environmental en-
gineering or environmental science. Most students spent less
than six hours per week on the course, but some students
spent significantly more time. Overall, the students enrolled
in the pilot test of "Molecular Methods in Environmental
Engineering" could be categorized as mature students (i.e.,
in their late twenties working toward their doctoral degrees).
Furthermore, the class contained a significant number of stu-
dents with extensive previous experience in biology. Thus,
the students enrolled in the pilot course were well prepared
in maturity and previous biology experience to actively par-
ticipate in this novel course. As the course continues to be
offered, I plan to track the success of the course in relation-
ship to the demographics of the enrolled students.
In addition to collecting demographic information, at the
end of the class the students were asked to respond to three
open-ended questions. In response to the question, "In your
opinion, were the objectives of the course met?" students re-
sponded:
The course met some of the objectives, but some students


Fall 2002


Number of Previous N=13
Biolovy Courses
<2 2
<5 4
<10 1
<15 1
15+ 4
Hours per week on N=13
course
<4 2
<6 7
<8 1
<10 2
<12
<15 1


II 1 .I *1


f sruaenrs enrolled in the pilot
an anonymous, in-class survey.











[ Graduate Education


are not convinced why we use molecular biology to
identify microorganisms in systems that have been proved
or have been operating successfully.
SYes. I am equipped with knowledge about this approach,
and I can interpret research results and publications
from this developing field.
In response to the question, "What was the best aspect of this
course?" students responded:
Most of the procedures are basic/universal operations in
molecular biology which means that we understand how to
study biology and biotechnology at the molecular level.
Experimental work-because it is through applications
that a student gets a tight grip on ideas and concepts. In
addition, the challenging experiments and the value of
the final result make the work more interesting.
The lectures were interesting and informative. I learned
a great deal, and my ideas about environmental
engineering and science have been positively affected by
the knowledge I have gained.
Your perspective. We will never see "cutting edge"
developments in a book.
The whole structure of the course is similar to a research
project.
The best aspect was carrying the concepts from the
classroom to the lab in a manner relevant to our field.
Also, having a class that is new gives afresh perspective
into the future of environmental engineering.
In response to the question, "What part of the course would
you suggest improving?" students responded:
More theoretical basis, especially for the background of
molecular biology methods.
From their responses to the open-ended questions, it is ap-
parent that the students felt the pilot course was a success. It
is interesting to note that the students appreciated that the
pilot course represented an effort to integrate research into
the classroom. One of the greatest difficulties for developing
a role for molecular biology in an engineering curriculum is
discovering a mechanism for moving these "state-of-the-art"
research skills into a classroom setting. In the future, we plan
to expand the enrollment for "Molecular Methods in Envi-
ronmental Engineering" to include undergraduate environ-
mental engineering students as well as graduate and under-
graduate students from related disciplines, including chemi-
cal engineering and biomedical engineering.

CONCLUSIONS
To address the growing national need for integrating
genomics and molecular biology into the engineering cur-
riculum, the author developed and pilot tested a new course,
"Molecular Methods in Environmental Engineering." Fifteen
graduate students were successfully introduced to molecular
biology through lectures and hands-on laboratory exercises
following the "full-cycle 16S rRNA approach." Although the


Chemical Engineering Education


pilot course can be considered a success, future offerings of
this course must be modified to reduce the difficulty of com-
prehending molecular biology by inexperienced engineering
students. One of the most daunting challenges for this type
of "state-of-the-art" course is providing a supportive, yet in-
dependent learning environment. For highly motivated gradu-
ate students, the author demonstrated that the format for this
course is successful. To offer this course to undergraduate
students or poorly prepared graduate students represents a
future challenge. In upcoming course offerings, the author
plans to open enrollment for "Molecular Methods in Envi-
ronmental Engineering" to undergraduate students in envi-
ronmental engineering as well as students in chemical engi-
neering and biomedical engineering. As genomics and mo-
lecular biology become as common to an engineering cur-
riculum as chemistry and physics, engineering faculty need
to take the lead in developing courses that introduce these
topics from an engineering perspective with a focus upon
quantitative approaches and the application of science to find
cost-effective solutions to society's problems.

ACKNOWLEDGMENTS
This laboratory course would not have been possible with-
out the commitment of significant resources from the De-
partment of Civil and Environmental Engineering of the Uni-
versity of Cincinnati. For the success of the pilot test, the
author is grateful to the Department.

REFERENCES
1. Amann, R., W. Ludwig, and K.H. Schleifer, "Phylogentic Identifica-
tion and In Situ Detection of Individual Microbial Cells without Cul-
tivation," Microbiol. Rev., (59), p. 143, (1995)
2. Rittman, B. "Editorial: Molecular Understanding," Water Environ. Res.,
(70), p. 1107, (1998)
3. Stensel, H.D., 2001, "Editorial: Probing the Black Boxes, Water
Environ Res., (73), p. 259, (2001)
4. Woese, C.R., "Bacterial Evolution," Microbiol. Rev., (51), p. 221,
(1987)
5. Woese, C.R., "There Must be a Prokaryote Somewhere: Microbiology's
Search for Itself," Microbiol. Rev., (58), p. 1, (1994)
6. Hugenholtz, P., B.M. Goebel, and N.R. Pace, "Impact of Culture-In-
dependent Studies on the Emerging Phylogenetic View of Bacterial
Diversity," J. Bact., (180), p. 4765, (1998)
7. Catalog # 12800-100, MoBio, Solano Beach, CA
8. Applied Biosystems, Foster City, CA
9. PanVera Corp., Madison, WI
10. Invitrogen Corp., Carlsbad, CA
11. Eppendorf Scientific, Westbury, NY
12. Model Ultima II, Revco, Inc., Asheville, NC
13. Biospec Products, Bartlesville, OK
14. Catalog # CSSU1214 and EC105, E-C Apparatus Corp., Holbrook,
NY
15. Spectronic Unicam, Rochester, NY
16. Model C24, New Brunswick Scientific, Edison, NJ
17. Model E600, Nikon, Inc. Melville, NY










18. de los Reyes, M.F, FL. de los Reyes, M. Hernandez, and L. Raskin,
"Quantification of Gordona amarae Strains in Foaming Activated
Sludge and Anaerobic Digester Systems with Oligonucleotide Hybrid-
ization Probes," Appl. Environ. Microbiol., (64), p. 2503, (1998)
19. E-C Apparatus Corp., Holbrook, NY
20. Promega, Inc., Madison, WI
21. Cel-Line Associates, New Field, NJ


22. Oerther, D.B., J. Pernthaler, A. Schramm, R. Amann, and L. Raskin,
"Monitoring Precursor 16S rRNA of Acinetobacter spp. in Activated
Sludge Wastewater Treatment Systems," Appl. Environ. Microbiol.,
(66), p. 2154 (2000)
23. Type FF, Cedar Grove, NJ
24. Nikon Instruments, Inc., Melville, NY
25. Diagnostic Instruments, Inc. Sterling Heights, MI J


M letter to the editor


To The Editor:
This letter is motivated by the paper "An Undergraduate
Course in Applied Probability and Statistics" that appeared
in the Spring 2002 issue of Chemical Engineering Educa-
tion.1l Probability and statistics are difficult subjects to teach
to engineering students, and Professor Fahidy is to be con-
gratulated on his efforts in this area.
In this letter we would like to refer to the discussion and
examples related to regression analysis. Professor Fahidy dis-
cusses in detail the use of numeric information (such as error
variance, confidence intervals, correlation coefficient, etc.)
for regression analysis, but does not mention graphic infor-
mation (residual plots) and physical insight for regression
analysis. Using the examples presented by Professor Fahidy,tl
we would like to demonstrate the importance of including
graphical information and physical arguments in the regres-
sion analysis.
Let us refer first to Example 4 in the paper. In this example,
the integral method of rate data analysis is used for a (sup-
posedly) first-order reaction. Nonlinear regression can be used

TABLE 1
Regression Results for Example 4 in Reference 1
Reaction Order P'Order "' Order 0'h Order 2"d Order
Model logY=-k*t Y=exp(-k*t) Y=Y,+k*t l/Y=1/Y,+k*t
k (value) 0.0039888 0.0038126 -0.0042162 0.0059893
95% Conf. Interval +0.0011009 0.0010816 0.0015209 +0.0059893
Y, (or 1/Y., value) -- 1.0329275 0.9365288
95% Conf. interval 0.586582 +0.1012594
R2 0.7620164 0.7770319 00.8362884 0.7757433
Variance (based on Y) 0.0023055 0.002271 0.0018759 0.0021994













Figure 1. Residual plot for Example 4 in Fahidy paper.'1

Fall 2002


for finding the reaction rate coefficient (k) using concentra-
tion (Y) versus time (t) data, on the regression model Y =
exp(-kt). Alternatively, this equation can be linearized to yield
lnY=-kt, where linear regression can be applied. The results
of the linear and nonlinear regression that were obtained us-
ing POLYMATH 5.1 are shown in the first two columns of
Table 1. Note that these results are different from what is
presented in [1], but they are correct and were confirmed by
the author of the original article.121 Looking at the numerical
information presented in Table 1 (parameter values, confi-
dence intervals, correlation coefficients, and variances) leads
to the conclusion that there is no significant difference be-
tween linear and nonlinear regression for determining k (the
variances are almost the same, contrary to what is argued in
[1]). The same information may also lead to the conclusion
that the model fits the data reasonably well. This conclusion,
however, is contradicted by the residual plot shown in Figure
1. The residuals are not randomly distributed around a zero
value. This may indicate either lack of fit of the model, or
that the underlying assumption of a random error distribu-
tion for the dependent variables is incorrect.
Physical insight can suggest alternative regression models,
but more information regarding the reaction involved is
needed. Since no such information is available, we will as-
sume a homogeneous reaction, just for the sake of the dem-
onstration. Assuming 0'h order reaction or 2nd order reaction
yields the models shown in the third and fourth columns of
Table 1, respectively. The numeric information presented in
the Table points on the 0'h order reaction as the most appro-
priate one (smallest variance value-note that in order to be
on a unique scale, all the variance calculations must be based
on Y). The residual plot for the 0'h order reaction is not sig-
nificantly different, however, from that shown in Figure 1;
thus, this model is not supported by the residual plot either.
The conclusion from proper analysis of this example is that
the data available are insufficient (in quality, quantity, or both)
to determine in any certainty the order of the reaction it rep-
resents. To obtain a more definite result, additional measure-
ments must be made.
In Example 5, a linear model Y=a+bx is fitted to data of
mean fuel consumption rate (Y) versus vehicle mass (x).
The numerical results that were obtained for this example,
using POLYMATH, are: parameter values (including
95% confidence intervals) a=-0.86959752.0733031;
Continued on page 277










Classroom


A New Approach to Teaching

TURBULENT

THERMAL CONVECTION




STUART W. CHURCHILL
University of Pennsylvania Philadelphia, PA 19104-6393


At AIChE's annual meeting in 2000, I gave an oral
presentation of an early version of a pair of new ex-
pressions, completely free of explicit empiricism, for
the prediction of fully developed turbulent thermal convec-
tion in all channels and for all thermal boundary conditions.
At the same venue, In 2001 I also presented a greatly im-
proved version, although at the expense of a smidgen of em-
piricism. Both presentations prompted the same question from
participants: "Is this approach being taught to current stu-
dents, and if not, why not?" I explained in both instances that
this material is very new and is not in any textbooks, and
furthermore, that it may not appear in textbooks for some
time to come since the authors of transport textbooks must
first become aware of the concept and its results, and then be
convinced of its educational (as well as predictive superior-
ity) over the method they are currently teaching. Also, as
Andersontl1 has noted, textbooks in chemical engineering
seem to have a unique longevity, and the more successful of
them are replaced or revised only after long intervals of time.
Undoubtedly with these textbook characteristics in mind,
my mentor and departmental chairman, Donald L. Katz, long
ago made the suggestion (which to a young assistant profes-
sor was virtually an order) that every year I replace at least
20% of the graduate transport course content by embracing
new developments in the literature. Throughout my career,
that suggestion led to my use of notes incorporating these
new segments, together with using a book or books as a
supplement rather than the other way around. I conclude, a
full half-century later, that this process of annual supplemen-
tation and revision has, by virtue of the associated forced
self-study and self-learning in the fields of my teaching, more
than compensated me (and perhaps my students) for the ef-
forts, and that it is a worthy complement of the new materials
most of us introduce periodically from our own research and


consulting. I am here taking advantage of the platform pro-
vided by Chemical Engineering Education to encourage and
assist the process of supplementation for transport teachers
with respect to a new approach for the description and pre-
diction of turbulent thermal convection.
In a previous CEE article,11 I presented a new approach to
the description and teaching of turbulent flow with the same
objective. For that simpler and more restricted topic, it was
possible to include in the presentation a virtually complete
set of supplementary notes for direct use by any interested
faculty member. For the much more complex process of tur-
bulent thermal convection and the much more complex pro-
cess of development of the new model, however, the presen-
tation of a work ng set of supplemental notes in this format is
simply not feasible. Rather, this article has the more limited
objective of outlining the new approach with the hope that
faculty members who teach transport will be inspired to study
the more complete documentation in the key references and
make the effort to formulate their own supplemental notes.
Perhaps I will eventually find the time and motivation to pre-
pare a monograph on this topic, but I do not recommend that
anyone procrastinate with that as the excuse.
When an analogue of the approach that was so simple,


Stuart W. Churchill is the Carl V.S.
Patterson Professor Emeritus at the Univer-
sity of Pennsylvania, where he has been
since 1967. His BSE degrees (in ChE and
Math), MSE, and PhD were all obtained at
the University of Michigan, where he also
taught from 1950 to 1967. Since his formal
retirement in 1990, he has continued to teach
and carry out research on heat transfer and
combustion. He is also currently completing
books on turbulent flow and correlation.


Copyright ChE Division of ASEE 2002


Chemical Engineering Education










straightforward, and successful for turbulent flow was first
attempted for the closely related topic of turbulent thermal
convection, I anticipated that the path of development would
closely parallel the previous one. While convection is inher-
ently more complex than flow in several respects, it is also
simpler in the sense that it merely consists of the superposi-
tion of a scalar quantity, the temperature, on the flow. The
path of development that emerged after considerable trial and
error proved to reflect the greater complexity that had been
anticipated, and the final results proved to reflect the antici-
pated greater simplicity.
The predictive equations for turbulent thermal convection
that are described in this paper are, by a significant margin,
more accurate, fundamentally sound, and general than any
prior ones. They also provide better insight into the relation-
ship between flow and convection and a better conception of
thermal convection itself that more than compensates for the
greater detail. This new material should therefore, as sug-
gested by audience members at the AIChE presentations, be
given serious consideration for inclusion in the final portfo-
lios of both our undergraduate and graduate students.
Apart from the merit of the predictive equations for turbu-
lent thermal convection that emerged, the path of their devel-
opment appears to have merit itself in an educational sense.
On the one hand, it provides insight into a creative process of
correlation that is within the capabilities of our students. On
the other hand, it provides a perspective within which the
strengths and weaknesses of all forms of correlation can be
evaluated, not only in flow and convection but also in every
aspect of chemical engineering. Our students should be
made to realize that whatever career they follow after
graduation, they will spend considerable time using and/
or formulating correlations.
I have a predilection for presentations in narrative and his-
torical contexts under the presumption that the personal char-
acteristics, as well as the triumphs and failures, of our prede-
cessors not only stimulate interest but also provide a mne-
monic for students. In this instance, a description of the ser-
endipitous and irregular path of development of a completely
new formulation in a relatively mature field may serve a simi-
lar role. Teachers who prefer a more orderly and skeletal ap-
proach are welcome to eliminate such diversionary material.
Many details concerning origins, proofs, uncertainties, and
limitations are deferred to the references, and in particular to
Churchill and Zajic.13' It is, however, essential that the teacher
present these details, or perhaps in the instance of graduate
students, assign key references as required collateral read-
ing. In either event, students should be encouraged to ques-
tion the validity of the many assertions and simplifications in
this article rather than accept them "on faith." Undergradu-
ate students may require more guidance than do graduate stu-
dents with respect to the new approach, but they have the


counterbalancing advantage of less to unlearn.


THE NEW APPROACH
FOR TURBULENT FLOW
A thorough understanding by students and faculty alike of
the new approach for the description and teaching of turbu-
lent flow, as previously described[2], is an essential prereq-
uisite for the complementary new approach presented here
for turbulent thermal convection. Because of space limita-
tions, however, only those results that are directly applied or
adapted for thermal convection will be reproduced here.
The time-averaged, once-integrated differential equation
of conservation for momentum in the radial (negative-y) di-
rection in steady-on-the-mean, full developed flow of a fluid
of invariant density and viscosity through a round tube can
be represented by

c(1 =g du -pu'V (1)
a) dy

Here, Tw is the shear stress on the wall, y is the distance
from the wall, a is the radius of the pipe, u is the time-aver-
aged velocity, and u' and v' are the fluctuating components
of the velocity in the x and y directions, respectively. The
superbar designates the time-average of their product, while
p and p are the dynamic viscosity and specific density of
the fluid. (Aside to teachers: The origin of this expression
and the physical meaning of the several variables and terms,
including the signs of the latter, should be described or reviewed
as appropriate. Any uneasiness of the students in this regard
can be expected to persist in what follows. Of course, this warn-
ing applies to some extent to subsequent details as well.)
Equation (1) can be rewritten in terms of the dimension-
less "wall" variables of Prandtl, namely

u = u(p / )/2

y+ = /y(,p)2 /

a+ = a(wp)1l2 / 2

and one new variable, namely the fraction of the transport of
momentum (or the total shear stress) due to the turbulent fluc-
tuations (u'v') =-pu'v' / as

1 yxF -7++1] du
1-- + = (2)
a dy+

Equation (1), with y+/a+ replaced by 1-R, can be integrated
formally to obtain the following expression for the radial dis-
tribution of the time-averaged velocity:

u+ = u )++dR2 (3)
2
R2


Fall 2002









The velocity distribution can in turn be integrated over the
cross-section to obtain, after utilizing integration by parts,
the following integral expression for the mixed-mean veloc-
ity and thereby the Fanning friction factor:
= u+dR2 1 u'v') dR4 (4)

[tf Um 4)
0 0
Equations (1) through (4) are exact insofar as the restrictions
mentioned above with respect to Eq. (1) are fulfilled. In or-
der to implement Eqs. (3) and (4), an expression is required
for (u'v') in terms of y+ and a+. For this purpose, Churchill14'
proposed the following semi-empirical expression:

I / \3i -i-8/7
++ 8/7 = 0.7 ( 8/7


+ exp -1 1 +6.9 y 8/(5)
0.436y+ 0.436a+ (

It is essential for the students to be aware of the origins and
uncertainties of Eq. (5) since this expression has a critical
role, both numerically and functionally, in all of the develop-
ments that follow for both flow and convection. The third-
power dependence on y+ for small values of y+ was originally
postulated on the basis of asymptotic analyses, but has since
been confirmed by direct numerical simulations, which have
also produced a theoretical value of approximately 7 x 10-4
for the numerical coefficient. The exponential term for mod-
erate values of y+, as well as the deductive term for y a+
were both derived by speculative analysis, but the coefficients
of 0.436 and 6.95 were determined from recent, improved
experimental data for the time-averaged velocity distribution.
The power-mean form of Eq. (5) is arbitrary and the combin-
ing exponent of -8/7 is based on experimental data for u'v.
(See Churchill and Zajict3] for further details, including com-
plete references.)
Numerical integration of Eqs. (3) and (4) using (u'v')+ from
Eq. (5) results in almost exact values of u+ and u+ owing to
the smoothing associated with integration. Such values of u+
may be represented with a high degree of accuracy for a+ >
300 by the following expression that invokes no additional
empiricism beyond that of Eq. (5):

(2 1/2 3.2 227 502 + a+ (6)
m) u a 3 + a+ 0.4366

Equations (1) through (6) are the only ones for flow that will
be referred to directly in the developments that follow for
convection.
It may occur to teachers and graduate students at this point
that the relevant consideration of turbulent flow has been
completed without any mention of the eddy viscosity or the


mixing length. One merit of the new approach, which carries
over to thermal convection, is that the need to introduce such
heuristic quantities is avoided completely by the more direct
and simple development in terms of(u'v')



AN ASIDE ON A
GENERIC CORRELATING EQUATION

Equation (5) is a particular application of the generic cor-
relating equation proposed by Churchill and Usagi[51 for two
regions, namely

yb Y= + y (7)
Here, y = y{x}, y,, = {x-0}, y_ = y{x->o}, and b is an
arbitrary exponent. Either yo or y_ or both are necessarily
functions of x rather than fixed values. For three regions, Eq.
(7) can be extended either directly as


ybq=(yb+yb) +ybq

or in staggered form as


(yb yb y qy b -y) (9)
Here, y, is an intermediate asymptote and q is a second arbi-
trary exponent. The reverse order of combination of y,, y,
and y_ leads to equally valid and, in general, fundamentally
different representations. Equations (7) through (9) have been
introduced here to avoid interrupting the continuity of the
development in which they are used.


DEVELOPMENT OF A NEW FORMULATION
FOR TURBULENT CONVECTION
The analogue of Eq. (1), with the additional idealization of
negligible viscous dissipation, is
kT
j = -k + pcT'v' (10)
ay
and that of Eq. (2) is

SI (T'v)++ T (11)
Jw ay+
Here, j is the heat flux density in the y-direction, T is the
temperature of the fluid, j and Tw are their values at the wall,
T+ = k(wp)/2(Tw T) / jw, T'v' is the time-averaged prod-
uct of these fluctuating quantities, (T'v') = pcT'v' / j is the
fraction of the radial heat flux density due to the turbulent
fluctuations, and k is the thermal conductivity of the fluid.
The terms j/j, and (T'v')+ in Eq. (11) depend on two param-
eters, namely the Prandtl number Pr = cp/k and the mode of
heating at the wall, as well as on y+ and a.


Chemical Engineering Education










From an energy balance over an inner cylindrical segment
of the fluid stream, it follows that


R I
j 1wRI u aT/ / ax
j, R 0 um Tm / ax


Here, Tm is the mixed-mean temperature of the fluid stream.
As contrasted with / Iw, which may be inferred from Eq.
(1) to vary linearly with R, j/j varies non-linearly because of
its dependence on the velocity distribution and in some in-
stances on the temperature distribution as well. Also, as can
be inferred from Eq. (12), T varies with x as well as with y,
even in fully developed thermal convection, whereas u var-
ies only with y in fully developed flow. Fully developed ther-
mal convection is ordinarily defined by two criteria, namely


a T -T
ax T, T,


Then T+, weighted by u+ / u can be integrated over the
cross section to obtain


Nu- ya
Nu 2a+= 4
Tm+= R2
R/


U dR2
Um )


and 0
ax


where h = j /(T Tm) is the local heat transfer coefficient.
Equation (11) can be put in a more tractable form for both
formal and numerical solution by introducing new variables
y and Prt defined as follows, in place ofj/jw and (T'v')

j j u1 R aT /dX
1+= I dR2 (13)
jw T jR R2 T /ax
0


For uniform heating at the wall, it follows from the criteria
for fully developed thermal convection that
aT / ax = aTm /I x. It then follows from the correspondingly
reduced form of Eq. (13), together with Eqs. (3) and (4), that
y is a function only of y+ and a+. Equation (17) can then by
virtue of the same considerations, be integrated by parts to
obtain


Pr, 1 v' (Tu'vuv
Pr 1 J(v lT +


The result is


(1+ y)R dT+ (15)
1+Pr (u + d(15)
++
Pr ( dy+



The use of y, the perturbation of the heat flux density distri-
bution from that of the shear stress distribution, was suggested
by Reichardt.'61 The variable Pr, was originally introduced in
connection with modeling in terms of the eddy viscosity and
eddy conductivity, and accordingly, by analogy with the cor-
responding ratio of molecular quantities, was called the tur-
bulent Prandtl number. Although the redefinition of Pr in
terms of (u'v') and (T'v') avoids these heuristic vari-
ables, the traditional name and symbol for this quantity are
retained herein out of respect for its historical origin. It should
be noted that Pr is not necessarily proportional to Pr since
(Tv')) is, in general, a function of Pr.
Equation -=R can be integrated formally to obtain


Equation (18) can be reduced for three special cases. For Pr
= 0, it can be expressed as

Nuo -Nu{Pr= 0}= 8 (l+)2dR =8/( l+y)2mR (19)

while for Pr = Pr, it can be reduced by virtue of Eq. (4) to


NuI =Nu{Pr = Prt}


8

f(l+y)2[1- (- )++ dR4
o


2a+
Um(1 + 1 mR


Fall 2002


+ 1 (1
2 f
R' Pr
1+-
Prt









Here, as can be inferred, ( +y))R4 designates the integrated-
mean value over R4, and (I+y)2mr 4 the integrated-mean
value weighted by 1 (u'v') Both quantities may readily
be evaluated numerically, using Eqs. (3), (4), and (5), and the
reduced form of Eq. (13). For Pr M-, the temperature field
develops almost completely very near the wall where (u'v')
can be approximated by 0.7 (y+/10)3 and y can be neglected.
Equation (16) can then be integrated in closed form to obtain

Nu- = Nu{Pr -* }= 33/2 (0.0007)/3a+(Pr/ Pr )1/3 / K =

0.07343Re(f / 2)1/2(Pr/Prt)/3 (21)

For uniform wall temperature, the criteria for fully devel-
oped convection require that

(aT / ax) / (aT, / ax) T+ / Tg+
Integration of Eq. (17) by parts is no longer possible, but
from the limiting form of Eq. (16) for R = 0, it follows that

Nuo = 4(T /T /(l + Y)mR2 (22)


Su+ (T+) Re(f2)
Nul = (1+ )wmR
u|=4 T| f+ Y)wmR2


(23)


Here, Tc is the temperature at the axis of the pipe. Equation
(21) remains applicable as is. The determination of numeri-
cal values of Y, T+, and Tn+ from Eqs. (13), (16), and (17)
now requires iteration, but the functional forms of Eqs. (22)
and (23) are adequate for the development herein.
On the basis of the previous experiences with various as-
pects of turbulent flow, I anticipated that Eqs. (19) through
(23) could be combined in appropriate pairings in the form
of Eq. (7) to construct satisfactory correlating equations for
Pr 2 Pr and for Pr < Pr, or alternatively, in appropriate trip-
lets in the form of Eq. (8). All such attempts failed, however.
I then found (somewhat serendipitously) that a successful cor-
relating equation for turbulent thermal convection could be
devised by using a particular analogy between momentum
and energy transfer in which the exact solutions for three par-
ticular values of Pr occur in the form of Eq. (9). Accordingly,
a brief and very selective review of such analogies is appro-
priate at this point.


SELECTIVE ANALOGIES
Reynolds171 postulated that the transport of both momen-
tum and energy between a turbulent stream and its confining
surface occurred wholly by means of a mass flux of eddies
and thereby derived the equivalent of
Nu = PrRe(f /2) (24)


Prandtl'81 improved upon the Reynolds analogy by postulat-
ing an added resistance due to linear molecular diffusion of
momentum and energy across a viscous boundary layer of
thickness 8 in series with transport by the eddies of Reynolds
in the turbulent core, thereby obtaining the equivalent of

N Pr Re(f / 2)
1+ 8+(Pr- 1)(f / 2)1/2
Equation (25), just as Eq. (24), is inapplicable for Pr < 1,
owing to neglect of thermal conduction in the turbulent core,
and also for Pr >> 1, owing to neglect of eddy transport within
the viscous boundary layer. Even so, it represents a great ad-
vance in that it correctly predicts a coupled, non-power de-
pendence on both Pr and Re, in the latter case by virtue of the
dependence of f on Re. Of the many analogies that have been
proposed to eliminate the deficiencies of the Prandtl analogy
for large and small values of Pr (see, for example, Churchill['),
only two need to be examined here.
Reichardt161 eliminated dy+ between the equivalents of Eqs.
(2) and (15) and made several ingenious approximations that
allowed him to integrate the resulting combined equation in
closed form. Churchill[19 assembled the fragments of this so-
lution into a single expression for Nu and corrected the erro-
neous expression used by Reichardt for the shear stress near
the wall, thereby obtaining


(1 + Y)mu T+ (Yu+ )Pr
1 -P
Nu Re(f/2) T + )u --Pr

13.62 T1 Prt Pr 1/3
Re(f / 2) 2T, Pr Pr


Equation (26) is limited in applicability to Pr 2 Prt by virtue
of one of the simplifications made by Reichardt in order to
be able to integrate analytically.
Churchill10 (also Churchill and Zajic'31) followed a com-
pletely different path to derive an expression, which for Pr 2
Prr, is exactly equivalent to Eq. (26) except for replacement
of the term 1 Pr/Pr by 1 (Pr/Pr)2/3. In retrospect, the differ-
ence in these expressions is a consequence of the approxima-
tion of Reichardt of du+ by dy+ in the differential term lead-
ing to the right-most term of Eq. (26).


FINAL FORMS
The final predictive expressions for turbulent thermal con-
vection emerged from the various expressions above by means
of the following lengthy series of insights, postulates, and
inferences, all of which were essential.

O Churchill, et al.,l 'I recognized that Eq. (26) was equiva-
lent, with Tm / Tc evaluated at the limiting conditions, to


Chemical Engineering Education










( Pr N 1 Pr )
tPr) Nu+ 1 Pr )Nu


(27)


O They further recognized that when Eq. (17) was rear-
ranged as

Nu Nu1 Nu Pr1
Nu=-Nui 1 [+ Nu (28)
Nu- Nul NuI Pr- Prt

it had the form of Eq. (9), with

b=-q=l
Yo =Nul
y = Nu-

yi = Nu (Nu Nu) Pr -I
Nu- Prt

The staggered independent variable, Pr/Pr 1, has the essen-
tial role of converting Nu, from a particular value to an as-
ymptote. According to Eq. (28), Nu goes through a sigmoi-
dal transition from Nu, to N-, a nuance of behavior that had
previously been overlooked. In retrospect, correlation in terms
of Eq. (7), that is, direct interpolation between Nu, and Nu-,
was doomed to fail. The relationship provided by the
Reichardt analogy was essential to the derivation of Eq. (27).


O The identification of Eq. (28) with Eq. (9) suggested
that the analogue of Eq. (28) in terms of Nu0 and Nu, might
be applicable for Pr < Pr1. That concept led to an expression
with a discrete step in the derivative of Nu with respect to Pr/
Prt at Pr = Pr1, but elimination of this discontinuity by means
of an arbitrary but ultimately vanishing coefficient resulted
in

Nu Nuo -/L Nui Nu Nu, (Pr-P
Nu1 -Nuo + Nu Nu Nuo Pr (29)

where Nu = Nu {Pr = Prt }= 0.07343 Re(f / 2)/2.


O4The absence of any allusion to geometry or to the ther-
mal boundary condition suggested that Eqs. (28) and (29)
might be applicable for all geometries and all thermal bound-
ary conditions. Plots of numerically computed values of Nu
versus Pr/Pr for round tubes with uniform heating and uni-
form wall temperature, and for parallel-plate channels with
equal uniform heating and with unequal uniform tempera-
tures, confirmed the validity of this speculation.


0 These plots in logarithmic coordinates appeared to pro-
vide an excellent overall representation for all values of Pr/


Pr, for all values of a+ or b* (where b is the half-spacing of
the parallel plates) greater than 145, which is the lower limit
for the existence of fully turbulent flow, for all geometries,
and for all thermal boundary conditions. The more critical
test provided by arithmetic plots, however, reveal errors in
Nu of up to 20% for both Pr/Prt = 0 {10} and Pr/Pr = 0 {0.01 }.
After many attempted correctives, substitution of the anal-
ogy of Churchill for that of Reichardt to obtain

1 Pr 1 Pr2/3 (30)
Nu Pr Nu Pr Nu(

was found to result in an almost perfect representation for
the dependence of Nu on Pr/Pr.
@ The analogue of Eq. (30) for Pr < Pr, corrected as was
Eq. (29) to remove the singularity in the derivative, and with
the arbitrary inclusion of the empirical factor (Pr/Pr)"/, is

Prt 1 Nu 2-Nu Nug
Nu Nuo = 1P r 3 (31)
NuI -Nuo (Prt/Pr) /8(Nu, -Nuo)NuL


This expression results in almost exact representations for
Pr < Pr, for all of the previously mentioned conditions-
thereby it is a complement in every respect to Eq. (30).


IMPLEMENTATION
The numerical calculation of values of Nu for specified
values of Re and Pr and for particular geometries and
boundary conditions requires numerical values or expres-
sions for f, Nu,,, Nu,, and Pr,. For a round tube, values of
f of sufficient accuracy can be determined from Eq. (6)
by noting that Re = 2 au+,. Values of Nu0 and Nu, can be
calculated from Eqs. (19) and (20), but an array of such val-
ues has already been calculated for representative values of
a+, and correlating equations have been devised for interpo-
lation. The slight inaccuracy associated with Eq. (5) is totally
negligible when it is used in conjunction with Eqs. (19) and
(20). Equivalent expressions for f, and values and expres-
sions for Nu0 and Nu, are also available or can readily be
derived and calculated for other geometries and thermal
boundary conditions. Equation (21) is directly applicable as
an asymptote for large values of Pr for all geometries and
conditions. Current correlative and predictive equations for
Pr, are quite uncertain (see, for example, Kays'121 or
Churchill131). However, Nu as predicted by Eqs. (30) and (31)
is fortuitously insensitive to the expression used for Prt, and
the following purely empirical equation
0.015
Pr, = 0.85 + 05 (32)
Pr
appears to be adequate for that purpose. The dividing value


Fall 2002











of Pr with respect to the use of Eq. (30) or (31), that is, the
value of Pr for which Pr = Pr, is 0.867 according to Eq. (32).
Other correlating equations for Pr, give only slightly differ-
ent numerical values for this pivotal value of Pr. Either Eq.
(30) or Eq. (31) can be used without serious error for 0.45 <
Pr < 1.7, which suggests that Eq. (30) is a sufficient expres-
sion for all fluids other than liquid metals.

SUMMARY
Equations (30) and (31), together with Eq. (32), predict
values of Nu within 1% or 2% of numerically calculated val-
ues for all geometries and conditions in the fully turbulent
regime. This is to be compared with deviations of 10% to
40% on the mean for all expressions in current use, many of
which are greatly restricted with respect to range and condi-
tions (see Churchill and Zajic131). The remarkable improve-
ment in accuracy for Pr 2 Prt, as provided by Eq. (27), is a
consequence of using the Reichardt analogy, which is free of
any explicit empiricism. This expression fails in exactness
only due to some minor mathematical simplifications made
in its derivation. This slight inaccuracy is in turn virtually
eliminated by use of the analogy of Churchill. On the other
hand, the greatly improved accuracy of Eq. (31) for Pr < Pr,
is a consequence of the identification of the structure of the
analogy of Reichardt with that of the generic correlating equa-
tion of Churchill and Usagi for three regimes in staggered
form, together with a minor empiricism. This same identifi-
cation revealed a virtual regime and a point of inflection for
Pr < Pr,, and another such pair that had never before been
recognized for Pr > Pr. The existence of these virtual regimes
explains the numerical and functional failures of most prior
correlating equations.
The generality of the new expressions for all geometries
and thermal boundary conditions is a consequence of the rec-
ognition that the analogy of Reichardt could be expressed in
terms of Nu0, Nu,, Nu_, and Pr/Pr. The supplementary ex-
pressions for Nu0, Nu,, and Nu, which are exact insofar as
Pr, is independent of y+, follow directly from formulation of
the equations of conservation in terms of the fraction of the
transport due to the turbulent fluctuations. They could have been
derived using eddy diffusional models, but not so simply.
Implementation of the new expressions for specified val-
ues of Re and Pr, and for particular geometries and thermal
boundary conditions, is not onerous since the entire calcula-
tion can be preprogrammed.
The path of development leading to Eqs. (30) and (31) could
now be streamlined, but the description of the irregular path
that was actually followed has educational value in that all
students and practicing engineers should be concerned with
the evaluation if not the construction of correlating equations.
Although the process of derivation of the new relationships
for thermal convection is much more complicated, and the
relationships themselves are slightly more complicated to


employ, these deficiencies appear to be a small price to pay
for their greater accuracy, sounder rationale, and broader ap-
plicability.
Students should be prompted to question any of the as-
sertions and non-obvious steps that were made in the ab-
breviated development herein and not expanded upon by
the teacher. Justifications may generally be found in the
references.

REFERENCES
1. Anderson, T.J., "Chemical Processing of Electrons and Holes," Chem.
Eng. Ed., 24(1), 26 (1990)
2. Churchill, S.W., "A New Approach to Teaching Turbulent Flow," Chem.
Eng. Ed., 32(2), 142 (1999)
3. Churchill, S.W., and S.C. Zajic, "The Prediction of Turbulent Con-
vection with Minimal Explicit Empiricism," AIChE J., 48, 927 (2002)
4. Churchill, S.W., "New Simplified Models and Formulations for Tur-
bulent Flow and Convection," AIChE J., 42, 1125 (1997)
5. Churchill, S.W., and R. Usagi, "A General Expression for the Correla-
tion of Rates of Transfer and Other Phenomena," AIChE J., 18, 1121
(1972)
6. Reichardt, H., "Die Grundlagen des Turbulenten Warmeii-
bertraganges,"Archivges. Wiirmetechn., 2, 129 (1951): English trans-
lation, "The Principles of Turbulent Transfer," Nat. Advisory Comm.
Aeronaut., TM 1408, Washington, DC (1957)
7. Reynolds, O., "On the Extent and Action of the Heating Surface of
Steam Boilers," Proc. Lit. Soc., Manchester 14, 7 (1874)
8. Prandtl, L., "Ein Beziehung zwischen Wirmeaustaush und
Strimungswiderstand der Fliissigkeiten," Phys. Z., 11, 1072 (1910)
9. Churchill, S.W., "Critique of the Classical Algebraic Analogies be-
tween Heat, Mass, and Momentum Transfer," Ind. Eng. Chem. Res.,
36, 3878 (1987)
10. Churchill, S.W., "New Wine in New Bottles: Unexpected Findings in
Heat Transfer. Part III. The Prediction of Turbulent Convection with
Minimal Explicit Empiricism," Thermal Sci. Eng., 5(3), 13 (1997)
11. Churchill, S.W., M. Shinoda, and N. Arai, "A New Concept of Corre-
lation for Turbulent Convection," Thermal Sci. Eng., 8(4), 49 (2000)
12. Kays, W.M., "Turbulent Prandtl Number: Where are We?" J. Heat
Transfer Trans ASME, 116, 234 (1994)
13. Churchill, S.W., "A Reinterpretation of the Turbulent Prandtl Num-
ber," Ind. Eng. Chem. Res., in press O



letter to the editor


Dear Editor:
Late last year, you published our Letter to the Editor re-
garding a survey we were carrying out on the use of Inher-
ently Safer Design (ISD), meant to make the process indus-
try a lot safer. Several of your readers downloaded our ques-
tionnaire and sent their responses to us. We got responses
from eleven countries world wide.
The findings of the survey have just been published under
the title "Inherently Safer Design: Present and Future" in the
Transactions of the Institution of Chemical Engineers, Pro-
cess Safety and Environmental Progress, 80, Part B, May
2002.
We are pleased to enclose a copy of the publication for


Chemical Engineering Education










your reference. Further, the following is a brief summary of
the survey paper. It's appearance would be a fitting finale to
the effort that started with the initial publication of our letter
in your journal.

Summary
A recent survey of the current use of Inherently Safer Design
(ISD) concepts attracted responses from 63 people in 11 coun-
tries. These included industrialists, consultants, regulators,
and academics. The salient results of the survey are noted
below in bullet form to focus attention, followed by recom-
mendations to expedite the adoption and spread of ISD.
Almost everyone responding knows of ISD. Their
knowledge stems from specialized lectures, short
courses, books, conferences, and training videos.
ISD has been practiced by some for decades, whereas
others started only recently.
ISD is used in almost all stages of chemical process
development, design, and operation.
ISD is used during the manufacture of a whole range of
products.
Almost all hazards have been targeted, both on-shore
and off-shore.
The above attests to the universality of ISD applica-
tions.
There is a favorable impact on balance sheets.
It is important to use "Management of Change" when
implementing ISD to avoid introducing any new
hazards.
There is very little additional cost if implemented early.
Payback is fast.
Some applications/practitioners have won awards.
ISD is included in lectures at several institutions. More
will do so now.
Many are not familiar with the current Inherent Safety
(IS) indices. Those familiar with them have used them
sparingly. A simple, realistic index is needed that also
shows economic benefits. Detailed examples of use at
different stages of process development are necessary.
ISD concepts can influence R&D in various areas of
chemical engineering and chemistry.
ISD should encompass inherent safety, health, and
environment (ISHE).
ISD concepts, suitably modified, can be used for other
branches of engineering such as mining, construction,
transport, etc.
Current regulations do not force the use of ISD.

Recommendations
The sad truth is that ISD is applied when an ISD enthusiast is
on the team and not otherwise. Implementation of the recom-


mendations below might encourage the uptake of ISD.
Every chemist and chemical engineer should be trained
in ISD. Academics and professional bodies should lead
in this.
Other scientists and engineers should be given intro-
ductory lectures in ISD with examples from different
industries.
IChemE should make ISD a part of its approved degree
syllabus. Subsequently, it should persuade other
engineering and science accrediting societies to do
likewise.
There is a need to teach IS to management and finan-
cial people also since their role is crucial in encourag-
ing applications of ISD.
Dedicated funding by government and industry for
research and teaching in ISD will encourage many
academics to take it up.
Incentives by the government to cost share demonstra-
tion plants and provide tax breaks for ISD.
Expand ISD to encompass ISHE since the environment
and occupational health are day-to-day concerns. It
may eventually be extended to ISHEQ (Q for Quality)
since improvements in SHE will decisively impact
quality of product.
Companies should provide examples of ISD use in
various situations and the economic benefits reaped in
order to convince other industries, regulators, govern-
ment, the media, the public, academics, R&D funding
agencies, etc.
Involve the mainstream print and audiovisual media to
favorably impact public opinion.
Amend regulations to enforce the use of ISD.
Insistence by international agencies to include ISD in
projects that they fund in the same way that the World
Bank now insists on environmental impact assessment
studies in projects funded by it.
Some expected results
Tall columns of chemical plants will be reduced to one-
or two-story heights. This will improve the image of the
chemical industry.
Increased investment in process industry.
Less restrictive regulations.
Greater enrolments in UG and PG courses.
Significantly enhanced funding for R&D.
Adoption of ISD by other engineering disciplines,
especially the more accident-prone ones such as
construction, mining, transportation, etc.
J.P. Gupta
David W. Edwards
Loughborough University


Fall 2002


271











curriculum


NOVEL CONCEPTS FOR TEACHING


PARTICLE TECHNOLOGY



WOLFGANG PEUKERT, HANS-JOACHIM SCHMID
Munich University of Technology 85748 Garching, Germany


Particle technology is an interdisciplinary subject deal-
ing with disperse systems, including all types of solid
particles (aerosols, suspensions), liquid particles (drop-
lets, emulsions), and gaseous particles (bubbles). The main
focus of our current research and curriculum, however, is on
solid particles.
The goal of particle technology is producing and handling
disperse materials under economical and ecological con-
straints. The materials are produced due to a surplus value of
the product properties. Typical examples for these properties
are the taste of chocolate, the color of pigments, the strength
of concrete, or the electrical properties of semiconductors.
Consequently, this is also a key point in our curriculum.
In order to prepare a young engineer for his possible tasks
in industry and research, we have organized the curriculum
to reflect the structure of the field (see Figure 1). The field
can be structured generally in four levels. The first and most
fundamental level covers the elementary processes, i.e., the
physical fundamentals. They include the statistical founda-
tions of particle technology, multiphase flow, bulk mechan-
ics and powder flow, interfacial phenomena, and the interac-
tions of dispersed matter with electromagnetic radiation. On
the second level, we apply the fundamentals to machines and
unit operations. In our curriculum, we concentrate on separa-
tion processes, further strengthening students' capabilities in
multiphase flow phenomena. The third level considers whole
processes. Here, we teach the concept of product engineering,
i.e., how to tailor product properties. Consequently, we have a
close link to the applications, which are actually very broad:
Materials science (e.g., all ceramics manufacturing is in
fact applied particle technology)
Life science (e.g., proteins may be treated as small
particles in some respects, drug delivery)
Information technology (e.g., quantum dots, clean room
technology, chemical mechanical polishing)
Environmental engineering (e.g., particle separation)


How can the new areas be included in the
curriculum without disregarding the conven-
tional ones? In our opinion, the only answer
is that teaching the fundamentals is even
more important, but the examples given
to the students should change.

Traditionally, chemical engineering has been taught in
Germany using the unit-operations concept. In most univer-
sities, teaching particle technology has followed the concept
of Hans Rumpf, who stressed the physical fundamentals in
the basic course, which is followed by courses in agglomera-
tion, solid-liquid separation, or particle characterization, to
name just a few. Unfortunately, in the USA particle technol-
ogy is taught extensively in only a few universities. Students
learn how to design machines and processes that either keep
the particle size constant (i.e., separation, mixing) or change
the particle size (i.e., size reduction and size enlargement). In
the past, only mechanical means to produce and handle par-

Wolfgang Peukert got his diploma degree in
Chemical Engineering (1984) and PhD (1990)
at Karlsruhe University In 1998 he became a
full professor at Munich University of Technol-
ogy. He is the chair of solids and interface pro-
cess technology. He also leads the particle
technology research group and teaches par-
ticle technology.



Hans-Joachim Schmid got his diploma de-
gree in chemical engineering (1993) and PhD
in mechanical process engineering (1998)
from the University of Karlsruhe. He is a re-
search assistant in the particle technology
group at MUT His main research interests
are multiphase flows and particle character-
ization.


Copyright ChE Division of ASEE 2002


Chemical Engineering Education











tides were considered; therefore, particles larger than approxi-
mately Iim were mainly dealt with while the non-mechani-
cal methods of particle synthesis (e.g., crystallization, gas
phase processes) that lead to submicron particles were ne-
glected.
By introducing product properties, we address the overall
goal of a chemical process, i.e., the production of well-de-
fined product properties under economical and ecological
constraints. The concept of product engineering transcends
educational traditions and recognizes the end value of deal-

Main topics
Statistical foundations
-Fundamentals Physical-Chemical Aspects Multiphase flow
.Bulk mechanics
0 Interfaces
S(Interaction w. radiation)
-Unit operations Design Skills Particle separation
a CFD

L I Property and process function
L-Processes Particle formation
Particle consolidation
Application and
Characterization Information- Environmental -
Materials Life -
Sciences
Figure 1. Structure of particle technology curriculum and
courses offered at Munich University of Technology.


100 0,14


80- 0,10

property
S60-
handling 0,06
o property \ ,,
8 40- -
\------ ------------ -- 0,0o
0

0 0,1 0,2 0,35
particle size x / pm

Figure 2. Property functions of a typical pigment.

Showing the whole picture







molecule process
elementary unit operations









SIneraces and separation balance '


Figure 3. Teaching concept and new topics (gray).

Fall 2002


ing with process technology, i.e., the product property. Al-
though this point of view is not new, it is largely neglected in
the curriculum. Rumpf" coined the expression "property
function" for the end-product qualities as well as handling
characteristics. The property function is defined as
Product property = F(disperse properties and microstruc-
ture, chemical composition)
Disperse properties are particle-size distribution, particle
shape, particle morphology, and particle-surface characteris-
tics. As an example, Figure 2 shows the product quality of a
pigment (in this case the color strength per unit mass of pig-
ments) that improves with decreasing particle diameter. The
yield stress of the powder, as an important handling property,
also increases with smaller particles, indicating prohibitive
high resistance against powder flow. Obviously, there exists
an optimum where both product and handling quality are ac-
ceptable. One solution to this problem may be to optimize
powder formulation allowing both high product quality and
acceptable handling properties. Of course, there are many
other end-product qualities, such as taste (e.g., of chocolate),
strength (e.g., of concrete), activity (e.g., of a catalyst or a
drug), or the band gap (e.g., of a nanocrystalline semicon-
ductor). Typical handling characteristics are flowability, dust
development, filtration resistance, risk of explosion, and
abrasiveness, to name only a few. Polke and Krekel'2' intro-
duced the term "process function" to relate the disperse prop-
erties of the product to the production process and the educts
Disperse properties = F(process parameters, educts)
Process parameters include the types of machines and unit
operations as well as their interconnection, the operational
parameters. The art of chemical engineering in this context
involves designing the best process for producing the correct
dispersed properties, leading to the desired product quality
with a minimum of costs, including environmental costs.
This way, the product would achieve the highest profit
since it is the most competitive. Our point of view in-
cludes both the economical aspects and a global perspec-
tive of environmental responsibility.

EDUCATION IN PARTICLE TECHNOLOGY
AT TU MUNICH

Teaching Concept and New Topics

The particle technology courses are a part of the chemical
engineering and process engineering ("Verfahrenstechnik" in
German) curricula at the Munich University of Technology.
On one hand, the traditional education of chemical engineers
prepares students for well-known applications such as the
design of cyclones or heat exchangers, but many of the tradi-
tional applications have reached the point where their eco-
nomic success is decreasing. On the other hand, new oppor-
tunities are evolving in areas that are less familiar to engi-
neers, e.g., information technology or various aspects of ma-










trials science. The question is: How can the new areas
be included in the curriculum without disregarding the
conventional ones? In our opinion, the only answer is
that teaching the fundamentals is even more important,
but the examples given to the students should change.P3,4
In Figure 3, our approach is shown schematically. We
explain the whole picture to the students by showing
them the progression from molecular precursors to the
whole process, which actually covers many orders of
magnitude in both geometrical dimensions and time
scale. In other words, we pave the way from feed mate-
rials to end-product properties-this is the horizontal line.
In the vertical, depth is gained by explaining certain as-
pects in a detailed way. By reflecting the first three lev-
els of Figure 1, we stress particulate interfaces (funda-
mental level) since we believe that this aspect has not
been sufficiently covered in the past. Moreover, with the
advent of nanotechnology, interfacial aspects have be-
come increasingly important. The second level, compris-
ing unit operations, is handled in a more-or-less tradi-
tional way, although new aspects such as CFD model-
ing are included. On the process level, disperse systems
have to be treated mathematically by means of population
balance equations, which have so far not been covered in
traditional particle technology curricula.

Courses
The courses are organized into three levels. The first
and most fundamental level comprises a two-semester
course in "Fundamentals of Particle Technology" (see
Figure 4). In this course, the important foundations (rang-
ing from statistics, motion of particles in fluids, fracture
mechanics, to dimensional analysis) and their implica-
tion in mechanical process engineering are covered. In
addition, new elements such as population balances
(which are increasingly used in industry) and interfacial
phenomena are introduced. The latter comprise the fun-
damentals of interactions between molecules and par-
ticles, characterization of particulate interfaces and as-
pects of nanoparticle technology (e.g., coagulation and
stabilization of colloidal suspensions).
The second level stresses unit operations. Here, we
concentrate on "Particle Separation" (see Figure 5). This
course is principally organized in the traditional way,
focusing on separation of particles from gases as well as
solid-liquid separation. Different unit operations in gas-
solid separation are introduced systematically by focus-
ing on common principles, i.e., on transport mechanisms
of particles to the collecting surfaces of the respective
separators. In this way, various unit operations are treated
very efficiently, which allows for introduction of new,
modern methods such as CFD and its use for optimizing
such apparatuses. We also offer a complementary course


Figure 4. Fundamentals of Particle Technology course
(particle characterization included in separate course).


Gas solid separation
(dilute systems)
Fundamentals:
CFD and particle tracking


Solid liquid separation
(dense systems)
* suspension rheology
* sedimentation
* filtration
* flocculation


Figure 5. Particle Separation course.


) Particle production

process design property function
top down particle size and shape color
grinding
classification crystallinity taste
bottom up particle surface strength
gas phase synthesis
-crystallization particulate systems
agglomeratess, thin films...)
consolidation


S Pardti.
Populati


Figure 6. Product Engineering course.


Chemical Engineering Education












* relevant physics,
constituing equations,
assumptions
* realization:
arrangement,
sensor & signal
* how to calculate property
distribution? (-> inversion)
* derive capability and limits
of method
* practical aspects


Figure 7. Particle Characterization course.


Figure 8. Methodological approach.


Figure 9. Integrated approach of university education.


Aim:




promoting
understanding of
principles and
system
intercorrelations


physical-chemical
foundation


Technical Skills


Soft Skills





Soft Skills I


Fall 2002


dealing with "Downstream Processing of Biotechnologi-
cal Products" that focuses primarily on different unit op-
erations for separation, disintegration, and purification of
bioproducts as well as their interactions in the whole pro-
duction process. In several aspects, bioproducts such as
proteins can be regarded as nanoparticles, although the lim-
its of this point of view should be kept in mind.
A completely new course is being offered in product en-
gineering (see Figure 6). The key question is how to pro-
duce the physical properties that define the product prop-
erty, from the point of view of both handling and applica-
tion. Examples for property functions are presented to-
gether with various methods for producing the particles
(e.g., comminution and classification, gas phase synthesis
of nanoparticles, crystallization, and precipitation). Han-
dling and formulation topics round out this course. The
students learn key concepts for formation of structured
solids, product design, and powder processing systems. In
this context, the systems engineering approach is impor-
tant. There is also a course in particle characterization that
teaches the main principles in characterizing particle prop-
erties, e.g., concentration, size, shape, surface, and zeta
potential (see Figure 7). The purpose of this course is to
enable the students to choose an appropriate setup for ar-
bitrary particle characterization tasks. This is accomplished
by emphasizing the basic aspects of a measuring technique
(e.g., physical principle, signal recording, conditioning, and
evaluation) as well as a complete measurement system (in-
cluding sampling, transport, and preconditioning). These
principles are explained in conjunction with a choice of
the most important measurement techniques.
Whereas Fundamentals of Particle Technology I and II
are mandatory for all chemical engineering students, Par-
ticle Separation is one of a group of three courses (together
with Process and Plant Design and Design of Thermal Pro-
cesses) from which the students must choose two. The re-
maining courses are elective.
Methodology and Didactics
The course in particle technology follows several guide-
lines:
The key item is the product property approach, i.e.,
particles have physical properties such as particle
size distribution, particle shape, or particle morphol-
ogy that are closely related to product properties.
Although it is difficult to describe complete process
chains, we enhance the student's awareness of the
complete process.
From a methodological point of view, we believe that teach-
ing should follow a double-tracked approach. On one hand,
the teacher should stress the important physical founda-
tions, since excellent skills in the fundamental principles
will be essential for the students throughout their studies
and their professional lives. This implies that a large num-










ber of facts have to be taught, thus assigning an important
role to the teacher. On the other hand, to promote the stu-
dents' understanding of the underlying principles as well as
to sharpen their view of the complete process, active learn-
ing appears to be a key issue.13.5'61 We try to support this ac-
tive learning in different ways (see Figure 8).
Lab and virtual experiments are conducted so that students
can apply and transfer their acquired knowledge and get in-
volved with more realistic problems. This is accomplished
by a mandatory lab course (one semester) as well as lab com-
ponents that are integrated into the courses described above.
The lab experiments include a wide field of exemplary tasks
that include, for example, dust separation in cyclones, filtra-
tion, mixing, and particle characterization by laser diffrac-
tion as well as the investigation of the stability of colloidal
suspensions by dynamic light scattering. Furthermore, a com-
pletely new virtual lab is currently being established in the
course Product Engineering, with computer simulations of
disperse systems (e.g., crystallization, comminution) based
on population balances using commercial software (e.g.,
LabView and Parsival).
We also encourage the students to take an active role
throughout the courses wherever it is appropriate, for example,
in the particle characterization course. After introducing the
basic principles and the important characteristics of a mea-
surement systems (e.g., assessed equivalent particle size, sig-
nal recording, conditioning and evaluation, necessary sample
preparation, etc.) as well as discussing their application to
the most important measurement techniques, the students are
arranged in small groups. Each group is then assigned the
task of analyzing one measurement technique that is so far
unknown to them. They also have to prepare a presentation
of their results that will relay the most important facts to their
fellow students. The groups are supposed to work autono-
mously, with the teacher playing a more passive role and only
giving guidelines or help when asked. In this way, several
goals can be achieved.

The students work and access information autonomously,
e.g., from literature in a foreign language.
The group work necessitates that students find their roles
in a group and work together productively. 71
Finally, the students are given the chance to prepare and
give a presentation. Even listening and assessing the
presentation of other groups increases their ability in this
respect. This is a capability that is not practiced
enough."81

By actively preparing a small part of the course, the stu-
dents not only acquire valuable technical knowledge, but they
also get a chance to increase their "soft skills." Personal de-
velopment is often neglected in a university education. Stu-
dents should concentrate on both their technical skills and
their personal growth (see Figure 9). This includes an ability
for self-organization and focusing on defined targets, intrin-


sic motivation to reach goals, and an ability to communicate
results. On a deeper level, internal self-reflection is indis-
pensable for accepting personal strengths and weaknesses as
well as those of others. This is a precondition for all social skills.

CONCLUSIONS
Particle technology is a much wider field than many people
realize since it also comprises biochemical, chemical, and
thermal processes dealing with particles. Hence, it is not only
of the utmost importance in the chemical industry, where about
60-70% of all products are fabricated in dispersed form, but
also for a number of other fields, such as materials science
and information technology. Product properties and the sub-
sequently developed product engineering approach is at the
center of our considerations. With a continuously growing
number of applications for dispersed systems, we feel a need
to stress the fundamental aspects even more. With the gen-
erally observed trend toward finer particle sizes, new topics
such as particle interactions and population dynamics have
been included in order to prepare our students for newly de-
veloping areas such as nanotechnology. The technical courses
are complemented by various activities to strengthen the soft
skills of the students.
Recently, suggestions have been made by Cussler, et al.,[91
on how to change chemical engineering curriculae. Consid-
ering the shift in industrial practice from large-scale processes
producing commodities toward more specialized product
design, we feel that particle technology and particle design
methods deserve a prominent place in the curriculum.

ACKNOWLEDGMENTS
The authors would like to thank Professor Helmar Schubert
from the University of Karlsruhe for very valuable discussions.

REFERENCES
1. Rumpf, H. Uber die Eigenschaft von Nutzstiuben, Stab-Reinhaltung
derLuft, 27(1), p. 3 (1967)
2. Polke, R. and J. Krekel, "QualitAtssicherung bei der
Verfahrensentwicklung," Chem. Ing. Tech., 64(6), p. 528 (1992)
3. J.L. Cano, Garces, A., and Saenz, M.J. "Oral Presentations of Stu-
dents in Product Engineering Lectures." Int. J. Engg. Ed., 13(3), p.
175 (1997)
4. Cussler, E.L. "Do Changes in the Chemical Industry Imply Changes
in the Curriculum?" Chem. Eng. Ed., 33(1), p. 12 (1999)
5. Davis, R.H. "Helpful Hints for Effective Teaching," Chem. Eng.
Ed., 32(1), p. 36 (1998)
6. Felder, R.M., D.R. Woods, J.E. Stice, and A. Rugarcia. "The Future
of Engineering Education Part 2: Teaching Methods that Work."
Chem. Eng. Ed., 34(1), p. 26 (2000)
7. Humphreys, P., V. Lo, F. Chan, and G. Duggan, "Developing Trans-
ferable Groupwork Skills for Engineering Students," Int. J. Engg.
Ed., 17(1), p. 59 (2001)
8. Brostow, W., "Instruction in Materials Science and Engineering:
Modem Technology and the New Role of the Teacher," Mat. Sci.
andEng., A302, p. 181 (2001)
9. Cussler, E.L., D.W. Savage, A.P.J. Middelberg, and M. Kind. "Re-
focusing Chemical Engineering," Chem. Eng. Progr, 98(1), p. 26S
(2002) O


Chemical Engineering Education











Letter to the Editor
Continued from page 262.
b=8.5164364+1.5315505; the error variance
s2=0.467503; and correlation coefficient R2=0.953603.
Professor Fahidy advises not to put too much faith in the
linear regression model, in spite of the relatively large
R2 value, because of the extremely wide confidence in-
tervals on the parameter a. The fairly random distribu-
tion of the residuals (see Figure 2) suggests, however,
that the linear model may be the correct one. Further-
more, both physical considerations (fuel consumption
should be zero for a zero mass vehicle) and the wide
confidence intervals on the free parameter a, indicate that
the model can be improved by setting the free parameter
at zero. Indeed, carrying out the regression while setting
a=0 yields: b=7.8929160.3599903; s'=0.4641509, and
R2=0.9481781. Thus, this model is now acceptable, even
with respect to the confidence interval values.
One of Professor Fahidy's objectives in presenting this
example was to warn against accepting relatively large
R2 values as proof of good linear relationship between
the dependent and independent variables. The limitations
of the R2 statistics in this respect can be most strikingly
demonstrated using residual plots. Shacham, et al.,'31 for
example, fitted vapor pressure data of 1-propanol with
the two-parameter Clapeyron equation. This regression
yields the values: R2=0.9998818 and s-=1.659E-05
(based on log P). Such a high value of R2 can be inter-

m











Figure 2. Residual plot for Example 5 in Fahidy
paper.'




p
am




-D -- ---- .. .------------------------------------ -----------

Figure 3. Residual plot for vapor pressure data from
Reference 3.
Regression model: log P = 7.6380342-1622.8666/T

Fall 2002


preted as a perfect fit. But the residual plot (seen in Figure 3) shows
that the vapor pressure data set exhibits a curvature, which is not
predicted by the Clapeyron equation. Indeed, using the four-param-
eter Riedel equation for representation of the same data yields: R2=1;
s2= 1.327E-09 and randomly distributed residuals.
The last example, given in the Appendix of the article deals with a
linear model for representing coded effectiveness indicators versus
catalysts containing various coded platinum mass units. Analysis of
this example shows that if the free parameter, a, is set at zero (as
suggested by the wide confidence intervals on a and physical con-
siderations) the linear model is appropriate to represent the data with
8=1.64376590.0845917, R'=0.8860414, and s2=0.8508906.
We can conclude that teaching statistical analysis of data and re-
gression models is very important, but interpretation of numeric sta-
tistical indicators must be complemented by graphical analysis and
consideration of the physical nature of the model in order to arrive
at the correct conclusions.
Mordechai Shacham
Ben-Gurion University of the Negev
Neima Brauner
Tel-Aviv University
References
1. T.Z., "An Undergraduate Course in Applied Probability and Sta-
tistics," Chem. Eng. Ed., 36(2), 170 (2002)
2. Fahidy, T.Z., Personal communication (2002)
3. Shacham, M., N. Brauner, and M.B. Cutlip, "Replacing the Graph
Paper with Interactive Software in Modeling and Analysis of Ex-
perimental Data," Comp. Appl. Eng. Ed., 4(1), 241 (1996) 0


Author's Response
I am delighted at Professor Shacham's interest in my paper. I also
fully concur with the argument that the residual plots are an impor-
tant and integral part of regression analysis. This is now standard
textbook material, and I do routinely discuss this subject in my course.
Although my intention was to keep the article from being too long,
in retrospect I should have spent a paragraph or two on residual
analysis, and I regret the omission.
In Example 4 it was stated that the reaction mechanism was first-
order irreversible, but perhaps not strongly enough to imply an a
priori knowledge of non-statistical origin, so that 0'h and 2nd order
models are beyond consideration. With limited data and given a
physically correct model, the method that provides regression pa-
rameters relating data to model with the smallest error variance may
be acceptable in lack of something better, even if the residual plot
does not show randomness of a desired degree. The quest for addi-
tional measurements is almost universal in the case of limited-size data.
My views about R2 versus confidence intervals for true regression
parameters do not fully coincide with the respondents', but may I point
out the redundancy of seven-digit values, computer printouts notwith-
standing. An R2=0.8860414 is not more meaningful than R2=0.89
Thomas Z. Fahidy











, -classroom


GAS STATION PRICING GAME


A Lesson in Engineering Economics

and Business Strategies


AARON SIN, ALFRED M. CENTER
Cornell University Ithaca, NY 14850


he School of Chemical Engineering at Cornell Uni-
versity recently undertook an evaluation of its Mas-
ters of Engineering program to assess the curriculum
and the amount of value added to the student's education by
their participation in the program. One conclusion that we
reached was that students in a professional masters program
were most likely to go on, at least initially, to some kind of a
position in a corporate environment. To increase the likeli-
hood of their success in those early years on the job, we felt
that some level of knowledge of how a business unit works
and how an engineer fits into such a unit would be of signifi-
cant importance to their careers.
With this in mind we added a requirement that all M. Eng.
Candidates take a course that would give them some insight
into these areas. While there are a number of different courses
at Cornell that deal with related topics, there was no one course
that covered all of the areas that we thought were relevant.
This led to the development of a new course, primarily for
Masters of Engineering students, titled "Managing New Busi-
ness Development."
The course is an attempt to explain the business develop-
ment process as it is likely to be carried out in a major corpo-
ration. It deals with concept development, feasibility assess-
ment, front-end analysis to select the best implementation
strategy, tactics to take the concept forward, implementa-
tion of the selected strategy, and ongoing improvement
of the process once it is implemented to either increase or
maintain profitability.
The students are exposed to a number of different concepts.
As the course advances, they are asked to demonstrate their
knowledge through several case studies. The first case study
involves producing plans for executing a feasibility study to


introduce a new line of cosmetics in a newly opened over-
seas market. The second involves maximizing value from a
feedstock that contains a number of different components.
One of the concepts we found particularly difficult to get
across to the students was pricing strategy. To provide a means
for hands-on experience with this concept, we developed what
we call the "gas station game." Unlike most games in busi-
ness schools that generally involve multiple inputs and fo-
cuses at sitewide or businesswide optimization in a qualita-
tive manner, this is a quantitative pricing game that aims at
illustrating market forces at work. Since most people in the
U.S. regularly deal with the fluctuation of gas prices, it is
easy for the students to relate to it. We play this game every
time the class meets.

THE GAS STATION GAME
In the game, students are divided into four groups, with
each of them managing a gas station. Operating under differ-
ent restrictions ("mom and pop" versus "big chain"), students
are asked to decide on their business goals and facility sizes,
which in turn lead to pricing structure and marketing tactics.
We found that it is generally effective to have students per-


Aaron Sin received his B. ChE. in 1998 from the University of Delaware,
where he was trained to become a practical engineer. At Cornell, he
used this knowledge to design microfluidic devices for pharmaceutical
testing with his research advisor. Aaron is completing his Ph.D. thesis
and considering a career in academia.
Alfred Center is a registered professional engineer with over thirty years
of experience in the petroleum industry. He is now a senior lecturer in
chemical engineering at Cornell, teaching classes in unit operations labo-
ratory, senior design, project management process control, and busi-
ness development strategies.


Copyright ChE Division of ASEE 2002


Chemical Engineering Education











form cash flow analyses for different scenarios. (The project
assignment is shown in Appendix A.) The cost parameters
are approximated and tested to produce realistic profit fig-
ures in the end. Capital costs include the storage tank mate-
rial and installation, gas pumps, land requirement, engi-
neering costs, etc. The operating costs are estimated as
10% of the capital investment, assuming a ten-year project
lifetime.
When the students are ready for the actual price bidding, a
simulation is used to determine the demand in each station,
based on the four stated prices (see Figure 1). The simulation
is modified from the Monte Carlo Gillespie algorithm from
reaction kinetics. Simply, the probability of customers visit-
ing each gas station is inversely proportional to the price dif-
ference between that particular station and the minimum bid-
der. The simulation then uses a random number generator
to determine the exact demand for each station. An extra
station with a fixed price is added to model gas stations
from outside this town.
To account for different levels of service provided by each
station (e.g., method of payment that is accepted), the prices
are adjusted before the probabilities are calculated. These ad-


justment amounts are based on polls conducted among stu-
dents regarding their own consumer preferences. The simu-
lation also includes some proportion of cars that stop at the
first gas station in sight instead of comparing prices, which
again is determined using a Gillespie algorithm with a prede-
termined probability.
The profit of each company is calculated based on the num-
ber of gallons sold minus operating costs of the gas station.
As mentioned before, each group decides in advance what
the suitable underground storage capacity will be, which gives
rise to certain capital costs and operating costs. In the event
that the gas station sells more gas than its capacity al-
lows, it will have to obtain extra gas at 115% of the maxi-
mum price among the four gas stations. In this way, each
gas station is equally profitable if the right price relative
to each other is found.

RESULTS AND DISCUSSIONS
The results of the game are quite encouraging. We are try-
ing to teach the concepts of customer perception of product
value, convenience, and price differentiation based on those
perceptions. We are also trying to show that the strategy of


cM 6 l v:fc Ed4iet Y 'w nsr ofrrr locs Dali Wiidow eHt;p







iM S Peaned Period 2 P,,od3 PeIod 4 Penod S Penod 6
4 PnI -' Gs Sttion Maome Car o 51mulaMon
5 N Cars 51 430
f agals Gas Scanon Monte Curio a87
7 R*nvnue 89ro
S u:sIall Ei ow 0 r60r
11 Cars 4
12' #gulu *9 1 1 *whcb-*1 496
13 Revenue 160
14 Pro Staot 1 2aAl0 2 lh I s 2 an4 1542
1i S1tti4ll II .18813
IaPtreo i 3 t"O 1401 [ | 1t33
17 #Cars 150
S. gals PaeI La I i0l i ratIoin c8 ton
19 Rvenu 2360
218lrM m" I Ahfol I >hlll Hohfr F ^r 3S r t 2 r1 I:ri
21i .illkn ( IV .466 I6
22 Pnca 1rpi I E0i ot I (iiE1 I al Im t |
23'Cars 1 1 470
24 i.-ia Trot [~jji SaaiBJ El iiiEl 2W6
2S R2venu 25450
25 Profo PerloO | t Owi 7 412
-i --- .3.' 66
2s:Tatal #cad
297

1 r1


Figure 1. The gas station game simulation in action.


Fall 2002











maximizing an individual player's revenue did not necessar-
ily mean defeating the others. And, in fact, the most favor-
able revenue picture is one in which all participants were able
to share the market in some fashion.
We found that within approximately ten iterations, the stu-
dents were able to arrive at the conclusion that a shared mar-
ket created more revenue and that cutthroat competition was
unlikely to succeed. With this realization, the students go on
to develop pricing strategies that allow each of them to sell
close to their facility's capacity and to maximize their in-
dividual revenues.
Figure 2 shows a typical adjustment process based on root-
mean-squared deviations in prices and revenues, as compared
to values at the last iteration. At around the tenth iteration,
prices begin to converge to the range where a reasonable profit
is sustained among all stations. The revenues continue to fluc-
tuate, on the other hand, since students often react to price
changes of the other stations after their demands have
changed, instead of anticipating the behavior of the oth-
ers. These fluctuations are likely to stabilize if we carry
the game further.

CONCLUSION
We think this game provides an easy way to teach pricing
strategy in a fairly simplistic business model, and we are happy
to pass along this game for your interest and use.



APPENDIX A
Assignment Sheet
for the Gas Station Pricing Game


There are four gas stations on Rt. 13, coming into Ithaca.
They are about a block apart, as indicated in the figure be-
low.


Figure 1A: Map of the four gas stations

Preliminary market research indicates a demand of about
120 cars/hr in the day and 20 cars/hr at night, at 10 gals/car.
While some percentage of the drivers go to the first gas sta-
tion in sight, most make that decision based on things such as
price, convenience (credit card/speed pass), and brand name.
They also have the choice of getting gas from the next town
if they feel prices are too high.
Your first task is to decide on the amount of investment,


15.00%a
*-7500
-o-Price
S12.50% Deviation
P -Revenue
o.o Deviation 5000
10.00%


.00% 2500


> 0
n0 &

2.50%

0.00% -2500
1 2 3 4 5 6 7 8 9 1011121314151617
Iteration
Figure 2. The adjustment process: root mean squared de-
viation in prices relative to final average price (left axis)
and root mean squared deviation in revenues (right axis)
plotted against iteration number.


TABLE 1
Differences between Mom/Pop Operations
and Chain Companies

Investment Supply Cost Personnel Service
Mom/Pop $300,000 $1.45/gal I @ $5/hr 12 hr
Chain Unlimited $1.47/gal 2 @ $5/hr Speed pass



TABLE 2
Gas Station Configurations and Costs

Capacities 20,000gal 25,000 gal 30,000 gal 40,000 gal
Capital Cost $200,000 $300,000 $400,000 $500,000

Operating Cost $56/day $84/day $111/day $138/day


level of service, and pricing strategy for your gas station. Your
decision will depend on the nature of your company (mom/
pop vs. chain), as listed in Table 1. Table 2 lists the available
gas station configurations.
The supply trucks come every seven days to refill the
underground gas tanks. If you sell more gas than your
designed capacity, the extra gas will be available at 115%
x Max gas price in Ithaca.
The goal of this exercise is to achieve the highest return on
investment among all groups, with a minimum acceptable
ROI at 12% per year. You will be able to change your
prices (and only prices) every week, depending on the
market situation. O


Chemical Engineering Education


I II IV
- Rt. 13 to Ithaca -

III












Mfjannouncements


CONFERENCE


TEACHING
ENTREPRENEURIAL ENGINEERING

Monterey, California
January 13-16, 2003

Engineering educators have done a great job of teaching
students engineering science and engineering design. In ad-
dition, engineering schools are beginning to address the de-
velopment of "soft skills" such as communications, team-
work, and ethics. In the current environment, it is increas-
ingly important for the engineering education system to also
find ways of teaching entrepreneurship and motivating stu-
dents toward such activities. This conference will set the stage
for a continuing and fruitful dialog between engineering edu-
cators and the business community.
The conference will assemble entrepreneurs, engineering
educators, and business school faculty to discuss

What are the attributes of successful entrepreneurs?
What are models of successful programs teaching
entrepreneurship to engineers?
What is the culture at a university that fosters a spirit
of innovation and entrepreneurship?
*How can engineering faculty become role models of
innovation and entrepreneurship?

The outcomes of the conference will be a set of recom-
mendations to engineering faculty, curricular integration op-
tions, model programs available for replication, and contacts
between academic and business that will be published in the
journals of various professional societies.
The Chairs of the Conference are Eleanor Baum of The
Cooper Union and Carl McHargue of the University of Ten-
nessee.
Additional information about this Conference, and a regis-
tration form, can be found at the Conference's web site:

Engineering Conferences International offices are located
at
6 MetroTech Center, Brooklyn, NY 11201
Telephone at 212-591-8144 Fax at 212-591-8145
e-mail at bhconf@poly.edu
web at www.engconfintl.org.


CONFERENCE


ENHANCEMENT OF THE GLOBAL PERSPECTIVE
FOR ENGINEERING STUDENTS BY PROVIDING
AN INTERNATIONAL EXPERIENCE

Tomar, Portugal
April 6-11, 2003

This conference will provide a forum for exchange of ideas
on methods of enhancing the global perspective of engineer-
ing students, identify the key obstacles, and discuss progress
toward eliminating the obstacles. The conference is jointly
sponsored by Engineering Conferences International, Ordem
des Engenheiros, Portugal, and E4 (Enhancing Engineering
Education in Europe). Thematic Network is financed by the
European Commission under SOCRATES II and co-financed
by the University of Florence. Contact
for more information
or go to
.
The conference will focus on the recognition that exposure
to other cultures brings personal enrichment to individuals
and can be an important component of the educational expe-
rience. With the increased globalization of economies, the
need extends beyond personal enrichment and has become
an important asset to student mobility. Among the issues that
must be addressed are compatibility of degree systems, ac-
creditation of courses and/or degrees, quality assurance, an
accepted credit system, language of instruction, and legal and
social issues such as visas, taxation, and financial support.
The Chairs of the Conference are Carl McHargue of the
University of Tennessee and Eleanor Baum of The Cooper
Union (New York, NY). The Co-Chairs are Antonio Salgado
Baros of the Orem dos Engenheiros (Portugal), G. Augusti
of the University of Rome (LaSapienza, Italy), and C. Borri
of the University of Florence (Italy).
Additional information about this conference, and a regis-
tration form, can be found at the Conference's web site

Engineering Conferences International (ECI) is the suc-
cessor to the United Engineering Foundation Conferences.
ECI offices are located at 6 MetroTech Center, Brooklyn,
NY 11201
Telephone at 212-591-8144,-Fax at 212-591-8145
e-mail at bhconf@poly.edu- web at www.engconfintl.org.


Fall 2002














Random Thoughts...






SPEAKING OF EDUCATION III





RICHARD M. FIELDER
North Carolina State University Raleigh, NC 27695


here is a theory which states that if ever anyone
discovers exactly what the Universe is for and why it
is here, it will instantly disappear and be replaced by
something even more bizarre and inexplicable. There is
another theory which states that this has already happened.
(Douglas Adams)


A lecture is a process by which the notes of the professor
become the notes of the students without passing through the
minds of either.


If a professor can be replaced by a CD-ROM, he/she should
be.
(Jack Wilson)


I'm sure the reason such young nitwits are produced in our
schools is because they have no contact with anything of any
use in everyday life.

(Petronius, d. ~66 AD)


(R.K. Rathbun)


Times are bad. Children no longer obey their parents, and
everyone is writing a book.


A teacher who is attempting to teach without inspiring the
pupil with a desire to learn is hammering on a cold iron.


(Horace Mann)


What's on your mind, if you'll forgive the overstatement?


Teachers who cannot keep students involved and excited for
several hours in the classroom should not be there.


(John Roueche)


(Cicero)


(Fred A lien)


Everything should be made as simple as possible, but not
simpler.

(Albert Einstein)



In theory, there is no difference between theory and practice;
in practice, there is.

(Chuck Reid)


Copyright ChE Division of ASEE 2002


Chemical Engineering Education


Richard M. Felder is Hoechst Celanese Pro-
fessor Emeritus of Chemical Engineering at
North Carolina State University. He received
his BChE from City College of CUNY and his
PhD from Princeton. He is coauthor of the text
Elementary Principles of Chemical Processes
(Wiley, 2000) and codirector of the ASEE Na-
tional Effective Teaching Institute

















To state a theorem and then to show examples of it is literally
to teach backwards.
(E. Kim Nebeuts)


Setting an example is not the main means of influencing
another, it is the only means.
(Albert Einstein)


There is a legend that the difference between classes of
freshmen and post-graduates is that if you say "Good
Morning" to the first, they reply "Good Morning." But the
graduate students write it down.


(Donald Bligh)


I used to keep my college roommate from reading my
personal mail by hiding it in her textbooks.


Education is what happens to the other person, not what
comes out of the mouth of the educator.


(Joan Welsh)


(Miles Horton)


Education is the ability to listen to almost anything without
losing your temper or your self-confidence.

(Robert Frost)


Lack of education is an extraordinary handicap when one is
being offensive.


Predicting the future is easy. It's trying to figure out what's
going on now that's hard.
(Fritz Dressier)



If I knew what I was looking for, it wouldn't be research,
would it?

(Richard Feynmann)


(Josephine Tey)


Education is one of the few things a person is willing to pay
for and not get.
(William Lowe Bryan)


Education is what survives when what has been learned has
been forgotten.


If I accept you as you are, I will make you worse; however if
I treat you as though you are what you are capable of
becoming, I help you become that.


(Goethe)


Teaching is the greatest act of optimism.


(B.F Skinner)


(Colleen Wilcox)


A graduation ceremony is an event where the commencement
speaker tells thousands of students dressed in identical caps
and gowns that individuality is the key to success.


Try not to have a good time...this is supposed to be educa-
tional.


(Robert Orben)


(Charles Schulz)


Fall 2002


All of the Random Thoughts columns are now available on the World Wide Web at
http://www.ncsu.edu/effectiveteaching and at http://che.ufl.edu/-cee/











e,] classroom


MAKING PHASE EQUILIBRIUM MORE


USER-FRIENDLY



MICHAEL J. MISOVICH
Rose-Hulman Institute of Technology Terre Haute, IN 47803


I believe phase equilibrium thermodynamics is the most
conceptually difficult undergraduate chemical engineer
ing class. Even students who perform calculations sat-
isfactorily seem confused over the meaning of what they
have learned.
Phase equilibrium is the single undergraduate chemical
engineering class in which abstract concepts are presented to
the near exclusion of practical applications. Table 1 gives
examples of practical or physically intuitive subject matter
found in classes that students typically consider abstract, theo-
retical, or mathematical. These actually contain some bal-
ance of theory and practice, giving students a point of refer-
ence to physical processes and equipment. Calculations such
as bubble and dew points are needed for practical design, of
course, but most phase equilibrium courses do not connect
these to real processes or equipment. Practical applications
of the material are taught as part of unit operations, mass
transfer, or distillation courses.
Students frequently have more intuition about the physical
meaning of abstract quantities in classes other than phase equi-
librium. Heat transfer students could define the Prandtl num-
ber as Cp/! k, give a physical interpretation for all three
variables, and potentially recognize related facts. For example,


"The Prandtl number could be derived by applying
the Buckingham Pi theorem to a heat transfer prob-
lem," or "Larger Prandtl numbers result in larger con-
vective heat transfer coefficients." They know that
the Prandtl number for liquid water at 100 atm and
1500C is unlikely to be 100 or 0.01.
When phase equilibrium students define chemical
potential, it is typically in terms of other abstract con-
cepts-free energy, standard states, fugacity, and ac-
tivity. They are unlikely to know whether a certain
chemical potential is positive or negative, nor what
practical significance its sign would have. Without
doing a calculation, how many phase equilibrium stu-
dents know whether the fugacity of liquid water at


100 atm and 1500C is closest to 5 atm, 50 atm, or 500 atm?
Most are at a complete loss when asked to apply abstract
quantities such as activity coefficients to practical questions,
e.g., "Is ethanol more likely to form an azeotrope with n-
hexane or n-octane?" Lacking qualitative understanding,
their only approach for answering this question is detailed
quantitative calculation.

STRATEGIES FOR BUILDING INTUITION
Prausnitz, et al.,"11 describes the phase equilibrium prob-
lem as a three-step process. First, a real problem is translated
into an abstract mathematical problem. Second, the math-
ematical problem is solved. In the final step, the mathemati-
cal solution is translated back into physically meaningful


TABLE 1
Content of "Theoretical" ChE Classes


Class
Fluid Mechanics

Mass Transfer
Transport Phenomena


Phase Equilibrium


Theoretical Concepts
Shear stress tensor,
Dimensional Analysis
Fluxes of all sorts
Partial differential
equations, Dimensionless
Greek variables
Chemical potential
fugacity, activity


Practical Concepts
Pumps, Valves, Piping

Packed absorption towers
Viscometers, Heat transfer
with free convection,
Wetted wall columns
Bubble and Dew Points,
Flash, Solubilities


@ Copyright ChE Division of ASEE 2002


Chemical Engineering Education


Michael Misovich will be Associate Profes-
sorin the Physics and Engineering Department
of Hope College in August, 2002. His research
interests include thermodynamic property pre-
dictions from equations of state, physical chem-
istry of polymer solutions, chemical engineer-
ing education, and its assessment.












TABLE 2
Common Intuition about Chemical Engineering Data

* High molecular weight compounds have high boiling points
* A substance with a density order of magnitude less than water is
probably a gas
* A Reynolds number in the laminar range for flow of water in
typical process piping is not typical
* Convective heat transfer coefficients are very low for gases as
compared to liquids





TABLE 3
Uncommon Intuition about Phase Equilibrium Data

* The fugacity of a liquid is approximately its vapor pressure, as
long as the pressure is not extremely high
* The fugacity of a component in an ideal gas mixture is its partial
pressure
* Substances we consider noncondensible gases have fugacity
coefficients larger than one; liquids and condensible vapors have
fugacity coefficients smaller than one
* Substances with large differences in boiling points are unlikely to
form azeotropes; substances with very close boiling points are
almost certain to form them
* Activity coefficients larger than approximately seven indicate
that liquid-liquid phase separation is possible
* The dilute component in either of two nearly immiscible phases
obeys Henry's Law up to its solubility limit


terms. Typically, this step consists of transforming highly
abstract variables into physically significant ones.
Chemical Potential -) Fugacity Activity 4 Composition
Each transformation results in a less abstract variable than
the previous step. Students do not seem to recognize this,
perhaps because we do not teach it explicitly. Instead, they
see chemical potential, fugacity, and activity as equally nebu-
lous and abstract concepts upon which a rote series of math-
ematical operations will hopefully produce a physically mean-
ingful variable such as composition, pressure, or temperature.
One of my principal goals in teaching phase equilibrium
thermodynamics is to help students develop an intuitive un-
derstanding of the topic. I point out to them in the beginning
that this class deals with techniques for generating data to
use in other classes to the nearly total exclusion of applica-
tions. Since students will not be able to rely on processes or
equipment to provide intuition, I emphasize understanding the
data and its significance. This type of intuition about data, rather
than equipment, occurs in other classes as the Prandtl number
example above and as similar examples in Table 2 indicate.
To promote this, I emphasize calculation and use of data
having an obvious physical interpretation, e.g., temperature,
pressure, volume, vapor pressure, composition, and enthalpy.
When concepts such as free energy, chemical potential, fugac-
ity, and activity are presented, the focus is partly on their use
in solving for the more physical variables. Whenever pos-
sible, I encourage students to examine how the abstract vari-
ables affect the physical variables, and thus to develop some
intuition about the significance of the abstract variables. Ex-


TABLE 4
Comparison of Graphical Figure Use in ChE Textbooks


Non-graph
Graph Figures Figures


Introduction to Chemical
Engineering Thermodynamics'2'
(Chapters 10-15)
Chemical and Process
Thermodynamics'3'
(Chapters 9-13)
Transport Phenomenal'4
Elementary Principles of Chemical
Processes'5'
(Chapter 6)
Momentum, Heat, and Mass
Transfer"5'
(Chapters 35, 37-40)


Graphs per Percent Graph
Pes" 100 paes Figures


44 568
(11) (199)

60 541
(6) (253)
105 711

15 587
(0) (71)


773
(143)


71
(84)

66
(91)
40

53
(100)


21 60
(44) (77)


'Graph figures include all two- and three-dimensional coordinate plots and nomographs. Any figure that
included both graphical and nongraphical information was treated as a graph figure. Only numbered, captioned
figures in text and examples were counted; figures with problems and in appendices were excluded.
bPages include all text, examples, questions, and problems but exclude appendices.


amples are given in Table 3;
these are sometimes
present, but not frequently
emphasized, in phase equi-
librium texts.

More so than in many
chemical engineering
classes, phase equilibrium
data are most useful and un-
derstandable when pre-
sented graphically. This is
evident from observations
given in Table 4 of how fre-
quently graphical material
is presented in textbooks.

Thermodynamics and
unit operations texts contain
more graphs and a higher
proportion of figures that
are graphs, as opposed to
schematic diagrams and
other drawings. Within each
text, the chapters more


Textbook


Fall 2002











closely related to phase equilibrium have a higher proportion
of graphs than the text as a whole, as indicated by the num-
bers in parentheses in Table 4.
Furthermore, many students have a visual learning style.
These students may struggle with equations and textual in-
formation, especially in an abstract context, and it is crucial
that they see data presented graphically and also learn how to
prepare data in a format that is most comprehensible to them.
Hence, students need to make the connection between calcu-
lations and equations discussed in class and graphical pre-
sentation of phase equilibrium data. To assure they are ca-
pable of both understanding and generating graphical data, I
assign a significant number of computer problems requiring
this, as explained in further detail later in this article. Com-
puter spreadsheets have been previously suggested17,' for use
in solving phase equilibrium and equation-of-state calcula-
tions, and they are well suited both for the calcula-
tions and for subsequent graphical presentation. One
recent text[91 includes a number of example spread-
sheets that may be used for applications similar to those
described in this article, although I prefer to have stu-
dents write their own spreadsheets. 10


DETAILS OF
PHASE DIAGRAM
COMPUTER ASSIGNMENT
As an illustration of such assignments, consider the
construction of a binary Pxy diagram for an ideal so-
lution at some constant temperature. Figure 1 is an
example generated by repetitive dew point pressure
and bubble point pressure calculations. Taking liquid
mole fraction x, as the independent variable, and as-
suming component vapor pressures plsat and p2at are
known, Eqs. (1-3) allow calculation of all dependent
variables in the problem. To generate the diagram, al-
low x, to vary over the range 0.0 to 1.0. These calcu-
lations are easily done using computer spreadsheet
software.


X2 = 1 1

P = XlPsat + x2P2at
X Psat
Pxl P
Yl-
P


Figure 2 shows the general organization of this spread-
sheet. The upper rows contain headings and constants
such as the vapor pressures. The middle rows are used
for calculations. The leftmost column is initially filled
with values between 0 and 1 at intervals of 0.01, or a
suitable small increment. (This should be done using
spreadsheet commands or formulas; occasionally, a
student will attempt to enter the numbers manually
and become frustrated that using the computer appar-

286


ently makes solving the problem too time-consuming.) Fill
the remaining three columns in the middle rows of the spread-
sheet with formulas given by Eqs. (1-3). If these formulas
are entered correctly in the first of the middle rows, a single
copy/paste command generates the entire table through the
remaining middle rows.
There may be one complication in producing a graph from
these results. In a conventional Pxy diagram, pressure is taken
as the vertical coordinate twice. With liquid composition as
the horizontal coordinate, a bubble point curve is produced,
then with vapor composition as the horizontal coordinate, a
dew point curve is produced. To do this on the spreadsheet, a
single y-coordinate must be paired with two different x-co-
ordinates. At one time, few spreadsheet packages included
this capability, but many recent versions (including Microsoft
Excel) now allow it. If using an older package without this

P-x-y DiagramatT= 100deg C
Methyl isopmpy keone (1) ietyl ketone(2)









,-- ---- -- -






0 01 0.2 0.3 0.4 05 0.6 07 0.8 0.9 1
xl. yt

Figure 1. Pxy diagram prepared using spreadsheet.


Headings
and
Constants
(xl values)
0.00
0.01
0.02
x2 values P values yi values (Blank)

0.99
1.00



Copy of (Blank) Copy of
yi values P values





Figure 2. General structure of spreadsheet for Pxy diagram.


Chemical Engineering Education


1000




soO
800

700

600











capability, set up the lower rows of Figure 2 as shown, then
define the first column as the x-coordinate for graphing and
each of the two columns containing pressure values as sepa-
rate y-coordinates. The lower rows of Figure 2 can be omit-
ted when using current versions of Excel and other spread-
sheets that allow multiple xy pairs to be graphed.

ADDITIONAL COMPUTER ASSIGNMENTS
Table 5 lists other thermodynamic data graphs prepared
using computer spreadsheets. A very brief discussion of each
follows. Many were prepared by students as homework as-
signments using techniques similar to those outlined for the
Pxy diagram. Copies of these assignments are available upon



TABLE 5
Graphs Prepared Using Spreadsheets
for Phase Equilibrium Class

Binary phase diagrams for ideal solutions
Pxya
Txyb
xya

Fugacity versus pressure
Numerical integration of PV datab
Generalized viral coefficient
Redlich-Kwong equation of state'

Volumetric properties of binary nonideal solutions
Excess volume
Partial molar excess volumes"

Activity coefficients in binary solutions versus composition
Margulesa
Van Laarb
Wilson"

Infinite dilution activity versus temperature
Wilson"

Phase diagram for nonideal azeotrope forming binary mixture
Pxyb
Txyb
xya

Excess free energy of homogeneous azeotrope forming binary
mixture versus composition
Experimental data"
Margules equation (fit to azeotrope data)"
Margules equation (best fit to VLE data)"
Wilson equation (literature constants)b

Excess free energy of heterogeneous azeotrope forming binary
mixture versus composition
Experimental data"
Margules equation (best fit to VLE data)"
Margules equation (best fit to LLE solubility data)"


"Prepared by students as homework assignment
"Prepared by instructor for class discussion


request. Some graphs were not assigned but were generated
by the instructor and presented during class discussion.
The same spreadsheet data used to produce a Pxy diagram
as described above could be used to plot an xy diagram at
constant temperature. Pxy and Txy are the predominant rep-
resentations of VLE data in phase equilibrium classes, but
xy is probably the most frequently used format of the phase
equilibrium data in other classes, e.g., distillation, absorp-
tion, mass transfer.
Using the method described above, generating Pxy data
for an ideal binary system at constant temperature does not
require trial and error. Calculation of a single Txy datum for
an ideal binary system at constant pressure requires iteration
or trial and error since the vapor pressures are functions of
temperature. But generating a Txy diagram for such a system
-the locus of dew and bubble point temperatures for all pos-
sible compositions- does not require trial and error. Taking
temperature as the independent variable rather than liquid
composition, all other variables can be calculated directly by
Eqs. (1-3). Selecting a range of temperatures in increments be-
tween the pure-component boiling points generates the diagram.
Plotting y versus x instead of T versus y and T versus x pro-
duces an xy diagram at constant pressure from the same data.
For nonideal binary mixtures, activity coefficients are func-
tions of liquid composition and possibly temperature. Pxy
and xy diagrams at constant temperature are generated in a
straightforward fashion without iteration since temperature
is fixed and liquid composition is taken as the independent
variable for generating the table as described above.
Iteration cannot be avoided when generating Txy and xy
diagrams at constant pressure for nonideal binaries. To find
activity coefficients and vapor pressures, liquid composition
and temperature are needed. Only one can be assumed. Di-
rect calculation of liquid composition from vapor pressure,
as in the ideal case, is not possible. If temperature is used as
the independent variable, as suggested for the ideal case, a
unique composition may not result because azeotropes are
possible. I recommend using liquid mole fraction as the in-
dependent variable ranging from 0 to 1, as in the Pxy dia-
grams. Iteration can be performed by circular recalculation
on the spreadsheet. Unfortunately, spreadsheets vary signifi-
cantly in their implementation of circular recalculation, even
from version to version, and it is difficult to give a "recipe"
that works in all cases. Often, particular rearrangements of
equations or ordering of the columns is necessary. No matter
what package was being used, however, I have always been
able to find some method that eventually worked.
Thermodynamics textbooks commonly contain graphs of
excess and partial excess properties such as volume and en-
thalpy for binary solutions. In the volumetric properties as-
signment, students generate similar graphs for ethanol-water
using density data as a function of composition taken from
Continued on page 291.


Fall 2002











MM laboratory


CHEM-E-CAR

DOWNUNDER


Victoria 3800 Australia


he Chem-E-Car competition has been run for under-
graduates by the AIChE for the past three years with
finals at the AIChE annual meetings. The idea is for
teams of undergraduate students to design and build a small
car powered by a chemical reaction. The objective is for the
car to travel a certain distance and then stop. The distance to
be traveled and the weight to be carried by the car are not
announced until the day of the competition. The emphasis is
on control of a chemical reaction, with a keen eye on safety
and the environmental impact of the design. The winner is
the team whose car stops nearest to the required distance. In
addition to designing and building the car, each team must
make a poster that describes the car's operation and include a
safety and environmental assessment.
Having witnessed the enthusiasm of the participating stu-
dents and spectators at the AIChE Chem-E-Car Competition
finals held in Dallas and Los Angeles, I decided to organize a
Chem-E-Car competition here in Australia. Early in 2001, I
contacted all chemical engineering departments in Australia
and New Zealand, sent them copies of the rules (for the AIChE
competition), and invited them to join. Six departments re-
sponded enthusiastically, and within a couple of months teams
of students were working away. The original plan was to have
local competitions within each department, with these com-
petitions generating finalists for the grand Australasian final.
University work and the difficulty of the Chem-E-Car task
took its toll, however. Several teams fell by the wayside, in-
cluding the team from my department. As time went on, it


Martin Rhodes is Professor in the Depart-
ment of Chemical Engineering at Monash
University in Melbourne, Australia. He has a
keen interest in chemical engineering educa-
tion and specializes in particle technology, a
subject on which he has written an under-
graduate textbook. His research interests in-
clude fluidization, gas-particle flows, interpar-
ticle forces, and particle mixing.


Copyright ChE Division of ASEE 2002


became clear that the grand final would be a fight between
five teams-four from Australia and one from the National
University of Singapore, who, upon hearing about the com-
petition, asked if they could take part. The grand final was
held on day three of the World Congress of Chemical Engi-


Figure 1. The NUS car (a) with bodywork removed to
reveal the inner detail and (b) in motion.


Figure 2. The UNSW car drifting through its self-
generated mist.


Chemical Engineering Education


MARTIN RHODES
Monash University Melbourne,


--~- '










neering at the Melbourne Exhibition Centre in late September.

THE TEAMS AND THE CARS
National University of Singapore (NUS)
The NUS car (Figure 1) used the decomposition of 15%
hydrogen peroxide solution with dilute potassium perman-
ganate solution as a catalyst to generate oxygen, which was
stored in the stainless steel reactor. Opening the ball valve at
the rear of the reactor released the contents in short order,
propelling the car along. The car was stopped by friction.
The distance traveled was controlled by adjusting the quanti-
ties of reactant used and the time for reaction.
During the test runs prior to the competition, this car an-
nounced itself with a loud bang and blew away the plastic
sheeting that had been specially erected as a splashguard be-
hind the start line. Race helpers hurriedly modified and re-
erected the splashguard. The valve on the rear of the reactor
was equipped with a lengthened handle. Starting the car in-


figure 3. The Sydney University
three-wheeled, two-cell car.


Figure 4. The Newt
experiencing ter
probl


Figure 5. The Newcastle Two team's car a) running without
b) in full sparkling glory.


volved swinging an oversized pair of laboratory tongs, golf-
iron style, to hit the handle and swiftly open the valve. The
swipe with the tongs only happened at the precise time, dic-
tated by the reaction countdown.
On its first official competition run, the team member wield-
ing the tongs was either a little too enthusiastic or had poor
aim; the result was that the car turned onto its side within a
few meters of the start line.
University of New South Wales (UNSW)
The UNSW car, named "Cold Power," was powered by a
1.5-3V electric motor running from an electrochemical cell.
The cell used solutions zinc sulfate and copper sulfate with
zinc and copper electrodes. The electrodes were made from
Imm sheet, totaling around 200cm2 for each metal. The dis-
tance was controlled using a switch that involved measuring
the speed of sublimation of solid carbon. A quantity of solid
carbon dioxide was placed in a container on one side of a
pulley. On the other side were a number of counterweights
such that the solid carbon dioxide con-
tainer rested on a metal electrode,
which completed the circuit. As the
solid carbon dioxide vaporized, the
weight on that side of the pulley de-
creased until it was outweighed by the
counterweights. Once this occurred,
the solid carbon dioxide container
lifted off the electrode and cut the
power to the motor. The amount of
solid carbon dioxide initially placed
in the container (anywhere from 20g
to 50g) was determined by the dis-
castle One team car tance to be traveled. The UNSW car
rminal technical was interesting to observe as it glided
lems. along in a white cloud generated by
the subliming carbon di-
oxide (see Figure 2).
Sydney University
The Sydney University
car (see Figure 3) was de-
signed and built by a team
of first-year engineering
students (mechanical and
chemical). It was driven
by an electric motor pow-
ered by an electrochemi-
cal cell comprised of
1.8M sulfuric acid and
potassium dichromate so-
lution (lg/100ml) with
zinc electrodes. This car
had three wheels and a
its sparkler timing device and low center of gravity. It


Fall 2002











was able to travel well in a straight line. The inventory of
acid was only 5ml, and the cell was enclosed to minimize
spillage problems in the event of a crash. The first run of the
Sydney team was good, but unfortunately, it started without
the required weight.

Newcastle University Team One
The Newcastle Team One car was driven by a small 3.5V
1A motor and powered by a zinc/copper copper sulfate bat-
tery, using 1M copper sulfate solution and 1M sulfuric acid.
This car made a promising start, getting third closest to the
line on its first run. Technical problems (a broken electrical
connection to the motor), however, prevented it from leaving
the starting line on its second run (see Figure 4).

Newcastle University Team Two
The Newcastle Team Two car (see Figure 5) was driven by
a 3V electric motor via a six-speed gearbox. The motor was
powered by a battery of four cells each producing 1.45V-two
cells in series with another two cells in series. The cell used
was an alkaline battery, very similar in chemistry to com-
mercial batteries.
A children's sparkler was used as a timing fuse to stop the
car. When the sparkler burned to the end, it melted through a
section of solder wire incorporated into the cell wiring and
disconnected the power supply from the car motor. The length
of the sparkler determined the running time of the car and
was decided according to the results of previous trials. Spar-

I


Chem-E-Car


University of Newcastle

The Cell
Th Cl


The car is powered by an electrolytc reaction taking place In a dry cell. The cell used Is
an alkaline battery, very similar in chemistry to commercial batterle.
.1 1 1 ncshere
Ionic Reaction in Cell: a n EMCrphal P a. I
Zn n2 + 2e [ .
Mn4+ + e--s Mn3* ,


ml I


I Features I d l fts produce 1.45 V. nn the car


klers were found to be remarkably consistent and had a burn-
ing rate of around 0.28 cm/s. Extensive safety testing had
been carried out on sparklers used indoors to ensure mini-
mum smoking or sparking.
With the sparkler burning away as the car rolled along, it
was pleasing to the eye. In practice on home turf, it had man-
aged to consistently stop only a few centimeters from the
desired distance. On this day it was the most consistent car
and eventually achieved second place.


THE RESULT

Team Newcastle Two won the poster competition with a
concise, informative display (see Figure 6). The performance
competition winner was the team from the National Univer-
sity of Singapore; after a crash on its first run, their car stopped
only 135cm short of the 20m designated distance on its sec-
ond and final attempt. Team Newcastle Two took second place
when their car stopped 180cm after the line. The trophy, a
polished Plexiglas CSTR on wheels, was made by the work-
shop staff at Monash University and is now in the hands of
the NUS team.


Reports from faculty involved in supervising the local de-
partment competitions suggested that the students benefited
greatly from the experience. To get to the start line with a car
that was competitive and worked according to the rules, each
team had to solve the series of specific engineering prob-
lems. Several teams went beyond mere functionality and con-
sidered aesthetics.
The concentration
and enthusiasm of
the participants was
1 palpable, and I was
privileged to witness
it. It is not often that
SThe Stopping Mechanism our students engage
in something that is
Coanrnrdal sparklers are used as
..r A- SS r...a.. fun and also a great
th sparkler bu to the and. it
ma 0 Ito a end oo learning exercise.
we Inoopor-etd into the o *
sup"' from the "ar to'r Th The Chem-E-Car
length of the spkler deterlines
he ruling m of the M...nd Is Competition was this
diddWl accotdng sto the result of
s* 1, x" o" and more.


lour calls ars arrangdasa below to gm u
.maimn perormenr e:
/Car dlimension 225 *200mm (top vi29eV S e a
-Weight (tar) = o1028 g: _*__ a
-car = 320g ed ou pars inhdoors, to
-zinc=4x37g' min. i smoking or-
-. -I=4xos I Safety _
-EMD=4x35g ': .
3V moo MSS orade Safety procdurs developed for sparkler use:
-6sedgearox Su contldaineril ld to hold c l foilrtspar :
High purity chemicals mean negligible No fmmabe material within aparkl
go-o by-products radius of 450 mm
Minimal in nc required wth cell. Skle to be handled with cuton for
-Minimal interferece required with cell, three minutes after uset
acomponentsalstforseveNal runs
Chem-E-CarTeam jamndidklrn tmdUpre mbennn ja skemp johnmcchy lukMorgn tnlar m KyIrollihmon salonnlker Wonmth rtahlkron


Figure 6. The winning poster of the Newcastle Two team.


The Chem-E-Car
Competition will be
held again next year
with the grand final
in Christchurch,
New Zealand, at the
CHEMECA 2002,
the annual confer-
ence of chemical en-
gineers in Australia
and New Zealand. O


Chemical Engineering Education


mo
_/


pw

rio-


290











User-Friendly Phase Equilibrium
Continued from page 287.

handbooks.10 "' By doing this assignment, students can de-
velop a better intuitive understanding of the meaning of such
excess property data because they see where the data came
from. Additionally, the magnitude of the variation of ac-
tivity coefficient with pressure is related to the partial
molar excess volume. Using these results, students can
prove to themselves why activity coefficients are typi-
cally assumed pressure-independent.
Before using activity coefficients in VLE calculations, stu-
dents prepare a few plots of activity coefficient versus com-
position or of infinite dilution activity coefficient versus tem-
perature. When they produce graphs similar to those in the
textbook, students reinforce their concept of what "shape"
these functions should have. Also, by plotting results from
several different equations on one graph, students see that
it makes little difference which correlation is chosen in
most cases. For subsequent VLE and LLE calculations,
they typically use the Margules equation because it is the
most simple mathematically.
In conjunction with VLE phase diagrams, students produce
plots of excess free energy functions. These plots can be used
to determine constants in an activity coefficient correlation.
For example, a plot of GE/RTx x, versus xi can be used to
determine Margules equation parameters by a straight-line
fit. When constants determined by several methods are used
to plot an xy diagram, students learn the fit of the data is as
important as which equation is used.
Phase separation and LLE are analyzed with graphs of free
energy of mixing versus liquid composition. For LLE, it is
the shape of these curves-convex or concave-that is the
determining factor in phase stability. As with the VLE data,
students generate plots of these functions from experimental
data points and, by fitting activity coefficient correlations in
various ways, compare the results.
Phase equilibrium and chemical reaction equilibrium are
often taught in one course. I have also successfully used com-
puter spreadsheet assignments or demonstrations for class dis-
cussion in the reaction equilibrium portion of the course.
It is a fundamental belief of mine that students will choose
to use the computer and specific software in cases where it
makes a problem easier to solve. When I assigned these prob-
lems, I did not require the use of specific software. (In fact, I
did not require the use of a computer at all, but with the avail-
ability of computing resources and the students' general fa-
miliarity with computers, no hand-plotted solutions have been
submitted in about ten years!) I typically discussed how to
structure a spreadsheet for the assignment and frequently had
the students work through a hand calculation for a single data
point as an in-class exercise.


The majority of students "follow the path of least resis-
tance" and complete the assignment using the standard spread-
sheet package, currently Microsoft Excel. The specific choice
of spreadsheet has little effect. Students have solved the prob-
lems using Quattro Pro, Lotus 1-2-3, SuperCalc, and the Smart
Spreadsheet in past years. Moreover, it is unnecessary to use
a spreadsheet, as a few students have demonstrated by solv-
ing the problems using programming languages (FORTRAN,
C), graphics packages, and math solvers (Mathcad, Maple).
All students eventually gravitated to spreadsheets by the end
of the class, however. The only warning I give to students
who use nonstandard computer software is that I may not be
able to assist them with computer-related problems if they
are using a package with which I am unfamiliar.

CONCLUSIONS
In teaching phase equilibrium thermodynamics, I have at-
tempted to promote understanding and intuition of the course
material. Initial explanation that the goals of the class relate
mainly to data handling and generation, unlike other chemi-
cal engineering classes, prevents confusing expectations from
developing. Meaning and consequences of data are empha-
sized, particularly for abstract quantities such as activity co-
efficients for which interpretation is not necessarily explicit.
Widespread presentation and students' use of graphical data
is made convenient using computer spreadsheet software.

ACKNOWLEDGMENTS
These computer assignments were developed over a series
of courses taught at Michigan State University and Villanova
University.

REFERENCES
1. Prausnitz, J.M., R.N. Lichtenthaler, and E.G. de Azevedo, Molecular
Thermodynamics of Fluid-Phase Equilibria, 2nd ed., Prentice-Hall Inc.,
Englewood Cliffs, NJ, p. 4 (1986)
2. Smith, J.M., H.C. Van Ness, and M.M. Abbott, Introduction to Chemi-
cal Engineering Thermodynamics, 5th ed., McGraw-Hill, New York
(1996)
3. Kyle, B.G., Chemical and Process Thermodynamics, 2nd ed., Prentice-
Hall, Englewood Cliffs, NJ (1992)
4. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena,
John Wiley & Sons, New York (1960)
5. Felder, R.M., and R.W. Rousseau, Elementary Principles of Chemical
Processes, John Wiley & Sons, New York (1986)
6. Bennett, C.O., and J.E. Myers, Momentum, Heat, and Mass Transfer,
McGraw-Hill, New York (1985)
7. Savage, Phillip E., "Spreadsheets for Thermodynamics Instruction,"
Chem. Eng. Ed., 29(4), p. 262 (1995)
8. Pratt, R.M., "Thermodynamic Properties Involving Derivatives: Us-
ing the Peng-Robinson Equation of State," Chem. Eng. Ed., 35(2), p.
112(2001)
9. Elliott, J.R., and C.T. Lira, Introductory Chemical Engineering Ther-
modynamics, Prentice Hall PTR (1999)
10. Green. D.W., and J.O. Maloney, eds, Perry's Chemical Engineers'
Handbook, 7th ed., McGraw-Hill, New York, NY (1997)
11. Weast, R.C., ed., CRC Handbook of Chemistry and Physics, 60th ed.,
CRC Press, Boca Raton, FL, D-227 (1979) 1


Fall 2002











: laboratory


ON IMPROVING "THOUGHT WITH HANDS"



G.K. SURESHKUMAR, K.C. KHILAR
Indian Institute of Technology, Bombay India 400 076


L laboratory exercises are essential"1,21 toward the devel-
opment of a good chemical engineering graduate with
desirable skills such as independent learning, inter-
dependent learning, problem solving, critical thinking, cre-
ative thinking, interpersonal skills, teamwork, leadership,
integration, communication, and change management.'31 The
standard laboratory exercise in chemical engineering, how-
ever, revolves around an apparatus that remains unchanged
for several years and can lead to unethical practices among
students',41 such as submission of data/reports from previous
years. Moreover, the application of thought, which is crucial
for laboratory work and developing the skills mentioned
above, is almost nonexistent in the standard laboratory exer-
cise. From an instructional-objectives viewpoint,151 most labo-
ratory exercises are designed to be at Bloom level 2 (com-
prehension) out of the possible six levels. This leads to se-
vere resentment toward laboratory work among students and
professors alike. Students consider lab courses as a formality
to be completed, while faculty treat them as poor cousins of
theory courses, relegating the entire responsibility for lab
courses to lab supervisors or teaching assistants.
We believe that if students are challenged to think criti-
cally on laboratory exercises and encouraged to be creative,
their interest in and respect for laboratory work would im-
prove, and in turn, the faculty would be further motivated to
offer better laboratory courses/projects. With this belief, a
laboratory course consisting of both dual-step laboratory ex-
ercises and a recommendation/innovation exercise was con-
ceived and assigned to third-year (junior) undergraduate stu-
dents taking the fluid mechanics laboratory at the Indian In-
stitute of Technology, Bombay.
Our laboratory guidelines state that the overall aim of this
laboratory course is to inspire students to appreciate the un-
derlying themes of the experimental aspects/approaches to
engineering/science with fluid-flow aspects as a model sub-
ject. The goal is to develop students' abilities to "think with
their hands." Another purpose of this course is to improve
understanding of fluid-flow principles, to develop a physical
feel for some fluid-flow situations, to develop a familiarity


with some commonly used fluid-flow equipment, to incul-
cate a concern for safety, to improve communication of ex-
perimental results, to improve the quality of analysis and in-
quiry, and to kindle the spirit of discovery in students. Fur-
ther, we expect the exercise to develop some of the above-
mentioned skills in a chemical engineering graduate.

THE LABORATORY EXERCISES
The activities for the laboratory consisted of dual-step labo-
ratory experiments (performed by student groups) and a
recommendations report (an individual activity).
The Dual-Step Laboratory Exercise
Each laboratory experiment was conducted over two lab
sessions. During the first session, student groups were ex-
pected to follow the procedures given in the manual to carry
out the experiment. Students were expected to become com-
fortable with the equipment and the experiment, and the first-
session experiments were designed accordingly.
After the first session, students were required (as home-
work) to analyze the data taken during the lab session based on
the theoretical principles in the lab manual/fluid mechanics text-
book/notes and examine whether the results obtained were as

G.K. Sureshkumar (G.K.) is currently Associ-
ate Professor in the Chemical Engineering De-
partment at Indian Institute of Technology,
Bombay. He received his BTech. in Chemical
SEngineering from Indian Institute of Technol-
ogy, Madras, and his PhD from Drexel Univer-
sity. His research interest is free radical-based
improvements in the productivity of bioreactors.
SHe can be reached at


Kartic C. Khilar is currently Professor in the
Chemical Engineering Department at Indian
Institute of Technology, Bombay He earned
his BTech degree in Chemical Engineering
from Indian Institute of Technology, Kharagpur,
and his PhD from University of Michigan. He
and his students work in nanoparticle produc-
tion and colloid-associated contaminants
transport in porous media.


Copyright ChE Division of ASEE 2002
Chemical Engineering Education










expected. The following ensued:
a) If the experimental results matched the expected results,
students were expected to think of additional experi-
ments, preferably new ones, that could be done with the
same (or slightly modified) setup. But the additional
experiments need to be done within the time frame of
the second lab session. We believe that working with
these practical constraints would help students acquire
"street smarts," which are useful in handling real-world
problems.
b) If the experimental results did not match the expected
results, students were required to form hypotheses based
on the results and design ways to experimentally (with
certain calculations) prove or disprove their various
hypotheses in the second lab session. The emphasis was
on the technical/scientific rigor in proofs. The students
were also warned that their theories could be proved
false by their experiments and that it was acceptable to
admit they did not understand the reasons for disagree-
ment within the time available to them and therefore,
additional study would be required.
After the second lab session, each student group was ex-
pected to submit a single report in the regular format, i.e., (a)
Aim and Objectives, (b) Methodology, (c) Results and Dis-
cussion (which was required to be significant), (d) Conclu-
sions, and (e) the original data sheets. The reports were graded
on the following bases:
If the actual results matched the expected results:
Ability to follow procedures 10%
Data analysis (1st session) 15%
Discussion (1st session) 15%
Creativity/originality aspects (2nd session) 20%
Data analysis (2nd session) 15%
Discussion (2nd session) 15%
Presentation (mainly communication) 10%
Reports that addressed novel aspects to study in their sec-
ond session were rewarded handsomely in grading the cre-
ativity/originality criterion (see the student examples pre-
sented later).
If the actual results did not match the expected results:
Ability to follow procedures 10%
Data analysis (1st session) 15%
Discussion 15%
Clarity in thought and situation/problem
analysis (2nd session) 20%
Rigor (2nd session) 15%
Discussion (2nd session) 15%
Presentation (mainly communication) 10%
Reports that were well developed on both the possible rea-
sons for the disagreement between actual and expected data
and the experiments to prove or disprove them were given
high marks for the clarity-in-thought criterion. The difficulty
level in problem analysis was also recognized in that crite-
rion-reports that fully analyzed a difficult situation received
higher marks than those that, as a matter of chance, analyzed


a simple, easy-to-identify situation. Also, reports that un-
equivocally proved or disproved their points received high
marks for the rigor criterion. Other criteria, such as data analy-
sis, discussion, and presentation, carry their usual weight.
The Recommendations Report
Over the duration of the course, each student was expected
to think about an experiment or a set of experiments that could
be done in the fluid mechanics lab. Students were encour-
aged to be as creative as possible. Near the end of the course
(a week before the last day of classes), each student was ex-
pected to submit a detailed report on this experiment (or set
of experiments) and the equipment and instruments needed.
The reports were evaluated on the following bases:
Creativity/originality aspects 30%
Clarity in thought 20%
Detail 30%
Doability 10%
Presentation (mainly communication) 10%

The dual-step exercises evaluated through the reports carried
a 70% weight, and the recommendation report carried a 30%
weight toward the final grade.

IMPLEMENTATION OF DETAILS /RATIONALE
In the beginning of the semester before the experiments
began, the instructor met the class and discussed the exer-
cises and recommended strategies. In addition to experimen-
tal details for the first session, the laboratory manual carried
information on safety procedures for the lab, error analysis,
technical writing, and the unacceptability of academic dis-
honesty, all of which were seriously discussed in the initial
meeting. The instructor also emphasized the need for safety
procedures whenever he observed lapses during the lab ses-
sions. Student groups were asked to select their own leaders
who would assign duties for the group members and be gener-
ally responsible for the group's activities. This ensured that an
avenue for the development of teamwork and leadership skills
existed. Also, on many occasions, the instructor communicated
to the groups through their leaders.
Before the start of the first session, the groups were ad-
vised to familiarize themselves with the details for each ex-
periment using the lab manual and the textbook. The first-
session experiments were designed as shorter versions of the
experiments given in the usual lab course, and students were
encouraged to spend the additional time becoming comfort-
able with the setup and the various equipment used. For ex-
ample, the instructor encouraged the students to raise ques-
tions regarding the equipment or the reasoning behind the
various experimental steps, which the students normally took
for granted. The students took the first session seriously be-
cause they knew they had to consider the setup, the experi-
mental methods, and the underlying theory in order to have
an interesting second session. During the experiment (both
sessions), groups were advised to record the data in duplicate


Fall 2002









using a carbon sheet, and the members were asked to sign each
data sheet. The duplicate copy was submitted to the instructor
at the end of each session, and nonsubmission would result in a
grade of zero for that session. The instructor has never had to
give a zero over the past two years for this reason.
After the data analysis for the first session, the groups were
required to meet the instructor to discuss their plans for the


second session. This meeting was not to guide
the students on what they could do in the sec-
ond session, but for the instructor to listen and
comment on the possibility of doing the experi-
ments. This meeting was normally scheduled a
few days before the second session, primarily
to address any special requirements for the ex-
periment that needed to be communicated to
the lab superintendent. Also, this meeting
helped the instructor ensure that the second-
session experiments were of proper scope (nei-
ther too large nor too small) and reasonably well
thought out, especially if the actual data
matched the expected data in the first session.
In addition, it was communicated to the stu-
dents at the beginning of the semester that no
complete dismantling of the set-ups would be
allowed, except in rare cases. This encouraged


SAMPLES FROM STUDENT EXERCISES
Samples from the Dual-Step Laboratory Exercises
Agreement Between Actual and Expected Data An ex-
periment for the lab involved studying the relationship be-
tween Power number and Reynolds number in an agitated
system. One of the groups found good agreement between


... the overall
aim is...
to improve
the quality of
analysis and
inquiry,
and to kindle
the spirit of
discovery in
students.


the students to think of "non-invasive" means for testing their
theories. Also, this precaution was necessary because some
piping networks in our lab had packing to prevent leaks that
would be difficult for an inexperienced person to reassemble.
The lab reports for the dual-step exercises were due before
the start of the next experiment; the instructor graded them
and offered constructive criticism and feedback within a week
of submission. Students appreciated the timely feedback.
The grading of the recommendations report was time con-
suming (three to four consecutive, full days). As long as
grades are important, some students may cheat to get the best
grade;'6,7] therefore, a significant amount of time was spent
establishing the originality of submitted reports. This was
achieved through one-on-one interviews with students who
had submitted "doubtful" reports. During an interview, it was
easy to ascertain whether cheating had taken place by ask-
ing relevant questions, most of which were on the experi-
ment submitted.
All experiments were run on existing equipment; therefore,
this dual-step exercise does not require additional funds for
equipment. It can be run anywhere, even in the face of fund
crunches. It also provides a greater probability for disagree-
ment between actual and expected data, and thus helps stu-
dents develop lateral-thinking abilities while forming hypoth-
eses for the disagreement. Therefore, the dual-step labora-
tory exercise provides a way to turn a seeming disadvantage
in running an existing laboratory course into an advantage of
improving thought in students.


actual and expected data and therefore had to
think of additional experiments to do on the
same setup. They decided to compare the rela-
tionship between Power and Reynolds numbers
for an aqueous system with and without a sur-
factant. They found that the Power number for
the corresponding Reynolds number was lower
for the system with surfactant than for plain
water. Therefore, they concluded that the power
requirements for an aqueous system with sur-
factant are lower than that for plain water. They
also provided qualitative explanations for the
observed results from a molecular viewpoint.
Another experiment involved studying two-
phase flow characteristics in a vertical transpar-
ent tube such as the relationships between slug
length and slug velocity and between pressure
drop and void fraction, etc. The group that ob-


trained results as expected decided to study the relationship
between the radius of curvature of the slug's leading edge
and its length. They developed a theory based on geometri-
cal considerations for the variation of the leading-edge cur-
vature with slug length; they also showed correspondence
between the theoretically expected results and measured data.
Disagreement Between Actual and Expected Data An-
other experiment involved a piping network with various types
of pipes, fittings, and valves. The objectives for the first ses-
sion included determination of the frictional losses across the
pipe fittings and valves. The experiment required recording
readings from manometers attached to the pressure taps
across relevant fittings or valves and determining the water
flow rate using the pressure difference measured across
the orifice meter.
The first group that worked on the experiment found that
the friction loss constants obtained for the various fittings on
the network were higher by almost an order of magnitude
than literature values. Therefore, the group first postulated
that scale formation led to higher loss constants. To test the
postulate, they arranged for the network to be cleaned thor-
oughly and repeated the experiment in the second session.
This did not yield significantly different loss constants,
thereby partly disproving the postulate that the scale forma-
tion alone resulted in the discrepancy. Students in one of the
other groups that worked on the experiment postulated that
the water-flow rate measurements using the calibration curve
for the orifice meter may not have been correct; they noticed


Chemical Engineering Education


294










a discrepancy between flow rates measured using a measur-
ing jar/stop watch arrangement and the orifice meter read-
ings. So, the students prepared a fresh calibration graph for
the orifice meter and found it to be different from the exist-
ing, erroneous calibration chart. They also proved that the fric-
tion loss constants obtained using the new calibration graph
were comparable to the values found in the literature.

Samples from the Recommendations Report

A student named Nikhil Agarwal suggested an inexpen-
sive, simple method for determining the viscosity of a solu-
tion by allowing it to flow over a smooth, inclined flat plate
from a reservoir and taking measurements. Using suitable
balances, Nikhil expressed the viscosity as a function of mea-
surable parameters (with origins from the thickness of the
liquid layerE81) as:
pg3 cosp
3Q
where p is the fluid density, g is the acceleration due to grav-
ity, 8 is the film thickness, 3 is the angle between the plate
and the vertical, and Q is the flow rate. He carefully consid-
ered the details and limitations of the experimental proce-
dure and suggested a method to study the variation of viscos-
ity with temperature using the same setup.
Another student, Sikander Siraj, using input from a friend
in electrical engineering, suggested a photoelectric diode-
based (PED) device for the measurement of slug lengths in
the two-phase flow experiment. The idea had its origins in
the burglar alarm principle. For the measurement, he used
the deviation caused by the refraction of the infrared beam
when it passes through media of different refractive indices.

STUDENT AND STAFF FEEDBACK

The students were asked to send their comments through
e-mail to their class representative, who removed details per-
taining to the authors of the comments, compiled without ed-
iting, and forwarded the comments as a single file to the in-
structor. For the improved version of the lab, comments from
82 out of 83 students were received, and all except nine ex-
plicitly stated that the lab was useful to them. They said that
their learning included fluid-mechanics principles, applica-
tion of thought to a lab, leadership qualities, thinking cre-
atively, and working in a group. Some positive comments
over the past two years include, "Due to this lab alone, I can
say that I know some 'chemical engineering,'" and "This is
the first time I feel what a lab course is all about." Also, many
students suggested minor changes in equipment, etc., to im-
prove the lab. Of the nine students who did not state their
liking for the lab, seven were neutral, and the other two said
that the lab was not useful to them.
The staff associated with the lab were enthusiastic about
fulfilling the requirements of the lab. They also said that they


enjoyed setting up the various experiments although it in-
volved additional time.

INITIAL CHALLENGES
The first time it was offered, almost all students expressed
that the lab demanded a lot of their time. We believe this was
because students compared it with previous editions of the
same course. In addition, the same experiments that were
given in previous editions were packaged into a two-session
(dual-step) format, significantly increasing the work. There-
fore, in the next edition of the course, the experiments were
consolidated into half the original number, with all other de-
tails unchanged. Afterwards, there were very few comments
(3 out of 83) that there was too much work.
The first time the course was offered, the groups were as-
signed according to student roll numbers, which the students
hated. The next time, the students were asked to form their
own groups with the average cumulative performance index
(CPI) of the group members being close to the class average
CPI; this incorporates cooperative learning elements. Com-
plaints about unsuitable groups were almost eliminated.
The remaining challenge is group size. Six students in a
group is nonideal and should be reduced. We intend to re-
duce the number by running the experiments more frequently
in the future. The logistics constraint needs to be addressed
first, however.
In short, a focus on developing the critical thought process
in students made the laboratory course interesting to both
students and instructors and also developed students' respect
for experimental work.

ACKNOWLEDGMENTS
We would like to thank the students of CL333 for their
enthusiastic participation in the exercise as well as O.S.
Sawarkar, V.B.V. Nair, V. Ramachandran, and A.D. Kadam
for their contributions.

REFERENCES
1. Middleberg, A.P.J., "Laboratory Projects: Should Students Do Them
or Design Them?" Chem. Eng. Ed., 29(1), p. 34, (1995)
2. Jones. W.E., "Basic Chemical Engineering Experiments," Chem. Eng.
Ed., 27(l), p. 188. (1993)
3. Rugarcia, A., R.M. Felder, D.R. Woods, and J.E. Stice, "The Future of
Engineering Education. I. A Vision for a New Century," Chem. Eng.
Ed., 34(1), p. 16, (2000)
4. Macias-Machin, A., G. Zhang, and O. Levenspiel, "The Unstructured
Student-Designed Research Type of Laboratory Experiment," Chem.
Eng. Ed., 24(2), p. 78, (1990)
5. Felder, R.M., D.R. Woods, J.E. Stice, and A. Rugarcia, "The Future of
Engineering Education. II. Teaching Methods that Work," Chem. Eng.
Ed., 34(1), p. 26, (2000)
6. Felder, R.M., "Cheating: An Ounce of Prevention...Or the Tragic Tale
of the Dying Grandmother," Chem. Eng. Ed., 19(1), p. 12 (2000)
7. Sureshkumar, G.K., "A Choose-Focus-Analyze Exercise in ChE Un-
dergraduate Courses," Chem. Eng. Ed., 35(1), p. 80, (2001)
8. McCabe, W.L., J.C. Smith, and P. Harriott, Unit Operations of Chemi-
cal Engineering, McGraw-Hill, Singapore, 6th ed., (2000) D


Fall 2002










ref m curriculum


THE EARTH'S

CARBON CYCLE

Chemical Engineering Course Material



ROGER A. SCHMITZ
University of Notre Dame Notre Dame, IN 46556


On three occasions in recent years, I have taught an
elective course at the University of Notre Dame for
chemical engineering seniors titled "Topics on Ecol-
ogy and the Environment." I developed the course because I
felt it was important for our students (and myself as well) to
have a greater appreciation-from a chemical engineer's per-
spective-for the workings of Earth's natural processes, both
biotic and abiotic, and a knowledge of how human and in-
dustrial activities are disturbing or might disturb them.
One of the significant components is a module on the car-
bon cycle-the subject of this article. In gathering and devel-
oping material for this module and others in the course, I was
struck by these observations:
Many of the Earth's processes, including the carbon
cycle, though fundamentally very complex in detail, can
be represented by simple models that are useful for study
purposes and even for quantitative estimates, at least as
a first approximation.
The development, analysis, and application of models
are well within the scope of an undergraduate chemical
engineering curriculum.
The subject matter or bits and pieces of it, can be
integrated advantageously, straightforwardly, and nearly
seamlessly into core chemical engineering courses.
My objectives in this article are to demonstrate all of this,
using the carbon cycle as the means, and to provide conve-
nient material for others who may be persuaded by my third
observation.
Of the biogeochemical cycles of the six major "life" ele-
ments, C, N, P, S, O, and H, the carbon cycle receives the
lion's share of the attention in the literature. That's no sur-
prise inasmuch as most of our energy needs are met by the
burning of carbon-based fuels and inasmuch as the conse-
quent increasing level of atmospheric carbon dioxide and its


potential effect on the Earth's climate is a frequent focus of
attention in technical and nontechnical publications. What's
more, chemical engineers will have opportunities to play a
prominent role in any steps taken to moderate that level,
whether those steps be toward alternate energy sources or
toward sequestering or otherwise preventing emissions di-
rectly into the atmosphere.

THE CONCEPTUAL MODEL
Carbon is found in all of Earth's compartments or reser-
voirs-in the biota and in the atmosphere, hydrosphere, and
lithosphere. Mathematical models describing the cycle ac-
count for the movement of carbon among and within those
reservoirs and for anthropogenic disturbances, which are prin-
cipally due to fossil fuel burning and deforestation (i.e., mainly
burning of removed trees) for land use changes.
Figure 1 presents a schematic diagram of a conceptual
model of the carbon cycle consisting of six reservoirs, num-
bered one through six. (A seventh reservoir for fossil fuels
enters dynamically into the model later only as a disturbance
to the six-reservoir natural cycle.) Other reservoirs, includ-
ing sediments, marine biota, and lakes, rivers, and streams,
are omitted for reasons given later. In one way or another, all
models are based on this starting picture, which is sometimes

Roger Schmitz is the Keating-Crawford Pro-
fessor of Chemical Engineering at the Univer-
sity of Notre Dame. He received his bachelor's
degree from the University of Illinois and his PhD
from the University of Minnesota, both in Chemi-
cal Engineering. His current interests are in the
modeling and analysis of environmental and
ecosystem dynamics.


Copyright ChE Division of ASEE 2002


Chemical Engineering Education










modified to include one or more of the omitted reservoirs.
Models differ primarily in the extent of detail and correspond-
ingly in the objectives of the modeler. For example, highly
detailed climate studies employ general circulation models
based on fundamental transport equations to describe pro-
cesses in the atmosphere and/or ocean reservoirs and several
types of vegetation to describe the atmosphere-biota ex-
change."' At the other extreme, so-called "box" (or "com-
partment" or "lumped") models that are intended to give es-
timates of global averages of carbon in major reservoirs, are
based on spatially aggregated descriptions, often with no more


detail, sometimes even less,
than that shown in Figure
1.[27] Except to allude to the
structure of high-end models
and their purposes (and
sometimes to compare re-
sults), I choose to work with
simple box models in the
course. In short, as tools for
study, they have suited my
purposes. Further, if prop-
erly calibrated and tuned,
they have proven useful for
quantitative purposes so
long as the principal interest
is in global averages, par-
ticularly in atmospheric car-
bon dioxide levels.
The conceptual model rep-
resented in Figure 1 and the
mathematical description to
follow are amalgamations of
several box models that I
have studied and used in the
course. The version pre-
sented here is closely pat-
terned after, but not identi-
cal to, that described in a re-
cent publication by Lenton.1'
I usually have the students
go through the development


The numbers in parentheses beside the arrows in Figure 1
represent estimates, in petagrams of carbon per year (PgC/
y), of the transport (commonly termed "fluxes" in the rel-
evant literature) of carbon between reservoirs. Such fluxes
are estimates, adjusted so that each box is balanced at a steady
state, where it would remain unless disturbed. There is no
common agreement on the values of the reference pre-indus-
trial masses and fluxes, or even on the reference year (gener-
ally between 1800 and 1860), but the variation from one ref-
erence source to another is of little significance. The values
shown in Figure 1 are in line with those used in the refer-
ences cited above.


1 M1
ATMOSPHERE (612)


F61 F15 F51 F F F21 F3 F3
(50) (100 (50) (57) (58) (19) (18)


lerrestal arm ocean cool ocean
biola surface waers surface walers
N5 I FdiI NlN3
1580s 17301 1 140-


\
6 4
soils & deep
detritus ocean waters
M6 M4
(1500) 1 370(K)0
Ff
Ff- -



Figure 1. Schematic diagram of a six-box model of the car-
bon cycle. Values shown for reservoir masses (M, in PgC)
and fluxes (F., in PgC/y) are representative of the pre-in-
dustrial steady state (- 1850).


of other models as complementary outside work.

THE REFERENCE PRE-INDUSTRIAL STATE

The quantities shown in parentheses in the boxes in Figure
1 represent estimates of the "pre-industrial" distribution of
carbon (i.e., the mass of element C in all of its compounds) in
petagrams (PgC, 1 Pg = 10lg.) These are typical reference
values presumed to represent the balanced (steady-state)
conditions around the year 1850-early in the industrial
revolution when there was little or no observable change
from year to year.


M the mass of carbon
in the atmosphere reser-
voir can be taken to be en-
tirely in the form of CO2.
The 612 PgC in that reser-
voir corresponds to a CO2
concentration of 286 ppmv
(parts per million by vol-
ume) -the concentration
unit used in most illustra-
tions to follow. (The con-
version factor of 2.128
PgC/ppmv is based on a
total atmosphere mass of
5.14 x 106 with a molecu-
lar weight of 29.)
Notice the notation in
Figure 1. M, stands for the
mass of carbon in box i; F..
for the flux of carbon from
box i to box j. The anthro-
pogenic disturbance flux
F moves carbon from a
nonrenewable fossil fuel
reservoir to the atmo-
sphere.* The other anthro-
pogenic disturbances, Fd
and F, take carbon from
the renewable terrestrial


biota reservoir to the atmosphere (deforestation) and from
the atmosphere to the terrestrial biota (reforestation), respec-
tively. (There is increasing interest in sequestering part of Ff
by redirecting it to cavities in the lithosphere and/or to the
deep ocean.'8"91 Those slight but interesting variations to the
model will be mentioned in suggested exercises near the
end.) The following list gives a succinct description of
the other fluxes:

Actually, Ff accounts for all carbon emissions to the atmosphere except
those due to deforestation. It is commonly termed "emissions due to fossil
fuel burning"-a term that I shall use throughout. Other industrial sources,
such as cement manufacturing, account for only a few percent of the total.


Fall 2002










SF1,, F F and F31 are simply mass transfer rates for the
exchange of carbon (as carbon dioxide in this case since
nearly all atmospheric carbon is in that form) between
the atmosphere and the ocean waters. Basically, the rates
are described by the product of a mass transfer coeffi-
cient and a concentration driving force, but the nuances
involved in using that description warrant further
attention later.
SF23 represents the advective flow of carbon from the
warm to cool surface ocean reservoirs. This flow, which
accounts for most of the ocean mixing, results from the
downflow of cool surface water at high latitudes and the
corresponding upwelling to the warmer surfaces at low
latitudes. There is also an eddy-mixing component
contained in the fluxes between the surface and deep
ocean waters. The model could be further simplified
without affecting results noticeably by lumping boxes 2
and 3 into a single box.
D F5 is the rate of photosynthetic uptake of carbon from
the atmosphere by terrestrial vegetation. This flux,
assumed often in models of this type to be describable by
a single overall rate expression, gets special attention
later. M5 is the total carbon in terrestrial biota, but we
might think of it as being the mass of vegetation since
about 90% of it is in forests.
F56 is the flux of carbon in litter fall-mostly dead leaves
and the like, but generally including all dead and waste
products from the terrestrial biota.
SF 5 and F are the fluxes of carbon, mostly as carbon
dioxide with small amounts as methane and other
compounds, to the atmosphere by biotic respiration.

As mentioned above, a more complete box structure would
include additional elements for aquatic biota; sediments; and
rivers, streams, and lakes. Such additions are more suited for
discussions and assigned work than for incorporation into a
working model for the following reasons: The inventory of
carbon in aquatic biota and in rivers, streams, and lakes is
negligibly small; sediments, the largest of all reservoirs with
a total carbon mass of about 108 PgC, are the most sluggish
by far; the small fluxes (~0.3 PgC/y) into and out of the sedi-
ments lead to a first-order time constant of the order of sev-
eral hundred million years! For the reservoirs represented in
Figure 1, first-order time constants, calculated as the ratio of
the mass of carbon in a reservoir to the flux of carbon out of
it, range from 1.19 years for the cool surface waters in box 3
to 330 years for the deep ocean waters in box 4. For the at-
mosphere, box 1, it's 3.48 years. The illustrations in simula-
tions to come will cover time spans up to 250 years, over
which time the sediment reservoirs are virtually steady.


THE EQUATIONS
The mathematical description of the box model of Figure 1
consists of a set of carbon balance equations. For the atmo-


sphere, box 1, for example
dM1
dt
F21 -F12 + F31 F13 + F51 F15 + F61 +(Ff +Fd Fr) (1)

In general
dMi 6
d- = (Fi Fi + disturbances (2)
jdt

If a particular F.. does not appear in Figure 1, its value in Eq.
(2) is zero. The disturbances, as represented in Figure 1, ap-
pear only in the balances for boxes 1 and 5.
To keep account of the fossil fuel supply, a seventh box is
added, an out-of-cycle, nonrenewable reservoir of the car-
bon in fossil fuels. The following balance describes the deple-
tion of that reservoir:
dM = -Ff (3)
dt
All terms in these equations have units of petagrams of car-
bon per year (PgC/y).
The initial conditions are the reference pre-industrial res-
ervoir levels in 1850. I use 5300 PgC for the initial value of
M7, somewhat arbitrarily, but based on rather common state-
ments that while the total carbon stored in fossil fuels is
about 10,000 PgC, only about half of it can actually be
recovered for use.
Since most of the reservoirs undergo relatively small
changes over periods of interest, as later simulations will show,
the fluxes can be related to the reservoir masses by first-or-
der processes. That is
Fij = kijMi (4)

Such relationships are frequently employed in box models
of the biogeochemical cycles, including the carbon cycle, with
three exceptions: F5, F21, and F31. For the others, the numeri-
cal value of k can be obtained readily from the reference
data given in Figure 1.
If the carbon in the ocean were present simply as carbon
dioxide in aqueous solution, we would expect all four of the
F's connecting the ocean surface waters to the atmosphere to
be describable by Eq. (4)-under the safe assumption that
Henry's law applies to the dilute CO2 solution. The situation
is complicated, however, by the fact that CO2 in aqueous so-
lution enters into equilibrium chemical reactions involving
carbonate and bicarbonate forms. Therefore, while the fluxes
F21 and F3 can be related linearly to aqueous CO2, they are
not linearly related to the total C; that is, to M2 and M3. The
relationship to the total carbon in solution is complicated. It
is affected by all of the factors that affect acid-base equilib-
rium in ocean water-total alkalinity, salinity, temperature,
and dissolved salts of weak bases, such as boron. A rigorous
treatment requires linking a set of equations for ocean chem-


Chemical Engineering Education


29R










istry dynamics to the above set. Some studiesi3.5 have fol-
lowed that procedure, as have I in some instances. Others'2.471
have opted for a simpler empirical approach that uses the
following relationships:
F21 =k21M2 F31 k31M3 (5)
Values of the exponents p2 and [3, called buffer factors or
Revelle factors, can be obtained from charts of the type given
in the book by Butcher, et al.1 I0 They can also be obtained by
delving into the intricacies of ocean chemistry dynamics and
correlating results of calculations. I used the latter approach
to obtain the values shown later, but to save space and to stay
on track, I shall spare further detail.
My testing has shown that results of computations using
constant values of the 's hardly differ from those obtained
by appending detailed ocean dynamics to the model, so long
as changes in M, and M3 are relatively small, generally less
than 5%. The numerical values of P range between 9 and 15;
the nonlinearity is surprisingly strong. Notice that with val-
ues of P2 and 03 given, numerical values of the rate con-
stants k,, and k31 can be determined from the reference con-
ditions given in Figure 1.
The rate of photosynthetic uptake, F of carbon from the
atmosphere cannot be represented realistically as a linear func-
tion of M,. The basic reason is that the function should ac-
count for a saturation effect with regard to the nutrient CO,.
That is, the rate increases with increasing CO, but approaches
a limit. For small changes in M,, the function may be ap-
proximated by a linear relationship, but as a later illustration
will show, changes in M, are large over the periods of interest.
There seems to be no clear consensus as to what form to
use for F5 in models of this type. Whatever the specific form,
a common feature is a dependence on atmospheric carbon
that suggests an ultimate saturation. The particular one cho-
sen does not seem to be a critical matter so long as the con-
stants are calibrated or tuned to fit existing data. Neverthe-
less, this is a fertile item for classroom discussion, debate,
and outside work. Here I shall use the form employed by
Lenton'[3

k 5 M-y forM1 >
15M8M-- forM>Y
F,15 = M, +r (6)
0 forM1 where
y is the threshold value of M, (I used Lenton's value of
62 PgC.)
F is a saturation parameter (Lenton used it as a tuning
parameter and arrived at a value of 194 PgC. By methods
described later, I arrived at a value of 198 PgC.)
k,, is a rate coefficient to be calculated from the reference
state.
M is a function that depends on the disturbances Fr and
Fd as explained and described below. In short, it accounts


for changes in the Earth's capacity for terrestrial biota.

The role of the function M8 is important but not obvious at
first glance, and definitions and explanations do not come
easily. Let me first define it by way of the following equation
and then offer brief explanations.

M8(t)=+ +I (krFr -kdFd)dt ()
M.((t) = I + f (7)
1850 M5.ref
where
kd is the fraction of forested area or mass (or forest
capacity) that cannot be reforested (is not available for
regrowth) following deforestation activities-for
example, forest areas cleared for urban development.
k is that fraction of the reforested area or mass that
increases the Earth's capacity for terrestrial biota. (This is
sometimes termed "aforestation" as opposed to "reforesta-
tion" that directly renews deforested areas.
Ms.r is a normalizing factor inserted arbitrarily to make
M, dimensionless. I take it to be the initial value of M,.


Lenton used this form but did not include kr and Fr explic-
itly in his formulation. Reforestation can be accounted for
without those factors if Fd is allowed to have negative values.
I prefer to show F and Fd separately for clarity in simulations
later.
Simply stated, the integral in Eq. (7) accounts for perma-
nent effects of the disturbances Fd and Fr. Were that integral
not included, the model equations would lead to the follow-
ing illogical conclusion, among others: If F -= 0, and if Fd
and Fr eventually settle to zero, the ultimate steady state of
carbon in the reservoirs would be identical to the starting ref-
erence state; the effects of the temporary nonzero values of
the disturbances would die away, according to the model. But
obviously the effects of some land use changes must per-
sist-for example, if forest areas are cleared and urbanized
with no offsetting reforestation. With the integral included in
M, with kd # 0 and F = 0, such land use change would per-
manently affect the distribution of carbon, not its total amount.
Other illustrations can be given to justify the form of M8, but
perhaps further explanation, if needed, is better sought in stu-
dent exercises later.
An alternate form of the integral equation above is this dif-
ferential equation:

dM8 krFr kd d
dM8- krFr kdFd withinitialcondition Ms(1850)= 1 (8)
dt Ms5,ref

The numerical value of the coefficient k,5 in Eq. (6) can be
calculated from the reference values shown in Figure 1, given
values for F and y and taking M8 = 1 (its initial state).
With Eq. (8) added to the material balance equations, the
complete mathematical model consists of the following set
of eight ordinary differential equations:


Fall 2002














dM, =_ M Y +k2 MP
dM1=- (kl2 +k3)M1 1-k M +k21 2
dt Mi +F

+k31M3 +k51M5 +k61M6 +Ff(t)+Fd(t)-Fr(t)

dM kl2M -(k23 + k24)M2 k21M2 +k42M4
dt
dM3 MP3 +k
dM3= kM3 +k23M2-k34M3-k31M3 +k43M4
dt

dM4 = k24M2 +k34M3 (k42 +k43 )M4 (9)
dt
dM5 -k M8 M1 (k51+k56)M5-Fd(t)+Fr(t)
dt M, +F
dM6 =k56M5 k61M6
dt
dM7 -Ff(t)
dt
dM8 _-[kdFd(t)-krFr(t)]/
dt /M5,ref



Numerical values for the constants are given in Table 1.
Determining the values of the k's, as described earlier, cali-
brates the model to the data for the reference year 1850. The
value for y is taken from Lenton's model. The value for kd is
somewhat arbitrary and could be adjusted by tuning the model,
but I have taken it to be constant throughout at 0.23. (Lenton
used a value of 0.27.) I have arbitrarily chosen a value of
unity for k,. My method for determining the value for F, the
only tuning parameter, will be described in the next section.
The values for P2 and 33 were determined as described earlier.
Implicit in this development is the assumption that the car-
bon cycle is independent of all other state variables, or that
all others are constant, such as temperature, moisture, and
other nutrient levels. That assumption is frequently invoked,
but it may be an oversimplification if the model results are to
be applied to global climate dynamics, for example. In the
aforementioned work of Lenton[31 the carbon cycle is coupled
to the Earth's energy balance, and in that of Ver et al.1[7 to
other nutrient cycles.

TUNING AND TESTING
WITH HISTORICAL DATA

Extensive historical records are available for testing and
tuning the model. Figure 2 shows data on emissions due to
fossil fuel consumption, F, taken from Marland et al.,'"i and
deforestation, Fd, taken from Houghton and Hackler,1"2 as well
as the total of the two over the period 1850 through 1990. (I
used 1990 as the endpoint because the deforestation data given


by Houghton and Hackler are not tabulated beyond that year.
We can safely assume that reforestation, F, has been negligi-
bly small in the past.) The dramatic increase in fossil fuel emis-
sions since the middle of the twentieth century is evident.
The solid curves in Figure 2 show my empirical fit of the
reported data. In order to get a rather precise representa-
tion I used separate functions over four segments of Ff
and over six segments of Fd. This detailed fitting may seem
to be overkill. I simply wanted to eliminate an inaccurate


1850 1870 1890 1910 1930 1950 1970 1990
year
Figure 2. Historical record of carbon emissions to the at-
mosphere. Symbols represent reported data;'11'12 solid
curves are empirical fits.


Chemical Engineering Education


TABLE 1
Numerical Values and Unitsfor
Model Constants
symbol value units
k1, 0.0931 y-
k,, 0.0311 y-'
k,, 147 y-I
k,, 58(730 1' ) PgC(-2)y-
k3 0.0781 y-'
k 0.0164 yI
k,, 18(140- 3) PgC('- y3)y-
k3 0.714 y-
k42 0.00189 y-
k,, 0.00114 y1
k,, 0.0862 y-
k16 0.0862 y_
k6, 0.0333 y_
P2 9.4
P3 10.2
7 62.0 PgC
r 198 PgC
k, 0.230
k 1.0











representation of the disturbance record as an explana-
tion for any model failure.
With this representation of the historical disturbances and
the model constants in Table 1, the system of ordinary differ-
ential equations in Eq. (10) can be solved readily, by numeri-
cal routines available in a number of software packages, to
obtain a model-generated record of carbon in the reservoirs
from 1850 through 1990. (I used Mathcad for this particular
exercise and extensively throughout the course.) The solid
curve of Figure 3 shows the result for atmospheric CO,; the
data points are reported estimates or measurements from the
Worldwatch Institute database."31 The good agreement be-
tween model results and reported data was assured over a
portion of the curve, at least by my method of determining
the value of F. Its value of 198 PgC, as given in Table 1, was
determined by an iterative search aimed at minimizing the
total squared difference between model results and reported
data over the period 1980-1990. Admittedly, the good agree-
ment over the early years was also virtually assured because
model constants were calculated to give a perfect fit of the

TABLE 2
Model Computed
Quantitiesfor 1990
i M'
1 753
2 744
3 143
4 37071
5 577
6 1489
7 5086
8 0.952
*Units of M are PgC, except
Ms, which has no units.


1850 1875 1900 1925 1950 1975 2000
year


reference data of 1850. Over the other years, the maximum
disagreement, which occurs around 1925, is less than 1.3%.
All such things considered, this test of the model lends legiti-
macy to its use in predicting carbon distributions through some
years ahead.
Table 2 lists the calculated 1990 levels of carbon for all
reservoirs. Notice that changes in the five of the six reser-
voirs have been relatively small over the 140-year period,
according to the model. The terrestrial biota in box 5 increased
only from 577 to 580 PgC owing to the offsetting effects of
decreases by deforestation and increases by atmospheric CO,
fertilization. The atmospheric reservoir increased by 23% by
1990 and is obviously destined to go higher, but changes in
others have amounted to about 2% or less.
A total of 214 petagrams of new carbon was injected into
the cycle from the fossil fuel reservoir and distributed among
the other reservoirs over the period 1850 through 1990. Even-
tually most of that will reside in the deep oceans, box 4, but
by 1990 that reservoir has increased by only 71 petagrams.
Atmospheric carbon increased by 141 petagrams. Some of
that redistribution of carbon, but not any of the increase in
the total, is due to deforestation with a nonzero value of kd.
In the simulations to follow, the ending values of the M's
for 1990, given in Table 2, are used as the initial state.

SIMULATIONS
The simulations described in this section engage the stu-
dents in the use of the model and exhort them to learn about
current trends, issues, and possible future actions-and to
become informed about likely consequences regarding fu-
ture disturbances to the carbon cycle. The principal interest
is in the prediction of atmospheric carbon dioxide levels
through the 21" century. Such predictions, based on models
of varying degrees of complexity, have been reported in a
number of recent studies. '1..5,7.14]*

Disturbance Scenarios
Postulated scenarios for future carbon emissions over a
century of time when human activities, worldwide econo-
mies, and international politics are involved are naturally laden
with uncertainty, the effects of which, in fact, probably over-
shadow the effects of the assumptions and simplifications in
the model itself. Notwithstanding such, predictions through
simulations require inserting the disturbance functions F,, Fd,
and Fr into the model equations.
The most commonly employed scenarios for carbon emis-
sions are those in a set of five that were suggested in a 1992
report to the International Panel on Climate Change, IPCC.[1315

The list given in the References section is only a small sample. The inter-
ested reader will be led to a much larger assortment of models and
related subjects simply by entering the keyword "carbon" on a web
browser.


Fall 2002


Figure 3. Reported and model-calculated records of
atmospheric carbon dioxide since 1850.










Known by the names IS92a, IS92b,.. .IS92e, they are based
on likely or possible trends in population changes, economic
growth, energy supplies, etc. in developed and developing
countries. There is also a Kyoto protocol, which, if en-
acted according to Article 3 of the agreement, would call
for a worldwide decrease in emissions to 95% of the 1990
level by the year 2012.[161
Shown in Figure 4 are slightly modified versions of three
of the IS92 scenarios for total carbon emissions for 1990 on-
ward, including the most pessimistic (IS92e) and the most
optimistic (IS92c) cases, and what's usually referred to as
the "business-as-usual" scenario (IS92a).* The latter is the
most commonly used version, and as its description im-
plies, is based on the assumption that carbon emissions
can be predicted from current trends with no major
changes in policies and practices.
Also shown in Figure 4 is a representation of the scenario
for the Kyoto protocol, based on the assumption that emis-
sions would be held constant after 2012. (Ver, et al., used a
similar representation.t71) The IS92 scenarios break down the
anticipated emissions into fossil fuel use and deforestation.
All of them use the same deforestation pattern, which de-
clines to zero by 2100. A curve showing the modified defor-
estation scenario is also included in Figure 4. The differences
between that curve and the others in the figure are the fossil
fuel components. Reforestation is not included in the sce-
narios as a separate disturbance.

Some Results
I use two different approaches for simulations, each hav-
ing certain advantages over the other. One is a straightfor-
ward numerical solution of the differential equations using
Mathcad-basically similar to the method used to generate
the historical curve in Figure 3. It's the workhorse that I
incorporate into classroom presentations and the major tool
used by the students for assigned work. I constructed the other
using LabVIEW** to give a convenient user interface, a vir-
tual laboratory, for certain classroom demonstrations and stu-
dent experiments. It provides the user with hands-on control
of the disturbances during a simulation, showing effects of
manipulations "live" on virtual strip-chart recorders and digi-
tal displays. (Actually, I've used the LabVIEW simulation
for classroom demonstration at the very beginning of the

I modified the IS92 scenarios for both the fossil fuel and deforestation
components in order to bring the 1990 values of the scenarios in agree-
ment with the data actually reported for that year'"t121 This amounted to
adding 0.1 PgC to all of the IS92fossilfuel quantities and increasing all
of the deforestation values by about 50%. These modifications are more
for refinement and fastidiousness than for any significant effect on cal-
culations.
** LabVIEW developed by the National Instruments Corporation in Aus-
tin, Texas, is graphical programming software developed mainly for data
acquisition and instrument control. It also serves as a powerful tool for
constructing virtual laboratories.


module because it is illustrative and serves to introduce goals
and whet the appetite for learning about model development
and simulations.) Space limitations prohibit a full descrip-
tion of the LabVIEW simulator and its operation here, but
the gist of it is shown in the photo of the user's panel in Fig-
ure 5 and the brief description in the caption. Notice that those
features afford the user an option of sequestering carbon by
reforestation and by capturing a fraction of emissions, F,, in
the deep ocean and geologic reservoirs.
Figure 6 presents an example of the results of Mathcad
simulations using the four scenarios of Figure 4. (For those
simulations, I used linear interpolation between the data points
shown in Figure 4 for the period 1990-2100.) The results in
Figure 6 are based on the parameters listed in Table I ex-
cept that here the values used for P2 and P3 are 11.0 and
12.3, respectively. (As I mentioned above, those values
depend on the total carbon in the surface ocean reservoirs.
I used the 1990 values of M, and M, given in Table 2 as a
basis for the new p values for the period 1990-2100.) F,
is taken to be zero.
Notice that the model predicts atmospheric CO, would in-
crease to 702 ppmv by the year 2100 if the IS92a business-
as-usual scenario were followed. Based on that scenario, pre-
dictions by models used by others1,3,141 range between 697
and 724 ppmv. Over the entire 110-year period, the maxi-
mum difference in atmospheric CO, between any two of the
four models (the three cited above and the present one) is
about 4%, an observation that buttresses confidence in dis-
cussions of quantitative results from the model at hand. No-
tice the wide range of predicted CO, levels in 2100 resulting
from the different scenarios for carbon emissions. The high-
est is nearly twice the lowest; both are probably unrealis-
tic extremes. Business-as-usual would result in nearly
doubling the 1990 CO2 level by the year 2100, according
to the model prediction.


Figure 4. Carbon emissions to the atmosphere; historical
data and possible future scenarios.


Chemical Engineering Education













































Additional Work
Using Mathcad and LabVIEW simulations, students obvi-
ously can be involved in examining all sorts of questions,
model variations, and parameter effects. Here is a partial list
of exercises that I have used, some of which require consult-
ing outside references.
I Extend simulations beyond 2100 to address a number of
questions raised about the ultimate steady state. (Actu-
ally, I ask the students to use the steady-state forms of
the equations to address some of these.) What would that
ultimate state be if emissions were halted immediately?



950
o reported data to 2000
850 ------ for IS92e scenario from 1990 -
E IS92a
S750 -- --- IS92c
702
I650 -- Kyoto
650 /


472
450

350 ---
a a o o a o o o 0
250
1850 1900 1950 2000 2050 2100
year

Figure 6. Atmospheric carbon dioxide levels; reported
historical data and model predictions.


Fall 2002


What would it be if all carbon in the fossil fuel reservoir
were eventually used? How long will it take to approach
a steady state if carbon emissions to the atmosphere are
halted at a certain time?
> Carry out simulations to clarify, if necessary, the roles
and effects of kd, kr, and M,-or to test entirely different
forms of F,,, the rate of photosynthetic uptake of car-
bon.
> What is a realistic mathematical description for the dis-
turbance, F, if reforestation begins with new trees that
require a number of years for maturation?
> Examine the predicted changes in the strengths of the
terrestrial and oceanic sinks (or sources?) of atmospheric
carbon over the 21s" century.
It is sometimes suggested that the most realistic goal that
can be achieved regarding the control of atmospheric CO2
is to "stabilize" it at twice the pre-industrial level by the
year 2100. Try to achieve that goal by manipulating the
emissions (or by fabricating an emissions scenario) in
such a way that atmospheric CO2 lines out at about 1224
PgC (572 ppmv) by the year 2100. (This is an ideal exer-
cise-even an entertaining one-for the LabVIEW simu-
lator. In fact, the data shown on the digital displays and
charts in Figure 5 are the end states of this exercise.)
Notice that the difference between the emissions level
so achieved in 2100 and that dictated by the IS92a sce-
Continued on page 309.

303











,M1 laboratory


DETERMINING THE

FLOW CHARACTERISTICS OF A

POWER LAW LIQUID




JAMES R. HILLIER, DALE TING, LISA L. KOPPLIN, MARGARET KOCH, SANTOSH K. GUPTA
University of Wisconsin Madison, WI 53706


Non-Newtonian liquids present unique problems with
respect to their flow behavior. These problems are
seldom addressed in undergraduate courses in chemi-
cal/mechanical engineering and are possibly covered only
through a single experiment in one of the laboratory courses.
Tjahjadi and Guptal' extended the work of Walawender and
Chen'2' and developed an experimental scheme that illustrates
how the apparent viscosity, ir, of a pseudoplastic liquid (di-
lute aqueous solution of Na-CMC) decreases with increasing
shear rate, y. They also suggested performing additional
experiments after adding some sodium chloride to the
CMC solution, to observe a dramatic decrease in Tr and
relate it to the contraction of the polyelectrolyte molecules
in an ionic medium.
Although the results had considerable educational value,
the equations used were quite complex and cumbersome
to use, with the result that a student obtained little insight
into the method of analysis-this limits the value of their
experiment.
In the present work (developed as part of the "informal"
experiments'31 at the Summer 2000-I laboratory at the Uni-
versity of Wisconsin-Madison), a much simpler experiment
has been developed that uses the easily understood macro-
scopic energy balance (the engineering Bernoulli equation[4])
to obtain experimental results.
A 0.07% (by weight) solution of a sodium salt of carboxy-
methyl cellulose (Na-CMC; weight average molecular weight
= 7 x 105; DS = 0.9; Aldrich Chemicals, Milwaukee, WI) in
deionized water was used for our study. CMC was selected
because of its pseudoplastic nature over a range (1 105 s-')
of shear rates. In addition, CMC is an inexpensive, nontoxic,
biodegradable, water-soluble polymer, commonly used in
mining applications, food thickeners, adhesives, and textiles.


The results obtained could also be compared to existing val-
ues in the literature'' for consistency.

EXPERIMENTAL SET-UP
The experimental set-up is similar to that used for studying
the flow characteristics of Newtonian liquids, as described
by Crosby.'si Flush-mounted glass capillaries (in one case, a
copper tube) of different diameters and lengths are used with
a drain tank,"'1 as shown in Figure 1. Two different kinds of
experimental units were made so as to vary the shear rate
over a reasonable range. The detailed dimensions are pro-
vided in Table 1.

PROCEDURE
The CMC solution to be used in all the experimental runs
was prepared using laboratory-grade carboxymethyl cellu-
lose powder. A solution of 0.07 wt% CMC in deionized wa-

James R. Hillier received his BS degrees from the University of Wiscon-
sin-Madison in Chemical Engineering (2000), Biochemistry (2000), and
Molecular Biology (2000). He is currently the Plant Engineer for Equistar
Chemicals in Fairport Harbor, OH, while working on a master's degree in
polymer engineering and a diploma in disaster management.
Dale Ting received his BS in Chemical Engineering from the University of
Wisconsin-Madison in 2000. He is currently working in process develop-
ment at The Procter and Gamble Co. in Cincinnati, OH.
Lisa Kopplin received a BS in Chemical Engineering from the University
of Wisconsin-Madison (2000). She is currently serving as a Project Engi-
neer for General Mills, Inc., in their West Chicago manufacturing facility.
Margaret R. Koch graduated from the University of Wisconsin-Madison
with a BS in Chemical Engineering in 2000. She is currently working in
Process Development at S.C. Johnson & Son, Racine, WI.
Santosh K. Gupta received his BTech (1968) from I.I.T, Kanpur, and his
PhD (1972) from the University of Pennsylvania-Philadelphia. He has been
on the faculty of /.l.T, Kanpur, since 1973, and has also been a Visiting
Professor at the University of Notre Dame, National University of
Singapore, and the University of Wisconsin-Madison. His research inter-
ests include polymerization engineering and optimization using Al tech-
niques.
Copyright ChE Division of ASEE 2002


Chemical Engineering Education

























-ri-2ro -Zro 2ro I
(a) (b) (c)
Figure 1. Experimental set-ups for Phases 1 and 2.
a and b, 50 ml graduated tube (buret with lower end cut) con-
nected to aligned glass capillaries, flush-mounted to minimize
entrance losses.
c, 5 lit SS tank (diameter 0.158 m) with sight glass to measure
h, used. Glass or Cu capillaries/tubes used. Details provided in
Table 1.


Fall 2002


ter was prepared well in advance to guarantee the ho-
mogeneity of the solutions."' The solution was heated
to 30-500C for about 4 to 8 hours and stirred for over
24 hours. Homogeneity of the solution was con-
firmed by observing its clarity against a very bright
light source."1.6
In each experimental run, a specified amount of poly-
mer solution was added to the holding tank. The ini-
tial values, ho, of the level of solution in the tank (see
Figure 1) are given for the different experimental runs
(Table 1). Flow was started, and data on h was recorded
over time, t, starting at the calibration mark. This al-
lowed flow patterns to establish so that data would not
be altered by flow development. Experimental runs
were stopped prior to complete efflux of the liquid
from the tank, so as to reduce the significance of
end effects.

THEORY

Since CMC solutions behave like pseudoplastics,
their apparent viscosities, ir, decrease with increasing
shear rates, y. The general dependence of 11 on is
quite complex, but over small ranges of the shear rate,
y, the following power law model[4.6.71 is followed quite
well:

T = Ky" (1)
where t is the shear stress. In Eq. (1), the constant, K,
is referred to as the consistency index, and the expo-
nent, n, is the power law index. The apparent viscosity
is then given by


y
r -= K (2)

A macroscopic (mechanical energy balance for this
system. Eq 5201 leads to (see Appendix 1 for details)

(3n+l+n vn
pg(L + h) 2 KL n ) rn+l (3)

In Eq. (3), p is the density of the solution, ro and L are
the (inner) radius and length of the capillary (Figure
1), h is the height of the solution above the capillary
entrance at time, t, g is the acceleration due to grav-
ity, and v is the mass-average velocity inside the
capillary at time t.
The mass-average velocity of the solution inside the
capillary can be obtained using the continuity equa-
tion

TR )2(-dh (
v=J -s T (4)
where R is the inner ra dthe drain tank. A second
where R is the inner radius of the drain tank. A second











The primary advantage of the present study is that analysis of the raw data can be
performed using equations that are easily understood by juniors in chemical
engineering, and standard computer packages can be used...


or third degree polynomial can be fitted to data on h(t). This
gives excellent values of the coefficient-of-determination of
about 0.999 and higher. This polynomial is then used with
Eq. (4) to obtain v. Eqs. (3) and (4) can be combined and
integrated for Newtonian fluids (n = 1) to give the standard'4n
equation for the efflux time for a vertical tank-pipe assembly
under laminar-flow conditions. The students find these deri-
vations easier to comprehend (in fact, they can make the
derivations themselves) than the equations described by
Tjahjadi and Gupta.i '
The validity of the assumption of laminar flow should be
confirmed by calculating the Reynolds number for the
pseudoplastic liquid using[7: Eq 550]

Re= 23-n( n n Dnpv2-n
3,3n+l) K (5)

For pseudoplastic flows present in the laminar region, as in
this study, the sudden contraction/entrance losses are expected
to be negligible."'21 In the more general case where the en-
trance losses are important, the Bagley correction'8'9 can
be used. This could be a possible avenue of further study
for a student.
Equation (3) can be rewritten as

i 2KL (3n+l .
log [pg(L + h)] = log 2 KL (3 n + n log (v) (6)
r_ i- I n ) I

An appropriate log-log plot of Eq. (6) gives n (= slope). K
can then be obtained using n and the intercept, a, using


K = exp fn (7)
S2L 3n+l 1 (

Once values are obtained for both n and K, the shear rate (at
the wall of the tube, r = r ) can be evaluated using[4'7;App 1]


Spg(L + h)ro ]n (8)
S2LK J I

The apparent viscosity, r, can then be evaluated (at this wall
shear rate) using Eq. (2). Equation (8) assumes that the power
law dependence is valid, and so the value of y obtained is
inferred from the data-fitting procedure.
Unfortunately, use of the power law assumption, though
helpful in simplifying the experiment at the undergraduate
level, can give a false idea of the complexity of the method
of analysis routinely used by professional, non-Newtonian


rheologists (who commonly use the Rabinowitsch tech-
nique'6'91). An alternative procedure of data analysis that is
not as difficult and that can be attempted by an undergradu-
ate student, is the use of the Schummer approximation'101 (de-
scribed in Appendix 2). Such an analysis preserves, to some
extent, the physics of mechanical energy balance and closely
follows the steps that would be employed in the professional
theological evaluation of non-Newtonian viscosity. One set
of experimental data generated herein is analyzed later to
compare the results using the power law and the
Schummer approaches.

RESULTS AND DISCUSSION
Details of the several experimental set-ups and runs are
given in Table 1. These experiments were designed and per-
formed in two phases-Runs 1 and 11 through 16 in Table 1
comprising the first phase, followed by Runs 2-10. The re-
sults of the first phase were analyzed and used to help im-
prove the designs for Phase 2. Figure 2 shows data from Phase
1. It demonstrates the decrease of the apparent viscosity with
increasing shear rates. Although the viscosity vs. shear rate
diagram is incomplete, the shear-thinning effect characteris-
tic of pseudoplastic fluids is quite evident. The straight-line
segments on this log-log plot confirm the validity of the
power-law model over small ranges of shear rate. The data
overlap in some regions, which confirms the accuracy of the
results. The value of the power law index varies from about
0.3 to 1.0 (see Table 1). The range of shear rates covered
extends over almost two decades, and the data appears to fall






0 12






o Ra 1oo 00


Figure 2. Apparent viscosity vs. shear rate for a 0.07 wt%
Na-CMC aqueous solution, assuming power law behavior
of the liquid. Phase 1 results shown with Runs indicated.
Results from Ref. 11 also shown for comparison. Tempera-
ture = 23C.


Chemical Engineering Education










on a smooth curve over this range.
The data is also found to be consistent with some earlier
workE"' performed using the same solution, using a stainless
steel tank with a copper tube, similar to that used in Run No.
16. Our data is also consistent with the earlier data"' on a 0.07
wt% Na-CMC solution having a slightly larger weight-aver-
age molecular weight of 7.5 x 105 (the apparent viscosity at
1000 s- was about 7 cP earlier, and is about the same in Figure
2). The replicability of our results was found to be excellent.
It should be mentioned here that an interesting activity would
be to confirm the experimental results obtained here with those
using more sophisticated capillary-flow or Couette viscom-
eters available in research laboratories. Use of the former
would also illustrate the use of the more exact Rabinowitsch
technique of analysis.'"9
The experimental results shown in Figure 2 were then used
to design a few additional experiments (Phase 2) so as to ex-


Figure 3. Results for Phase 2, assuming power law
behavior of the liquid. Run Nos. 2,3, x; 4, ; 5, -;
6, --; 7, o; 8, +; 9, D; 10 0; Temperature = 23 C.


01
Schummer
0 Power Law

'3

0.0





0 001
100 1000 10000
Shear Rate (1/s)

Figure 4. Comparison of r1 vs y obtained assuming power
law behavior of the liquid with that using the Schummer
correction. Set 9 (Table 1) data used.


tend the range of shear rates. The corresponding plot for the
apparent viscosity vs. shear rate for these runs is given in
Figure 3, and the values of K and n in Table 1. It was found
that the data for the two sets of experimental runs, in the
range of shear rates of about 300 to 1000 s superposed
very well (these have not been shown since the data points
get too cluttered). It is interesting to observe that Runs 9
and 10 give data over a very large range of shear rate, and
one could as well use just one or both of these set-ups for a
routine laboratory experiment.
It should be emphasized that Eq. (3) is applicable only
over small ranges of shear rate (and so over a small range of
t, as the meniscus falls). A log-log plot of this equation does
not show straight lines for some cases, and one must exer-
cise some judgment to fit the points. Moreover, the viscos-
ity of CMC (a polyelectrolyte) solutions in deionized water
is very sensitive to the concentration of small amounts of
salts that may be present.'" The addition of small quantities
of NaCI to the solution could help improve the reproduc-
ibility of the results substantially, and would help if one were
to compare the results obtained by different groups of stu-
dents taken over several weeks.
Figure 4 shows one set of data (Run 9, Table 1) that has
been analyzed using both the power law assumption for the
solution as well as the more accurate Schummer technique.
The results superpose quite well, but a shift in the curves is
quite evident, as discussed in Ref. 10.

CONCLUSIONS
A simple experimental set-up was developed to study the
decrease of the apparent viscosity of a 0.07% (by weight)
aqueous solution of Na-CMC with increasing shear rate. Two
experimental units were found that covered a reasonably
large range of shear rates of 500 to 6000 s-. The primary
advantage of the present study is that analysis of the raw
data can be performed using equations that are easily un-
derstood by juniors in chemical engineering, and standard
computer packages (e.g., Excel, etc.) can be used for this
purpose.
Additional experimental data can easily be taken after
adding sodium choride to the CMC solution, to study the
effect of molecular contraction of the polyelectrolyte.I'1 The
results obtained using the power law assumption are com-
pared to more elaborate methods of analysis, and a few ad-
ditional experiments have been suggested for the more
enterprising student.



APPENDIX 1

Details of the Derivation of Eqs. (3) and (8)

The macroscopic mechanical energy balance[4] is applied


Fall 2002










between points 1 and 2 (Figure la) with the following as-
sumptions:
The column is vertical
The kinetic energies of the liquid at 1 and 2 are
negligible
Entrance or other losses are negligible, and the only
losses are due to viscous effects in the capillary
This leads to


g(L + h)= c -
SP capillary to


(Al.1)


where to is the shear stress at the capillary wall, r = ro, and
(AP)capiary is the pressure drop across the length, L, of the
capillary.
A force balance over a control volume of radius, r, and hav-
ing a differential length, dz, gives[4'
-P =21 (A1.2)
dz r


-dP( AP) 2T
dz L Jcapillary ro


(AI.3)


Equations (A1.2) and (Al.3) give


-^o


Kvn (3n+ln _ro (AP
o0 = ro n ) 2 I L )capillary


(A1.9)


Equation (Al.9) can be combined with Eq. (A1.1) to give
Eq. (3).
Equation (Al.6) can be simplified to give


( tor p=/n( g(L +h) rl
which leads to Eq. (8) (with r = r).
which leads to Eq. (8) (with r = rQ).


(Al.10)


APPENDIX 2

Details of the Schummer Approximationt[1


The apparent shear rate Yap, and the apparent viscosity,
lap, are defined'"' by


4v 4Q
Yap 3-

o_ rgrpg(L+h)
pYap 8vL


(a)


(b) (A2.1)


Schummer states that the "true" shear rate, j, corresponding
to 'ap (at which the viscosity is equal to Tlap) is given by


Using the following variation of Eq. (1)

:= K du (A1.5)

where u is the axial velocity at location, r, in Eq. (A1.4), we
obtain

-du It0o /n
(r) = I rl/n (A1.6)
S d r = roK

This can be integrated fromr=r0(T=t0)tor=r(t=t)to


/r /1I/n I/n+l I/n+1
t0 r0 -
u(r) = K ro 1+l
Kr01 i+ 1


(A1.7)


Equation (A1.7) can easily be integrated over 0 < r < r0 to
give the mass average velocity, v, as


v= ro I+
K 13+


(Al.8)


which can be rearranged (and Eq. A1.1 used) to give


03.32v
/=0.83ap -


(A2.2)


The experimental data can be used to give the average veloc-
ity, v, in the capillary, as a function of time. This can be used
with Eqs. (A2.lb) and (A2.2) to evaluate rlap and the "true"
(or the corresponding) shear rate, ,, to give a more accurate
plot of rl vs y.

REFERENCES
1. Tjahjadi, M., and S.K. Gupta, Chem. Eng. Ed., 20, 84 (1986)
2. Walawender, W.P., and T.Y. Chen, Chem. Eng. Ed., 9, 10 (1975)
3. Sather, G.A., and J. Coca, Chem. Eng. Ed., 22, 140 (1988)
4. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena,
2nd ed., John Wiley and Sons, New York, NY (2001)
5. Crosby, E.J., Experiments in Transport Phenomena, Department of
Chemical Engineering, University of Wisconsin, Madison, WI (1961)
6. Kumar, A., and S.K. Gupta, Fundamentals of Polymer Science and
Engineering, Tata McGraw Hill, New Delhi, India (1978)
7. McCabe, W.L., J.C. Smith, and P. Harriot, Unit Operations of Chemi-
cal Engineering, 5th ed., McGraw Hill, New York, NY (1993)
8. Bagley, E.B., J. Appl. Phys., 28, 624 (1957)
9. McKelvey, J.M., Polymer Processing, John Wiley and Sons, New York,
NY (1962)
10. Dealy, J.M., and K.F. Wisbrun, Melt Rheology and Its Role in Plastics
Processing, van Nostrand Reinhold, New York, NY (1990)
11. Zhang, J., J. Jenkins, B. Linden, and A. Kristopeit, UW-Madison Trans-
port Lab Memo, Madison, WI (2000) J


Chemical Engineering Education


(A1.4)











The Earth's Carbon Cycle
Continued from page 303.

nario (i.e., the difference between the end points of curves
of the lower strip chart of Figure 5) is the amount of
carbon that would have to be replaced by an equivalent
energy source. Follow-up questions for consideration
and/or further simulations: What alternate sources of
energy might fill the gap? Could it be filled by seques-
tering carbon in the terrestrial biota (reforestation ac-
tivities)? ...in geologic storage? ...in the deep ocean
waters? Would those possibilities lead to a permanent
stabilization? What is the trend of the fabricated emis-
sions curve in 2100? What is its ultimate fate if atmo-
spheric CO2 is to stay level at 572 ppmv?
0 Start from the beginning with an alternative model that
presumably improves on this one (e.g., by adding layers
to the ocean or atmosphere, a spatial variation to the ter-
restrial reservoirs). Calibrate, tune, and test the model
against the results shown here.

CONCLUDING COMMENTS
Many of the Earth's biogeochemical processes can be stud-
ied and modeled within the context of the usual chemical
engineering curricular material. The carbon cycle, the focus
of this article, is a particularly apt example because, though
basically complex, it can be usefully described by a simple
mathematical model. Additionally, it is being disturbed and
altered by human activities, possibly to the extent of causing
global warming and other climate changes, and is therefore a
subject of current interest and concern.
Aside from students learning about this particular subject,
important and timely as it is, in my view another worthwhile
outcome is that they gain confidence in their ability to ana-
lyze physical situations that may not be on their usual bill-of-
fare and to apply their chemical engineering tools to the for-
mation of a mathematical description. Never mind that the
description is soaked with simplifications and assumptions-
such as perfectly mixed boxes for oceans, single-rate expres-
sions for all of the Earth's photosynthesis, and so on. A great
deal is learned by pondering, investigating, and debating the
bases for such simplifications and assumptions.
This article describes my coverage of the subject in a course
devoted to topics on ecology and the environment. The cov-
erage is scalable-downward to a brief treatment and selected
homework assignments integrated into some of the usual core
course offerings, or upward to the development of more so-
phisticated models and the application of more advanced de-
scriptions of the rate processes, mathematical analysis, and
computational methods. Whatever the scope, students ben-
efit from the broadening experience of applying their chemi-
cal engineering tools in a quantitative way to an important
subject outside the mainstream.


Readers who would like to have an electronic copy of this
module, which consists of a slide show with links to spread-
sheets, simulations, etc., including the LabVIEW simulator,
should contact me at .


ACKNOWLEDGMENT
Development of the material for this article was part of a
project supported by the CRCD program (Grant EEC97-
00537-CRCD) of the National Science Foundation.


REFERENCES

1. Cox, P.M., R.A. Betts, C.D. Jones, S.A. Spall, and I.J. Totterdell, "Ac-
celeration of Global Warming Due to Carbon-Cycle Feedbacks in a
Coupled Climate Model," Nature, 408, 184 (2000)
2. Chameides, W.L., and E.M. Perdue, Biogeochemical Cycles: A Com-
puter-Interactive Study of Earth System Science and Global Change,
Oxford University Press (1997)
3. Lenton, T.M., "Land and Ocean Carbon Cycle Feedback Effects on
Global Warming in a Simple Earth System Model," Tellus, 52B, 1159
(2000)
4. Rodhe, H., and A. Bjorkstrom, "Some Consequences of Non-Propor-
tionality Between Fluxes and Reservoir Contents in Natural Systems,"
Tellus, 31, 269 (1979)
5. Schnoor, J.L., Environmental Modeling: Fate and Transport of Pol-
lutants in Water, Air and Soil, John Wiley & Sons (1996)
6. Siegenthaler, U., and F. Joos, "Use of a Simple Model for Studying
Oceanic Tracer Distributions and the Global Carbon Cycle," Tellus,
44B, 186(1992)
7. Ver, L.M.B., FT. Mackenzie, and A. Lerman, "Biogeochemical Re-
sponses of the Carbon Cycle to Natural and Human Perturbations:
Past, Present, and Future," Ami. J. of Sci., 299, 762 (1999)
8. Herzog, H., B. Eliasson, and O. Kaarstad. "Capturing Greenhouse
Gases," Sci. Am., February 2000, 72 (2000)
9. Kane, R.L., and D.E. Klein, "Carbon Sequestration: An Option for
Mitigating Global Climate Change," Chem. Eng. Prog., June 2001,44
(2001)
10. Butcher, S.S., R.J. Charlson. G.H. Orians, and G.V. Wolfe (eds), Glo-
bal Biogeochemical Cycles, Academic Press (1992)
11. Marland, G., T.A. Boden, R.J. Andres, A.L. Brenkert, and C.A.
Johnston, Trends: A Compendium of Data on Global Change, Carbon
Dioxide Information Analysis Center, Oak Ridge National Labora-
tory, Oak Ridge. TN (1998)
12. Houghton, R.A., and J.L. Hackler, Trends: A Compendium of Data on
Global Change, Carbon Dioxide Information Analysis Center, Oak
Ridge National Laboratory, Oak Ridge, TN (1998)
13. Worldwatch CD-ROM, Worldwatch Institute, Washington, DC (2001)
(This CD-ROM and downloadable datasets are available at www.worldwatch.org/pubs/>
14. Houghton, J.T., L.G. Meira Filho, B.A. Callander, N. Harris, A.
Kattenberg, and K. Maskell (eds), Climate Change 1995: The Science
of Climate Change, Contribution of Working Group I to the Second
Assessment Report of the Intergovernmental Panel on Climate Change,
See Figure 5 of Technical Summary (Published for the Intergovern-
mental Panel on Climate Change, IPCC), Cambridge University Press
(1995) (This and other reports of the IPCC are available online at /www.ipcc.ch/pub/reports.htm>
15. Leggett, J., W.J. Pepper, and R.J. Swart, "Emissions Scenarios of the
IPCC: An Update," Climate Change 1992: The Supplementary Re-
port to the IPCC Scientific Assessment (J.T. Houghton, B.A. Callander,
and S.K. Varney, eds), p. 69-95, Cambridge University Press (1992)
16. United Nations Framework Convention on Climate Change, COP 3
Report, Document FCCC/CP/1997/7/Add. 1. (The full text of this re-
port is available at O


Fall 2002











[S assessment


PORTFOLIO

ASSESSMENT

In Introductory ChE Courses



SURITA R. BHATIA
University of Massachusetts Amherst, MA 01003-9303


As defined by Feuer and Fulton,111 performance-based
assessment refers to assessment techniques that re-
quire students to create a final product, such as a
written report, oral presentation, or portfolio of their work,
as opposed to the more conventional assessment techniques
of written quizzes or exams. Performance assessment can also
be defined as an assessment method that evaluates a student's
ability to perform a specific procedure or task;121 in this con-
text, the assessment must contain a performance task, a stu-
dent-response format, and a scoring system. Examples
would include judging a student's ability to manipulate
laboratory equipment or respond to an open-ended prob-
lem.121 Slater suggests designing a performance task that
is "somewhat undefined, complex, and has multiple entry
and exit points;" that is, a task that has more than one
correct solution path.[21
The advantages of performance-based assessment tech-
niques have been documented by several studies in the edu-
cational literature." '6 Many studies emphasize the "real-
world" nature of performance assessment;l"3 student work is
evaluated in a manner that is much closer to what will be
encountered in the work environment. Perhaps most impor-
tantly, research has shown that alternative assessment helps
in the evaluation of students with various learning styles and
educational backgrounds, promoting excellence among a
more diverse student population.14'
These "alternative assessment" techniques131 are not new
to engineering education. Traditional performance-based as-
sessment is often used (although not often acknowledged as
such) in junior- and senior-level courses in the form of labo-
ratory experiments, written lab reports, design projects, and
oral presentations; and the ABET EC 2000 guidelines have
brought increased attention to outcomes-based assessment.17'81
But alternative assessment is not widely used in the fresh-


man- and sophomore-level courses for a variety of reasons.
Educators may worry that freshmen and sophomores do not
have the depth and breadth of knowledge to complete a de-
sign project or written paper, or that there is simply not enough
class time to have students give oral presentations...after
all, there is barely enough class time to teach these stu-
dents mass and energy balances and thermodynamics.
There is another means of implementing performance-
based assessment in these courses, however-one that has
remained largely under-used in engineering education:
student portfolios.

WHAT IS A PORTFOLIO?
Portfolios are collections of student work, typically selected
according to guidelines set forth by the instructor.131 These
guidelines may have a one-to-one correspondence with the
course objectives, or an instructor may choose to highlight
particular course objectives. An example of required items
from the freshman chemical engineering course at UMass,
which I will discuss in more detail below, is given in Table 1.
Along with each item, students are asked to submit a state-
ment of why the item was chosen. This element of self-analy-
sis or self-reflection is crucial if portfolios are to be more
than just "student folders."['9 For comparison, the course ob-

Surita R. Bhatla is an assistant professor in the
ChE Department at the University of Massachu-
setts. She received her BChE from the Univer-
sity of Delaware, her PhD from Princeton Uni-
versity, and held a postdoctoral position at the
CNRS/Rhodia Complex Fluids Laboratory. Her
research interests are associative polymers, rhe-
ology, shear-induced structure, and structured
cell encapsulation materials. She has taught
mass balances and heat transfer at the under-
graduate level and coteaches a graduate course
on colloidal dispersions.


Copyright ChE Division of ASEE 2002


Chemical Engineering Education













TABLE 1
Required Portfolio Entries for Freshman Course in
Chemical Engineering Fundamentals


1. A problem with a "nonroutine" solution, where students had to
employ new strategies or methods of solution

2. A homework problem that involved teamwork or group work

3. A problem that gave the student a good sense of real-world
applications

4. A problem involving data analysis or data fitting

5. A problem involving the use of MathCAD

6. A problem involving the use of Microsoft Excel

7. A self-analysis of the student's strengths and weaknesses with
regards to concepts learned in class

8. Reflections on chemical engineering, this class, and any thoughts
on career choices




TABLE 2
Course Objectives for Freshman Course in
Chemical Engineering Fundamentals

At the end of this course, students should

E[ Understand concepts of engineering calculations, including
significant figures and dimensional analysis, and be able to
perform unit conversions

E[ Understand process flowsheets, know how to draw and label a
flowsheet, and be able to clearly define subsystems within
processes to set up conservation equations

[ Understand conservation of mass and be able to solve material
balances on steady processes

E[ Understand thermodynamic quantities such as internal energy,
enthalpy, and heat capacity

[ Understand the concept behind distillation and be able to perform
simple vapor-liquid equilibria calculations using Raoult's Law
and Henry's Law

1 Understand conservation of energy and be able to set up simple
energy balances

[ Be able to use software packages (for instance, Microsoft Excel
or MathCAD) to set up and solve engineering calculations and
aid in data analysis

[I Be able to use the principles and tools learned in this course to
solve problems not covered in detail as part of the course and to
continue learning related material as needed in the future.


Fall 2002


Many studies emphasize the
"real-world" nature of performance
assessment; student work is evaluated in a
manner that is much closer to what will be
encountered in the work environment.


jectives are listed in Table 2.
A widely cited benefit of portfolio assessment is an im-
provement in communication skills and creative-thinking
skills, particularly in mathematics and science, two disciplines
where students often have difficulty communicating their
results.1"49' These assessment techniques also promote stu-
dent self-assessment and reflection. This allows students
to become better at selecting and presenting their best
work, which helps them gain confidence in their abili-
ties.141
Studies in college physics classest61 have shown that port-
folios may serve to help students organize work and internal-
ize concepts; however, preliminary studies of portfolio use
in undergraduate chemistry coursesi"01 indicate that there is a
disconnect between student performance on exams and in
portfolio entries with regard to specific course objectives.
Educators in chemical engineering may feel uncomfortable
with the concept of "student self-reflection"; after all, we are
here to teach students, not to ask them how they "feel" about
engineering, right? We prefer hard numbers and are more
accustomed to quantitative assessment methods. But the util-
ity of portfolios has been demonstrated in several science,
mathematics, and engineering courses.14"60 161 Many states
require use of portfolios in all subject areas for grades
four through twelve,14-5 and portfolios have been success-
fully used in undergraduate physics, chemistry, and geol-
ogy courses.1691
The chemical engineering program at the Colorado School
of Mines has relied heavily on portfolio assessment for over
a decade, and Olds and Miller"I4' give an excellent descrip-
tion of the use of portfolios in the ChE curriculum. Both
Alvero CollegeE"5 and Rose-Hulman Institute of Technol-
ogyt16' have implemented an electronic portfolio system for
all students. Preliminary results from the Rose-Hulman project
indicate that students find the electronic portfolio system easy
to use, and that use of a web-based system reduced some of
the disadvantages of conventional portfolios, including stor-
age, user access, and availability."6'
It is important to keep in mind the difficulties and limita-
tions associated with portfolio assessment. Portfolios are not
appropriate for assessing factual knowledge or recall abili-
ties; thus, they should be used in conjunction with conven-
tional, quantitative assessment techniques.'91 Portfolios can
be difficult to manage and time-consuming to grade, which

311












Perhaps most importantly, research has shown that alternative assessment
helps in the evaluation of students with various learning styles and
educational backgrounds, promoting excellence
among a more diverse student population.


makes them easiest to implement in courses with small to
medium enrollments. Slatert'9 and Winkl101 have reported tech-
niques to extend the use of portfolios to large lecture courses,
however.
Although there has been an emphasis on the use of portfo-
lios in upper-level "capstone" courses, such as senior design
and the unit operations laboratory,1'4 I focus on their use in
introductory chemical engineering courses. I believe portfo-
lio assessment has unique benefits to beginning engineering
students, as described further in the following paragraphs.

GRADING PORTFOLIOS
Implementing innovative assessment is all well and good,
but how are we going to evaluate and grade student portfo-
lios? Since the portfolio entries have presumably been graded
as part of a homework assignment or exam earlier in the se-
mester, it does not seem fair to me to place the students in
"double jeopardy" by basing the portfolio grade on whether
or not the problems are correct. I chose to grade portfolios by
giving equal weight to three criteria:

Completeness and organization
Quality and style of writing
Level of thought, analysis, and reflection in each entry

The first two criteria are easy to evaluate. The first refers to
whether students have all the required items, including a table
of contents and page numbers. The second criterion refers to
writing style and grammar, again fairly straightforward to
evaluate.
The third criterion is a little more subjective and requires
some planning on the part of the instructor. I evaluated the
level of thought and analysis by judging the extent to which
each entry addressed two to three "thought questions," which
are listed in Table 3. Students were given these questions at
the start of the semester to help guide them through the self-
analysis process.
Slater'91 recommends developing a "scoring rubric,"
whereby the portfolio grade is based on the extent to which
students demonstrate mastery of the required number of ob-
jectives. For example, you may require students to have at
least eight entries, each of which is related to a specific course
objective. A simple scoring rubric could then be an "A" grade
for demonstrating adequate mastery in seven or more objec-


tives (as evidenced by the portfolio entries), a "B" grade in
five or more objectives, and so on. More detailed examples,
developed for a unit operations course, are given by Olds
and Miller;"4' see also the examples given by Slater.[91

EXAMPLE
Portfolios in the Introductory ChE Course
In the spring of the freshman year, students at UMass take
a course titled Chemical Engineering Fundamentals. The
course content covers units and dimensions, mass balances,
simple reactive systems (i.e., CSTRs and PFRs), and forms
of energy. The typical enrollment is 40-50 students, most of
whom are engineering majors with an interest in chemical
engineering. After completing the freshman year require-
ments, students can apply for admission into the chemi-
cal engineering major. Thus, many students in the ChE
Fundamentals course are still unsure of their choice of
major.
I chose to implement portfolio assessment in this course as
an optional assignment. The portfolio assignment could be
used to replace a low grade on either of two midterm exams
or a low homework grade, but not the final exam. Many in-
structors give students the option of "dropping" one low grade,
so I did not feel that the use of portfolios would cause grade


TABLE 3
Questions for Student Self-Analysis
in Portfolio Entries

E[ What concept or topic was involved with this problem? What
skills did you use in solving it?
E How did this problem help you learn something new?
E[ Did you learn anything about yourself, your thought process, or
your strengths and weaknesses as a result of this activity?
E What strategies did you use? What were you thinking as you
worked the problem?
E[ Would you do anything differently if you had more time?
E[ Can you describe any connections between the activity and other
concepts, subject areas, or real-life situations?
El Does the problem represent a special achievement for you, a
sense of accomplishment at having learned a particular concept,
or a sense of improvement over time?


Chemical Engineering Education




































































Figure 1. Results from student surveys after complet-
ing course. Responses to questions are as follows:
1 Strongly agree; 2 Agree; 3 No strong opin-
ion; 4 Disagree; 5 Strongly disagree.
Columns and error bars represent the average and stan-
dard deviation for each question, from a sample size
of 13 surveys for questions 1-3 and 28 surveys for ques-
tions 4-7. Question numbers correspond to those given
in Table 4.


TABLE 4
Student Evaluation Survey

0. Did you complete the optional portfolio assignment for this
class?
1. (If"Yes" to the first question) I enjoyed completing the portfolio
assignment.
2. (If "Yes" to the first question) I felt that I learned more about
myself and my strengths and weaknesses in chemical engineer-
ing and problem solving as a result of completing the portfolio.
3. (If "Yes" to the first question) My written communication skills
have improved as a result of completing the portfolio assign-
ment.
4. I feel that the use of both qualitative (e.g., written reports, oral
reports, and portfolios) and quantitative (e.g., exams and
homework) methods of assessment were appropriate for this
class.
5. I dislike qualitative methods of assessment (e.g., written reports,
oral reports, and portfolios) because I feel that they are
subjective.
6. I feel that quantitative methods of assessment (e.g., exams and
homework) are most appropriate for engineering and science
classes.
7. I would like to see qualitative methods of assessment (e.g.,
written reports, oral reports, and portfolios) incorporated into
other science and engineering classes.


inflation.
On the first day of class, I gave students a handout de-
scribing the portfolio assignment, including the informa-
tion in Tables 1 through 3, and a summary of the grading
protocol for portfolios. I also held a short class discus-
sion on what portfolios are and why they were being used
for this course.
Students were required to have at least eight portfolio en-
tries, which are listed in Table 1. Six of these entries were
related to course objectives or outcomes, with a focus on
objectives that are difficult to assess using conventional exam
techniques (i.e., the use of Microsoft Excel, data-fitting tech-
niques, etc.). These entries were expected to be copies of prob-
lems, either from the homework or exams. Students were re-
quired to attach a copy of their solution to the problem and a
short (one paragraph to one page) explanation of why the
problem was chosen.
In addition, two one-page essays (the last two items in Table
1) were required. I also handed out a list of questions to keep
in mind as they wrote their portfolio entries (listed in Table
3). Finally, students were asked to organize their entries, num-
ber each page, and include a table of contents in the portfo-
lio. Periodically throughout the semester, I reminded students
to work on the portfolio assignment and to come see me if
they had questions on the assignment.



RESULTS
Student Feedback and Assessment Survey
The class enrollment was 41 students. Forty-one percent
of the students (17 students) completed the portfolio assign-
ment. Grades on the portfolios were roughly in the low "C"
to high "A" range. For most students, the portfolio grade was
used to replace a low homework grade, but the difference in
the final grade for the course with and without the portfolio
was never more than a letter grade.
I was somewhat distressed to find that several students
counted on the portfolio to bring up their low homework grade
and thus did not spend as much time on the homework as-
signments throughout the semester as I would have liked. I
have since altered the portfolio guidelines to allow students
to replace a low midterm exam grade, but not the final exam
or a low homework grade.
I found that grading of the portfolios was time consuming,
but I did not feel that it took longer than grading exams. The
time commitment is similar to that required for evaluating
written reports, and I made comments on all portfolios re-
garding grammar and writing style.
Students were asked to complete a survey upon comple-
tion of the course, and the survey questions and student re-
sponses are given in Table 4 and Figure 1, respectively.


5
5 *--

4

3

P 2



1


1


2 3 4 5 6 7
Question number


Fall 2002












Portfolios can be particularly useful for beginning chemical engineering students,
who often do not have class projects that require them to synthesize concepts
and present their results in a written format.


These are preliminary results; obviously, data need to be
taken on a larger sample size before conclusions can be
drawn. The results also may be biased due to wording of
the survey questions. This needs to be addressed before
definitive conclusions can be reached, and I am currently
updating and redesigning the survey questions for future
classes.
On the whole, the response from students was quite posi-
tive. The strongest and most uniform response was to Ques-
tions 2 and 4; 86% of students who completed a portfolio
strongly agreed or agreed that the portfolio helped them to
learn more about themselves and their strengths and weak-
nesses in chemical engineering and problem solving, and
89% of all students felt that the use of both quantitative
and qualitative assessment methods were appropriate in
the course. It remains unclear whether or not the portfo-
lio assignment helped students improve their written com-
munication skills.
Several of the written comments that accompanied port-
folio entries were quite encouraging, and I have listed some
of the more memorable comments in Table 5. There were
also comments both positive and negative, that were useful
to me as an educator. Students were very honest about com-
ponents of the class that they liked and disliked. Most of
these comments were made in response to Item 8, Table 1,
reflections on chemical engineering and the class. Examples
of these comments are also given in Table 5.

CONCLUSIONS AND RECOMMENDATIONS
Portfolios can be particularly useful for beginning chemi-
cal engineering students, who often do not have class projects
that require them to synthesize concepts and present their
results in a written format. Interestingly, students did not feel
as though the assignment improved their written communi-
cation skills, but the portfolio assignment did seem to give
these incoming students an opportunity to reflect on their
abilities and their choice of major. Portfolios can also be used
to assess course objectives that are difficult to evaluate using
traditional techniques.
Based on my experience, I have some guidelines and rec-
ommendations for implementation of portfolios:


Be prepared to read up on assessment tech-
niques. Several of the references listed contain


excellent examples of student entries and grading
schemes.'45,9 I" I found the National Institute of
Science Education Field-Tested Learning
Assessment Guide website particularly useful.
(Found at flag/default.asp>.)


- Be clear about expectations for portfolios at the
start of the semester. You may want to give
students sample entries.


N Remind students that they should be saving
homework sets and collecting problems for
entries in their portfolio. This is extremely
important for freshman-level students who are
still learning how to organize their coursework.


P If you allow students to use a portfolio grade as a
replacement, make sure their expectations are
realistic. One fabulous portfolio assignment will
not pull a final "D" grade up to an "A"-as I
mentioned above, the overall effect on the final
grades in the course was never more than a letter
grade.
It is worth noting that implementing portfolios as
a "replacement" for a poor exam could allow a
student to bring a failing grade up to a "D."
Instructors need to decide for themselves
whether this is permissible and to develop their
own guidelines accordingly.
For example, I specified that if students received
a zero grade on an exam or homework due to
academic dishonesty, this grade could not be
"replaced" under any circumstances. One could
imagine extending this rule to any failing grade
to prevent the above scenario. Finally, I found
that it was problematic to allow students to
replace a low homework average with the
portfolio grade.


> Create a grading scheme that places emphasis on
what you think is most important, whether this is
good writing, clear organization, self-reflection,


Chemical Engineering Education















TABLE 5
Sample Comments from Student Portfolios

New Strategies of Problem Solving (Item 1)
and Self-Analysis (Item 7)

"I now have more confidence knowing that if I can't solve a problem
using the accepted method of solution, I will be able to come up with
a new method, perhaps something nonroutine, in order to solve the
problem."

"This problem showed me that I should have more confidence in my
ability to find a solution when it doesn't simply present itself after a
series of steps."

"I could apply things I had learned in a completely different context
to other situations. This is actually quite comforting, as I've always
wondered if I'll be able to use the things I learn now later on in life
when I might actually need them."
"I've had trouble [with] time management, as I have usually been
able to understand the problems but have not left myself enough time
to gather it all in a presentable format."

"My weakness is that every time I hit a wall, I tend not to do anything
about it. I can only blame myself for not attempting, [but] I already
made my choice in staying in this major and it is all up to me in
keeping that choice."


Reflections on Chemical Engineering
and The Fundamentals Course (Item 8)

"All in all I enjoyed the class, I enjoy being a chemical engineering
student, and I look forward to the day when I am employed as a
fabulous chemical engineer."

"I dislike computers and I dreaded using them for this class. I
probably would have stuck with this major if it were not for
MathCAD and Excel. I do not think being taught [MathCAD] for one
class period is enough class time."

"Since the class is almost over, I feel a real sense of accomplishment.
I know that it is only a freshman level class, but I put a great deal of
effort and time into the class...It makes me proud to say that I'm a
chemical engineering major when people ask me."

"I feel like I've gotten a much better idea about what chemical
engineers do through the various assignments and from the oral
presentations of my peers."
"I feel that we did not [spend] much time on using the computer."

"Before taking this class I wasn't positive that chemical engineering
was the right major for me. I felt that perhaps I would not be able to
handle the workload or grasp all of the material that I needed to
know. However, I now feel that I am actually capable of becoming an
engineer."

"I love going to my chemical engineering classes, they are the only
ones that I don't purposely skip."

"As a result of this class I am much more confident about my choice
of major and the preparation it will give me to succeed in the career I
want to pursue."


or assessment of a specific course objective.
Make sure your grading scheme is clear to the
students at the start of the semester.


ACKNOWLEDGMENTS

I would like to acknowledge my Chemical Engineering
Fundamentals students for participating in this work. Pro-
fessor Donald Wink (Chemistry, University of Illinois at
Chicago) provided me with a copy of his recent ACS pre-
sentation on portfolio assessment and suggested several of
the works cited in this article, which was greatly appreci-
ated. The manuscript reviewers, particularly Reviewer #3,
made several useful and constructive comments. Mrs.
Kanak Bhatia (Ed.D. candidate, University of Delaware)
also suggested several helpful references and made com-
ments on the manuscript.


REFERENCES
1. Feuer, M.J., and K. Fulton, "The Many Faces of Performance As-
sessment," Phi Delta Kappan, 74, 473 (1993)
2. Slater, T.F., "Performance Assessment," in Field-Tested Learning
Assessment Guide, National Institute of Science Education (2000)

(accessed 6/6/02)
3. Herman, J.L., P.R. Ashbach, and L. Winters, A Practical Guide to
Alternative Assessment, Association for Supervision and Curricu-
lum Development, Alexandria, VA (1992)
4. Lambin, D.V., and V.L. Walker, "Planning for Classroom Portfolio
Assessment," Arithmetic Teacher, 41, 318 (1994)
5. Abruscato, J., "Early Results and Tentative Implications from the
Vermont Portfolio Project," Phi Delta Kappan, 74, 474 (1993)
6. Slater, T.F., "The Effectiveness of Portfolio Assessments in Science,"
J. Coll. Sci. Teach., 26, 315 (1997)
7. Shaeiwitz, J.A., "Outcomes Assessment: Its Time Has Come," Chem.
Eng. Ed., 33(2), 102 (1999)
8. DiBiasio, D.A., "Outcomes Assessment: An Unstable Process?"
Chem. Eng. Ed., 33(2), 116 (1999)
9. Slater, T.F, "Portfolios," in Field-Tested Learning Assessment Guide,
National Institute of Science Education (2000) www.wcer.wisc.edu/nise/cll/flag/cat/perfass/perfass.htm> (ac-
cessed 2/15/02)
10. Wink, D.J., "Portfolio Assessment in Large Lecture Class," Ab-
stracts of Papers of the ACS, 220, 49 (2000)
11. Johnson, J.M., "Portfolio Assessment in Mathematics: Lessons from
the Field," The Computing Teacher, 21, 22 (1994)
12. Adamchik, Jr., C.E, "The Design andAssessment of Chemistry Port-
folios," J. Chem. Ed., 73, 528 (1996)
13. Phelps, A.J., M.M. LaPorte, and A. Mahood, "Portfolio Assessment
in High School Chemistry: One Teacher's Guidelines," J. Chem.
Ed., 74, 528 (1997)
14. Olds, B.M., and R.L. Miller, "Using Portfolios to Assess a ChE
Program," Chem. Eng. Ed., 33(2), 110 (1999)
15. "Alverno's Diagnostic Digital Portfolio," academics/ddp.html> (accessed 6/6/02)
16. Rogers, G.M., and J. Williams, "Building a Better Portfolio," PRISM,
8, (1999) 0


Fall 2002










, curriculum


ASPECTS OF

ENGINEERING PRACTICE

Examining Value and Behaviors in Organizations



RAMON L. ESPINO
University of Virginia Charlottesville, VA 22904-4741


Since 1995, the School of Engineering and Applied Sci-
ences at the University of Virginia has offered an elec-
tive course that examines human values and practices
in engineering organizations. The course is available to all
fourth-year engineering students and is taken by 40 to 50 stu-
dents each year. It is taught by the Brenton S. Halsey Visiting
Professor of Chemical Engineering, who is selected annu-
ally from individuals with high-level experience in industry.
Support for the Chair comes from a generous endowment by
The James River Corporation in honor of its founding CEO,
Brenton Halsey. Previous Halsey Professors and their affilia-
tions are given in Table 1.
The details of the course content and execution are left to
the discretion of the Halsey Professor, but its core objective
is to provide engineering students with significant insight into
the professional and nontechnical aspects of engineering prac-
tice. The intention is to better prepare the University of Vir-
ginia engineering graduates to succeed in the business and
technical world that they will be entering after graduation.
This paper describes the course materials, assignments, and
assessments for the spring semester of 2001, which is repre-
sentative of recent offerings.

DEVELOPING THE COURSE
The teaching experiences of previous Halsey Professors
contributed significantly to the current course content. Al-
though the objectives have remained the same, there is now
more emphasis on the students reading and analyzing infor-
mation prior to class. This information is generally in the form
of Harvard Business School (HBS) Cases and Notes. The
result of this approach is more in-depth discussion in class.
I built the course syllabus around the HBS Cases and Notes.
Harvard Business School Publishingm' offers an Index of
Cases and Notes available for purchase. I suggest one HBS


The objective of the course was to
increase student awareness of the non-
technical competencies they should pos-
sess in order to succeed in
the work world.

Case and two HBS Notes per week, requiring about nine hours
of homework (reading and writing a summary) per week.
Lectures to reinforce and elaborate upon the major themes of
the course are strongly recommended. We have found that
many of these should be given by outside speakers from busi-
ness and government in order to emphasize the broad appli-
cability of the concepts being discussed. Finally, additional
reading material can be used to round out the course.

COURSE STRATEGY
AND TEACHING METHOD
I developed the syllabus to follow the chronological order
of the professional and business career of an engineering
graduate. Selecting the first employer is the starting point,
followed by early career assignments and culminating with
the complex organizational, personal, and business challenges
of a senior manager. HBS Cases provide a well-written plat-


Ramon L. Espino received his BS degree from
Louisiana State University in 1964 and his Doc-
tor of Science degree from the Massachusetts
Institute of Technology in 1968, both in chemi-
cal engineering. Hejoined the faculty at the Uni-
versity of Virginia in 1999 after twenty-six years
with Exxon Mobil. His research interests are in
fuel cell technology and methane conversion to
clean fuels and chemicals.


Copyright ChE Division of ASEE 2002


Chemical Engineering Education











form that describes specific situations with no direct answers
or outcomes.
The additional reading assignment consisted mainly of HBS
Notes, which provided a conceptual framework for the stu-
dents to analyze the cases with some knowledge of basic con-
cepts on business practices, interpersonal behavior, and hu-
man values. The students were all expected to read two books:
Getting to Yes12i and The Seven Habits of Highly Effective
People. 1'
The classes were designed to be highly interactive, with
the bulk of the time spent discussing the HBS Cases and Notes.
In addition, there were lectures on
Styles of communicating and interacting
Individual competencies


TABLE 2
HBS Cases


Title
Kevin Simpson
Elizabeth Fisher
Lisa Benton
Amelia Rodgers
Anne Livingston
Tech Transfer at...
Thurgood Marshall...
Conflict in a diverse...
David Fletcher
MOD IV Product...
PPG-Developing...
John Smithers at Sigtek
Jenssen Shoes
Coming Glass Works


Topic
Interviewing and selecting your employer
Dual career decisions
Conflicts in your first assignment
First group-leader assignment
Changing jobs and new leadership role
Conflict between development and production
Leader of middle-level managers
Harassment and social conflict
Hiring your ideal business team
Effective teamwork
Risks and rewards of empowerment
Leading a quality process initiative
Managing a diversity conflict
Leadership during a business downturn


Conflict management
Teams and team performance
Strategic planning
Developing a personal career plan
Six outside speakers led discussions on various aspects of
their business careers. These included
Managing family and business life
How to improve leadership skills
Conflict management and negotiation
Working with consulting companies
Attending business school
Reinforcing organizational values

A detailed outline of the course is presented in Table 3 (next
page). The two 75-minute class periods each week allowed
adequate time for discussion of the Case and the Notes, as
well as for the lectures given by the Halsey Professor or by
invited speakers.


LEARNING THROUGH THE HBS CASES

The "Case Method" is based on real-life situations that rep-
resent the kind of challenges that engineers and managers
are likely to face during their work life. The cases helped
students sharpen their analytical skills, their ability to com-
municate clearly and forcefully, and most importantly, helped
them to develop their problem-solving abilities. Table 2 indi-
cates the topic being discussed in each case.
The students were assigned the HBS Case a week in ad-
vance. They were required to write a 3-to-4-page summary
of their assessment of the situation and their proposed
solutionss. They were also asked to document the key learn-
ings they had derived from the case. It was gratifying to ob-
serve their increasing sophistication in analysis and problem
solving during the course of the semester.
There were a number of interesting observations that re-
sulted from discussion of the HBS Cases. The students paid a
lot of attention to the interpersonal style of the protagonists
and were quite sensitive to antisocial behavior. They were, to
my surprise, expecting to experience such behavior in the
workplace. This applied even to harassment situations. An-
other class-wide attitude was to view most conflicts as rooted
in poor communication, and it took a lot of discussion for
them to see poor communication simply as the external mani-
festation of a more profound conflict.

LEARNING KEY CONCEPTS
THROUGH THE HBS NOTES
The course provides an introduction to a number of critical
competencies engineers need in order to succeed in organi-
zations. These were provided mainly through reading and
discussion of HBS Notes. The Notes were also given to the
students a week in advance of the class discussion. There


TABLE 1
Halsey Professors
at the University of Virginia

Year Name Company/Position
1995 N.H. Prater Mobay/CEO
1996 J.M. Trice, Jr. Monsanto/Director-HR
1997 R.A. Moore, Jr. International Paper/VP
1998 D.L. Ashcraft Temple-Island/VP
1999 J.D. Stein BASF/CEO
2000 V.A. Russo Scott Paper/VP
2001 R.L. Espino Exxon/R&D Manager
2002 A.R. Hirsig ARCO Chemical/CEO


Fall 2002












was a close coupling between the teachings in the Notes and
the Case being discussed in parallel. This worked well, as
confirmed by the frequent references to concepts presented
in the Notes in the students' analyses of Cases. It is unrealis-
tic to expect the students to fully master all the concepts, but
it was clear that they became very aware of their importance.
The hope is that when they are confronted with similar situa-
tions, they will refer to these Notes for guidance.

We discussed the differences between management and
leadership and the many complex and ambiguous issues that


most managers face. We spent very productive time on the
influence of culture and history on subtle but important dif-
ferences in managers' behavior in the USA, Europe, Japan,
India, China, and Latin America. Having some students from
outside the USA gave immediacy to these discussions.

As expected, issues of business ethics grabbed the students'
attention and elicited strong and quite varied opinions. In fact,
I was surprised at the diversity of viewpoints, how strongly
they were held, and that there was no correlation with gen-
der, race, or economic background.


TABLE 3
Course Outline


Week 1
Homework/Class Discussion HBS Notes on "Learning by the case
method" and "How to choose a leadership pattern"
Lecture Individual and team competencies

Week 2
Homework/Class Discussion HBS Notes on "Understanding
context" and "Conflicting responsibilities"
HBS Case "Kevin Simpson"
Lecture Styles of communicating and interacting

Week 3
Homework/Class Discussion HBS Notes on "Managing your career"
HBS Case "Elizabeth Fisher"
Lecture Invited Speaker-Managing family and business life

Week 4
Homework/Class Discussion HBS Notes on "Power dynamics in
organizations"
HBS Case "Lisa Benton"
Lecture The seven habits of highly effective people

Week
Homework/Class Discussion HBS Notes on "Managing your boss"
and "Exercising influence"
HBS Case "Amelia Rodgers"
Lecture Invited Speaker-Improving your leadership skills

Week 6
Homework/Class Discussion HBS Notes on "Evaluating an action
plan" and "Understanding communications in one-to-one
relationships"
HBS Case "Ann Livingston and Power Max Systems"
Lecture The seven habits of highly effective people

Week 7
Homework/Class Discussion HBS Notes on "Beyond the myth of a
perfect mentor" and "Managing networks"
HBS Case "Technology transfer at a defense contractor"
Lecture Invited Speaker-Conflict management and negotiation

Week 8
Homework/Class Discussion HBS Notes on "Power dependence and
effective management" and "Influence tactics"
HBS case "Thurgood Marshall High School"
Lecture Conflict management styles


Week 9
Homework/Class Discussion HBS Notes on "Integrity management"
and "Managing a task-force"
HBS Case "Managing conflict in a diverse environment"
Lecture Invited Speaker-Working in a consulting company

Week 10
Homework/Class Discussion HBS Notes on "Barriers and gateways
to communications" and "On good communications"
HBS Case "David Fletcher"
Lecture Invited Speaker-Should you get an MBA?

Week 11
Homework/Class Discussion HBS Notes on "The power of talk" and
"The discipline of teams"
HBS case "Mod IV product development team"
Lecture Getting to Yes

Week 12
Homework/Class Discussion HBS Notes on "The challenge of
commitment" and "A note on high-commitment work systems"
HBS Case "PPG-Developing a self-directed workforce"
Lecture Strategic planning

Week 13
Homework/Class Discussion HBS Notes on "Organization
structure," "Organization effectiveness," and "The challenge of
change"
HBS Case "John Smithers at Sigtek"
Lecture Invited Speaker-Reinforcing organizational values

Week 14
Homework/Class Discussion HBS Notes on "Business ethics: the
view from the trenches," "Ethics without a sermon," and "Ways
of thinking about and across differences"
HBS Case "Jenssen Shoes"
Lecture Developing a personal career plan

Week 15
Final Homework:
A personal career plan
Analysis of the "Most admired company..."
Group report of HBS Case "Coming Glass Works"


Chemical Engineering Education










I was disappointed in the students' lack of interest in learn-
ing about team building, task-force management, and build-
ing commitment in the workplace. The students felt that they
knew about these topics and that they were already profi-
cient. I do not believe I ever convinced them there was a lot
for them to learn and that success in these areas requires skills
they actually did not possess.

OTHER FEATURES OF THE COURSE

The students were given a three-part final homework as-
signment. One element was a personal mission statement with
an associated five-year career development plan. The plan
could also include other facets of their life, such as family,
health, religion, community involvement, etc. For each of
the elements they were encour-
aged to follow a disciplined ap-
proach that included short-term
(6 months), midterm (2-3 TA
years), and long-term (5 years) Courst
plans. For each time period,
Not Useful 1 2
they were asked to state goals
and specific objectives and to February %
define strategies and action March -
steps. They were initially unen- April %
thusiastic about this task, but
the final product indicates that
they thought hard about it and
put together a realistic and credible plan.
The second element of the final homework was a team
project. Groups of four students were asked to analyze a fairly
complex HBS Case of a Coring Glass Works Division un-
dergoing a change in management during a business down-
turn. They were asked to devise strategies and specific action
plans for the division as well as a self-assessment of their
team performance. The reports indicated a wide range of team
performance, with the key problems being an inability to agree
on an action plan, finding time to work together, and uneven
participation by team members. This assignment came at the
very end of the semester, which was too late to refute their
earlier assertions that "teamwork was something they knew
how to handle."
The third element of the final homework was an analysis
of a company's performance during the last four years. Each
student selected a company from those reviewed by Fortune
Magazine in its annual publication of "America's Most Ad-
mired Companies.""-45 They were asked to analyze the per-
formance of the company they chose, to identify reasons for
any change in rankings during the four-year period, and to
forecast future trends.
The objective of this exercise was to allow the students to
apply to a specific company-wide situation what they had
learned about effective management, leadership, and manag-


ing change. The companies chosen reflected the students' wide
range of career interests and included, among others, enter-
tainment, communications, financial, computer technology,
oil and chemicals, consumer products. They were asked to
suggest the future direction the company needed to take to
improve performance. A majority suggested expanding glo-
bal reach and more technology investment, while only a few
focused on improving cost competitiveness.

STUDENT ASSESSMENT AND FEEDBACK
During the semester, the students were asked to provide
feedback on course content and to assess its effectiveness.
The data are summarized in Table 4 and show that the major-
ity of the class found the course very useful. They rated the
discussions of HBS Cases and Notes, my work experiences
and personal stories, and the
outside speakers the highest.
E 4 They were less enthusiastic
essment about the other reading mate-
rial, perhaps because they
5 6 7 8 Very Useful were not used to this amount
25 45 30 of reading in an engineering
3 29 50 18 course.
3 25 37 35 SUMMARY

The objective of the course
was to increase student aware-
ness of the nontechnical competencies they should possess
in order to succeed in the work world. It is unrealistic to ex-
pect that at the end of a semester they would have mastered
all these competencies, but it was evident that they were much
more sensitive to the importance of such skills and had grasped
the essentials. Also, they were left with an excellent collec-
tion of HBS Cases and Notes that could serve them well when
confronted with similar situations. As I frequently indicated
to them, I wished that I had such a learning experience in my
engineering schooling and early career.
The main reason for writing this article is to encourage other
colleges and universities to consider offering a course along
the general outline that I have described. I also encourage
experienced business practitioners to teach such a course. The
Halsey Professors are unanimous: it was an exciting and grati-
fying experience to share what you have learned with the
next generation of engineering and business leaders.

REFERENCES
1. Harvard Business School Publishing, 60 Harvard Way, Boston MA
02163
2. Fisher, R., W. Ury, and B. Patton, Getting to Yes, 2nd ed., Penguin
Books
3. Covey, S.R., The 7 Habits of Highly Effective People Simon and
Schuster
4. Fortune Magazine, March 6, 1997
5. Fortune Magazine, February 21, 2001 0


Fall 2002


BL
eAss

3 4
















I*NG D*EREEX



GRADUATE EDUCATION ADVERTISEMENTS


Akron, University of.................................. 321
Alabama, University of .............................. 322
Alabama, Huntsville; University of.............. 323
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Brigham Young University ........................... 427
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Bucknell University .................................... 428
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Worcester Polytechnic Institute .................. 425
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Chemical Engineering Education














Graduate Education in Chemical Engineering


Teaching and
research assistantships
as well as
industrially sponsored
fellowships
available
up to
$20,000.

In addition to
stipends,
tuition and fees
are waived.

PhD students
may get
some incentive
scholarships.

The deadline for
assistantship
applications
is
April 15th.


G. G. CHASE
Multiphase Processes,
Fluid Flow, Interfacial
Phenomena, Filtration.
Coalescence




H. M. CHEUNG
Nanocomposite Materials,
Sonochemical Processing,
Polymerization in
Nanostructured Fluids,
Supercritical Fluid
Processing


S. S. C. CHUANG
Catalysis, Reaction
Engineering, Environ-
mentally Benign
Synthesis




J. R. ELLIOTT
Molecular Simulation,
Phase Behavior, Physical
Properties, Process
Modeling


E. A. EVANS
Materials Processing and
CVD Modeling


L. K. JU
Biochemical Engineering,
Environmental






S. T. LOPINA
BioMaterial Engineering
and Polymer Engineering






B.Z. NEWBY
Surface Modification,
Polymer Thin film






H. C. QAMMAR
Nonlinear Control,
Chaotic Processes






P. WANG
Biocatalysis and
Biomaterials


For Additional Information, Write
Chairman, Graduate Committee
Department of Chemical Engineering The University of Akron Akron, OH 44325-3906
Phone (330) 972-7250 Fax (330) 972-5856 www.ecgf.uakron.edu/-chem


Fall 2002












THE UNIVERSITY OF

ALABAMA



Chemical

Engineering


A dedicated faculty with state of the art
facilities offer research programs leading to
Doctor of Philosophy and Master of Science
degrees.


Research Areas:
Biomaterials, Catalysis and Reactor Design,
Drug Delivery Materials and Systems,
Electrohydrodynamics, Electronic Materials,
Environmental Studies, Fuel Cells, Interfacial
Transport, Magnetic Materials, Membrance
Separations and Reactors, Microelectro-
Mechanical Systems, Nanoscale Modeling,
Polymer Processing and Rheology, Process
Dynamics, Self-Assembled Materials,
Suspension and Slurry Rheology, Transport
Process Modeling
For Information Contact:
Director of Graduate Studies
Department of Chemical Engineering
The University of Alabama
Box 870203
Tuscaloosa, AL 35487-0203
Phone: (205) 348-6450


Faculty:
G. C. April, Ph.D. (Louisiana State)
D. W. Arnold, Ph.D. (Purdue)
C. S. Brazel, Ph.D. (Purdue)
E. S. Carlson, Ph.D. (Wyoming)
P. E. Clark, Ph.D. (Oklahoma State)
W. C. Clements, Jr., Ph.D. (Vanderbilt)
R. A. Griffin, Ph.D. (Utah State)
D. T. Johnson, Ph.D. (Florida)
T. M. Klein, Ph.D. (NC State)
A. M. Lane, Ph.D. (Massachusetts)
M. D. McKinley, Ph.D. (Florida)
S. M. C. Ritchie, Ph.D. (Kentucky)
L. Y. Sadler III, Ph.D. (Alabama)
J. M. Wiest, Ph.D. (Wisconsin)
M. L. Weaver, Ph.D. (Florida)


An equal employment / equal
educational opportunity institution


Chemical Engineering Education


,4,1










Chemical &


Materials Engineering




_ FACULTY & RESEARCH AREAS


he Department of Chemical and Materi-
als Engineering at the University of Ala-
bama in Huntsville offers you the oppor-
tunity for a solid and rewarding graduate career
that will lead to further success at the forefront
of academia and industry.
We will provide graduate programs that educate
and train students in advanced areas of chemical
engineering, materials science and engineering,
and biotechnology. Options for an MS and PhD
degree in Engineering or Materials Science are
available.
Our faculty are dedicated to international lead-
ership in research. Projects are ongoing in Mass
Transfer, Fluid Mechanics, Combustion,
Biosparations, Biomaterials, Microgravity Mate-
rials Processing, and Adhesion. Collaborations
have been established with nearby NASA/
Marshall Space Flight Center as well as leading
edge biotechnology and engineering companies.
We are also dedicated to innovation in teaching.
Our classes incorporate advances in computational
methods and multi-media presentations.

Department of Chemical Engineering
The University of Alabama in Huntsville
130 Engineering Building
Huntsville, AL 35899


Ram6n L. Cero Ph.D. (UC-Davis)
Professor and Chair
Capillary hydrodynamics, multiphase flows, enhanced heat transfer
surfaces.
(256) 824-7313, rlc@che.uah.edu
Chien P. Chen Ph.D. (Michigan State)
Professor
Multiphase flows, spray combustion, turbulence modeling,
numerical methods in fluids and heat transfer.
(256) 824-6194, cchen@che.uah.edu
Krishnan K. Chittur Ph.D. (Rice)
Professor
Protein adsorption to biomaterials, FTR/ATR at solid-liquid
interfaces, biosensing.
(256) 824-6850, kchittur@che.uah.edu
Douglas G. Hayes Ph.D. (Michigan)
Associate Professor
Enzyme reactions in nonaqueous media, separations involving
biomolecules, lipids and surfactants, surfactant-based colloidal
aggregates.
(256) 824-6874, dhayes@che.uah.edu
James E. Smith Jr. Ph.D. (South Carolina)
Professor
Kinetics and catalysis, powdered materials processing, combustion
diagnostics and fluids visualization using optical methods.
(256) 824-6439, jesmith@che.uah.edu
Jeffrey J. Weimer Ph.D. (MIT)
Associate Professor, Joint Appointment in Chemistry
Adhesion, biomaterials surface properties, thin film growth, surface
spectroscopies, scanning prode microscopies.
(256) 824-6954, jjweimer@matsci.uah.edu






UAH
The University of Alabama in Huntsville
An Affirmative Action/Equal Opportunity Institution
Web page: http://chemeng.uah.edu
Ph: 256*824*6810 FAX: 256-824-6839


Fall 2002














































The University of Alberta is well known
for its commitment to excellence in teach-

ing and research. The Department of

Chemical and Materials Engineering has

37 professors and over 100 graduate

students. Degrees are offered at the M.Sc.

and Ph.D. levels in Chemical Engineer-

ing, Materials Engineering, and Process
Control. Allfull-time graduate students in

the research programs receive a stipend

to cover living expenses and tuition.



For further information, contact

Graduate Program Officer
Department of Chemical and Materials Engineering
University of Alberta
Edmonton, Alberta, Canada T6G 2G6

PHONE (780) 492-1823 FAX (780) 492-2881
e-mail: chemical. engineering@ ualberta. ca
web: www.ualberta.ca/chemeng


M. BHUSHAN, Ph.D. (I.I.T. Bombay)
Sensor Location Fault Diagnosis Process Safety
R.E. BURRELL, Ph.D. (University of Waterloo)
Nanostructured Biomaterials Drug Delivery Biofilms Tissue Integration with Materials
P. CHOI, Ph.D. (University of Waterloo)
Molecular Modeling of Polymers Thermodynamics of Polymer Solutions and Blends
K. T. CHUANG, Ph.D. (University of Alberta)
Fuel Cell Catalysis Separation Processes Pollution Control
I. G. DALLA LANA, Ph.D. (Univ. of Minnesota) EMERITUS
Chemical Reaction Engineering Heterogeneous Catalysis
J. A. W. ELLIOTT, Ph.D. (University of Toronto)
Thermodynamics Statistical Thermodynamics Interfacial Phenomena
D. G. FISHER, Ph.D. (University of Michigan) EMERITUS
Process Dynamics and Control Real-Time Computer Applications
J.F. FORBES, Ph.D. (McMaster University) CHAIR
Real-Time Optimization Scheduling and Planning
M. R. GRAY, Ph.D. (California Inst. of Tech.)
Bioreactors Chemical Kinetics Bitumen Processing
R. E. HAYES, Ph.D. (University of Bath)
Numerical Analysis Reactor Modeling Computational Fluid Dynamics
B. HUANG, Ph.D. (University of Alberta)
Controller Performance Assessment Multivariable Control Statistics
S. M. KRESTA, Ph.D. (McMaster University)
Turbulent & Transitional Flows Multiphase Flows CFD
S. LIU, Ph.D. (University of Alberta)
Fluid-Particle Dynamics Transport Phenomena Kinetics
D. T. LYNCH, Ph.D. (University of Alberta) DEAN OF ENGINEERING
Catalysis Kinetic Modeling Numerical Methods Polymerization
J. H. MASLIYAH, Ph.D. (University of British Columbia)
Transport Phenomena Colloids Particle-Fluid Dynamics Oil Sands
A. E. MATHER, Ph.D. (University of Michigan)
Phase Equilibria Fluid Properties at High Pressures Thermodynamics
E. S. MEADOWS, Ph.D. (University of Texas)
Process Control Fuel Cell Modeling and Control Optimization
W. C. MCCAFFREY, Ph.D. (McGill University)
Reaction Kinetics Heavy Oil Upgrading Polymer Recycling Biotechnology
K. NANDAKUMAR, Ph.D. (Princeton University)
Transport Phenomena Distillation Computational Fluid Dynamics
A.E. NELSON, Ph.D. (Michigan Technological University)
Heterogeneous Catalysis UHV Surface Science Chemical Kinetics
M. RAO, Ph.D. (Rutgers University)
AIl Intelligent Control Process Control
S. L. SHAH, Ph.D. (University of Alberta)
Computer Process Control System Identification Process and Performance Monitoring
J.M. SHAW, Ph.D. (University of British Columbia)
Petroleum Thermodynamics Multiphase Mixing Process Modeling
U. SUNDARARAJ, Ph.D. (University of Minnesota)
Polymer Processing Polymer Blends Interfacial Phenomena
H. ULUDAG, Ph.D. (University of Toronto)
Biomaterials Tissue Engineering Drug Delivery
S. E. WANKE, Ph.D. (University of California, Davis)
Heterogeneous Catalysis Kinetics Polymerization
M. C. WILLIAMS, Ph.D. (University of Wisconsin) EMERITUS
Rheology Polymer Characterization Polymer Processing
Z. XU, Ph.D. (Virginia Polytechnic Institute and State University)
Surface Science & Engineering Mineral Processing Waste Management
T. YEUNG, Ph.D. (University of British Columbia)
Emulsions Interfacial Phenomena Micromechanics


Chemical Engineering Education













ROBERT G. ARNOLD, Professor (CalTech)
Microbiological Hazardous Waste Treatment, Metals Speciation and Toxicil
PAUL BLOWERS, Assistant Professor (Illinois, Urbana-Champaign
Chemical Kinetics, Catalysis, Surface Phenomena
JAMES C. BAYGENTS, Associate Professor (Princeton)
Fluid Mechanics, Transport and Colloidal Phenomena, Bioseparations

WENDELL ELA, Assistant Professor (Stanford)
Particle-Particle Interactions, Environmental Chemistrn
JAMES FARRELL, Associate Professor (Stanford)
Sorption/desorption of Organics in Soils
JAMES A. FIELD, Associate Professor (Wagenigen Agricultural Un
Bioremediation, Microbiology, White Rot Fungi, Hazardous Waste
ROBERTO GUZMAN, Associate Professor (North Carolina State)
Affinity Protein Separations, Polymeric Surface Science
ANTHONY MUSCAT, Assistant Professor (Stanford)
Kinetics, Surface Chemistry, Surface Engineering, Semiconductor Processir
Microcontamination
KIMBERLY OGDEN, Associate Professor (Colorado)
Bioreactors, Bioremediation, Organics Removal from Soils
THOMAS W. PETERSON, Professor and Dean (CalTech)
Aerosols, Hazardous Waste Incineration, Microcontamination
ARA PHILIPOSSIAN, Associate Professor (Tufts)
Chemical/Mechanical Polishing, Semiconductor Processing
JERKER PORATH, Research Professor (Uppsala)
Separation Science
EDUARDO SAEZ, Associate Professor (UC, Davis)
Rheology, Polymer Flows, Multiphase Reactors
FARHANG SHADMAN, Professor (Berkeley)
Reaction Engineering, Kinetics, Catalysis, Reactive Membranes,
Microcontamination
JOST 0. L. WENDT, Professor and Head (Johns Hopkins)
Combustion-Generated Air Pollution, Incineration, Waste
Management


For further information, write to

http://ww.che.arizona.edu

or write

Chairman, Graduate Study Committee
Department of Chemical and
Environmental Engineering
P.O. BOX 210011
The University ofArizona
Tucson, AZ 85721

The University of Arizona is an equal
opportunity educational institution/equal opportunity employer.
Women and minorities are encouraged to apply.


(


CHEMICAL AND


ENVIRONMENTAL


ENGINEERING

at


THE

UNIVERSITY

OF -


ARIZONAN A

The Chemical and Environmental Engineering Department
at the University of Arizona offers a wide range of research
opportunities in all major areas of chemical engineering and
environmental engineering, and graduate courses are offered in
most of the research areas listed here. The department offers a fully
accredited undergraduate degree as well as MS and PhD graduate
degrees. Strong interdisciplinary programs exist in bioprocessing
and bioseparations, microcontamination in electronics manu-
facture, and environmental process modification.
Financial support is available through fellowships, government
and industrial grants and contracts, teaching and
research assistantships.
Tucson has an excellent climate and many
recreational opportunities. It is a growing modern city that
retains much of the old Southwestern atmosphere.


Fall 2002


I












S ARIZONA STATE


UNIVERSITY


Department of Chemical and Materials Engineering


A Distinguished and Diverse Faculty A multi-disciplinary research
environment with opportunities
Chemical Engineering in electronic materials
Jonathan Allen, Ph.D., MIT. Atmospheric aerosol chemistry, single-particle measurement processing biotechnology *
techniques, environmental fate of organic pollutants processing, characterization,
Stephen Beaudoin, Ph.D., North Carolina State. Semiconductor materials processing, environ- and simulation of materials *
mentally-benign semiconductor processing, particle and thin-film adhesion, chemical- ceramics air and water
mechanical polishing, polymer dielectrics
purification atmospheric
James Beckman, Ph.D., Arizona. Unit operations, applied mathematics, energy-efficient water
purification, fractionation, CMP reclamation chemistry process control
Veronica Burrows, Ph.D., Princeton. Surface science, environmental sensors, semiconductor
processing, interfacial chemical and physical processes in sensor processing
Ann Dillner, Ph.D., Illinois, Urbana-Champaign. Atmospheric particulate matter (aerosols)
chemistry and physics, ultra fine aerosols, light scattering, climate and health effects of
aerosols
Chan Beum Park, Ph.D., POSTTECH, South Korea. Bioprocess in extremis, novel cell-free
protein synthesis, biolab-on-a-chip technology
Gregory Raupp, Ph.D., Wisconsin. Gas-solid surface reactions mechanisms and kinetics,
interactions between surface reactions and simultaneous transport processes, semiconductor
materials processing, thermal and plasma-enhanced chemical vapor deposition (CVD)
Anneta Razatos, Ph.D., Texas at Austin. Bacterial adhesion, colloid interactions, AFM, biofilms,
genetic engineering
Daniel Rivera, Ph.D., Caltech. Control systems engineering, dynamic modeling via system
identification, robust control, computer-aided control system design
Michael Sierks, Ph.D., Iowa State. Protein engineering, biomedical engineering, enzyme
kinetics, antibody engineering


Materials Science and Engineering
James Adams, Ph.D., Atomistic stimulation of metallic surfaces, adhesion, wear, and automotive
catalysts, heavy metal toxicity
Terry Alford, Ph.D., Cornell. Electronic materials, physical metallurgy, electronic thin films
Nikhilesh Chawla, Ph.D., Michigan. Lead-free solders, composite materials, powder metallurgy
Sandwip Dey, Ph.D., Alfred. Electro-ceramics, MOCVD and ALCVD, dielectrics: leakage, loss
mechanisms and modeling
Stephen Krause, Ph.D., Michigan. Characterization of structural changes in processing of semiconductors
Subhash Mahajan (Chair), Ph.D., Berkeley. Semiconductor defects, high temperature semiconductors, structural materials deformation
James Mayer, Ph.D., Purdue. Thin film processing, ion beam modification of materials
Nate Newman, Ph.D., Stanford. Growth, characterization, and modeling of solid-state materials
S. Tom Picraux, Ph.D. Caltech. Nanostructured materials, epitaxy, and thin-film electronic materials
Karl Sieradzki, Ph.D. Syracuse. Fracture of solids, thin-film deposition and growth, corrosion
Mark van Schilfgaarde, Ph.D. Stanford. Methods and applications of electronic structure theory, dilute magnetic semiconductors, GW approximation

For details concerning graduate opportunities in Chemical and Materials Engineering atASU, please call Marlene Bolf
at (480) 965-3313, or write to Subhash Mahajan, Chair, Chemical and Materials Engineering, Arizona State University,
Tempe, Arizona 85287-6006 (smahajan@asu.edu).


Chemical Engineering Education













AUBURN UNIVERSITY'


Chemical Engineering


Robert P. Chambers University of California, Berkeley
Harry T. Cullinan Carnegie Mellon University
Christine W. Curtis Florida State University
Steve R. Duke University of Illinois
Said Elnashaie University of Edinburgh
James A. Guin University of Texas, Austin
Ram B. Gupta University of Texas. Austin
Gopal A. Krishnagopalan University of Maine
Y. Y. Lee Iowa State University
Glennon Maples Oklahoma State University
David R. Mills Washington State University
Ronald D. Neuman The Institute of Paper Chemistry
Stephen A. Perusich University of Illinois
Timothy D. Placek University of Kentucky
Christopher B. Roberts University of Notre Dame
A. R. Tarrer Purdue University
Bruce J. Tatarchuk University of Wisconsin


Research Areas
* Biochemical Engineering
* Pulp and Pper
* Process Systems Engineering
SIntegrated Process Design
* Environmental Chemical Engineering
* Catalysis and Reaction Engineering
* Materials lymers
* Surface and Interfacial Science
* Thermodynamics Supecritical Fluids
* Electrochemical Engineering
* Transport Phenomena
* Fuel CellTechnoloy'
* Microfibrous Materials
* Nanotechnology


-Inquiriesto:.
Director of Graduate Recruting '
Department of Chemical Engineering
Auburn University. AL 36849 F
Phone (334) 844-4827 '
Fax (334)844-2063 .
http:!lwwwrAg.aubiimied -
I-e i:t che ickal@enauburn.edu
Financial assistance is available to qualified applicants.


Fall 2002


I












DEPARTMENT OF CHEMICAL

AND PETROLEUM ENGINEERING


FACULTY
R. G. Moore, Head (Alberta)
J. Azaiez (Stanford)
H. Baheri (Saskatchewan)
L. A. Behie (Western Ontario)
C. Bellehumeur (McMaster)
P. R. Bishnoi (Alberta)
P. J. Farrell (Calgary)
R. A. Heidemann (Washington U.)
J.M. Hill (Wisconsin)
A. A. Jeje (MIT)
M. S. Kallos (Calgary)
A. Kantzas (Waterloo)
B. B. Maini (Univ. Washington)
A. K. Mehrotra (Calgary)
S. A. Mehta (Calgary)
B. J. Milne (Calgary)
M. Pooladi-Darvish (Alberta)
A. Settari (Calgary)
S. Srinivasan (Stanford)
W. Y. Svrcek (Alberta)
M. A. Trebble (Calgary)
H. W. Yarranton (Alberta)
B. Young (Canterbury, NZ)
L. Zanzotto (Slovak Tech. Univ., Czechoslovakia)


The Department offers graduate programs leading to the M.Sc. and Ph.D.
degrees in Chemical Engineering (full-time) and the M.Eng. degree in Chemical
Engineering, Petroleum Reservoir Engineering or Engineering for the
Environment (part-time) in the following areas:
Biochemical Engineering & Biotechnology
Biomedical Engineering
Catalysis and Fuel Cells
Environmental Engineering
Modeling, Simulation & Control
Petroleum Recovery & Reservoir Engineering
Polymer Processing & Rheology
Process Development
Reaction Engineering/Kinetics
Thermodynamics
Transport Phenomena
Fellowships and Research Assistantships are available to all qualified applicants.

SFor Additional Information Write *
Dr. W.Y. Svrcek Associate Head, Graduate Studies
Department of Chemical and Petroleum Engineering
University of Calgary Calgary, Alberta, Canada T2N 1N4
E-mail: gradstud@ucalgary.ca


The University is located in the City of Calgary, the Oil capital of Canada, the home of the world famous Calgary Stampede and the 1988
Winter Olympics. The City combines the traditions of the Old West with the sophistication of a modern urban center Beautiful Banff
National Park is 110 km west of the City and the ski resorts of Banff, Lake Louise,and Kananaskis areas are readily accessible. In the
above photo the University Campus is shown in the foreground. The Engineering complex is on the left of the picture, and the Olympic
Oval is on the right of the picture.


[ ~UNIVERSITY OF

S CALGARY


.0


Chemical Engineering Education














U i rtoC io i B r l


The Chemical Engineering Department at the
University of California, Berkeley, one of the pre-
eminent departments in the field, offers graduate pro-
grams leading to the Master of Science and Doctor
of Philosophy. Students also have the opportunity
to take part in the many cultural offerings of the San
Francisco Bay Area and the recreational activities
of California's northern coast and mountains.

FACULTY


Nitash P. Balsara
Harvey W. Blanch
Arup K. Chakraborty
David B. Graves
Alexander Katz
C. Judson King
Susan J. Muller
John M. Prausnitz
Jeffrey A. Reimer
Alexis T. Bell


Elton J. Cairns
Douglas S. Clark
Enrique Iglesia
Jay D. Keasling
Roya Maboudlan
John S. Newman
Clayton J. Radke
David V. Schaffer
Rachel A. Segalman


BIOENGINEERING
Blanch, Clark,
Keasling, Schaffer,
Chakraborty, Muller,
Prausnitz & Radke













I















POLYMERS &
SOFT MATERIALS

Balsara, Chakraborty,
Muller, Prausnitz, Radke,
Reimer & Segalman


Chairman: Arup K. Chakraborty I


FOR FURTHER INFORMATION, PLEASE VISIT OUR WEBSITE:

http://cheme.berkeley.edu/index.shtmi


Fall 2002


CATALYSIS &
REACTION ENG.

Bell, Chakraborty,
Iglesia, Katz & Reimer


ELECTROCHEMICAL
ENGINEERING

Cairns, Newman &
Reimer


ENVIRONMENTAL
ENGINEERING

Bell, Graves, Iglesia,
Keasling & King


MICROELECTRONICS
PROCESSING &
MEMS

Graves, Maboudian,
Reimer & Segalman













University of California, Davis


Department of Chemical Engineering & Materials Science
Offering M.S. and Ph.D. degree programs in both Chemical Engineering and Materials Science and Engineering

Faculty


David E. Block, Assistant Professor Ph.D., University of Minnesota, 1992 Industrialfermentation, biochemical processes in phannaceutical industry
Roger B. Boulton, Professor Ph.D., University of Melbourne, 1976 Fermentation and reaction kinetics, crstallization
Stephanie R. Dungan, Associate Professor Ph.D., Massachusetts Institute of Technology, 1992 Micelle transport, colloid and interfacial science in food
processing
Roland Faller, Assistant Professor Ph.D., Max-Planck Institute for Polymer Research, 2000 Molecular modeling of soft-condensed matter
Bruce C. Gates, Professor Ph.D., University of Washington. Seattle, 1966 Catalysis, solid superacid catalysis, zeolite catalysts, bimetallic catalysts,
catalysis by metal clusters
Jeffery C. Gibeling, Professor Ph.D., Stanford University, 1979 Deformation, fracture andfatigue of metals, layered composites and bone
Joanna R. Groza, Professor Ph.D., Polytechnic Institute, Bucharest, 1972 Plasma activated sintering and processing ofnanostructured materials
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Area-ti i -


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.r as ring/M etiBir hI


Chemical Engineering Education


I Jh" Ilullll J, ckd p.auJuJl luJt ".I '". L .' IIh',
Department of Chemical Engineering and Materials
Science allows students to choose research projects and
lih.- I .I I. In Il ..i I.j .u ll I lIh rr ,
,,', i,:.rT,jljII ll ..tL L ,,I h ,l, Lal.l ::.l. H I. .:. I a .d
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rd1 1.] I .. .ihri I l I.., [N.. M 1 -;.,J 4i h. I.-I'Iti
I' f,










UNIVERSITY OF



CALIFORNIA

Graduate Studies in
Chemical Engineering IR VINE
and Materials Science and Engineering
for Chemical Engineering, Engineering, and Materials Science Majors
Offering degrees at the M.S. and Ph.D. levels. Research in frontier areas
in chemical engineering, biochemical engineering, biomedical engineering, and materials
science and engineering. Strong physical and life science and engineering groups on campus.
FACULTY
Ying Chih Chang (Stanford University)
Nancy A. Da Silva (California Institute of Technology)
James C. Earthman (Stanford University)
Steven C. George (University of Washington)
Stanley B. Grant (California Institute of Technology)
Juan Hong (Purdue University)
Enrique J. Lavernia (Massachusetts Institute of Technology)
Henry C. Lim (Northwestern University)
Jia Grace Lu (Harvard University)
Martha L. Mecartney (Stanford University)
Farghalli A. Mohamed (University of California, Berkeley)
Frank G. Shi (California Institute of Technology)
Vasan Venugopalan (Massachusetts Institute of Technology)
Joint Appointments:
G. Wesley Hatfield (Purdue University)
Noo Li Jeon (University of Illinois)
Sunny Jiang (University of South Florida)
Roger H. Rangel (University of California, Berkeley)
William A. Sirignano (Princeton University)
Adjunct Professors
Russell Chou (Carnegie Mellon University)
Andrew Shapiro (University of Califoria, Irvine)
Victoria Tellkamp (University of Califoria, Irvine)

The 1,510-acre UC Irvine campus is in Orange County, five miles from the Pacific Ocean and 40 miles south of Los
Angeles. Irvine is one of the nation's fastest growing residential, industrial, and business areas. Nearby beaches,
mountain and desert area recreational activities, and local cultural activities make Irvine a pleasant city in which to
live and study.
For further information and application forms, please visit
http://www.eng.uci.edu/cbe/
or contact
Department of Chemical Engineering and Materials Science
School of Engineering University of California Irvine, CA 92697-2575


Fall 2002


* Biomedical

En
Engineering
* Bioreactor
Engineering
* Bioremediation
* Ceramics
* Combustion
* Composite
Materials
* Control and
Optimization
* Environmental
Engineering
* Interfacial
Engineering
* Materials
Processing
* Mechanical
Properties
* Metabolic
Engineering
* Microelectroi es
Processing and
Modeling
* Microsucture
of Materials
* Nanocrystalline
Materials
* Nucleation,
Chrystallization
and Glass
Transition-
Process ._


* Recomb- ant"---

og -- -
g*egeaia sL^


ing
.. -._; -- :;:- .:- ---* -----

SWater&- --tiotr
Control.


331









CHEMICAL ENGINEERING AT


RESEARCH
AREAS

* Aerosol Science and Technolog.
* Biochemical Engineering
* Combinatorial Catalysil
* Complex Systems Engineering
* Electrochemistry
* Membranes
* Molecular and Cellular
Bioengineering
* Pollution Prevention

* Polymer Engineering
* Process Design, Optimiiltion.
Dynamics, and Contriol
* Reaction Kinetics and
Combustion
* Semiconductor Manufacturing


FACULTY
J. P. Chang
P. D. Christofides
Y. Cohen
J. Davis
(Vice Chancellor for
Information Technology)
S. K. Friedlander
R. F. Hicks
E. L. Knuth (Prof Emeritus)
J. C. Liao
V. Manousiouthakis
H. G. Monbouquette
K. Nobe
L. B. Robinson (Prof Emeritus)
S. M. Senkan
Y. Tang
W. D. Van Vorst (Prof Emeritus)
V. L. Vilker (Prof Emeritus)
A.R. Wazzan


PROGRAMS


UCLA's Chemical Engineering Department offers a
program of teaching and research linking fundamental en-
gineering science and industrial practice. Our Department
has strong graduate research programs in Bioengineering,
Energy and Environment, Semiconductor Manufacturing,
Engineering of Materials, and Process and Control Sys-
tems Engineering.
Fellowships are available for outstanding applicants


interested in Ph.D. degree programs. A fellowship in-
cludes a waiver of tuition and fees plus a stipend.
Located five miles from the Pacific Coast,
UCLA's attractive 417-acre campus extends from Bel
Air to Westwood Village. Students have access to
the highly regarded science programs and to a vari-
ety of experiences in theatre, music, art, and sports
on campus.


CONTACT


5531 B -e Ha : *e. ll,, UCL-4, Lo Angeles, C 0-
Telehon at 310 825906 or isi us t ww~chmen+ucl~ed


Chemical Engineering Education


UCLAsm^^^^










University of California, Riverside
Department of Chemical and Environmental Engineering




The Graduate Program in Chemical and En- arlan and Rosemary Bourns College of
vironmental Engineering offers training lead-
ing to the degrees of Master of Science and engineering
Doctor of Philosophy. All applicants are re-
quired to submit scores from the general apti-
tude Graduate Record Examination (GRE).
For more information and application mate-
rials, write:
Graduate Advisor
Department of Chemical and
Environmental Engineering
University of California
Riverside CA 92521
Visit us at our website:
http://www.engr.ucr.edu/chemenv


Faculty
Wilfred Chen (Cal Tech) Environmental Biotechnology, Microbial Engineering, Biocatalysis
David R. Cocker (Caltech) Air Quality Systems Engineering
Marc Deshusses (ETH, Zurich) Environmental Biotechnology, Bioremediation, Modeling
Robert C. Haddon (Penn State) Carbon Nanotubes, Advanced Materials
Eric M.V. Hoek (Yale) Environmental Membrane Processes, Collodial and Interfacial Phenomena
Mark R. Matsumoto (UC Davis) Water and Wastewater Treatment, Hazardous Waste, Soil Remediation
Ashok Mulchandani (McGill) Bioengineering, Biomaterials, Biosensors, Environmental Biotechnology
Joseph M. Norbeck (Nebraska) Advanced Vehicle Technology, Air Pollutants, Renewable Fuels
Mihri Ozkan (UC Sn Diego) Biomedical Microdevices, Bio-MEMS and Bio-Photonics
Anders O. Wistrom (UC Davis) Particulate and Colloidal Systems
Jianzhong Wu (UC Berkeley) Molecular Simulation, Theory of Complex Fluids, Nanomaterials
Yushan Yan (CalTech) Zeolite Thin Films, Fuel Cells, Nanostructured Materials, Catalysis

The 1,200-acre Riverside campus of the University of California is located 50 miles east of Los Ange-
les within easy driving distance to most of the major cultural and recreational offerings in Southern
California. In addition, it is virtually equidistant from the desert, the mountains, and the ocean.


Fall 2002













UNIVERSITY OF CALIFORNIA


SANTA BARBARA


ERAY S. AYDIL Ph.D. (Houston) Microelectronics and Plasma Processing
SANJOY BANERJEE Ph.D. (Waterloo) Environmental Fluid Dynamics, Multiphase Flows, Turbulence, Computational Fluid Dynamics
BRADLEY F. CHMELKA Ph.D. (U.C. Berkeley) Molecular Materials Science, Inorganic-Organic Composites, Porous Solids, NMR, Polymers
PATRICK S. DAUGHERTY Ph.D. (Austin) Protein Engineering and Design, Library Technologies
MICHAEL F. DOHERTY Ph.D. (Cambridge) Design and Synthesis, Separations, Process Dynamics and Control
FRANCIS J. DOYLE III Ph.D. (Caltech) Process Control, Systems Biology, Nonlinear Dynamics
GLENN H. FREDRICKSON Ph.D. (Stanford) Statistical Mechanics, Glasses, Polymers, Composites, Alloys
G.M. HOMSY Ph.D. (Illinois) Fluid Mechanics, Instabilities, Porous Media, Interfacial Flows, Convective Heat Transfer
JACOB ISRAELACHVILI Ph.D. (Cambridge) Colloidal and Biomolecular Interactions, Adhesion and Friction
EDWARD J. KRAMER Ph.D. (Carnegie-Mellon) Fracture and Diffusion of Polymers, Polymer Surfaces and Interfaces
L. GARY LEAL Ph.D. (Stanford) Fluid Mechanics, Physics and Rheology of Complex Fluids, including Polymers, Suspensions, and Emulsions.
GLENN E. LUCAS Ph.D. (M.I.T) Mechanics of Materials, Structural Reliability.
DIMITRIOS MAROUDAS Ph.D. (M.I.T) Theoretical and Computational Materials Science, Electronic and Structural Materials
ERIC McFARLAND Ph.D. (M.I.T) M.D. (Harvard) Combinatorial Material Science, Environmental Catalysis, Surface Science
DUNCAN A. MELLICHAMP Ph.D. (Purdue) Computer Control, Process Dynamics, Real-Time Computing
SAMIR MITRAGOTRI Ph.D. (M.I.T) Drug Delivery and Biomaterials
DAVID J. PINE Ph.D. (Cornell) (Chair) Polymer, Surfactant, and Colloidal Physics, Multiple Light Scattering, Photonic Crystals
ORVILLE C. SANDALL Ph.D. (Berkeley) Transport Phenomena, Separation Processes
DALE E. SEBORG Ph.D. (Princeton) Process Control, Monitoring and Identification
MATTHEW V. TIRRELL Ph.D. (Massachusetts) Polymers, Surfaces, Adhesion Biomaterials
T. G. THEOFANOUS Ph.D. (Minnesota) Multiphase Flow, Risk Assessment and Management
JOSEPH A. ZASADZINSKI Ph.D. (Minnesota) Surface and Interfacial Phenomena, Biomaterials


PROGRAMS
AND FINANCIAL SUPPORT
The Department offers M.S. and
Ph.D. degree programs Finan-
cial aid, including fellowships,
teaching assistantships, and re-
search assistantships, is avail-
able.
THE UNIVERSITY
One of the world's few seashore
campuses, UCSB is located on
the Pacific Coast 100 miles
northwest of Los Angeles. The
student enrollment is over
18,000. The metropolitan Santa
Barbara area has over 150,000
residents and is famous for its
mild, even climate.

For additional information
and applications, write to
Chair Graduate Admissions Committee Department of Chemical Engineering University of California Santa Barbara, CA 93106


Chemical Engineering Education








Chemical Engineering at the


SCALIFORNIA


INSTITUTE


OF


TECHNOLOGY

"At the Leading Edge"


Frances H. Arnold
Anand R. Asthagiri
John F Brady
Mark E. Davis


~
CI
II
S
O


Richard C. Flagan
George R. Gavalas (Emeritus)
Konstantinos P. Giapis
Julia A. Korfield


John H. Seinfeld
David A. Tirrell
Nicholas W Tschoegl (Emeritus)
Zhen-Gang Wang


Aerosol Science
Applied Mathematics
Atmospheric Chemistry and Physics
Biocatalysis and Bioreactor Engineering
Biomaterials
Biomedical Engineering
Bioseparations
Catalysis
Chemical Vapor Deposition


Combustion
Colloid Physics
Fluid Mechanics
Materials Processing
Microelectronics Processing
Microstructured Fluids
Polymer Science
Protein Engineering
Statistical Mechanics


For further information, write
Director of Graduate Studies
Chemical Engineering 210-41 California Institute of Technology Pasadena, California 91125-4100
Also, visit us on the World Wide Web for an on-line brochure: http://www.che.caltech.edu


Fall 2002







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Case Western Reservei II UnivIerit
M .S .~~ an-h D r g a si C e i a n i e r n


Faculty

John Angus
Harihara Baskaran
Robert Edwards
Donald Feke
Jeffrey Glass
Uziel Landau
Chung-Chiun Liu
J. Adin Mann
Heidi Martin
Philip Morrison
Peter Pintauro
Syed Qutubuddin
Robert Savinell
Thomas Zawodzinski


Research Opportunities

Advanced Energy Systems
Fuel Cells and Batteries
Hydrogen Infrastructure
Membrane Transport
Sensors
Microfabrication
Biomedical Engineering
Transport in Biological Systems
Biomedical Sensors and Actuators
Wound Healing
Inflammation and Cancer Metastasis
Neural Prosthetic Devices
Advanced Materials and Devices
Diamond and Nitride Synthesis
Coatings, Thin Films, and Surfaces
In-Situ Diagnostics
Fine Particle Science and Processing
Polymer Nanocomposites
Electrochemical Microfabrication


For more information on
Graduate Research, Admission, and Financial Aid, contact:


Graduate Coordinator
Department of Chemical Engineering
E-mail: grad@cheme.cwru.edu
Web: http://www.cwru.edu/cse/eche


Case Western Reserve University
10900 Euclid Avenue
Cleveland, Ohio 44106-7217


Fall 2002









Opportunities for Graduate Study in Chemical Engineering at the







M.S. and Ph.D. Degrees in Chemical Engineering


Faculty

Carlos Co

Joel Fried

Rakesh Govind

Vadim Guliants

Daniel Hershey

Chia-chi Ho

Sun-Tak Hwang

Yuen-Koh Kao

Soon-Jai Khang

William Krantz

Jerry Y. S. Lin

Neville Pinto

Peter Smirniotis



The University of Cincinnati is
committed to a policy of
non-discrimination in
awarding financial aid.

For Admission Information
Director, Graduate Studies
Chemical Engineering
PO Box 210171
University of Cincinnati
Cincinnati, Ohio 45221-0171
E-mail:
mcarden@alpha.che.uc.edu
or
jlin@alpha.che.uc.edu


The faculty and students in the Department of Chemical Engineering are engaged in a diverse range
of exciting research topics. Assistantships and tuition scholarships are available to highly qualified
applicants to the MS and PhD degree programs.


E Advanced Materials
Inorganic membranes, nanostructured materials, microporous and mesoporous materials,
advanced materials processing, thin film technology, fuel cell and sensor materials, self-
assembly

E Biotechnology (Bioseparations)
Novel bioseparation techniques, affinity separation, biodegradation of toxic wastes, con-
trolled drug delivery, two-phase flow

O Catalysis and Chemical Reaction Engineering
Heterogeneous catalysis, environmental catalysis, zeolite catalysis, novel chemical reactors,
modeling and design of chemical reactors

O Environmental Research
Desulfurization and denitrication of flue gas, new technologies for coal combustion power
plant, wastewater treatment, removal of volatile organic vapors

O Membrane Technology
Membrane synthesis and characterization, membrane gas separation, membrane reactors,
sensors and probes, pervaporation, biomedical, food and environmental applications of
membranes, high-temperature membrane technology, natural gas processing by membranes

O Polymers
Thermodynamics, polymer blends and composites, high-temperature polymers, hydrogels,
polymer rheology, computational polymer science, polymerization technology

D Separation Technologies
Membrane separation, adsorption, chromatography, separation system synthesis, chemical
reaction-based separation processes


Chemical Engineering Education












Chemical


Engineering at


The City College of


New York CUNY

(The City University of New York)


A 154-year-old urban University, the oldest public
University in America, on a 35-acre Gothic and modern
campus in the greatest city in the world

FACULTY RESEARCH:


OAndreas Acrivos*oo<4 Rheology of
concentrated suspensions; Dielectro-
phoresis in flowing suspensions;
Dynamical systems theory and chaotic
particle motions

Alexander Couzis: Polymorph
selective templated crystallization;
Molecularly thin organic barrier layers;
Surfactant facilitated wetting of
hydrophobic surfaces; soft materials

"Morton Dennoo<: Polymer science
and rheology; non-Newtonian fluid
mechanics

Lane Gilchrist: Bioengineering with
cellular materials; Spectroscopy-guided
molecular engineering; Structural
studies of self-assembling proteins;
Bioprocessing
Robert Graff: Coal liquefaction;
Pollution prevention; Remediation
Leslie Isaacs: Preparation and charac-
terization of novel optical materials;
Recycling of pavement materials;
Application of thermo-analytic
techniques in materials research
Jae Lee: Theory of reactive distillation;
Process design and control; Separations;
Bioprocessing
OCharles Maldarelli: Interfacial fluid
mechanics and stability; Surface tension
driven flows and microfluidic applica-
tions; Surfactant adsorption, phase be-
havior and nanostructuring at interfaces
Irven Rinard: Process design
methodol-ogy; Dynamic process
simulation; Micro-reaction technology;
Process control; Bioprocessing

David Rumschitzki: Transport and
reaction aspects of arterial disease;

Fall 2002


Interfacial fluid mechanics and stability;
Catalyst deactivation and reaction
engineering
Reuel Shinnarm: Advanced process design
methods; Chemical reactor control;
Spinodal decomposition of binary solvent
mixtures; Process economics; Energy and
environment systems
Carol Steiner: Polymer solutions and
hydrogels; Soft biomaterials. Controlled
release technology
Gabriel Tardos: Powder technology;
Granulation; Fluid particle systems,
Electrostatic effects; Air pollution
Sheldon Weinbaum.m: Fluid mechanics,
Biotransport in living tissue; Modeling of
cellular mechanism of bone growth; bioheat
transfer: kidney function
Herbert Weinstein: Fluidization and
multiphase flows: multiphase chemical
reactor analysis and design, Multiphase
reactor analysis and design

ASSOCIATED FACULTY:
OJimmy Feng: (Mechanical Eng.) Liquid crystals
'Joel Koplik: (Physics) Fluid mechanics;
Molecular modeling; Transport in random media
Hernan Makse: (Physics) Granular mechanics
Mark Shattuck: (Physics) Experimental granular
rheology; Computational granular fluid dynamics:
Experimental spatio-temporal control of patterns
SLevich Institute
National Academy of Sciences
National Accadenn of Engineering


CONTACT INFORMATION:
Department of Chemical Engineering
City College of New York
Convent Avenue at 140th Street
New York. NY 10031
www-che.engr.ccny.cuny.edu
che.hr@aol.com













Cleveland State University


Grdut Stde in Chmia and Appie Bimdia Engneein


Engineering Degrees
M. Sc. Chemical Engineering
D. Eng. Applied Biomedical Engineering
D. Eng. Chemical Engineering

CSU Faculty
A. Annapragada (University of Michigan)
J.M. Belovich (University of Michigan)
G. Chatzimavroudis (Georgia Institute of Technology)
G.A. Coulman (Case Western Reserve University)
J.E. Gatica (State University of New York at Buffalo)
B. Ghorashi (Ohio State University)
E.S. Godleski (Cornell University)
R. Lustig (Institute of Thermo- and Fluiddynamics of the
Ruhr-University Bochum, Germany)
D.B. Shah (Michigan State University)
O. Taln (Arizona State University)
S.N. Tewari (Purdue University)
S. Ungarala (Michigan Technological University)
CCF Collaborating Faculty
J. Arendt (Ohio State University)
B. Davis (Pennsylvania State University)
K. Derwin (University of Michigan)
A. Fleischman (Case Western Reserve University)
M. Grabiner (University of Illinois)
S. Halliburton (Vanderbilt University)
G. Lockwood (University of Toronto, Canada)
C. McDevitt (University of London, U.K.)
S. Roy (Case Western Reserve University)
R. Shekhar (Ohio State University)
W. Smith (Cleveland State University)
A. van den Bogert (University of Utrecht, The Netherlands)
I. Vesely (University of Western Ontario, Canada)
G. Yue (University of Iowa)


For more information, write to:
Graduate Program Coordinator Department of Chemical Engineering
Cleveland State University Cleveland, OH 44115
Telephone: 216-687-2569 E-mail: ChE@csvax.egr.csuohio.edu
http://www.csuohio.edu/chemical_engineering/


Fenn College has more than 75 years of experience in provid-
ing outstanding engineering education.

Graduate Studies in Chemical and Applied Biomedical Engineering
at Cleveland State University's (CSU's) Fenn College of Engineering
offers a wealth of opportunity in a stimulating environment.
Research opportunities are available in collaboration with the Bio-
medical Engineering Department of the renowned Cleveland Clinic
Foundation (CCF), Cleveland's Ad-
vanced Manufacturing Center, local and
national industry, and Federal agencies,
to name a few. Assistantships and Tuition
Fee Waivers are available on a competi-
tive basis for qualified students.
Cleveland State University has 16,000
students enrolled in its academic pro-
grams. It is located in the center of the
city of Cleveland, with many outstand-
ing cultural and recreational opportuni-
ties nearby.


RESEARCH AREAS
Adsorption Processes
Agile Manufacturing
Artificial Heart Valves
Biomechanics
Bioreactor Design
Bioseparations
Blood Flow
Combustion
Computational Fluid Dynamics
Drug Delivery Systems
Environmental Pollution Control
Materials Synthesis and Processing
Medical Imaging
MEMS Technology
Orthopedic Devices
Process Modeling and Control
Reaction Engineering
Statistical Mechanics
Surface Phenomena and Mass Transfer
Thermodynamics and Fluid Phase Equilibrium
Tissue Engineering
Tribology
Ventricular Assist Devices
Zeolites: Synthesis, Adsorption, and Diffusion


Assistantships and Tuition/Fee Waivers are available on a competitive basis for qualified students.

340 Chemical Engineering Education













University of Colorado at Boulder


The Boulder campus has a controlled enrollment of about 22,000 undergraduates and 5,000 graduate students. The beautiful
campus has 200 buildings of rough-cut sandstone with red-tile roofs. The excellent educational opportunities and beautiful
location attract outstanding students from every part of the United States and 85 countries.
The University of Colorado has its main campus located in Boulder, an attractive community of 90,000 people located at the
base of the Rocky Mountains. Boulder has over 300 days of sunshine per year, with relatively mild and dry seasons. The city is
an active and innovative town that provides a rich array of recreational and cultural activities.

-- Department of Chemical Engineering Faculty and Research Interests -


Kristi S. Anseth
Polymers, Biomaterials, Tissue Engineering
Christopher N. Bowman
Polymers, Membrane Materials
David E. Clough
Process Control, Applied Statistics
Robert H. Davis
Fluid Mechanics, Biotechnology, Membranes
John L. Falconer
Catalysis, Zeolite Membranes
R. Igor Gamow
Biophysics, High Altitude Physiology, Human Performance,
Diving Physiology
Steven M. George
Surface Chemistry, Thin Films, Nanoengineering
Doug Gin
Polymers
Ryan Gill
Biotechnology


Christine M. Hrenya
Fluidization, Granular Systems, Fluid Mechanics
Dhinakar S. Kompala
Biotechnology, Animal Cell Cultures, Metabolic
Engineering
J. Will Medlin
Heterogeneous Catalysis, Solid-State Sensors,
Computational Chemistry
Richard D. Noble
Membranes, Separations
W. Fred Ramirez
Process Control, Biotechnology
Theodore W. Randolph
Biotechnology, Supercritical Fluids
Robert L. Sani
Transport Phenomena, Applied Mathematics
Daniel K. Schwartz
Interfacial and Colloid Science
Alan W. Weimer
Ceramics, Energy, Reaction Engineering


Graduate students may participate in the interdisciplinary Biotechnology Training Program and the
interdisciplinary NSF Industry/University Cooperative Research Center for Membrane Applied Science and Technology
and the Center for Fundamentals and Applications of Photopolymerizations.

For information and application
Graduate Admissions Committee Department of Chemical Engineering
University of Colorado Boulder, CO 80309-0424
Phone (303) 492-7471 Fax (303) 492-4341 E-mail chemeng@spot.colorado.edu
http://www.Colorado.EDU/che/


Fall 2002





















Evolving from its origins as a school of
mining founded in 1873, CSM is a unique,
highly-focused University dedicated to
scholarship and research in materials,
energy, and the environment.

The Chemical Engineering Department at
CSM maintains a high quality, active, and
well-funded graduate research program.
According to the NSF annual survey of
research expenditures, our department has
placed in the top 25 nationally each of the
last 5 years. Research areas within the
department include:
Materials Science and Engineering
Org aic and inorganic membranes (Way, Baldwin)
Polymeric materials (Dorgan, McCabe, Wu)
Colloids and complex fluids (Marr, Wu)
Electronic materials (Wolden)
Fuel cell membranes (Way)

Theoretical and Applied Thermodynamics
Natural gas hydrates (Sloan)
Molecular simulation and
modelling (Ely, McCabe)

Transport Properties and Processes
Dermal absorption (Bunge)
Microfluidics (Marr)

Space and Microgravity Research
Membranes on Mars (Way, Baldwin)
Water mist flame suppression (McKinnon)

Reacting Flows Finally, located at the
Flame kinetics (McKinnon, Dean) foot of the Rocky
Reaction mechanisms (Dean, McKinnon) Mountains and only 15
High-T fuel cell kinetics (Dean) miles from downtown
Denver, Golden enjoys
over 300 days of
sunshine per year.
These factors combine
to provide year-round
cultural, recreational,
and entertainment
opportunities virtually
unmatched anywhere
in the United States.


Chemical Engineering Education












tate University

CSU is located in Fort Collins, a pleasant commu-
nity of 100,000 people with the spirit of the West the
vitality of a growing metropolitan area, and the
friendliness of a small town. Fort Collins is located
about 65 miles north of Denver and is adjacent to
the foothills of the Rock, Mountains. The climate is
excellent, with 300 sunny days per year mild tem-
peratures, and low humidity. Opportunities for hik-
ing, biking, camping, boating, fishing, and skiing
"- -abound in the immediate and nearby areas. The cam-
S pus is within easy walking or biking distance of the
S .- __ town's shopping areas and its Center for the Per-
forming Arts.

I.S. and Ph.D. programs in

chemical engineering FACULTY


rESEARCH IN ... Brian C. Batt, Ph.D.
Advanced Process Control University of Colorado
I Biochemical Engineering Laurence A. Belfiore, Ph.D.
I Biomedical Engineering University of Wisconsin
Chemical Thermodynamics
David S. Dandy, Ph.D.
> Chemical Vapor Deposition California Institute of Technology
Computational Fluid Dynamics
Environmental Biotechnology M. Nazmul Karim, Ph.D.
Environmental Engineering University ofManchester
Magnetic Resonance Imaging James C. Linden, Ph.D.
I Membrane Separations Iowa State University
Metabolic Engineering
SPolymertic iMaterials Vincent G. Murphy, Ph.D.
University of Massachusetts
0 Porous Media Phenomena
Thin Films Kenneth F. Reardon, Ph.D.
Tissue Engineering California Institute of Technology

Kristina D. Rinker, Ph.D.
FINANCIAL AID AVAILABLE North Carolina State University
Teaching and research assistantships paying a
monthly stipend plus tuition reimbursement. A. Ted Watson, Ph.D.


For applications and further information, write
Graduate Advisor, Department of Chemical Engineering
Colorado State University
Fort Collins, CO 80523-1370


A


F


Fall 2002


California Institute of Technology

Ranil Wickramasinghe, Ph.D.
University of Minnesota


y
a,












University of Connecticut

Chemical Engineering Department
Graduate Study in Chemical Engineering

[1 Biochemical Engineering and Biotechnology
James D. Bryers, Ph.D., Rice University (Joint Appointment)
Biochemical Engineering, Biofilm Processes, Biomaterials
Robert W. Coughlin, Ph.D., Cornell University
Biotechnology, Biochemical and Environmental Engineering Catalysis, Kinetics, Separations,
Surface Science
Ranjan Srivastava, Ph.D., University of Maryland
Experimental and Computational Biology, Biomolecular Network Analysis, Stochastic Biological
Phenomena, Evolutionary Kinetics
Thomas K. Wood, Ph.D., North Carolina State University
Microbiological Engineering, Bioremediation with Genetically-Engineered Bacteria,
Enzymatic Green Chemistry, Biochemical Engineering, Biocorrosion

El Polymer Science
Patrick T Mather Ph.D., University of California, Santa Barbara

Richard Parnas, Ph.D., University of California, Los Angeles
Composites, Biomaterials
Montgomery T Shaw, Ph.D., Princeton University
Polymer Rheology and Processing, Polymer-Solution Thermodynamics
Robert A. Weiss, Ph.D., University ofMassachusetts
Polymer Structure-Property Relationships, Ion-Containing and Liquid Crystal Polymers,
Polymer Blends
Lei Zhu, Ph.D., University ofAkron
Polymer Phase Transitions, Structures of Morphologies of Block Copolymers, Polymeric
Nanocomposites, Biodegrabable Block Copolymers for Drug Delivery

El Computer Aided Modeling
Luke E.K. Achenie, Ph.D., Carnegie Mellon University
Modeling and Optimization, Molecular Design, Artificial Intelligence, Flexibility Analysis
Thomas F Anderson, Ph.D., Univesity of California at Berkeley
Modeling of Separation Processes, Fluid-Phase Equilibria
Douglas J. Cooper, Ph.D., University of Colorado
S-~_ Process Modeling, Monitoring and Control
Michael B. Cutlip, Ph.D., University of Colorado
Kinetics and Catalysis, Electrochemical Reaction Engineering, Numerical Methods
Suzanne Schadel Fenton, Ph.D., University of Illinois, Urbana-Champaign
Computational Fluid Dynamics, Turbulence, Two-Phase Flow

[1 Environmental and Energy Engineering
Can Erkey, Ph.D., Texas A&M University
Supercritical Fluids, Catalysis, Nanotechnology
James M. Fenton, Ph.D., University of Illinois, Urbana-Champaign
Electrochemical and Environmental Engineering, Mass Transfer Processes, Electronic
191 Auditorium Road, Unit 3222 Materials, Energy Systems, Fuel Cells
Storrs, CT 06269-3222
Joseph J. Helble, Ph.D., Massachusetts Institute of Technology
Tel: (860) 486-4020 Fax: (860) 486-2959 Air Pollution, Aerosol Science, Nanoscale Materials Sythesis and Characterization, Combustion
www.engr.uconn.edulcheg
www.engr.uconn.edu/cheg Emeritus Professors
cheginfo@engr.uconn.edu C.O. Bennett, J.P. Bell, A.T. DiBenedetto, G.M. Howard, H.E. Klei, D.W. Sundstrom


Chemical Engineering Education














CORN0LL


At Cornell University, graduate students in chemical engineering have the flexibility to
design research programs that take full advantage of Cornell's unique interdisciplinary
environment and enable them to pursue individualized plans of study.
Cornell graduate programs may draw upon the resources of many excellent departments
and research centers such as the Biotechnology Center, the Cornell Center for Materials
Research, the Cornell Nanofabrication Facility, the Comell Supercomputing Facility, and
the Nanobiotechnology Center.
Degrees granted include Master of Engineering, Master of Science, and Doctor of
Philosophy. All Ph.D. students are fully funded with tuition coverage and attractive
stipends.


A. Brad Anton
Lynden A. Archer
Paulette Clancy
Claude Cohen
Lance Collins
T. Michael Duncan
James R. Engstrom
Fernando A. Escobedo
Emmanuel P. Giannelis
Peter Harriott
Yong Lak Joo
Donald L. Koch
Kelvin H. Lee
Leonard W. Lion
Christopher K. Ober
William L. Olbricht
David Putnam
Ferdinand Rodriguez
Michael L. Shuler`,'
Paul H. Steen
Larry Walker
Ulrich Wiesner

member, National Academy of Engineering
member American Academy of
Arts & Science


Research Areas
* Advanced Materials Processing
* Biochemical and Biomedical Engineering
* Fluid Dynamics, Stability, and Rheology
* Molecular Thermodynamics and
Computer Simulation
* Polymer Science and Engineering
* Reaction Engineering: Surface Science,
Kinetics, and Reactor Design
Situated in the scenic Finger Lakes region of
New York State, the Cornell campus is one of
the most beautiful in the country. Students
enjoy sailing, skiing, fishing, hiking, bicycling,
boating, wine-tasting, and many other
activities.
For further information, write:
Director of Graduate Studies, School of Chemical Engineering, Cornell University, 120 Olin Hall, Ithaca, NY 14853-5201,
e-mail: DGS @CHEME.CORNELL.EDU, or "visit" our World Wide Web server at: http://www.cheme.comell.edu


Fall 2002










Graduate Study & Research in Chemical Engineering
at


Dartmouth's Thayer School of Engineering


Dartmouth and its affiliated professional schools offer PhD degrees in the full range of science disciplines as well as
MD and MBA degrees. The Thayer School of Engineering at Dartmouth College offers an ABET-accredited BE degree, as
well as MS, Masters of Engineering Management, and PhD degrees. The Chemical and Biochemical Engineering Pro-
gram features courses in foundational topics in chemical engineering as well as courses serving our areas of research
specialization:
Biotechnology and biocommodity engineering
Environmental science and engineering
Fluid mechanics
Materials science and engineering
Process design and evaluation
These important research areas are representative of those found in chemical engineering departments around the world.
A distinctive feature of the Thayer School is that the professors, students, and visiting scholars active in these areas have
backgrounds in a variety of engineering and scientific subdisciplines. This intellectual diversity reflects the reality that
boundaries between engineering and scientific subdisciplines are at best fuzzy and overlapping. It also provides opportu-
nities for students interested in chemical and biochemical engineering to draw from several intellectual traditions in
coursework and research. Fifteen full-time faculty are active in research involving chemical engineering fundamentals.


Faculty & Research Areas


Ian Baker (Oxford) 1- Structure/property relationships of materials, electron microscopy
John Collier (Dartmouth) > Orthopaedic prostheses, implant/host interfaces
Alvin Converse (Delaware) Kinetics & reactor design, enzymatic hydrolysis of cellulose
Benoit Cushman-Roisin (Florida State) > Numerical modeling of environmental fluid dynamics
Harold Frost (Harvard) N Microstructural evolution, deformation, and fracture of materials
Tillman Gerngross (Technical University of Vienna) > Engineering of glycoproteins, fermentation technology
Ursula Gibson (Cornell) 0 Thin film deposition, optical materials
Francis Kennedy (RPI) 0 Tribology, surface mechanics
Daniel R. Lynch (Princeton) 0 Computational methods, oceanography, and water resources
Lee Lynd (Dartmouth) Biomass processing, pathway engineering, reactor & process design
Victor Petrenko (USSR Academy of Science) 0 Physical chemistry of ice
Horst Richter (Stuttgart) > Thermodynamics, multiphase flow, energy conversion, process design
Erland Schulson (British Columbia) N Physical metallurgy of metals and alloys
Charles E. Wyman (Princeton) Biomass pretreatment & hydrolysis, cellulase synthesis & kinetics, process design



For further information, please contact:

Chemical Engineering Graduate Advisor Thayer School of Engineering Dartmouth College Hanover, NH 03755
http://thayer.dartmouth.edu/thayer/research/chem-biochem
5 Chemical Engineering Education




Full Text









capability, set up the lower rows of Figure 2 as shown, then
define the first column as the x-coordinate for graphing and
each of the two columns containing pressure values as sepa-
rate y-coordinates. The lower rows of Figure 2 can be omit-
ted when using current versions of Excel and other spread-
sheets that allow multiple xy pairs to be graphed.

ADDITIONAL COMPUTER ASSIGNMENTS
Table 5 lists other thermodynamic data graphs prepared
using computer spreadsheets. A very brief discussion of each
follows. Many were prepared by students as homework as-
signments using techniques similar to those outlined for the
Pxy diagram. Copies of these assignments are available upon



TABLE 5
Graphs Prepared Using Spreadsheets
for Phase Equilibrium Class

Binary phase diagrams for ideal solutions
Pxya
Txyb
xya

Fugacity versus pressure
Numerical integration of PV data
Generalized viral coefficient
Redlich-Kwong equation of state

Volumetric properties of binary nonideal solutions
Excess volumea
Partial molar excess volumes

Activity coefficients in binary solutions versus composition
Margulesa
Van Laarb
Wilsona

Infinite dilution activity versus temperature
Wilsona

Phase diagram for nonideal azeotrope forming binary mixture
Pxyb
Txyb
xya

Excess free energy of homogeneous azeotrope forming binary
mixture versus composition
Experimental data
Margules equation (fit to azeotrope data)a
Margules equation (best fit to VLE data)a
Wilson equation (literature constants)b

Excess free energy of heterogeneous azeotrope forming binary
mixture versus composition
Experimental dataa
Margules equation (best fit to VLE data)"
Margules equation (best fit to LLE solubility data)a


aPrepared by students as homework assignment
bPrepared by instructor for class discussion


request. Some graphs were not assigned but were generated
by the instructor and presented during class discussion.
The same spreadsheet data used to produce a Pxy diagram
as described above could be used to plot an xy diagram at
constant temperature. Pxy and Txy are the predominant rep-
resentations of VLE data in phase equilibrium classes, but
xy is probably the most frequently used format of the phase
equilibrium data in other classes, e.g., distillation, absorp-
tion, mass transfer.
Using the method described above, generating Pxy data
for an ideal binary system at constant temperature does not
require trial and error. Calculation of a single Txy datum for
an ideal binary system at constant pressure requires iteration
or trial and error since the vapor pressures are functions of
temperature. But generating a Txy diagram for such a system
-the locus of dew and bubble point temperatures for all pos-
sible compositions- does not require trial and error. Taking
temperature as the independent variable rather than liquid
composition, all other variables can be calculated directly by
Eqs. (1-3). Selecting a range of temperatures in increments be-
tween the pure-component boiling points generates the diagram.
Plotting y versus x instead of T versus y and T versus x pro-
duces an xy diagram at constant pressure from the same data.
For nonideal binary mixtures, activity coefficients are func-
tions of liquid composition and possibly temperature. Pxy
and xy diagrams at constant temperature are generated in a
straightforward fashion without iteration since temperature
is fixed and liquid composition is taken as the independent
variable for generating the table as described above.
Iteration cannot be avoided when generating Txy and xy
diagrams at constant pressure for nonideal binaries. To find
activity coefficients and vapor pressures, liquid composition
and temperature are needed. Only one can be assumed. Di-
rect calculation of liquid composition from vapor pressure,
as in the ideal case, is not possible. If temperature is used as
the independent variable, as suggested for the ideal case, a
unique composition may not result because azeotropes are
possible. I recommend using liquid mole fraction as the in-
dependent variable ranging from 0 to 1, as in the Pxy dia-
grams. Iteration can be performed by circular recalculation
on the spreadsheet. Unfortunately, spreadsheets vary signifi-
cantly in their implementation of circular recalculation, even
from version to version, and it is difficult to give a "recipe"
that works in all cases. Often, particular rearrangements of
equations or ordering of the columns is necessary. No matter
what package was being used, however, I have always been
able to find some method that eventually worked.
Thermodynamics textbooks commonly contain graphs of
excess and partial excess properties such as volume and en-
thalpy for binary solutions. In the volumetric properties as-
signment, students generate similar graphs for ethanol-water
using density data as a function of composition taken from
Continued on page 291.


Fall 2002











The primary advantage of the present study is that analysis of the raw data can be
performed using equations that are easily understood by juniors in chemical
engineering, and standard computer packages can be used...


or third degree polynomial can be fitted to data on h(t). This
gives excellent values of the coefficient-of-determination of
about 0.999 and higher. This polynomial is then used with
Eq. (4) to obtain v. Eqs. (3) and (4) can be combined and
integrated for Newtonian fluids (n = 1) to give the standard 41
equation for the efflux time for a vertical tank-pipe assembly
under laminar-flow conditions. The students find these deri-
vations easier to comprehend (in fact, they can make the
derivations themselves) than the equations described by
Tjahjadi and Gupta.E'1
The validity of the assumption of laminar flow should be
confirmed by calculating the Reynolds number for the
pseudoplastic liquid ' i "1

3-n n )n Dnpyn2-n
Re = 2 (5)
3 3n+l K

For pseudoplastic flows present in the laminar region, as in
this study, the sudden contraction/entrance losses are expected
to be negligible. 21 In the more general case where the en-
trance losses are important, the Bagley correctionE8'9' can
be used. This could be a possible avenue of further study
for a student.
Equation (3) can be rewritten as

2KL (3n +1 n
log [pg(L + h) = log L r + n log (v) (6)


An appropriate log-log plot of Eq. (6) gives n (= slope). K
can then be obtained using n and the intercept, c, using


K =exp (7)
2L 3n+l

Once values are obtained for both n and K, the shear rate (at
the wall of the tube, r = ro) can be evaluated umI'-'" 1]

= Pg(L + h)ro (8)
2LK

The apparent viscosity, iT, can then be evaluated (at this wall
shear rate) using Eq. (2). Equation (8) assumes that the power
law dependence is valid, and so the value of y obtained is
inferred from the data-fitting procedure.
Unfortunately, use of the power law assumption, though
helpful in simplifying the experiment at the undergraduate
level, can give a false idea of the complexity of the method
of analysis routinely used by professional, non-Newtonian


rheologists (who commonly use the Rabinowitsch tech-
niqueE6'9). An alternative procedure of data analysis that is
not as difficult and that can be attempted by an undergradu-
ate student, is the use of the Schummer approximationE10 (de-
scribed in Appendix 2). Such an analysis preserves, to some
extent, the physics of mechanical energy balance and closely
follows the steps that would be employed in the professional
theological evaluation of non-Newtonian viscosity. One set
of experimental data generated herein is analyzed later to
compare the results using the power law and the
Schummer approaches.

RESULTS AND DISCUSSION
Details of the several experimental set-ups and runs are
given in Table 1. These experiments were designed and per-
formed in two phases-Runs 1 and 11 through 16 in Table 1
comprising the first phase, followed by Runs 2-10. The re-
sults of the first phase were analyzed and used to help im-
prove the designs for Phase 2. Figure 2 shows data from Phase
1. It demonstrates the decrease of the apparent viscosity with
increasing shear rates. Although the viscosity vs. shear rate
diagram is incomplete, the shear-thinning effect characteris-
tic of pseudoplastic fluids is quite evident. The straight-line
segments on this log-log plot confirm the validity of the
power-law model over small ranges of shear rate. The data
overlap in some regions, which confirms the accuracy of the
results. The value of the power law index varies from about
0.3 to 1.0 (see Table 1). The range of shear rates covered
extends over almost two decades, and the data appears to fall




Run Nos.

012




oool

S1 Shear Rate 0ooo
(1fe|

Figure 2. Apparent viscosity vs. shear rate for a 0.07 wt%
Na-CMC aqueous solution, assuming power law behavior
of the liquid. Phase 1 results shown with Runs indicated.
Results from Ref. 11 also shown for comparison. Tempera-
ture = 230C.


Chemical Engineering Education


































































Question number

Figure 1. Results from student surveys after complet-
ing course. Responses to questions are as follows:
1 Strongly agree; 2 Agree; 3 No strong opin-
ion; 4 Disagree; 5 Strongly disagree.
Columns and error bars represent the average and stan-
dard deviation for each question, from a sample size
of 13 surveys for questions 1-3 and 28 surveys for ques-
tions 4-7. Question numbers correspond to those given
in Table 4.


TABLE 4
Student Evaluation Survey

0. Did you complete the optional portfolio assignment for this
class?
1. (If "Yes" to the first question) I enjoyed completing the portfolio
assignment.
2. (If "Yes" to the first question) I felt that I learned more about
myself and my strengths and weaknesses in chemical engineer-
ing and problem solving as a result of completing the portfolio.
3. (If "Yes" to the first question) My written communication skills
have improved as a result of completing the portfolio assign-
ment.
4. I feel that the use of both qualitative (e.g., written reports, oral
reports, and portfolios) and quantitative (e.g., exams and
homework) methods of assessment were appropriate for this
class.
5. I dislike qualitative methods of assessment (e.g., written reports,
oral reports, and portfolios) because I feel that they are
subjective.
6. I feel that quantitative methods of assessment (e.g., exams and
homework) are most appropriate for engineering and science
classes.
7. I would like to see qualitative methods of assessment (e.g.,
written reports, oral reports, and portfolios) incorporated into
other science and engineering classes.


inflation.
On the first day of class, I gave students a handout de-
scribing the portfolio assignment, including the informa-
tion in Tables 1 through 3, and a summary of the grading
protocol for portfolios. I also held a short class discus-
sion on what portfolios are and why they were being used
for this course.
Students were required to have at least eight portfolio en-
tries, which are listed in Table 1. Six of these entries were
related to course objectives or outcomes, with a focus on
objectives that are difficult to assess using conventional exam
techniques (i.e., the use of Microsoft Excel, data-fitting tech-
niques, etc.). These entries were expected to be copies of prob-
lems, either from the homework or exams. Students were re-
quired to attach a copy of their solution to the problem and a
short (one paragraph to one page) explanation of why the
problem was chosen.
In addition, two one-page essays (the last two items in Table
1) were required. I also handed out a list of questions to keep
in mind as they wrote their portfolio entries (listed in Table
3). Finally, students were asked to organize their entries, num-
ber each page, and include a table of contents in the portfo-
lio. Periodically throughout the semester, I reminded students
to work on the portfolio assignment and to come see me if
they had questions on the assignment.



RESULTS
Student Feedback and Assessment Survey
The class enrollment was 41 students. Forty-one percent
of the students (17 students) completed the portfolio assign-
ment. Grades on the portfolios were roughly in the low "C"
to high "A" range. For most students, the portfolio grade was
used to replace a low homework grade, but the difference in
the final grade for the course with and without the portfolio
was never more than a letter grade.
I was somewhat distressed to find that several students
counted on the portfolio to bring up their low homework grade
and thus did not spend as much time on the homework as-
signments throughout the semester as I would have liked. I
have since altered the portfolio guidelines to allow students
to replace a low midterm exam grade, but not the final exam
or a low homework grade.
I found that grading of the portfolios was time consuming,
but I did not feel that it took longer than grading exams. The
time commitment is similar to that required for evaluating
written reports, and I made comments on all portfolios re-
garding grammar and writing style.
Students were asked to complete a survey upon comple-
tion of the course, and the survey questions and student re-
sponses are given in Table 4 and Figure 1, respectively.


5 -

4

S3

S2 -






1 2


3 4 5 6 7


Fall 2002















TABLE 5
Sample Comments from Student Portfolios

New Strategies of Problem Solving (Item 1)
and Self-Analysis (Item 7)

S"I now have more confidence knowing that if I can't solve a problem
using the accepted method of solution, I will be able to come up with
a new method, perhaps something nonroutine, in order to solve the
problem."

"This problem showed me that I should have more confidence in my
ability to find a solution when it doesn't simply present itself after a
series of steps."

S"I could apply things I had learned in a completely different context
to other situations. This is actually quite comforting, as I've always
wondered if I'll be able to use the things I learn now later on in life
when I might actually need them."

S"I've had trouble [with] time management, as I have usually been
able to understand the problems but have not left myself enough time
to gather it all in a presentable format."

"My weakness is that every time I hit a wall, I tend not to do anything
about it. I can only blame myself for not attempting, [but] I already
made my choice in staying in this major and it is all up to me in
keeping that choice."


Reflections on Chemical Engineering
and The Fundamentals Course (Item 8)

"All in all I enjoyed the class, I enjoy being a chemical engineering
student, and I look forward to the day when I am employed as a
fabulous chemical engineer."

"I dislike computers and I dreaded using them for this class. I
probably would have stuck with this major if it were not for
MathCAD and Excel. I do not think being taught [MathCAD] for one
class period is enough class time."

"Since the class is almost over, I feel a real sense of accomplishment.
I know that it is only a freshman level class, but I put a great deal of
effort and time into the class...It makes me proud to say that I'm a
chemical engineering major when people ask me."

"I feel like I've gotten a much better idea about what chemical
engineers do through the various assignments and from the oral
presentations of my peers."

"I feel that we did not [spend] much time on using the computer."

"Before taking this class I wasn't positive that chemical engineering
was the right major for me. I felt that perhaps I would not be able to
handle the workload or grasp all of the material that I needed to
know. However, I now feel that I am actually capable of becoming an
engineer."

"I love going to my chemical engineering classes, they are the only
ones that I don't purposely skip."

"As a result of this class I am much more confident about my choice
of major and the preparation it will give me to succeed in the career I
want to pursue."


or assessment of a specific course objective.
Make sure your grading scheme is clear to the
students at the start of the semester.


ACKNOWLEDGMENTS

I would like to acknowledge my Chemical Engineering
Fundamentals students for participating in this work. Pro-
fessor Donald Wink (Chemistry, University of Illinois at
Chicago) provided me with a copy of his recent ACS pre-
sentation on portfolio assessment and suggested several of
the works cited in this article, which was greatly appreci-
ated. The manuscript reviewers, particularly Reviewer #3,
made several useful and constructive comments. Mrs.
Kanak Bhatia (Ed.D. candidate, University of Delaware)
also suggested several helpful references and made com-
ments on the manuscript.


REFERENCES
1. Feuer, M.J., and K. Fulton, "The Many Faces of Performance As-
sessment," Phi Delta Kappan, 74, 473 (1993)
2. Slater, T.F., "Performance Assessment," in Field-Tested Learning
Assessment Guide, National Institute of Science Education (2000)

(accessed 6/6/02)
3. Herman, J.L., PR. Ashbach, and L. Winters, A Practical Guide to
Alternative Assessment, Association for Supervision and Curricu-
lum Development, Alexandria, VA (1992)
4. Lambin, D.V., and V.L. Walker, "Planning for Classroom Portfolio
Assessment," Arithmetic Teacher 41, 318 (1994)
5. Abruscato, J., "Early Results and Tentative Implications from the
Vermont Portfolio Project," Phi Delta Kappan, 74, 474 (1993)
6. Slater, T.F., "The Effectiveness of Portfolio Assessments in Science,"
J. Coll. Sci. Teach., 26, 315 (1997)
7. Shaeiwitz, J.A., "Outcomes Assessment: Its Time Has Come," Chem.
Eng. Ed., 33(2), 102 (1999)
8. DiBiasio, D.A., "Outcomes Assessment: An Unstable Process?"
Chem. Eng. Ed., 33(2), 116 (1999)
9. Slater, T.E, "Portfolios," in Field-Tested LearningAssessment Guide,
National Institute of Science Education (2000) www.wcer.wisc.edu/nise/cll/flag/cat/perfass/perfassl.htm> (ac-
cessed 2/15/02)
10. Wink, D.J., "Portfolio Assessment in Large Lecture Class," Ab-
stracts of Papers of the ACS, 220, 49 (2000)
11. Johnson, J.M., "Portfolio Assessment in Mathematics: Lessons from
the Field," The Computing Teacher 21, 22 (1994)
12. Adamchik, Jr., C.E, "The Design andAssessment of Chemistry Port-
folios," J. Chem. Ed., 73, 528 (1996)
13. Phelps, A.J., M.M. LaPorte, and A. Mahood, "Portfolio Assessment
in High School Chemistry: One Teacher's Guidelines," J. Chem.
Ed., 74, 528 (1997)
14. Olds, B.M., and R.L. Miller, "Using Portfolios to Assess a ChE
Program," Chem. Eng. Ed., 33(2), 110 (1999)
15. "Alverno's Diagnostic Digital Portfolio," academics/ddp.html> (accessed 6/6/02)
16. Rogers, G.M., and J. Williams, "Building a Better Portfolio," PRISM,
8, (1999) O


Fall 2002











assessment


PORTFOLIO


ASSESSMENT

In Introductory ChE Courses


* Amherst, MA 01003-9303


A s defined by Feuer and Fulton,'" performance-based
assessment refers to assessment techniques that re-
quire students to create a final product, such as a
written report, oral presentation, or portfolio of their work,
as opposed to the more conventional assessment techniques
of written quizzes or exams. Performance assessment can also
be defined as an assessment method that evaluates a student's
ability to perform a specific procedure or task;E21 in this con-
text, the assessment must contain a performance task, a stu-
dent-response format, and a scoring system. Examples
would include judging a student's ability to manipulate
laboratory equipment or respond to an open-ended prob-
lem.[2] Slater suggests designing a performance task that
is "somewhat undefined, complex, and has multiple entry
and exit points;" that is, a task that has more than one
correct solution path.J21
The advantages of performance-based assessment tech-
niques have been documented by several studies in the edu-
cational literature.1-61] Many studies emphasize the "real-
world" nature of performance assessment;P31 student work is
evaluated in a manner that is much closer to what will be
encountered in the work environment. Perhaps most impor-
tantly, research has shown that alternative assessment helps
in the evaluation of students with various learning styles and
educational backgrounds, promoting excellence among a
more diverse student population.E4
These "alternative assessment" techniques[3' are not new
to engineering education. Traditional performance-based as-
sessment is often used (although not often acknowledged as
such) in junior- and senior-level courses in the form of labo-
ratory experiments, written lab reports, design projects, and
oral presentations; and the ABET EC 2000 guidelines have
brought increased attention to outcomes-based assessment.7E1,8
But alternative assessment is not widely used in the fresh-


man- and sophomore-level courses for a variety of reasons.
Educators may worry that freshmen and sophomores do not
have the depth and breadth of knowledge to complete a de-
sign project or written paper, or that there is simply not enough
class time to have students give oral presentations...after
all, there is barely enough class time to teach these stu-
dents mass and energy balances and thermodynamics.
There is another means of implementing performance-
based assessment in these courses, however-one that has
remained largely under-used in engineering education:
student portfolios.

WHAT IS A PORTFOLIO?
Portfolios are collections of student work, typically selected
according to guidelines set forth by the instructor.E31 These
guidelines may have a one-to-one correspondence with the
course objectives, or an instructor may choose to highlight
particular course objectives. An example of required items
from the freshman chemical engineering course at UMass,
which I will discuss in more detail below, is given in Table 1.
Along with each item, students are asked to submit a state-
ment of why the item was chosen. This element of self-analy-
sis or self-reflection is crucial if portfolios are to be more
than just "student folders."E'9 For comparison, the course ob-


Copyright ChE Division ofASEE 2002


Chemical Engineering Education


SURITA R. BHATIA
University of Massachusetts


Surita R. Bhatia is an assistantprofessor in the
ChE Department at the University of Massachu-
setts. She received her BChE from the Univer-
sity of Delaware, her PhD from Princeton Uni-
versity, and held a postdoctoral position at the
CNRS/Rhodia Complex Fluids Laboratory Her
research interests are associative polymers, rhe-
ology, shear-induced structure, and structured
cell encapsulation materials. She has taught
mass balances and heat transfer at the under-
graduate level and coteaches a graduate course
on colloidal dispersions.












I
hybridization buffer (20% [vol./vol.] formamide, 0.9 M NaC1,
100 mM Tris HC1 [pH 7.0], 0.1% SDS), and fluorescently
labeled oligonucleotide probe, 1 pl (50 ng), was added to
each sample well. Hybridizations were conducted in a mois-
ture chamber for two hours, in the dark, at 460C. The slides
were washed for 30 minutes at 480C with 50 ml of prewarmed
wash solution (215 mM NaC1, 20 mM Tris HC1 [pH 7.0],
0.1% SDS, and 5 mM EDTA). Fixed, hybridized cells were
mounted with Cargille immersion oil[23] and a cover slip.
Probe-conferred fluorescence was visualized with a model
E600 upright epifluorescence microscope,[24] and digital im-
ages were captured using
a Spot-2 charge coupled
device (CCD) cam- Sex N=13 Ap
era.[25] The results of the Male 5 <23
FISH analysis included 27-30
determining the abun-
dance and spatial orga- current Degree N=13 Current Degi
nization of phylo- A. Env Eng
B.S. 4 Env. Sci.
genetically defined mi- M S. 7 Engineerng
Ph.D. 1 Other
crobial populations Highest Degree N=13 Highest Degr
identified by unique M.S. 4 Env. Env.
oligonucleotide hybrid- Ph.D. 9 iEnv. Sci.
ization probes.
nation pbes. Figure 2. Demographic o
The students learned course as determined by c
the procedures for the
laboratory exercises through
a video series produced specifically for this course. They were
given a laboratory manual at the start of the class, and videos
of the laboratory exercises were distributed biweekly in VHS
format. The manual outlined all of the procedures for the labo-
ratory and provided step-by-step instructions to complete each
exercise. The videos gave the students an opportunity to
view the instructor completing all of the steps of each
exercise. The laboratory exercises were completed inde-
pendently by the three-student teams according to a sched-
ule arranged at the start of the class. Approximately the
first fifteen minutes of the weekly lectures were dedicated
to reviewing the progress of each team toward meeting
the schedule for completion of the laboratory exercises.

TOPICS FOR THE LECTURES
Each week, approximately two hours were spent in a lec-
ture discussion format with the entire class. The nine topics
that were covered in the pilot course included:
> Overview of methods including the value of differ-
ent methods and an answer to the question, "Why do
Environmental Engineers need to learn molecular bi-
ology?"
> Measuring microbial community structure
> Measuring microbial community function


Graduate Education J

> Quantitative molecular biology for Environmental
Engineering versus qualitative molecular biology for
Environmental Science
> Troubleshooting the laboratory exercises to improve
the course for the subsequent year
> What is this "phylogeny stuff' anyway?
> Historical development of molecular tools in Envi-
ronmental Science and Engineering
> Success stories for molecular tools in Environmen-
tal Science and Engineering
> Principles of microscopic examination


f students enrolled in the pilot
in anonymous, in-class survey.


STUDENT
FEEDBACK
Figure 2 summarizes
the results of students'
responses to a demo-
graphic survey. Thirteen
of the fifteen students
enrolled in the course re-
sponded to the survey.
The class was divided
almost equally between
male and female stu-
dents with a median age
of 27-30 years old. Five of


the students had received significant formal training in biol-
ogy, previously participating in more than ten biology courses.
The majority of the students had already completed their MS
degree (eight out of thirteen), but more than 50% of the stu-
dents had received their degree outside of environmental en-
gineering or environmental science. Most students spent less
than six hours per week on the course, but some students
spent significantly more time. Overall, the students enrolled
in the pilot test of "Molecular Methods in Environmental
Engineering" could be categorized as mature students (i.e.,
in their late twenties working toward their doctoral degrees).
Furthermore, the class contained a significant number of stu-
dents with extensive previous experience in biology. Thus,
the students enrolled in the pilot course were well prepared
in maturity and previous biology experience to actively par-
ticipate in this novel course. As the course continues to be
offered, I plan to track the success of the course in relation-
ship to the demographics of the enrolled students.
In addition to collecting demographic information, at the
end of the class the students were asked to respond to three
open-ended questions. In response to the question, "In your
opinion, were the objectives of the course met?" students re-
sponded:
The course met some of the objectives, but some students


Fall 2002


N=13 Number of Previous N=13
Biology Courses
0 <2 2
4 <5 4
5 <10 1
4 <15 1
15+ 4
ee Field N=13 Hours per week on N=13
course
5 <4 2
1 <6 7
2 <8 1
5 <10 2
ee Field N=13 <12
<15 1


(










[ Graduate Education J


The L-S technique solves Eq. (16) for c' by expanding it in
the parameter p as

c/=Ypici (17)
i=1
and by using the Fredholm Alternative (i.e., the fact c' lies
in the function space orthogonal to which (c) resides). Such
an expansion (Eq. 17) is possible, since for p = 0, the trans-
verse diffusion operator in Eq. (8) has a zero eigenvalue with
a constant eigenfunction. Thus, (u'c') could be determined
to any order in p, i.e., closure of the local equation could be
accomplished to any desired accuracy. In practice, the lead-
ing term (that is of order p) is sufficient to retain all the quali-
tative features of the full CDR equation. For example, for the
case of azimuthally symmetric feeding, we have

a(c) 1 2 v4
c'= -p 12- 4 +8 +(p2) (18)

Substituting Eq. (18) into Eqs. (12) and (13) gives the two-
mode model to O(p) as

3(C) + 1 32(C + Da r(c)) + Op2 0 (19)
at az Pe az2

(c) -cm = PpP +0(p2)
az (P'

=lppc + O(p2) (20)
az
with boundary and initial conditions given by

= c Cm,in @ z =0 (21)
Pe dz
= 0 @ z = 1 (22)
az
(c)= (c) @ t=0 (23)

where 1 / P, is called the exchange coefficient, which depends
on the local shear rates. For the case of fully developed lami-
nar flows, D_ = Dx = Dm (molecular diffusivity of the spe-
cies), and P1 =1/48. We refer to this model as the two-mode
axial dispersion model. (Further details of the spatial averag-
ing procedure using the L-S technique can be found in
Chakraborty and Balakotaiah.[14,15])
It should be noted that the spatially averaged CDR equa-
tion (Eqs. 19 and 20) retains all the parameters (p, Pe, Da) of
the three-dimensional CDR equation (Eq. 8) and hence all
the qualitative features of the latter. It should also be men-
tioned that this model is capable of capturing macromixing
effects through the axial Peclet number Pe in the global equa-
tion (Eq. 19), as well as micromixing effects through the ex-
change coefficient Pf1 and transverse Peclet number p in the

Fall 2002


local equation (Eq. 20). In fact, the L-S technique guarantees
that the solution of the averaged model (Eqs. 19-23) agrees
with the exact solution of the three-dimensional CDR equation
to O(p). [Three decimal accuracy is obtained for a second-or-
der reaction for the case of Pe -> if 02 < 1 (see ref. 14).]
Using the spatial averaging technique illustrated above,
accurate low-dimensional models could be obtained for dif-
ferent types of reactors and flow profiles. For example, the
two-mode model for a tubular reactor with fully developed
turbulent flow is the same as Eqs (19) through (23), where
D1 is the effective turbulent diffusivity and P1 is a function
of Reynolds number (Re) and friction factor f. This model is
obtained by starting with the time-smoothed (Reynolds aver-
aged) CDR equation, where the reaction rate R(C) in Eq. (5)
is replaced by the Reynolds averaged reaction rate (after clo-
sure) R,(C). Spatial averaging by the L-S technique is then
performed on the time-averaged CDR equation (i.e., spatial
averaging follows time averaging) to obtain the two-mode model
(see ref. 15 for details). In the next section, we will present the
two-mode models for other types of homogeneous reactors.

TWO-MODE MODELS
FOR HOMOGENEOUS REACTORS

Tubular Reactors

The steady-state two-mode model for a tubular reactor for
the case of Pe -> (i.e., no macromixing present) may be
obtained from Eqs. (19) through (21). In dimensional form,
it is given by

(u) -R((C)) with Cm(x = 0)= Cmin (24)

Cm -(C) = -tmx (u) = tmxR((C)) (25)

where the local mixing time tox (in the local Eq. 25 describ-
ing micromixing effects) is given by
2
a
tmix = Pi (26)
D_
where a is the local diffusional length scale over which spa-
tial averaging is performed, DI is the local diffusion coeffi-
cient, and p 1 is the exchange coefficient. In the limit of com-
plete micromixing (i.e., tmix 0), the two-mode convection
model reduces to the ideal one-mode zero-parameter PFR model.

Loop and Recycle Reactors
In a loop reactor of length L, a flow rate of qn, and with an
average velocity of (uin), enters and leaves the reactor at
points x = 0 and x = 1, respectively (where x is the length
coordinate along the loop). The total flow rate in the loop is
Q + qn between points x = 0 and x = 1, and is Q between










[ Graduate Education )


2i1


H~


Collect Sample Extract Genomc DNA









Polymerase Chain Reaction
Denature, Anneal, Extend for Exponential Growth
Cloning.--.


Cloning
Ligation, Transformation, Isolate Recombinants









FISH and Microscopic Examination

/9


Figure 1. Schematic of the principal steps in the "full-cycle
16S rRNA approach." Genetic material is isolated directly
from an environmental sample and the 16S rDNA genes
are amplified in a PCR. The product of the PCR is cloned,
and recombinants are isolated for extraction of plasmid
DNA. Automated sequencing is used to provide the primary
nucleotide structure of the clones, and probe design is ac-
complished using semi-automated procedures and readily
available software. Finally, individual microbial cells are
visualized through fluorescence in situ hybridization (FISH)
with fluorescently labeled 16S rRNA-targeted oligonucle-
otide probes.


isms in environmental samples. Arguably, one of the most
widespread families of new techniques for determinative
microbiology targets rRNA. Comparative studies of rRNA
nucleotide sequences collected from a variety of microorgan-
isms led to the development of a universal phylogenetic frame-
work for understanding the evolutionary history of microor-
ganisms.[4,5] Subsequently, these comparative approaches were
coupled with oligonucleotide probe hybridizations to study
microorganisms in situ without prerequisite culturing."1,6
The "full-cycle 16S rRNA approach" refers to the process
of obtaining genomic information directly from an environ-
mental sample and then employing molecular methods to
assay the abundance of nucleotide sequences directly within
an environmental sample. The steps of the cycle, as applied
in my course, are briefly described and outlined in Figure 1.
Genomic deoxyribonucleic acid (DNA) is extracted from an
environmental sample using chemical and physical disrup-
tion of the microorganisms. Subsequently, a polymerase chain
reaction (PCR) is used to selectively "grow-up" target genes
from the heterogeneous pool of genetic material. In our case,
the target genes are 16S rRNA. The target genes, amplified
in the PCR, are cloned into bacterial vectors and transformed
into competent cells of Escherichia coli. The recombinant
clones are cultured and plasmid DNA is extracted. The re-
sults from commercial dideoxy terminal sequencing are used
to design an oligonucleotide hybridization probe purchased
from a commercial vendor. The fluorescently labeled probe
is hybridized to a "fixed" sample, and individual microbial
cells are identified using an epifluorescence microscope.
For my class, commercially available kits were used to the
extent possible to minimize the time spent by students and
the teaching assistant in preparing reagents. Genomic DNA
was extracted using an UltraClean Soil DNA Isolation Kit.71
PCR was conducted using a model 2400 thermal cyclerE81 and
the Takara Ex Taq kit.[91 Cloning of the PCR products was
accomplished with the TOPO TA Cloning kit version K2,E10l
and plasmid DNA was prepared using PerfectPrep Plasmid
Mini preps.E11l Throughout the exercises a variety of equip-
ment was used including an ultra low temperature freezer,E12]
a Mini Beadbeater-8,E13' a system for agarose gel electrophore-
sis,[14] a Genesys 10uv,[15] a constant-temperature rotary
shaker,[16] and an epifluorescence microscope.E17]

FORMAT FOR LABORATORY EXERCISES
Step 1 Students arranged themselves into teams of three.
The selection of teammates was based both on a common
interest in one environmental sample and on an effort to spread
previous experience and expertise in molecular biology
among the groups.
Step 2 Teams identified, evaluated, and proposed an ap-
propriate environmental system for study. Each system se-


Fall 2002


i













form cash flow analyses for different scenarios. (The project
assignment is shown in Appendix A.) The cost parameters
are approximated and tested to produce realistic profit fig-
ures in the end. Capital costs include the storage tank mate-
rial and installation, gas pumps, land requirement, engi-
neering costs, etc. The operating costs are estimated as
10% of the capital investment, assuming a ten-year project
lifetime.
When the students are ready for the actual price bidding, a
simulation is used to determine the demand in each station,
based on the four stated prices (see Figure 1). The simulation
is modified from the Monte Carlo Gillespie algorithm from
reaction kinetics. Simply, the probability of customers visit-
ing each gas station is inversely proportional to the price dif-
ference between that particular station and the minimum bid-
der. The simulation then uses a random number generator
to determine the exact demand for each station. An extra
station with a fixed price is added to model gas stations
from outside this town.
To account for different levels of service provided by each
station (e.g., method of payment that is accepted), the prices
are adjusted before the probabilities are calculated. These ad-


justment amounts are based on polls conducted among stu-
dents regarding their own consumer preferences. The simu-
lation also includes some proportion of cars that stop at the
first gas station in sight instead of comparing prices, which
again is determined using a Gillespie algorithm with a prede-
termined probability.
The profit of each company is calculated based on the num-
ber of gallons sold minus operating costs of the gas station.
As mentioned before, each group decides in advance what
the suitable underground storage capacity will be, which gives
rise to certain capital costs and operating costs. In the event
that the gas station sells more gas than its capacity al-
lows, it will have to obtain extra gas at 115% of the maxi-
mum price among the four gas stations. In this way, each
gas station is equally profitable if the right price relative
to each other is found.

RESULTS AND DISCUSSIONS
The results of the game are quite encouraging. We are try-
ing to teach the concepts of customer perception of product
value, convenience, and price differentiation based on those
perceptions. We are also trying to show that the strategy of


Excel




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| I Run 3 ; MBI ik
*'Slalrion I. Fr'iuCr: j C'tii i a IF -7url Uurno~ A
74 Pr:' G. Slalnon Monte Ca'o SLmulaniH
a ar -. ... .. .... c1 a"
a P3f'1' C as SWati ~M7.n WCa 'l q *

9 Slailam r.ta.(,l East W l -,G
10 Pr,':q oa E -
It ad.'-al% 1 -4,-
13 Pti A- nu., 14-i
14 F-'O: V.!tn 1 SItlin Stflicn I Sl*ian 4 '?
15 Sulloin III
17 *,CJ1. 1 P m. .

19 P',,ri- a .n_ __:i .l
:0 PrDI- MDUfi r H |r sr 5 v .3 6-'
; Slim. IV .11 i ZECE & '
1i a CjiiI 73 .Cj

2; P,-I. Penc D P s ','"? 41:



3,



Figure 1. The gas station game simulation in action.


Fall 2002












TABLE 2
Common Intuition about Chemical Engineering Data

* High molecular weight compounds have high boiling points
* A substance with a density order of magnitude less than water is
probably a gas
* A Reynolds number in the laminar range for flow of water in
typical process piping is not typical
* Convective heat transfer coefficients are very low for gases as
compared to liquids





TABLE 3
Uncommon Intuition about Phase Equilibrium Data

* The fugacity of a liquid is approximately its vapor pressure, as
long as the pressure is not extremely high
* The fugacity of a component in an ideal gas mixture is its partial
pressure
* Substances we consider noncondensible gases have fugacity
coefficients larger than one; liquids and condensible vapors have
fugacity coefficients smaller than one
* Substances with large differences in boiling points are unlikely to
form azeotropes; substances with very close boiling points are
almost certain to form them
* Activity coefficients larger than approximately seven indicate
that liquid-liquid phase separation is possible
* The dilute component in either of two nearly immiscible phases
obeys Henry's Law up to its solubility limit


terms. Typically, this step consists of transforming highly
abstract variables into physically significant ones.
Chemical Potential -) Fugacity -) Activity -) Composition
Each transformation results in a less abstract variable than
the previous step. Students do not seem to recognize this,
perhaps because we do not teach it explicitly. Instead, they
see chemical potential, fugacity, and activity as equally nebu-
lous and abstract concepts upon which a rote series of math-
ematical operations will hopefully produce a physically mean-
ingful variable such as composition, pressure, or temperature.
One of my principal goals in teaching phase equilibrium
thermodynamics is to help students develop an intuitive un-
derstanding of the topic. I point out to them in the beginning
that this class deals with techniques for generating data to
use in other classes to the nearly total exclusion of applica-
tions. Since students will not be able to rely on processes or
equipment to provide intuition, I emphasize understanding the
data and its significance. This type of intuition about data, rather
than equipment, occurs in other classes as the Prandtl number
example above and as similar examples in Table 2 indicate.
To promote this, I emphasize calculation and use of data
having an obvious physical interpretation, e.g., temperature,
pressure, volume, vapor pressure, composition, and enthalpy.
When concepts such as free energy, chemical potential, fugac-
ity, and activity are presented, the focus is partly on their use
in solving for the more physical variables. Whenever pos-
sible, I encourage students to examine how the abstract vari-
ables affect the physical variables, and thus to develop some
intuition about the significance of the abstract variables. Ex-


Textbook G
Introduction to Chemical
Engineering Thermodynamics21'
(Chapters 10-15)
Chemical and Process
Thermodynamics'31
(Chapters 9-13)
Transport Phenomenal41
Elementary Principles of Chemical
Processest5s
(Chapter 6)
Momentum, Heat, and Mass
Transferi61
(Chapters 35, 37-40)


Non-graph
raph Figures Figures


Graphs per Percent Graph
Pa eb 100 aees Fiures


568
(199)

541
(253)
711


15 587
(0) (71)


3 53
(11) (100)


aGraph figures include all two- and three-dimensional coordinate plots and nomographs. Any figure that
included both graphical and nongraphical information was treated as a graph figure. Only numbered, captioned
figures in text and examples were counted; figures with problems and in appendices were excluded.
bPages include all text, examples, questions, and problems but exclude appendices.


amples are given in Table 3;
these are sometimes
present, but not frequently
emphasized, in phase equi-
librium texts.

More so than in many
chemical engineering
classes, phase equilibrium
data are most useful and un-
derstandable when pre-
sented graphically. This is
evident from observations
given in Table 4 of how fre-
quently graphical material
is presented in textbooks.

Thermodynamics and
unit operations texts contain
more graphs and a higher
proportion of figures that
are graphs, as opposed to
schematic diagrams and
other drawings. Within each
text, the chapters more


TABLE 4
Comparison of Graphical Figure Use in ChE Textbooks


Fall 2002











representation of the disturbance record as an explana-
tion for any model failure.
With this representation of the historical disturbances and
the model constants in Table 1, the system of ordinary differ-
ential equations in Eq. (10) can be solved readily, by numeri-
cal routines available in a number of software packages, to
obtain a model-generated record of carbon in the reservoirs
from 1850 through 1990. (I used Mathcad for this particular
exercise and extensively throughout the course.) The solid
curve of Figure 3 shows the result for atmospheric CO,; the
data points are reported estimates or measurements from the
Worldwatch Institute database."13 The good agreement be-
tween model results and reported data was assured over a
portion of the curve, at least by my method of determining
the value of F. Its value of 198 PgC, as given in Table 1, was
determined by an iterative search aimed at minimizing the
total squared difference between model results and reported
data over the period 1980-1990. Admittedly, the good agree-
ment over the early years was also virtually assured because
model constants were calculated to give a perfect fit of the


TABLE 2
Model Computed
Quantitiesfor 1990
i M'

1 753
2 744
3 143
4 37071
5 577
6 1489
7 5086
8 0.952
'Units of M are PgC, except
M., which has no units.


380
370
360
S350
340
- 330
S320
S310
300
290
280
1850


1875 1900 1925 1950 1975 2000
year


reference data of 1850. Over the other years, the maximum
disagreement, which occurs around 1925, is less than 1.3%.
All such things considered, this test of the model lends legiti-
macy to its use in predicting carbon distributions through some
years ahead.
Table 2 lists the calculated 1990 levels of carbon for all
reservoirs. Notice that changes in the five of the six reser-
voirs have been relatively small over the 140-year period,
according to the model. The terrestrial biota in box 5 increased
only from 577 to 580 PgC owing to the offsetting effects of
decreases by deforestation and increases by atmospheric CO2
fertilization. The atmospheric reservoir increased by 23% by
1990 and is obviously destined to go higher, but changes in
others have amounted to about 2% or less.
A total of 214 petagrams of new carbon was injected into
the cycle from the fossil fuel reservoir and distributed among
the other reservoirs over the period 1850 through 1990. Even-
tually most of that will reside in the deep oceans, box 4, but
by 1990 that reservoir has increased by only 71 petagrams.
Atmospheric carbon increased by 141 petagrams. Some of
that redistribution of carbon, but not any of the increase in
the total, is due to deforestation with a nonzero value of kd.
In the simulations to follow, the ending values of the M's
for 1990, given in Table 2, are used as the initial state.

SIMULATIONS
The simulations described in this section engage the stu-
dents in the use of the model and exhort them to learn about
current trends, issues, and possible future actions-and to
become informed about likely consequences regarding fu-
ture disturbances to the carbon cycle. The principal interest
is in the prediction of atmospheric carbon dioxide levels
through the 211t century. Such predictions, based on models
of varying degrees of complexity, have been reported in a
number of recent studies. 1,3,5,7,14]

Disturbance Scenarios
Postulated scenarios for future carbon emissions over a
century of time when human activities, worldwide econo-
mies, and international politics are involved are naturally laden
with uncertainty, the effects of which, in fact, probably over-
shadow the effects of the assumptions and simplifications in
the model itself. Notwithstanding such, predictions through
simulations require inserting the disturbance functions F, Fd,
and Fr into the model equations.
The most commonly employed scenarios for carbon emis-
sions are those in a set of five that were suggested in a 1992
report to the International Panel on Climate Change, IPCC.[3,15]

The list given in the References section is only a small sample. The inter-
ested reader will be led to a much larger assortment of models and
related subjects simply by entering the keyword "carbon" on a web
browser


Fall 2002


Figure 3. Reported and model-calculated records of
atmospheric carbon dioxide since 1850.













EDITORIAL AND BUSINESS ADDRESS:
Chemical Engineering Education
Department of Chemical Engineering
University of Florida Gainesville, FL 32611
PHONE and FAX: 352-392-0861
e-mail: cee@che.ufl.edu

EDITOR
Tim Anderson

ASSOCIATE EDITOR
Phillip C. Wankat

MANAGING EDITOR
Carole Yocum

PROBLEM EDITOR
James O. Wilkes, U. fI; 1;.., ii

LEARNING IN INDUSTRY EDITOR
William J. Koros, C .. Institute of Technology




-PUBLICATIONS BOARD

CHAIRMAN *
E. Dendy Sloan, Jr.
Colorado School of Mines

MEMBERS
Pablo Debenedetti
Princeton University
Dianne Dorland
Rowan University
Thomas F. Edgar
University of Texas at Austin
Richard M. Felder
North Carolina State University
Bruce A. Finlayson
University of Washington
H. Scott Fogler
University of Michigan
William J. Koros
Georgia Institute of Technology
David F. Ollis
North Carolina State University
Ronald W. Rousseau
Georgia Institute of Technology
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University of Delaware
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Iowa State University
C. Stewart Slater
Rowan University
James E. Stice
University of Texas at Austin
Donald R. Woods
McMaster University


Chemical Engineering Education


Volume 36


Number 4


Fall 2002


D GRADUATE EDUCATION
250 A Novel Approach for Describing Micromixing Effects in Homoge-
neous Reactors,
Vemuri Balakotaiah, Saikat Chakraborty
258 Introducing Moleculr Biology to Environmental Engineers Through
Development of a New Course,
Daniel B. Oerther

> CLASSROOM
264 A New Approach to Teaching Turbulent Thermal Convection,
Stuart W Churchill
278 Gas Station Pricing Game: A Lesson in Engineering Economics and
Business Strategies,
Aaron Sin, Alfred M. Center
284 Making Phase Equilibrium More User-Friendly,
Michael J. Misovich

D CURRICULUM
272 Novel Concepts for Teaching Particle Technology,
-..i '. ..:. Peukert, Hans-Joachim Schmid
296 The Earth's Carbon Cycle: Chemical Engineering Course Material,
RogerA. Schmitz
316 Aspects of Engineering Practice: Examining Value and Behaviors in
Organizations,
Ramon L. Espino

> RANDOM THOUGHTS
282 Speaking of Education-III,
Richard M. Felder

> LABORATORY
288 Chem-E-Car Downunder,
Martin Rhodes
292 On Improving "Thought with Hands,"
G.K. Sureshkumar K.C. Khilar
304 Determining the Flow Characteristics of a Power Law Liquid,
James R. Hillier Dale Ting, Lisa L. Kopplin, Margaret Koch,
Santosh K. Gupta

> ASSESSMENT
310 Portfolio Assessment in Introductory ChE Courses, Surita R. Bhatia

257, 263, 270 Letter to the Editor
281 Announcements
320 Index for Graduate Education Advertisements

CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the Chemical Engineering
Division, American Society for Engineering Education, and is edited at the University of Florida. Correspondence
regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical Engineering Department,
University of Florida, Gainesville, FL 32611-6005. Copyright 2002 by the Chemical Engineering Division, American
Society for Engineering Education. The statements and opinions expressed in this periodical are those of the writers and not
necessarily those of the ChE Division, ASEE, which body assumes no responsibility for them. Defective copies replaced if
notified within 120 days of publication. Write for information on subscription costs andfor back copy costs and availability.
POSTMASTER: Send address changes to Chemical Engineering Education, Chemical Engineering Department., University
of Florida, Gainesville, FL 32611-6005. Periodicals Postage Paid at Gainesville, Florida and additional post offices.


Fall 2002



















To state a theorem and then to show examples of it is literally
to teach backwards.
(E. Kim Nebeuts)



Setting an example is not the main means of influencing
another, it is the only means.
(Albert Einstein)



Education is what happens to the other person, not what
comes out of the mouth of the educator.


(Miles Horton)


Education is the ability to listen to almost anything without
losing your temper or your self-confidence.

(Robert Frost)


Lack of education is an extraordinary handicap when one is
being offensive.


There is a legend that the difference between classes of
freshmen and post-graduates is that if you say "Good
Morning" to the first, they reply "Good Morning." But the
graduate students write it down.


(Donald Bligh)


I used to keep my college roommate from reading my
personal mail by hiding it in her textbooks.

(Joan Welsh)




Predicting the future is easy. It's trying to figure out what's
going on now that's hard.
(Fritz Dressier)



If I knew what I was looking for, it wouldn't be research,
would it?

(Richard Feynmann)


(Josephine Tey)


Education is one of the few things a person is willing to pay
for and not get.
(William Lowe Bryan)


Education is what survives when what has been learned has
been forgotten.


If I accept you as you are, I will make you worse; however if
I treat you as though you are what you are capable of
becoming, I help you become that.


(Goethe)


Teaching is the greatest act of optimism.


(B.F Skinner)


(Colleen Wilcox)


A graduation ceremony is an event where the commencement
speaker tells thousands of students dressed in identical caps
and gowns that individuality is the key to success.


Try not to have a good time...this is supposed to be educa-
tional.


(Robert Orben)


Fall 2002


All of the Random Thoughts columns are now available on the World Wide Web at
http://www.ncsu.edu/effective_teaching and at http://che.ufl.edu/-cee/


(Charles Schulz)











curriculum


NOVEL CONCEPTS FOR TEACHING


PARTICLE TECHNOLOGY



WOLFGANG PEUKERT, HANS-JOACHIM SCHMID
Munich University of Technology 85748 G., .. in Germany


article tcchl in, l *, is an interdisciplinary subject deal-
ing with disperse systems, including all types of solid
particles (aerosols, suspensions), liquid particles (drop-
lets, emulsions), and gaseous particles (bubbles). The main
focus of our current research and curriculum, however, is on
solid particles.
The goal of particle tcdlin li 11-., is producing and handling
disperse materials under economical and ecological con-
straints. The materials are produced due to a surplus value of
the product properties. Typical examples for these properties
are the taste of chocolate, the color of pigments, the strength
of concrete, or the electrical properties of semiconductors.
Consequently, this is also a key point in our curriculum.
In order to prepare a young engineer for his possible tasks
in industry and research, we have organized the curriculum
to reflect the structure of the field (see Figure 1). The field
can be structured generally in four levels. The first and most
fundamental level covers the elementary processes, i.e., the
physical fundamentals. They include the statistical founda-
tions of particle technology, multiphase flow, bulk mechan-
ics and powder flow, interfacial phenomena, and the interac-
tions of dispersed matter with electromagnetic radiation. On
the second level, we apply the fundamentals to machines and
unit operations. In our curriculum, we concentrate on separa-
tion processes, further strengthening students' capabilities in
multiphase flow phenomena. The third level considers whole
processes. Here, we teach the concept of product engineering,
i.e., how to tailor product properties. Consequently, we have a
close link to the applications, which are actually very broad:
Materials science (e.g., all ceramics manufacturing is in
fact applied particle technology)
Life science (e.g., proteins may be treated as small
particles in some respects, drug delivery)
Information technology (e.g., quantum dots, clean room
technology, chemical mechanical polishing)
Environmental engineering (e.g., particle separation)


How can the new areas be included in the
curriculum without disregarding the conven-
tional ones? In our opinion, the only answer
is that teaching the fundamentals is even
more important, but the examples given
to the students should change.

Traditionally, chemical engineering has been taught in
Germany using the unit-operations concept. In most univer-
sities, teaching particle tclin, l1 ,-, has followed the concept
of Hans Rumpf, who stressed the physical fundamentals in
the basic course, which is followed by courses in agglomera-
tion, solid-liquid separation, or particle characterization, to
name just a few. Unfortunately, in the USA particle technol-
ogy is taught extensively in only a few universities. Students
learn how to design machines and processes that either keep
the particle size constant (i.e., separation, mixing) or change
the particle size (i.e., size reduction and size enlargement). In
the past, only mechanical means to produce and handle par-

Wolfgang Peukert got his diploma degree in
Chemical Engineering (1984) and PhD (1990)
at Karlsruhe University. In 1998 he became a
full professor at Munich University of Technol-
ogy. He is the chair of solids and interface pro-
cess technology. He also leads the particle
technology research group and teaches par-
ticle technology.



Hans-Joachim Schmid got his diploma de-
gree in chemical engineering (1993) and PhD
in mechanical process engineering (1998)
from the University of Karlsruhe. He is a re-
search assistant in the particle technology
group at MUT His main research interests
are multiphase flows and particle character-
ization.


Copyright ChE Division ofASEE 2002


Chemical Engineering Education












was able to travel well in a straight line. The inventory of
acid was only 5ml, and the cell was enclosed to minimize
spillage problems in the event of a crash. The first run of the
Sydney team was good, but unfortunately, it started without
the required weight.

Newcastle University Team One

The Newcastle Team One car was driven by a small 3.5V
1A motor and powered by a zinc/copper copper sulfate bat-
tery, using 1M copper sulfate solution and 1M sulfuric acid.
This car made a promising start, getting third closest to the
line on its first run. Technical problems (a broken electrical
connection to the motor), however, prevented it from leaving
the starting line on its second run (see Figure 4).

Newcastle University Team Two

The Newcastle Team Two car (see Figure 5) was driven by
a 3V electric motor via a six-speed gearbox. The motor was
powered by a battery of four cells each producing 1.45V-two
cells in series with another two cells in series. The cell used
was an alkaline battery, very similar in chemistry to com-
mercial batteries.
A children's sparkler was used as a timing fuse to stop the
car. When the sparkler burned to the end, it melted through a
section of solder wire incorporated into the cell wiring and
disconnected the power supply from the car motor. The length
of the sparkler determined the running time of the car and
was decided according to the results of previous trials. Spar-


Chem-E-Car


University of Newcastle


[ The Cell
The car is powered by an electrolytic reaction taking place in a dry cell. The cell used is
an alkaline battery, very similar in chemistry to commercial batteries.
T I Zinc sheet
Ionic Reaction in Cell: 3mm EMDOGrphite Past
Z h+ + -'Separator-
Zn -- ZnZ2 + 2e- Filtr Papr
Mnn* + e--Mn3 Wem o


[ Features

/ Car dimensions 225 *200 mm (top view)
-Weight (tare) = 1028 g:
-car = 320g
zinc =4 x 37g
-steel =4 x 105 g
EMD=4x35g '
-3V motor ,
- 6 speed gearbox

-,


Individual cells produce 1.45 V. Within Ihe car,
four cells are arranged as below to give
maximum performance:
-- | 29V



[ Safety
- MSDSs consulted
- Sealed container used to hold cell
- High purity chemicals mean negligible
gaseous by-products
Minimal interference required with cell,
as components last for several runs


klers were found to be remarkably consistent and had a burn-
ing rate of around 0.28 cm/s. Extensive safety testing had
been carried out on sparklers used indoors to ensure mini-
mum smoking or sparking.

With the sparkler burning away as the car rolled along, it
was pleasing to the eye. In practice on home turf, it had man-
aged to consistently stop only a few centimeters from the
desired distance. On this day it was the most consistent car
and eventually achieved second place.


THE RESULT

Team Newcastle Two won the poster competition with a
concise, informative display (see Figure 6). The performance
competition winner was the team from the National Univer-
sity of Singapore; after a crash on its first run, their car stopped
only 135cm short of the 20m designated distance on its sec-
ond and final attempt. Team Newcastle Two took second place
when their car stopped 180cm after the line. The trophy, a
polished Plexiglas CSTR on wheels, was made by the work-
shop staff at Monash University and is now in the hands of
the NUS team.

Reports from faculty involved in supervising the local de-
partment competitions suggested that the students benefited
greatly from the experience. To get to the start line with a car
that was competitive and worked according to the rules, each
team had to solve the series of specific engineering prob-
lems. Several teams went beyond mere functionality and con-
sidered aesthetics.
The concentration
and enthusiasm of
the participants was
] palpable, and I was
privileged to witness
it. It is not often that
The Stopping Mechanism our students engage
in something that is
Commerial sparklers are used as
S r bs to p thecren fun and also a great
th sparkler bums to the and, it
marte through a seton of solder learning exercise.
wM incorporated into the cell
w mg and diconned the power
supply from the cr =for The 1 Chem-E-Car
Sength of 'Ie spafrer determines
he running time o tht c.r, and Competition was this
decided according to the results of
pre.ous tials and more.
Blasted from the environment to a m .


]


ensure rmaumum safety

Sparkler burning rate = D 28 cmis
Extensive safety testing has been
cared out on sparders indoors, to
ensure mrnimum smoking or
qpadding


- Safety procedures developed for sparkler use:
Noflammable materials within spark
radius of 450 mm
Sparklers to be handled with caution for
three minutes after use


Chem-E-Car Team s Jamedikmn tomdupre roe heny jessekemp johnmca- hy lukeorgan taniarice kylelollnm alionwalker johnal rebe=ahnkrson


Figure 6. The winning poster of the Newcastle Two team.


The Chem-E-Car
Competition will be
held again next year
with the grand final
in Christchurch,
New Zealand, at the
CHEMECA 2002,
the annual confer-
ence of chemical en-
gineers in Australia
and New Zealand. J


Chemical Engineering Education


















Random Thoughts...






SPEAKING OF EDUCATION III





RICHARD M. FIELDER
North Carolina State University Raleigh, NC 27695


here is a theory which states that if ever anyone
discovers exactly what the Universe is for and why it
is here, it will iii ..i.,il, disappear and be replaced by
something even more bizarre and inexplicable. There is
another theory which states that this has already happened.
(Douglas Adams)


A lecture is a process by which the notes of the professor
become the notes of the students without passing through the
minds of either.


(R.K. Rathbun)


If a professor can be replaced by a CD-ROM, he/she should
be.
(Jack Wilson)


I'm sure the reason such young nitwits are produced in our
schools is because they have no contact with anything of any
use in everyday life.

(Petronius, d. -66 AD)



Times are bad. Children no longer obey their parents, and
everyone is writing a book.


A teacher who is attempting to teach without inspiring the
pupil with a desire to learn is hammering on a cold iron.


(Horace Mann)


What's on your mind, if you'll forgive the overstatement?


(Cicero)


(Fred Allen)


Teachers who cannot keep students involved and excited for
several hours in the classroom should not be there.


F 1.' i,;,_ should be made as simple as possible, but not
simpler.

(Albert Einstein)



In theory, there is no difference between theory and practice;
in practice, there is.

(Chuck Reid)


Copyright ChE Division of ASEE 2002


Chemical Engineering Education


(John Roueche)


Richard M. Felder is Hoechst Celanese Pro-
fessor Emeritus of Chemical Engineering at
North Carolina State University. He received
his BChE from City College of CUNY and his
PhD from Princeton. He is coauthorof the text
Elementary Principles of Chemical Processes
(Wiley, 2000) and codirector of the ASEE Na-
tional Effective Teaching Institute













tides were considered; therefore, particles larger than approxi-
mately 1lim were mainly dealt with while the non-mechani-
cal methods of particle synthesis (e.g., crystallization, gas
phase processes) that lead to submicron particles were ne-
glected.
By introducing product properties, we address the overall
goal of a chemical process, i.e., the production of well-de-
fined product properties under economical and ecological
constraints. The concept of product engineering transcends
educational traditions and recognizes the end value of deal-

Main topics
Statistical foundations
-Fundamentals Physical-Chemical Aspects Multiphase flow
SInterfaces
( (Interaction w. radiation)
g-Unit operations \ o ign Si iIN Particle separation
_CFD

a- Property and process function
L.Processes n Particle formation
Particle consolidation
Application and
Characterization Information Environmental -
Materials Life -
Sciences
Figure 1. Structure of particle technology curriculum and
courses offered at Munich University of Technology.


100 0,14


S80- -0,10
application
\ property
p 60- '
Handling -0,06 S
property % 5
8 40-
""----.....- 0,02

0 0,1 0,2 0,35

particle size x pm

Figure 2. Property functions of a typical pigment.

Showing the whole picture

elementary unit operations processes
processes

E i. r.m-
S feed -


e, molecule process


[ i.a.,,n part. formation p rpulil...
,: Ir.-al and separation il--ui:,-

Figure 3. Teaching concept and new topics (gray).

Fall 2002


ing with process t cl iii l --.,, i.e., the product property. Al-
though this point of view is not new, it is largely neglected in
the curriculum. Rumpf"1 coined the expression "property
function" for the end-product qualities as well as handling
characteristics. The property function is defined as
Productproperty = F(disperse properties and microstruc-
ture, chemical composition)
Disperse properties are particle-size distribution, particle
shape, particle morphology, and particle-surface characteris-
tics. As an example, Figure 2 shows the product quality of a
pigment (in this case the color strength per unit mass of pig-
ments) that improves with decreasing particle diameter. The
yield stress of the powder, as an important handling property,
also increases with smaller particles, indicating prohibitive
high resistance against powder flow. Obviously, there exists
an optimum where both product and handling quality are ac-
ceptable. One solution to this problem may be to optimize
powder formulation allowing both high product quality and
acceptable handling properties. Of course, there are many
other end-product qualities, such as taste (e.g., of chocolate),
strength (e.g., of concrete), activity (e.g., of a catalyst or a
drug), or the band gap (e.g., of a nanocrystalline semicon-
ductor). Typical handling characteristics are flowability, dust
development, filtration resistance, risk of explosion, and
abrasiveness, to name only a few. Polke and KrekelE21 intro-
duced the term "process function" to relate the disperse prop-
erties of the product to the production process and the educts

Disperse properties = F(process parameters, educts)

Process parameters include the types of machines and unit
operations as well as their interconnection, the operational
parameters. The art of chemical engineering in this context
involves designing the best process for producing the correct
dispersed properties, leading to the desired product quality
with a minimum of costs, including environmental costs.
This way, the product would achieve the highest profit
since it is the most competitive. Our point of view in-
cludes both the economical aspects and a global perspec-
tive of environmental responsibility.

EDUCATION IN PARTICLE TECHNOLOGY
AT TU MUNICH

Teaching Concept and New Topics

The particle tclhin l .1 courses are a part of the chemical
engineering and process engineering ("Verfahrenstechnik" in
German) curricula at the Munich University of Tcl.iii, .l -.,.
On one hand, the traditional education of chemical engineers
prepares students for well-known applications such as the
design of cyclones or heat exchangers, but many of the tradi-
tional applications have reached the point where their eco-
nomic success is decreasing. On the other hand, new oppor-
tunities are evolving in areas that are less familiar to engi-
neers, e.g., information tcolin ii : *.1, or various aspects ofma-











maximizing an individual player's revenue did not necessar-
ily mean defeating the others. And, in fact, the most favor-
able revenue picture is one in which all participants were able
to share the market in some fashion.
We found that within approximately ten iterations, the stu-
dents were able to arrive at the conclusion that a shared mar-
ket created more revenue and that cutthroat competition was
unlikely to succeed. With this realization, the students go on
to develop pricing strategies that allow each of them to sell
close to their facility's capacity and to maximize their in-
dividual revenues.
Figure 2 shows a typical adjustment process based on root-
mean-squared deviations in prices and revenues, as compared
to values at the last iteration. At around the tenth iteration,
prices begin to converge to the range where a reasonable profit
is sustained among all stations. The revenues continue to fluc-
tuate, on the other hand, since students often react to price
changes of the other stations after their demands have
changed, instead of anticipating the behavior of the oth-
ers. These fluctuations are likely to stabilize if we carry
the game further.

CONCLUSION
We think this game provides an easy way to teach pricing
strategy in a fairly simplistic business model, and we are happy
to pass along this game for your interest and use.



APPENDIX A )
Assignment Sheet
for the Gas Station Pricing Game


There are four gas stations on Rt. 13, coming into Ithaca.
They are about a block apart, as indicated in the figure be-
low.


Figure 1A: Map of the four gas stations

Preliminary market research indicates a demand of about
120 cars/hr in the day and 20 cars/hr at night, at 10 gals/car.
While some percentage of the drivers go to the first gas sta-
tion in sight, most make that decision based on things such as
price, convenience (credit card/speed pass), and brand name.
They also have the choice of getting gas from the next town
if they feel prices are too high.
Your first task is to decide on the amount of investment,


15.00% -
S7500
--Price
S12.50% Deviation
D -Revenue
Deviation 5000
10.00% f
0 2o
._.

S7.50% A 2500

2 5.00% \

2.50%

0.00% -2500
1 2 3 4 5 6 7 8 9 1011121314151617
Iteration
Figure 2. The adjustment process: root mean squared de-
viation in prices relative to final average price (left axis)
and root mean squared deviation in revenues (right axis)
plotted against iteration number.


TABLE 1
Differences between Mom/Pop Operations
and Chain Companies

Investment Supply Cost Personnel Service

Mom/Pop $300,000 $1.45/gal 1 @ $5/hr 12 hr

Chain Unlimited $1.47/gal 2 @ $5/hr Speed pass



TABLE 2
Gas Station Configurations and Costs

Capacities 20,000 gal 25,000 gal 30,000 gal 40,000 gal
Capital Cost $200,000 $300,000 $400,000 $500,000

Operating Cost $56/day $84/day $111/day $138/day


level of service, and pricing strategy for your gas station. Your
decision will depend on the nature of your company (mom/
pop vs. chain), as listed in Table 1. Table 2 lists the available
gas station configurations.
The supply trucks come every seven days to refill the
underground gas tanks. If you sell more gas than your
designed capacity, the extra gas will be available at 115%
x Max gas price in Ithaca.
The goal of this exercise is to achieve the highest return on
investment among all groups, with a minimum acceptable
ROI at 12% per year. You will be able to change your
prices (and only prices) every week, depending on the
market situation. J


Chemical Engineering Education


I II IV
- - Rt. 13 to Ithaca- - -

III










Here, as can be inferred, (1+y)24 designates the integrated-
mean value over R4, and (l+y)2mR4 the integrated-mean
-- mR ++
value weighted by 1 [u'v') Both quantities may readily
be evaluated numerically, using Eqs. (3), (4), and (5), and the
reduced form of Eq. (13). For Pr -> the temperature field
develops almost completely very near the wall where u'v')
can be approximated by 0.7 (y+/10)3 and 7 can be neglected.
Equation (16) can then be integrated in closed form to obtain

Nu, = Nu{Pr -> } = 33/2 (0.0007)1/3 a (Pr/ Prt)1/3 / I =

0.07343Re(f/ 2)1/2 (Pr/Prt)/3 (21)

For uniform wall temperature, the criteria for fully devel-
oped convection require that

(aT / ax)/ (aTm / ax) T+ / T+
Integration of Eq. (17) by parts is no longer possible, but
from the limiting form of Eq. (16) for R = 0, it follows that

Nuo =4(T+ / T +(1+y)m2 (22)

and

u+ T+' Re(f2)
Nu 4 (23)
u T1 (1 +y) mR2
Here, Tc is the temperature at the axis of the pipe. Equation
(21) remains applicable as is. The determination of numeri-
cal values of 7, T+, and T+ from Eqs. (13), (16), and (17)
now requires iteration, but the functional forms of Eqs. (22)
and (23) are adequate for the development herein.
On the basis of the previous experiences with various as-
pects of turbulent flow, I anticipated that Eqs. (19) through
(23) could be combined in appropriate pairings in the form
of Eq. (7) to construct satisfactory correlating equations for
Pr > Prt and for Pr < Prt, or alternatively, in appropriate trip-
lets in the form of Eq. (8). All such attempts failed, however.
I then found (somewhat serendipitously) that a successful cor-
relating equation for turbulent thermal convection could be
devised by using a particular a;i .ilI, between momentum
and energy transfer in which the exact solutions for three par-
ticular values of Pr occur in the form of Eq. (9). Accordingly,
a brief and very selective review of such analogies is appro-
priate at this point.


SELECTIVE ANALOGIES
ReynoldsE71 postulated that the transport of both momen-
tum and energy between a turbulent stream and its confining
surface occurred wholly by means of a mass flux of eddies
and thereby derived the equivalent of
Nu = Pr Re(f / 2) (24)


Prandtl 8l improved upon the Reynolds ;:II..ili by postulat-
ing an added resistance due to linear molecular diffusion of
momentum and energy across a viscous boundary layer of
thickness 6 in series with transport by the eddies of Reynolds
in the turbulent core, thereby obtaining the equivalent of

Pr Re(f / 2)
Nu = (25)
1 + +(Pr- )(f / 2)1/2

Equation (25), just as Eq. (24), is inapplicable for Pr < 1,
owing to neglect of thermal conduction in the turbulent core,
and also for Pr >> 1, owing to neglect of eddy transport within
the viscous boundary layer. Even so, it represents a great ad-
vance in that it correctly predicts a coupled, non-power de-
pendence on both Pr and Re, in the latter case by virtue of the
dependence of f on Re. Of the many analogies that have been
proposed to eliminate the deficiencies of the Prandtl : i.ilI '_
for large and small values of Pr (see, for example, ChurchillE'9),
only two need to be examined here.
ReichardtE61 eliminated dy+ between the equivalents of Eqs.
(2) and (15) and made several ingenious approximations that
allowed him to integrate the resulting combined equation in
closed form. ChurchillE91 assembled the fragments of this so-
lution into a single expression for Nu and corrected the erro-
neous expression used by Reichardt for the shear stress near
the wall, thereby obtaining


1 (1+y)mu+ T+ U Prt+
Nu Re(f / 2) T-/ u~ Pr)

13.62 (T Prt 3
Re(f / 2)1/ T Pr \ Pr


Equation (26) is limited in applicability to Pr > Prt by virtue
of one of the simplifications made by Reichardt in order to
be able to integrate analytically.
Churchill10l (also Churchill and Z.j ic' followed a com-
pletely different path to derive an expression, which for Pr >
Pr, is exactly equivalent to Eq. (26) except for replacement
of the term 1 Pr/Pr by 1 (Pr/Pr)2/ In retrospect, the differ-
ence in these expressions is a consequence of the approxima-
tion of Reichardt of du+ by dy+ in the differential term lead-
ing to the right-most term of Eq. (26).


FINAL FORMS
The final predictive expressions for turbulent thermal con-
vection emerged from the various expressions above by means
of the following lengthy series of insights, postulates, and
inferences, all of which were essential.

O Churchill, et al., 11 recognized that Eq. (26) was equiva-
lent, with Tm / T+ evaluated at the limiting conditions, to


Chemical Engineering Education













on a smooth curve over this range.
The data is also found to be consistent with some earlier
workE11 performed using the same solution, using a stainless
steel tank with a copper tube, similar to that used in Run No.
16. Our data is also consistent with the earlier data11 on a 0.07
wt% Na-CMC solution having a slightly larger weight-aver-
age molecular weight of 7.5 x 105 (the apparent viscosity at
1000 s-1 was about 7 cP earlier, and is about the same in Figure
2). The replicability of our results was found to be excellent.
It should be mentioned here that an interesting activity would
be to confirm the experimental results obtained here with those
using more sophisticated capillary-flow or Couette viscom-
eters available in research laboratories. Use of the former
would also illustrate the use of the more exact Rabinowitsch
technique of analysis.[1,9]
The experimental results shown in Figure 2 were then used
to design a few additional experiments (Phase 2) so as to ex-

01'












0001ooo ,
10100 ShearRate 1000 10000
(1/s)

Figure 3. Results for Phase 2, assuming power law
behavior of the liquid. Run Nos. 2,3, x; 4, *; 5, -;
6, --; 7, o; 8, +; 9, F[; 10 0; Temperature = 23 OC.


01
Schummer
O Power Law




S 0.01
0





0.001 I
100 1000 10000
Shear Rate (1/s)

Figure 4. Comparison of il vs y obtained assuming power
law behavior of the liquid with that using the Schummer
correction. Set 9 (Table 1) data used.


tend the range of shear rates. The corresponding plot for the
apparent viscosity vs. shear rate for these runs is given in
Figure 3, and the values of K and n in Table 1. It was found
that the data for the two sets of experimental runs, in the
range of shear rates of about 300 to 1000 s-1, superposed
very well (these have not been shown since the data points
get too cluttered). It is interesting to observe that Runs 9
and 10 give data over a very large range of shear rate, and
one could as well use just one or both of these set-ups for a
routine laboratory experiment.
It should be emphasized that Eq. (3) is applicable only
over small ranges of shear rate (and so over a small range of
t, as the meniscus falls). A log-log plot of this equation does
not show straight lines for some cases, and one must exer-
cise some judgment to fit the points. Moreover, the viscos-
ity of CMC (a polyelectrolyte) solutions in deionized water
is very sensitive to the concentration of small amounts of
salts that may be present.'1 The addition of small quantities
of NaCl to the solution could help improve the reproduc-
ibility of the results substantially, and would help if one were
to compare the results obtained by different groups of stu-
dents taken over several weeks.
Figure 4 shows one set of data (Run 9, Table 1) that has
been analyzed using both the power law assumption for the
solution as well as the more accurate Schummer technique.
The results superpose quite well, but a shift in the curves is
quite evident, as discussed in Ref. 10.

CONCLUSIONS
A simple experimental set-up was developed to study the
decrease of the apparent viscosity of a 0.07% (by weight)
aqueous solution of Na-CMC with increasing shear rate. Two
experimental units were found that covered a reasonably
large range of shear rates of 500 to 6000 s-1. The primary
advantage of the present study is that analysis of the raw
data can be performed using equations that are easily un-
derstood by juniors in chemical engineering, and standard
computer packages (e.g., Excel, etc.) can be used for this
purpose.
Additional experimental data can easily be taken after
adding sodium choride to the CMC solution, to study the
effect of molecular contraction of the polyelectrolyte.El The
results obtained using the power law assumption are com-
pared to more elaborate methods of analysis, and a few ad-
ditional experiments have been suggested for the more
enterprising student.



APPENDIX 1

Details of the Derivation of Eqs. (3) and (8)

The macroscopic mechanical energy balance[41 is applied


Fall 2002














two-scale approach may be used to present a unified theory
of homogeneous and heterogeneous reactors!)
To summarize, the two-mode models are the minimal mod-
els that provide a low-dimensional description of mixing, by
coupling the interaction between chemical reaction, diffusion,
and velocity gradients at the local scales to the macro-scale
reactor variables. Due to their simplicity and generality, it is
hoped that they will find applications in the preliminary de-
sign and optimization of homogeneous chemical reactors, as
well as provide an alternative method for teaching
micromixing effects in homogeneous reactors.

ACKNOWLEDGMENTS
This work was supported by grants from the Robert A.
Welch Foundation, the Texas Advanced Tcll I hi -. Program,
and the Dow Chemical Company. We thank David West of
Dow Chemical, Dr. Grigorios Kolios of the University of
Stuttgart and Prof. Dan Luss of the University of Houston
for their help in locating and translation of the articles by
Bodenstein and Wolgast and Forster and Geib.

REFERENCES
1. Langmuir, I., "The Velocity of Reactions in Gases Moving Through
Heated Vessels and the Effect of Convection and Diffusion," J. Am.
Ceram. Soc., 30, 656 (1908)
2. Damk6hler, G., "Einfliisse der Str6mung, Diffusion und
Warmeiiberganges auf die Leistung von Reaktions6fen. II Die
Isotherme, Raumbestindige, Homogene Reaktion Ester Ordnung," Z.
Elektrochem., 43, 1 (1937)
3. Danckwerts, PV., "Continuous Flow Systems: Distribution of Resi-
dence Times," Chem. Eng. Sci., 2, 1 (1953)
4. Taylor, G.I., "Dispersion of Soluble Matter in Solvent Flowing Slowly
Through a Tube," Proc. Roy. Soc. Lond. A, 219, 186 (1953)
5. Aris, R., "On the Dispersion of a Solute in a Fluid Flowing Through a
Tube," Proc. Roy. Soc. Lond. A, 235, 67 (1956)
6. Forster, V.T., and K.H. Geib, "Die Theorietische Behandlung
Chemischer Reaktionen in Str6menden Systemen," Annalen. der
I., 5, 250(1934)
7. Zwietering, T.N., "The Degree of Mixing in Continuous Flow Sys-
tems," Chem. Eng. Sci., 11, 1 (1959)
8. Ng, D.Y.C., and D.W. T. Rippin, "The Effect of Incomplete Mixing on
Conversion in Homogeneous Reactions," Chem. Eng. Sci., 22, 65
(1965)
9. Miyawaki, O., H. Tsujikawa, and Y. Uraguchi, "Chemical Reactions
Under Incomplete Mixing," J. Chem. Eng. Japan, 8, 63 (1975)
10. Harada, M., "Micromixing in a Continuous Flow Reactor (Coales-
cence and Redispersion Models)," The Memoirs of the Faculty of En-
gineering, Kyoto Univ., 24, 431 (1962)
11. Villermaux, J., and J.C. Devillon, "Representation de la Coalescence
et de la Redispersion des Domaines de Segregation dans un Fluide per
Modele d'Interaction Phenomenologique," Proc. 2ndInd. Symp. Chem.
React. Eng., Amsterdam, B1 (1972)
12. Baldyga, J., and J.R. Bourne, "Mixing and Fast Chemical Reaction-
VIII. Initial Deformation of Material Elements in Isotropic Homoge-
neous Turbulence," Chem. Eng. Sci., 39, 329 (1984)
13. Bodenstein, M., and K. Wolgast, "Reaktionsgeschwindigkeit in
Str6menden Gasen," Ztschr Phys. Chem., 61, 422 (1908)
14. Chakraborty, S., and V Balakotaiah, "Low Dimensional Models for
Describing Mixing Effects in Laminar Flow Tubular Reactors," Chem.


Graduate Education J

Eng. Sci., 57, 2545 (2002)
15. Chakrabory, S., and V Balakotaiah, "Two-Mode Models for Describ-
ing Mixing Effects in Homogeneous Reactors," AIChE J., in review
(2002)
16. Li, K.T., and H.L. Toor, "Turbulent Reactive Mixing with a Series-
Parallel Reaction-Effect of Mixing on Yield,"AIChE J., 32,1312 (1986)
a

= letter to the editor


Dear Editor:

I recently used the illustration below to explain the ben-
efits of countercurrent flow to students in a separation pro-
cesses subject that I teach. I've never heard this illustration
used before and it seems to be a good one, so I thought it
would be good to put it in the public domain for the benefit
of other lecturers. However, it is very short and does not war-
rant being a "peer-reviewed" paper.

E1',i'iiin;: Why Counter-Current is
More Ei..t. It than Co-Current

While washing the dishes one night, I realized that this ac-
tivity provides a useful everyday illustration of why counter-
current mass and heat transfer processes are more efficient
than co-current ones.
I asked the students in my class what would be the best
way to clean a pile of dirty dishes if they had at their disposal
one basin of dirty wash water and one basin of clean wash
water. The class quickly reached the consensus that it would
be best to first use the dirty water to clean off as much of the
dirt as possible and then use the clean water to perform a
second-stage clean. The dirty water would remove the bulk
of the dirt, minimizing the contamination of the clean water
and leaving it in better condition to clean off any remaining
stubborn dirt. Putting the dirty dishes straight into the clean
water would quickly dilute and waste its cleaning ability.
This is equivalent to having the countercurrent flow of
streams in a liquid-liquid extraction or gas-liquid absorption
column. The clean solvent is best used to perform the final
stage of cleaning, while the used solvent is still able to perform
some cleaning of the raw feed stream as it enters the column.
Students seemed to intuitively understand this illustration,
and it provides a non-graphical complement to the usual
method of explaining the benefits of countercurrent flow,
which involves showing how the average concentration (or
temperature) difference driving force differs between co- and
countercurrent flows.
Simon Iveson
University of Newcastle
Callaghan NSW 2308, Australia
cgsmi@ cc. newcastle.edu.au


Fall 2002












Portfolios can be particularly usefulfor beginning chemical engineering students,
who often do not have class projects that require them to synthesize concepts
and present their results in a written format.


These are preliminary results; obviously, data need to be
taken on a larger sample size before conclusions can be
drawn. The results also may be biased due to wording of
the survey questions. This needs to be addressed before
definitive conclusions can be reached, and I am currently
updating and redesigning the survey questions for future
classes.
On the whole, the response from students was quite posi-
tive. The strongest and most uniform response was to Ques-
tions 2 and 4; 86% of students who completed a portfolio
strongly agreed or agreed that the portfolio helped them to
learn more about themselves and their strengths and weak-
nesses in chemical engineering and problem solving, and
89% of all students felt that the use of both quantitative
and qualitative assessment methods were appropriate in
the course. It remains unclear whether or not the portfo-
lio assignment helped students improve their written com-
munication skills.
Several of the written comments that accompanied port-
folio entries were quite encouraging, and I have listed some
of the more memorable comments in Table 5. There were
also comments both positive and negative, that were useful
to me as an educator. Students were very honest about com-
ponents of the class that they liked and disliked. Most of
these comments were made in response to Item 8, Table 1,
reflections on chemical engineering and the class. Examples
of these comments are also given in Table 5.

CONCLUSIONS AND RECOMMENDATIONS
Portfolios can be particularly useful for beginning chemi-
cal engineering students, who often do not have class projects
that require them to synthesize concepts and present their
results in a written format. Interestingly, students did not feel
as though the assignment improved their written communi-
cation skills, but the portfolio assignment did seem to give
these incoming students an opportunity to reflect on their
abilities and their choice of major. Portfolios can also be used
to assess course objectives that are difficult to evaluate using
traditional techniques.
Based on my experience, I have some guidelines and rec-
ommendations for implementation of portfolios:


Be prepared to read up on assessment tech-
niques. Several of the references listed contain


excellent examples of student entries and grading
schemes.4,5,9'11 I found the National Institute of
Science Education Field-Tested L..,,,;ini..
Assessment Guide website particularly useful.
(Found at flag/default.asp>.)


- Be clear about expectations for portfolios at the
start of the semester. You may want to give
students sample entries.


- Remind students that they should be saving
homework sets and collecting problems for
entries in their portfolio. This is extremely
important for freshman-level students who are
still learning how to organize their coursework.


- If you allow students to use a portfolio grade as a
replacement, make sure their expectations are
realistic. One fabulous portfolio assignment will
not pull a final "D" grade up to an "A"-as I
mentioned above, the overall effect on the final
grades in the course was never more than a letter
grade.
It is worth noting that implementing portfolios as
a "replacement" for a poor exam could allow a
student to bring a failing grade up to a "D."
Instructors need to decide for themselves
whether this is permissible and to develop their
own guidelines accordingly.
For example, I specified that if students received
a zero grade on an exam or homework due to
academic dishonesty, this grade could not be
"replaced" under any circumstances. One could
imagine extending this rule to any failing grade
to prevent the above scenario. Finally, I found
that it was problematic to allow students to
replace a low homework average with the
portfolio grade.


- Create a grading scheme that places emphasis on
what you think is most important, whether this is
good writing, clear organization, self-reflection,


Chemical Engineering Education











istry dynamics to the above set. Some studies3 15] have fol-
lowed that procedure, as have I in some instances. Others1[2,4'7
have opted for a simpler empirical approach that uses the
following relationships:
F21 = kM2 F3 = k3M3 (5)
Values of the exponents ,2 and P3, called buffer factors or
Revelle factors, can be obtained from charts of the type given
in the book by Butcher, et al.E10' They can also be obtained by
delving into the intricacies of ocean chemistry dynamics and
correlating results of calculations. I used the latter approach
to obtain the values shown later, but to save space and to stay
on track, I shall spare further detail.
My testing has shown that results of computations using
constant values of the 's hardly differ from those obtained
by appending detailed ocean dynamics to the model, so long
as changes in M2 and M3 are relatively small, generally less
than 5%. The numerical values of P range between 9 and 15;
the nonlinearity is surprisingly strong. Notice that with val-
ues of P2 and P3 given, numerical values of the rate con-
stants k2 and k31 can be determined from the reference con-
ditions given in Figure 1.
The rate of photosynthetic uptake, F15, of carbon from the
atmosphere cannot be represented realistically as a linear func-
tion of M1. The basic reason is that the function should ac-
count for a saturation effect with regard to the nutrient CO,.
That is, the rate increases with increasing CO2 but approaches
a limit. For small changes in M1, the function may be ap-
proximated by a linear relationship, but as a later illustration
will show, changes in M1 are large over the periods of interest.
There seems to be no clear consensus as to what form to
use for F in models of this type. Whatever the specific form,
a common feature is a dependence on atmospheric carbon
that suggests an ultimate saturation. The particular one cho-
sen does not seem to be a critical matter so long as the con-
stants are calibrated or tuned to fit existing data. Neverthe-
less, this is a fertile item for classroom discussion, debate,
and outside work. Here I shall use the form employed by
Lenton 31

ki5M8 M- forM > y
F15 M + F (6)
0 forM1 M where
y is the threshold value of M1 (I used Lenton's value of
62 PgC.)
F is a saturation parameter (Lenton used it as a tuning
parameter and arrived at a value of 194 PgC. By methods
described later, I arrived at a value of 198 PgC.)
k1 is a rate coefficient to be calculated from the reference
state.
M is a function that depends on the disturbances Fr and
Fd as explained and described below. In short, it accounts


for changes in the Earth's capacity for terrestrial biota.

The role of the function M8 is important but not obvious at
first glance, and definitions and explanations do not come
easily. Let me first define it by way of the following equation
and then offer brief explanations.

t (krFr kdFd)dt
Ms(t)=l+ E(7)
1850 M5,ref
where
kd is the fraction of forested area or mass (or forest
capacity) that cannot be reforested (is not available for
regrowth) following deforestation activities-for
example, forest areas cleared for urban development.
k is that fraction of the reforested area or mass that
increases the Earth's capacity for terrestrial biota. (This is
sometimes termed "aforestation" as opposed to "reforesta-
tion" that directly renews deforested areas.
M,.f is a normalizing factor inserted arbitrarily to make
Ms dimensionless. I take it to be the initial value of M5.

Lenton used this form but did not include kr and Fr explic-
itly in his formulation. Reforestation can be accounted for
without those factors if F is allowed to have negative values.
I prefer to show Fr and Fd separately for clarity in simulations
later.
Simply stated, the integral in Eq. (7) accounts for perma-
nent effects of the disturbances Fd and Fr. Were that integral
not included, the model equations would lead to the follow-
ing illogical conclusion, among others: If Ff 0, and if Fd
and Fr eventually settle to zero, the ultimate steady state of
carbon in the reservoirs would be identical to the starting ref-
erence state; the effects of the temporary nonzero values of
the disturbances would die away, according to the model. But
obviously the effects of some land use changes must per-
sist-for example, if forest areas are cleared and urbanized
with no offsetting reforestation. With the integral included in
M with kd # 0 and Fr 0, such land use change would per-
manently affect the distribution of carbon, not its total amount.
Other illustrations can be given to justify the form of M,, but
perhaps further explanation, if needed, is better sought in stu-
dent exercises later.
An alternate form of the integral equation above is this dif-
ferential equation:

dM8 krFr kd d
dM krFr kFd withinitialcondition M(1850) = 1 (8)
dt M 5,ref

The numerical value of the coefficient k15 in Eq. (6) can be
calculated from the reference values shown in Figure 1, given
values for F and y and taking M. = 1 (its initial state).
With Eq. (8) added to the material balance equations, the
complete mathematical model consists of the following set
of eight ordinary differential equations:


Fall 2002












was a close coupling between the teachings in the Notes and
the Case being discussed in parallel. This worked well, as
confirmed by the frequent references to concepts presented
in the Notes in the students' analyses of Cases. It is unrealis-
tic to expect the students to fully master all the concepts, but
it was clear that they became very aware of their importance.
The hope is that when they are confronted with similar situa-
tions, they will refer to these Notes for guidance.

We discussed the differences between management and
leadership and the many complex and ambiguous issues that


most managers face. We spent very productive time on the
influence of culture and history on subtle but important dif-
ferences in managers' behavior in the USA, Europe, Japan,
India, China, and Latin America. Having some students from
outside the USA gave immediacy to these discussions.

As expected, issues of business ethics grabbed the students'
attention and elicited strong and quite varied opinions. In fact,
I was surprised at the diversity of viewpoints, how strongly
they were held, and that there was no correlation with gen-
der, race, or economic background.


TABLE 3
Course Outline


Week 1
Homework/Class Discussion HBS Notes on "Learning by the case
method" and "How to choose a leadership pattern"
Lecture Individual and team competencies

Week 2
Homework/Class Discussion HBS Notes on "Understanding
context" and "Conflicting responsibilities"
HBS Case "Kevin Simpson"
Lecture Styles of communicating and interacting

Week 3
Homework/Class Discussion HBS Notes on "Managing your career"
HBS Case "Elizabeth Fisher"
Lecture Invited Speaker-Managing family and business life

Week 4
Homework/Class Discussion HBS Notes on "Power dynamics in
organizations"
HBS Case "Lisa Benton"
Lecture The seven habits of highly effective people

Week 5
Homework/Class Discussion HBS Notes on "Managing your boss"
and "Exercising influence"
HBS Case "Amelia Rodgers"
Lecture Invited Speaker-Improving your leadership skills

Week 6
Homework/Class Discussion HBS Notes on "Evaluating an action
plan" and "Understanding communications in one-to-one
relationships"
HBS Case "Ann Livingston and Power Max Systems"
Lecture The seven habits of highly effective people

Week 7
Homework/Class Discussion HBS Notes on "Beyond the myth of a
perfect mentor" and "Managing networks"
HBS Case I ..hI, -. ...- transfer at a defense contractor"
Lecture Invited Speaker-Conflict management and negotiation

Week 8
Homework/Class Discussion HBS Notes on "Power dependence and
effective management" and "Influence tactics"
HBS case "Thurgood Marshall High School"
Lecture Conflict management styles


Week 9
Homework/Class Discussion HBS Notes on "Integrity management"
and "Managing a task-force"
HBS Case "Managing conflict in a diverse environment"
Lecture Invited Speaker-Working in a consulting company

Week 10
Homework/Class Discussion HBS Notes on "Barriers and gateways
to communications" and "On good communications"
HBS Case "David Fletcher"
Lecture Invited Speaker-Should you get an MBA?

Week 11
Homework/Class Discussion HBS Notes on "The power of talk" and
"The discipline of teams"
HBS case "Mod IV product development team"
Lecture Getting to Yes

Week 12
Homework/Class Discussion HBS Notes on "The challenge of
commitment" and "A note on high-commitment work systems"
HBS Case "PPG-Developing a self-directed workforce"
Lecture Strategic planning

Week 13
Homework/Class Discussion HBS Notes on "Organization
structure," "Organization effectiveness," and "The challenge of
change"
HBS Case "John Smithers at Sigtek"
Lecture Invited Speaker-Reinforcing organizational values

Week 14
Homework/Class Discussion HBS Notes on "Business ethics: the
view from the trenches," "Ethics without a sermon," and "Ways
of thinking about and across differences"
HBS Case "Jenssen Shoes"
Lecture Developing a personal career plan

Week 15
Final Homework:
A personal career plan
Analysis of the "Most admired company..."
Group report of HBS Case "Corning Glass Works"


Chemical Engineering Education










The velocity distribution can in turn be integrated over the
cross-section to obtain, after utilizing integration by parts,
the following integral expression for the mixed-mean veloc-
ity and thereby the Fanning friction factor:

= u+ udR2 = 4 1- ) dR4 (4)
0 0
Equations (1) through (4) are exact insofar as the restrictions
mentioned above with respect to Eq. (1) are fulfilled. In or-
der to implement Eqs. (3) and (4), an expression is required
for (uv') in terms of y+ and a+. For this purpose, Churchillh4
proposed the following semi-empirical expression:

r -1-7 Y+ 8/7

10
+-7( 8
1 1 6.95yT/I
+ exp0 1+ i (5)
0.436y 0.436a a \

It is essential for the students to be aware of the origins and
uncertainties of Eq. (5) since this expression has a critical
role, both numerically and functionally, in all of the develop-
ments that follow for both flow and convection. The third-
power dependence on y+ for small values of y+ was originally
postulated on the basis of asymptotic analyses, but has since
been confirmed by direct numerical simulations, which have
also produced a theoretical value of approximately 7 x 10-4
for the numerical coefficient. The exponential term for mod-
erate values of y+, as well as the deductive term for y -> a
were both derived by speculative analysis, but the coefficients
of 0.436 and 6.95 were determined from recent, improved
experimental data for the time-averaged velocity distribution.
The power-mean form of Eq. (5) is arbitrary and the combin-
ing exponent of -8/7 is based on experimental data for u'v'.
(See Churchill and ZajicE 3 for further details, including com-
plete references.)
Numerical integration of Eqs. (3) and (4) using (uv')from
Eq. (5) results in almost exact values of u+ and u+ owing to
the smoothing associated with integration. Such values of Um+
may be represented with a high degree of accuracy for a+ >
300 by the following expression that invokes no additional
empiricism beyond that of Eq. (5):


(2 1/
yf


+ 227 + 50 .4 1 rna+
m = 3.2 + + 0.436I
a+ a+ 0.436


Equations (1) through (6) are the only ones for flow that will
be referred to directly in the developments that follow for
convection.
It may occur to teachers and graduate students at this point
that the relevant consideration of turbulent flow has been
completed without any mention of the eddy viscosity or the


mixing length. One merit of the new approach, which carries
over to thermal convection, is that the need to introduce such
heuristic quantities is avoided completely by the more direct
and simple development in terms of(u'v-)



AN ASIDE ON A
GENERIC CORRELATING EQUATION

Equation (5) is a particular application of the generic cor-
relating equation proposed by Churchill and UsagiEl5 for two
regions, namely
b b b
y Y + +yb (7)
Here, y = y{x), y, = {x->0), y_ = y{x->), and b is an
arbitrary exponent. Either y0 or y_ or both are necessarily
functions of x rather than fixed values. For three regions, Eq.
(7) can be extended either directly as

ybq =(y + b y (8)

or in staggered form as

(ybyb = (y b + y) (9)
Here, yl is an intermediate asymptote and q is a second arbi-
trary exponent. The reverse order of combination of y0, y,
and y_ leads to equally valid and, in general, fundamentally
different representations. Equations (7) through (9) have been
introduced here to avoid interrupting the continuity of the
development in which they are used.


DEVELOPMENT OF A NEW FORMULATION
FOR TURBULENT CONVECTION

The analogue ofEq. (1), with the additional idealization of
negligible viscous dissipation, is
aT
j = -k + pcT'v' (10)
ay
and that of Eq. (2) is

1- = BT (11)
Jw ay+
Here, j is the heat flux density in the y-direction, T is the
temperature of the fluid, jw and T are their values at the wall,
T+ = k(tp)/2 (T T) / pj,, T'v' is the time-averaged prod-
uct of these fluctuating quantities, (Tv') = pcT'v' / j is the
fraction of the radial heat flux density due to the turbulent
fluctuations, and k is the thermal conductivity of the fluid.
The terms j/j and T'v'+ in Eq. (11) depend on two param-
eters, namely the Prandtl number Pr = cq/k and the mode of
heating at the wall, as well as on y+ and a+.


Chemical Engineering Education











classroom


MAKING PHASE EQUILIBRIUM MORE


USER-FRIENDLY



MICHAEL J. MISOVICH
Rose-Hulman Institute of Technology Terre Haute, IN 47803


I believe phase equilibrium thermodynamics is the most
conceptually difficult undergraduate chemical engineer
ing class. Even students who perform calculations sat-
isfactorily seem confused over the meaning of what they
have learned.
Phase equilibrium is the single undergraduate chemical
engineering class in which abstract concepts are presented to
the near exclusion of practical applications. Table 1 gives
examples of practical or physically intuitive subject matter
found in classes that students typically consider abstract, theo-
retical, or mathematical. These actually contain some bal-
ance of theory and practice, giving students a point of refer-
ence to physical processes and equipment. Calculations such
as bubble and dew points are needed for practical design, of
course, but most phase equilibrium courses do not connect
these to real processes or equipment. Practical applications
of the material are taught as part of unit operations, mass
transfer, or distillation courses.
Students frequently have more intuition about the physical
meaning of abstract quantities in classes other than phase equi-
librium. Heat transfer students could define the Prandtl num-
ber as Cp / k, give a physical interpretation for all three
variables, and potentially recognize related facts. For example,
"The Prandtl number could be derived by applying
the Buckingham Pi theorem to a heat transfer prob-
lem," or "Larger Prandtl numbers result in larger con-
vective heat transfer coefficients." They know that
the Prandtl number for liquid water at 100 atm and
1500C is unlikely to be 100 or 0.01.


When phase equilibrium students define chemical
potential, it is typically in terms of other abstract con-
cepts-free energy, standard states, fugacity, and ac-
tivity. They are unlikely to know whether a certain
chemical potential is positive or negative, nor what
practical significance its sign would have. Without
doing a calculation, how many phase equilibrium stu-
dents know whether the fugacity of liquid water at


100 atm and 1500C is closest to 5 atm, 50 atm, or 500 atm?
Most are at a complete loss when asked to apply abstract
quantities such as activity coefficients to practical questions,
e.g., "Is ethanol more likely to form an azeotrope with n-
hexane or n-octane?" Lacking qualitative understanding,
their only approach for answering this question is detailed
quantitative calculation.

STRATEGIES FOR BUILDING INTUITION
Prausnitz, et al.,' describes the phase equilibrium prob-
lem as a three-step process. First, a real problem is translated
into an abstract mathematical problem. Second, the math-
ematical problem is solved. In the final step, the mathemati-
cal solution is translated back into physically meaningful


TABLE 1
Content of "Theoretical" ChE Classes


Class


Fluid Mechanics

Mass Transfer
Transport Phenomena


Phase Equilibrium


Theoretical Concepts
Shear stress tensor,
Dimensional Analysis
Fluxes of all sorts
Partial differential
equations, Dimensionless
Greek variables
Chemical potential
fugacity, activity


Practical Concepts
Pumps, Valves, Piping

Packed absorption towers
Viscometers, Heat transfer
with free convection,
Wetted wall columns
Bubble and Dew Points,
Flash, Solubilities


@ Copyright ChE Division ofASEE 2002


Chemical Engineering Education


Michael Misovich will be Associate Profes-
sorin the Physics and Engineering Department
of Hope College in August, 2002. His research
interests include thermodynamic propertypre-
dictions from equations of state, physical chem-
istry of polymer solutions, chemical engineer-
ing education, and its assessment.










[ Graduate Education I


A Novel Approach for Describing

MICROMIXING EFFECTS IN


HOMOGENEOUS REACTORS



VEMURI BALAKOTAIAH, SAIKAT CHAKRABORTY
University of Houston Houston, TX 77204-4004


Reacting flow systems are hierarchical in nature, i.e.,
they are characterized by multiple length (or time)
scales. Scale separation exists in most reactors, how-
ever, and these disparate scales are typically characterized
by three representative ones, namely, micro (molecular), meso
(catalyst particle or tube diameter), and macro (reactor or pro-
cess) scales. In most cases of practical interest, a strong non-
linear coupling exists between reaction and transport at micro
and meso scales, and the reactor performance at the macro scale.
As a result, transport limitations at the smaller scales signifi-
cantly influence the reactor and hence the process performance.
Such effects could be quantified by numerically solving
the convection-diffusion-reaction (CDR) equation from the
macro down to the micro scale. But the solution of the CDR
equation from the reactor (macro) scale down to the local
diffusional (micro) scale, using computational fluid dynam-
ics (CFD), is prohibitive in terms of numerical effort and im-
practical for the purpose of reactor control and optimization.
Moreover, even with today's computational power, it is im-
practical to explore the different types of bifurcation features
and spatio-temporal behaviors that exist in the multidimen-
sional parameter space, using CFD codes. In such cases, low
dimensional models are a natural alternative.
Historically, chemical engineers have derived low dimen-
sional models for reactors using a top-down approach, which
is based on a priori assumptions on the length and time scales
of convection, diffusion, and reaction. The classical ideal re-
actor (CSTR and PFR) models are examples of such low-
dimensional models obtained on the basis of simplified (or
oversimplified) assumptions. These assumptions are usually
not justified since justification requires comparison of the
solution obtained from the simplified models with that ob-
tained from the CDR model.
In order to account for experimental observations that could
not be explained by these ideal reactor models, the latter have
been modified by introducing the concepts of dispersion co-


efficientsE1'5 and residence time distributionE3,6,71 to account
for macro- and micro-mixing effects. Several other reactive
mixing models followed in the next forty years: the two- and
three-environment model,[89] the coalescence-redispersion
model,o10' interaction by exchange with mean model,E1ll en-
gulfment-deformation-diffusion model,E121 and CFD models
using probability density functions (PDF) and direct numeri-
cal simulation (DNS).
This article presents an alternative (bottom-up) approach
and an elementary treatment of mixing effects on reactor per-
formance. We will present a brief historical review of homo-
geneous reactor models before discussing this new approach.

BRIEF HISTORY OF
HOMOGENEOUS REACTOR MODELS
The most widely used homogeneous reactor models are
the three classical ideal reactor models: the plug-flow reactor
(PFR) model, the continuous stirred tank reactor (CSTR)
model, and the batch reactor (BR) model. While the BR model
and the PFR model (which are identical for constant density
systems with time replaced by space time or dimensionless
distance along the tube) have existed since the late eighteenth
century. A conceptual leap came in the form of the CSTR
model through the work of Bodenstein and Wohlgast in
1908.E31 Unlike the PFR model, which assumes no gradients
in the radial direction and no mixing in the axial direction,

Vemuri Balakotaiah is Professor of Chemical Engineering at the Uni-
versity of Houston. He received his BTech from the Indian Institute of
Technology (Madras) in 1978 and his PhD from the University of Hous-
ton in 1982, both in chemical engineering. His teaching and research
interests are in the areas of chemical reaction engineering, multiphase
flows, and applied mathematics.
Saikat Chakraborty is a PhD candidate in the Department of Chemical
Engineering at the University of Houston. He received his BTech from
Jadavpur University in 1997 and his MS from the Indian Institute of Sci-
ence (Bangalore) in 1999, both in chemical engineering. His research
interests are in the areas of chemical reaction engineering and granular
materials.
Copyright ChE Division ofASEE 2002
Chemical Engineering Education











Known by the names IS92a, IS92b, .. IS92e, they are based
on likely or possible trends in population changes, economic
growth, energy supplies, etc. in developed and developing
countries. There is also a Kyoto protocol, which, if en-
acted according to Article 3 of the agreement, would call
for a worldwide decrease in emissions to 95% of the 1990
level by the year 2012.[16
Shown in Figure 4 are slightly modified versions of three
of the IS92 scenarios for total carbon emissions for 1990 on-
ward, including the most pessimistic (IS92e) and the most
optimistic (IS92c) cases, and what's usually referred to as
the "business-as-usual" scenario (IS92a).* The latter is the
most commonly used version, and as its description im-
plies, is based on the assumption that carbon emissions
can be predicted from current trends with no major
changes in policies and practices.
Also shown in Figure 4 is a representation of the scenario
for the Kyoto protocol, based on the assumption that emis-
sions would be held constant after 2012. (Ver, et al., used a
similar representation. []) The IS92 scenarios break down the
anticipated emissions into fossil fuel use and deforestation.
All of them use the same deforestation pattern, which de-
clines to zero by 2100. A curve showing the modified defor-
estation scenario is also included in Figure 4. The differences
between that curve and the others in the figure are the fossil
fuel components. Reforestation is not included in the sce-
narios as a separate disturbance.

Some Results
I use two different approaches for simulations, each hav-
ing certain advantages over the other. One is a straightfor-
ward numerical solution of the differential equations using
Mathcad-basically similar to the method used to generate
the historical curve in Figure 3. It's the workhorse that I
incorporate into classroom presentations and the major tool
used by the students for assigned work. I constructed the other
using LabVIEW** to give a convenient user interface, a vir-
tual laboratory, for certain classroom demonstrations and stu-
dent experiments. It provides the user with hands-on control
of the disturbances during a simulation, showing effects of
manipulations "live" on virtual strip-chart recorders and digi-
tal displays. (Actually, I've used the LabVIEW simulation
for classroom demonstration at the very beginning of the

I modified the IS92 scenarios for both the fossil fuel and deforestation
components in order to bring the 1990 values of the scenarios in agree-
ment with the data actually reported for that year. [,12 This amounted to
.. PgCtoallofthe S92 .'. f..1. ... ..... ... .. all
of the deforestation values by about 50%. These modifications are more
for refinement and fastidiousness than for any significant effect on cal-
culations.
** LabVIEW developed by the National Instruments Corporation in Aus-
tin, Texas, is graphicalprogramming software developed mainly for data
acquisition and instrument control. It also serves as a powerful tool for
constructing virtual laboratories.


module because it is illustrative and serves to introduce goals
and whet the appetite for learning about model development
and simulations.) Space limitations prohibit a full descrip-
tion of the LabVIEW simulator and its operation here, but
the gist of it is shown in the photo of the user's panel in Fig-
ure 5 and the brief description in the caption. Notice that those
features afford the user an option of sequestering carbon by
reforestation and by capturing a fraction of emissions, F, in
the deep ocean and geologic reservoirs.
Figure 6 presents an example of the results of Mathcad
simulations using the four scenarios of Figure 4. (For those
simulations, I used linear interpolation between the data points
shown in Figure 4 for the period 1990-2100.) The results in
Figure 6 are based on the parameters listed in Table I ex-
cept that here the values used for P2 and P3 are 11.0 and
12.3, respectively. (As I mentioned above, those values
depend on the total carbon in the surface ocean reservoirs.
I used the 1990 values of M2 and M3 given in Table 2 as a
basis for the new p values for the period 1990-2100.) Fr
is taken to be zero.
Notice that the model predicts atmospheric CO2 would in-
crease to 702 ppmv by the year 2100 if the IS92a business-
as-usual scenario were followed. Based on that scenario, pre-
dictions by models used by others[31,314] range between 697
and 724 ppmv. Over the entire 110-year period, the maxi-
mum difference in atmospheric CO2 between any two of the
four models (the three cited above and the present one) is
about 4%, an observation that buttresses confidence in dis-
cussions of quantitative results from the model at hand. No-
tice the wide range of predicted CO2 levels in 2100 resulting
from the different scenarios for carbon emissions. The high-
est is nearly twice the lowest; both are probably unrealis-
tic extremes. Business-as-usual would result in nearly
doubling the 1990 CO2 level by the year 2100, according
to the model prediction.


35
Historical total to 1990
30 ----IS92a total (modified)
2 -U-lS92c
25 --IS92e
20 ---Kyoto protocol total
20 a Historical deforestation to 1990
--IS92 deforestation (modified)



0


1850 1875 1900 1925 1950 1975 2000 2025 2050 2075 2100
year

Figure 4. Carbon emissions to the atmosphere; historical
data and possible future scenarios.


Chemical Engineering Education
















I N D E X



GRADUATE EDUCATION ADVERTISEMENTS


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Texas A&M University ................................ 411
Texas A&M University, Kingsville .............. 438
Toledo, University of .................................. 412
Tufts University ......................................... 413
Tulane University ....................................... 414
Tulsa, University of .................................... 415
Utah, University of ..................................... 439
Vanderbilt University ................................. 416
Villanova University................................... 439
Virginia, University of ................................ 417
Virginia Tech ..................... .................... 418
Washington, University of ............................ 419
Washington State University ...................... 420
Washington University ............................... 421
Waterloo, University of .............................. 440
Wayne State University .............................. 422
West Virginia University ............................ 423
Wisconsin, University of .............................. 424
Worcester Polytechnic Institute .................. 425
Wyoming, University of ............................... 440
Yale University ..................... .................... 426


Chemical Engineering Education











form that describes specific situations with no direct answers
or outcomes.
The additional reading assignment consisted mainly of HBS
Notes, which provided a conceptual framework for the stu-
dents to analyze the cases with some knowledge of basic con-
cepts on business practices, interpersonal behavior, and hu-
man values. The students were all expected to read two books:
Gcurin,g to Yes[2[ and The Seven Habits of Highly Effective
People.[3]
The classes were designed to be highly interactive, with
the bulk of the time spent discussing the HBS Cases and Notes.
In addition, there were lectures on
Styles of ,.. -,iiin,., i .,e and ii. ,# .. .
Individual competencies


TABLE 2
HBS Cases


Title
Kevin Simpson
Elizabeth Fisher
Lisa Benton
Amelia Rodgers
Anne Livingston
Tech Transfer at...
T l. . .... I \ l . h. 11
Conflict in a diverse...
David Fletcher
MOD IV Product...
PPG-Developing...
John Smithers at Sigtek
Jenssen Shoes
Coming Glass Works


Topic
Interviewing and selecting your employer
Dual career decisions
Conflicts in your first assignment
First group-leader assignment
Changing jobs and new leadership role
Conflict between development and production
Leader of middle-level managers
Harassment and social conflict
Hiring your ideal business team
Effective teamwork
Risks and rewards of empowerment
Leading a quality process initiative
Managing a diversity conflict
Leadership during a business downturn


Conflict management
Teams and team performance
Strategic pl, .iii,;i,.
D. .. I. 7i';i.' a personal career plan
Six outside speakers led discussions on various aspects of
their business careers. These included
I,, i .-1/;.* family and business life
How to improve leadership skills
Conflict management and ;. *. *i;, ,i. 1,
WT1.lin ;, with (.. ,.,l1li;:' companies
All. ,,. hr. business school
R i. ; i, i n.,. .*i:, ,%n ,i ii. n,, I values

A detailed outline of the course is presented in Table 3 (next
page). The two 75-minute class periods each week allowed
adequate time for discussion of the Case and the Notes, as
well as for the lectures given by the Halsey Professor or by
invited speakers.

LEARNING THROUGH THE HBS CASES

The "Case Method" is based on real-life situations that rep-
resent the kind of challenges that engineers and managers
are likely to face during their work life. The cases helped
students sharpen their analytical skills, their ability to com-
municate clearly and forcefully, and most importantly, helped
them to develop their problem-solving abilities. Table 2 indi-
cates the topic being discussed in each case.
The students were assigned the HBS Case a week in ad-
vance. They were required to write a 3-to-4-page summary
of their assessment of the situation and their proposed
solutionss. They were also asked to document the key learn-
ings they had derived from the case. It was gratifying to ob-
serve their increasing sophistication in analysis and problem
solving during the course of the semester.
There were a number of interesting observations that re-
sulted from discussion of the HBS Cases. The students paid a
lot of attention to the interpersonal style of the protagonists
and were quite sensitive to antisocial behavior. They were, to
my surprise, expecting to experience such behavior in the
workplace. This applied even to harassment situations. An-
other class-wide attitude was to view most conflicts as rooted
in poor communication, and it took a lot of discussion for
them to see poor communication simply as the external mani-
festation of a more profound conflict.

LEARNING KEY CONCEPTS
THROUGH THE HBS NOTES
The course provides an introduction to a number of critical
competencies engineers need in order to succeed in organi-
zations. These were provided mainly through reading and
discussion of HBS Notes. The Notes were also given to the
students a week in advance of the class discussion. There


TABLE 1
Halsey Professors
at the University of Virginia

Year Name Company/Position
1995 N.H. Prater Mobay/CEO
1996 J.M. Trice, Jr. Monsanto/Director-HR
1997 R.A. Moore, Jr. International Paper/VP
1998 D.L. Ashcraft Temple-Island/VP
1999 J.D. Stein BASF/CEO
2000 V.A. Russo Scott Paper/VP
2001 R.L. Espino Exxon/R&D Manager
2002 A.R. Hirsig ARCO Chemical/CEO


Fall 2002











trials science. The question is: How can the new areas
be included in the curriculum without disregarding the
conventional ones? In our opinion, the only answer is
that teaching the fundamentals is even more important,
but the examples given to the students should change.J341
In Figure 3, our approach is shown schematically. We
explain the whole picture to the students by showing
them the progression from molecular precursors to the
whole process, which actually covers many orders of
magnitude in both geometrical dimensions and time
scale. In other words, we pave the way from feed mate-
rials to end-product properties-this is the horizontal line.
In the vertical, depth is gained by explaining certain as-
pects in a detailed way. By reflecting the first three lev-
els of Figure 1, we stress particulate interfaces (funda-
mental level) since we believe that this aspect has not
been sufficiently covered in the past. Moreover, with the
advent of 1u.11i',ii' -h 'i;,, interfacial aspects have be-
come increasingly important. The second level, compris-
ing unit operations, is handled in a more-or-less tradi-
tional way, although new aspects such as CFD model-
ing are included. On the process level, disperse systems
have to be treated mathematically by means of population
balance equations, which have so far not been covered in
traditional particle technology curricula.

Courses

The courses are organized into three levels. The first
and most fundamental level comprises a two-semester
course in "Fundamentals of Particle Tecl i "li .i_" (see
Figure 4). In this course, the important foundations (rang-
ing from statistics, motion of particles in fluids, fracture
mechanics, to dimensional analysis) and their implica-
tion in mechanical process engineering are covered. In
addition, new elements such as population balances
(which are increasingly used in industry) and interfacial
phenomena are introduced. The latter comprise the fun-
damentals of interactions between molecules and par-
ticles, characterization of particulate interfaces and as-
pects of nanoparticle tclniii'.l -, (e.g., coagulation and
stabilization of colloidal suspensions).
The second level stresses unit operations. Here, we
concentrate on "Particle Separation" (see Figure 5). This
course is principally organized in the traditional way,
focusing on separation of particles from gases as well as
solid-liquid separation. Different unit operations in gas-
solid separation are introduced systematically by focus-
ing on common principles, i.e., on transport mechanisms
of particles to the collecting surfaces of the respective
separators. In this way, various unit operations are treated
very efficiently, which allows for introduction of new,
modem methods such as CFD and its use for optimizing
such apparatuses. We also offer a complementary course


Figure 4. Fundamentals of Particle Technology course
(particle characterization included in separate course).


Gas solid separation
(dilute systems)
Fundamentals:
CFD and particle tracking
classification
> dust separ .:.,- "'


'r...- V.


Figure 5. Particle Separation course.


Figure 6. Product Engineering course.


Chemical Engineering Education


Solid liquid separation
(dense systems)
Suspension rheology


Particle production Structure formain lor A itppliialion

process design property function
top down particle size and shape color
- grinding
-classification crystallinity taste
bottom up particle surface strength
- gas phase synthesis
-crystallization particulate systems
agglomeratess, thin films...)
consolidation


Partc:le characlerization *
-, Population balance modeling y, r "











EI n= laboratory


DETERMINING THE


FLOW CHARACTERISTICS OF A


POWER LAW LIQUID


JAMES R. HILLIER, DALE TING, LISA L. KOPPLIN,
University of Wisconsin Madison, WI 53706

Non-Newtonian liquids present unique problems with
respect to their flow behavior. These problems are
seldom addressed in undergraduate courses in chemi-
cal/mechanical engineering and are possibly covered only
through a .Iii 1.. experiment in one of the laboratory courses.
Tjahjadi and GuptaE'1 extended the work of Walawender and
Chenr2E and developed an experimental scheme that illustrates
how the apparent viscosity, rj, of a pseudoplastic liquid (di-
lute aqueous solution of Na-CMC) decreases with increasing
shear rate, j. They also suggested performing additional
experiments after adding some sodium chloride to the
CMC solution, to observe a dramatic decrease in rj and
relate it to the contraction of the polyelectrolyte molecules
in an ionic medium.
Although the results had considerable educational value,
the equations used were quite complex and cumbersome
to use, with the result that a student obtained little insight
into the method of analysis-this limits the value of their
experiment.
In the present work (developed as part of the "informal"
experiments13] at the Summer 2000-I laboratory at the Uni-
versity of Wisconsin-Madison), a much simpler experiment
has been developed that uses the easily understood macro-
scopic energy balance (the engineering Bernoulli equationE41)
to obtain experimental results.
A 0.07% (by weight) solution of a sodium salt of carboxy-
methyl cellulose (Na-CMC; weight average molecular weight
= 7 x 105; DS = 0.9; Aldrich Chemicals, Milwaukee, WI) in
deionized water was used for our study. CMC was selected
because of its pseudoplastic nature over a range (1 105 s-1)
of shear rates. In addition, CMC is an inexpensive, nontoxic,
biodegradable, water-soluble polymer, commonly used in
mining applications, food thickeners, adhesives, and textiles.


MARGARET KOCH, SANTOSH K. GUPTA


The results obtained could also be compared to existing val-
ues in the literatureE11 for consistency.

EXPERIMENTAL SET-UP
The experimental set-up is similar to that used for studying
the flow characteristics of Newtonian liquids, as described
by Crosby.15s Flush-mounted glass capillaries (in one case, a
copper tube) of different diameters and lengths are used with
a drain tank,E" as shown in Figure 1. Two different kinds of
experimental units were made so as to vary the shear rate
over a reasonable range. The detailed dimensions are pro-
vided in Table 1.

PROCEDURE
The CMC solution to be used in all the experimental runs
was prepared using laboratory-grade carboxymethyl cellu-
lose powder. A solution of 0.07 wt% CMC in deionized wa-

James R. Hillier received his BS degrees from the University of Wiscon-
sin-Madison in Chemical Engineering (2000), Biochemistry (2000), and
Molecular Biology (2000). He is currently the Plant Engineer for Equistar
Chemicals in Fairport Harbor, OH, while working on a master's degree in
polymer engineering and a diploma in disaster management.
Dale Ting received his BS in Chemical Engineering from the University of
Wisconsin-Madison in 2000. He is currently working in process develop-
ment at The Procter and Gamble Co. in Cincinnati, OH.
Lisa Kopplin received a BS in Chemical Engineering from the University
of Wisconsin-Madison (2000). She is currently serving as a Project Engi-
neer for General Mills, Inc., in their West Chicago manufacturing facility.
Margaret R. Koch graduated from the University of Wisconsin-Madison
with a BS in Chemical Engineering in 2000. She is currently working in
Process Development at S.C. Johnson & Son, Racine, WI.
Santosh K. Gupta received his BTech (1968) from I.I. T, Kanpur, and his
PhD (1972) from the Universityof Pennsylvania-Philadelphia. He has been
on the faculty of I.. T, Kanpur, since 1973, and has also been a Visiting
Professor at the University of Notre Dame, National University of
Singapore, and the University of Wisconsin-Madison. His research inter-
ests include polymerization engineering and optimization using Al tech-
niques.
Copyright ChE Division of ASEE 2002


Chemical Engineering Education










using a carbon sheet, and the members were asked to sign each
data sheet. The duplicate copy was submitted to the instructor
at the end of each session, and nonsubmission would result in a
grade of zero for that session. The instructor has never had to
give a zero over the past two years for this reason.
After the data analysis for the first session, the groups were
required to meet the instructor to discuss their plans for the


second session. This meeting was not to guide
the students on what they could do in the sec-
ond session, but for the instructor to listen and
comment on the possibility of doing the experi-
ments. This meeting was normally scheduled a
few days before the second session, primarily
to address any special requirements for the ex-
periment that needed to be communicated to
the lab superintendent. Also, this meeting
helped the instructor ensure that the second-
session experiments were of proper scope (nei-
ther too large nor too small) and reasonably well
thought out, especially if the actual data
matched the expected data in the first session.
In addition, it was communicated to the stu-
dents at the beginning of the semester that no
complete dismantling of the set-ups would be
allowed, except in rare cases. This encouraged


SAMPLES FROM STUDENT EXERCISES
Samples from the Dual-Step Laboratory Exercises

Agreement Between Actual and Expected Data An ex-
periment for the lab involved studying the relationship be-
tween Power number and Reynolds number in an agitated
system. One of the groups found good agreement between


... the overall
aim is...
to improve
the quality of
analysis and
inquiry,
and to kindle
the spirit of
discovery in
students.


the students to think of "non-invasive" means for testing their
theories. Also, this precaution was necessary because some
piping networks in our lab had packing to prevent leaks that
would be difficult for an inexperienced person to reassemble.
The lab reports for the dual-step exercises were due before
the start of the next experiment; the instructor graded them
and offered constructive criticism and feedback within a week
of submission. Students appreciated the timely feedback.
The grading of the recommendations report was time con-
suming (three to four consecutive, full days). As long as
grades are important, some students may cheat to get the best
l.idc,' -1 therefore, a significant amount of time was spent
establishing the originality of submitted reports. This was
achieved through one-on-one interviews with students who
had submitted "doubtful" reports. During an interview, it was
easy to ascertain whether cheating had taken place by ask-
ing relevant questions, most of which were on the experi-
ment submitted.
All experiments were run on existing equipment; therefore,
this dual-step exercise does not require additional funds for
equipment. It can be run anywhere, even in the face of fund
crunches. It also provides a greater probability for disagree-
ment between actual and expected data, and thus helps stu-
dents develop lateral-thinking abilities while forming hypoth-
eses for the disagreement. Therefore, the dual-step labora-
tory exercise provides a way to turn a seeming disadvantage
in running an existing laboratory course into an advantage of
improving thought in students.

294


actual and expected data and therefore had to
think of additional experiments to do on the
same setup. They decided to compare the rela-
tionship between Power and Reynolds numbers
for an aqueous system with and without a sur-
factant. They found that the Power number for
the corresponding Reynolds number was lower
for the system with surfactant than for plain
water. Therefore, they concluded that the power
requirements for an aqueous system with sur-
factant are lower than that for plain water. They
also provided qualitative explanations for the
observed results from a molecular viewpoint.
Another experiment involved studying two-
phase flow characteristics in a vertical transpar-
ent tube such as the relationships between slug
length and slug velocity and between pressure
drop and void fraction, etc. The group that ob-


stained results as expected decided to study the relationship
between the radius of curvature of the slug's leading edge
and its length. They developed a theory based on geometri-
cal considerations for the variation of the leading-edge cur-
vature with slug length; they also showed correspondence
between the theoretically expected results and measured data.
D;i.,0.... ,,. mt Between Actual and Expected Data An-
other experiment involved a piping network with various types
of pipes, fittings, and valves. The objectives for the first ses-
sion included determination of the frictional losses across the
pipe fittings and valves. The experiment required recording
readings from manometers attached to the pressure taps
across relevant fittings or valves and determining the water
flow rate using the pressure difference measured across
the orifice meter.
The first group that worked on the experiment found that
the friction loss constants obtained for the various fittings on
the network were higher by almost an order of magnitude
than literature values. Therefore, the group first postulated
that scale formation led to higher loss constants. To test the
postulate, they arranged for the network to be cleaned thor-
oughly and repeated the experiment in the second session.
This did not yield significantly different loss constants,
thereby partly disproving the postulate that the scale forma-
tion alone resulted in the discrepancy. Students in one of the
other groups that worked on the experiment postulated that
the water-flow rate measurements using the calibration curve
for the orifice meter may not have been correct; they noticed


Chemical Engineering Education















expected. The following ensued:
a) If the experimental results matched the expected results,
students were expected to think of additional experi-
ments, preferably new ones, that could be done with the
same (or slightly modified) setup. But the additional
experiments need to be done within the time frame of
the second lab session. We believe that working with
these practical constraints would help students acquire
"street smarts," which are useful in handling real-world
problems.
b) If the experimental results did not match the expected
results, students were required to form hypotheses based
on the results and design ways to experimentally (with
certain calculations) prove or disprove their various
hypotheses in the second lab session. The emphasis was
on the technical/scientific rigor in proofs. The students
were also warned that their theories could be proved
false by their experiments and that it was acceptable to
admit they did not understand the reasons for disagree-
ment within the time available to them and therefore,
additional study would be required.

After the second lab session, each student group was ex-
pected to submit a single report in the regular format, i.e., (a)
Aim and Objectives, (b) Methodology, (c) Results and Dis-
cussion (which was required to be significant), (d) Conclu-
sions, and (e) the original data sheets. The reports were graded
on the following bases:
If the actual results matched the expected results:
Ability to follow procedures 10%
Data analysis (1st session) 15%
Discussion (1st session) 15%
Creativity/originality aspects (2nd session) 20%
Data analysis (2nd session) 15%
Discussion (2nd session) 15%
Presentation (mainly communication) 10%

Reports that addressed novel aspects to study in their sec-
ond session were rewarded handsomely in grading the cre-
ativity/originality criterion (see the student examples pre-
sented later).
If the actual results did not match the expected results:
Ability to follow procedures 10%
Data analysis (1st session) 15%
Discussion 15%
Clarity in thought and situation/problem
analysis (2nd session) 20%
Rigor (2nd session) 15%
Discussion (2nd session) 15%
Presentation (mainly communication) 10%

Reports that were well developed on both the possible rea-
sons for the disagreement between actual and expected data
and the experiments to prove or disprove them were given
high marks for the clarity-in-thought criterion. The difficulty
level in problem analysis was also recognized in that crite-
rion-reports that fully analyzed a difficult situation received
higher marks than those that, as a matter of chance, analyzed


a simple, easy-to-identify situation. Also, reports that un-
equivocally proved or disproved their points received high
marks for the rigor criterion. Other criteria, such as data analy-
sis, discussion, and presentation, carry their usual weight.
The Recommendations Report
Over the duration of the course, each student was expected
to think about an experiment or a set of experiments that could
be done in the fluid mechanics lab. Students were encour-
aged to be as creative as possible. Near the end of the course
(a week before the last day of classes), each student was ex-
pected to submit a detailed report on this experiment (or set
of experiments) and the equipment and instruments needed.
The reports were evaluated on the f ,11-. in: bases:
Creativity/originality aspects 30%
Clarity in thought 20%
Detail 30%
Doability 10%
Presentation (mainly communication) 10%

The dual-step exercises evaluated through the reports carried
a 70% weight, and the recommendation report carried a 30%
weight toward the final grade.

IMPLEMENTATION OF DETAILS /RATIONALE
In the beginning of the semester before the experiments
began, the instructor met the class and discussed the exer-
cises and recommended strategies. In addition to experimen-
tal details for the first session, the laboratory manual carried
information on safety procedures for the lab, error analysis,
technical writing, and the unacceptability of academic dis-
honesty, all of which were seriously discussed in the initial
meeting. The instructor also emphasized the need for safety
procedures whenever he observed lapses during the lab ses-
sions. Student groups were asked to select their own leaders
who would assign duties for the group members and be gener-
ally responsible for the group's activities. This ensured that an
avenue for the development of teamwork and leadership skills
existed. Also, on many occasions, the instructor communicated
to the groups through their leaders.
Before the start of the first session, the groups were ad-
vised to familiarize themselves with the details for each ex-
periment using the lab manual and the textbook. The first-
session experiments were designed as shorter versions of the
experiments given in the usual lab course, and students were
encouraged to spend the additional time becoming comfort-
able with the setup and the various equipment used. For ex-
ample, the instructor encouraged the students to raise ques-
tions regarding the equipment or the reasoning behind the
various experimental steps, which the students normally took
for granted. The students took the first session seriously be-
cause they knew they had to consider the setup, the experi-
mental methods, and the underlying theory in order to have
an interesting second session. During the experiment (both
sessions), groups were advised to record the data in duplicate


Fall 2002











curriculum


ASPECTS OF

ENGINEERING PRACTICE

Examining Value and Behaviors in Organizations



RAMON L. ESPINO
University of Virginia Charlottesville, VA 22904-4741


Since 1995, the School of Engineering and Applied Sci-
ences at the University of Virginia has offered an elec-
tive course that examines human values and practices
in engineering organizations. The course is available to all
fourth-year engineering students and is taken by 40 to 50 stu-
dents each year. It is taught by the Brenton S. Halsey Visiting
Professor of Chemical Engineering, who is selected annu-
ally from individuals with high-level experience in industry.
Support for the Chair comes from a generous endowment by
The James River Corporation in honor of its founding CEO,
Brenton Halsey. Previous Halsey Professors and their affilia-
tions are given in Table 1.
The details of the course content and execution are left to
the discretion of the Halsey Professor, but its core objective
is to provide engineering students with significant insight into
the professional and nontechnical aspects of engineering prac-
tice. The intention is to better prepare the University of Vir-
ginia engineering graduates to succeed in the business and
technical world that they will be entering after graduation.
This paper describes the course materials, assignments, and
assessments for the spring semester of 2001, which is repre-
sentative of recent offerings.

DEVELOPING THE COURSE
The teaching experiences of previous Halsey Professors
contributed significantly to the current course content. Al-
though the objectives have remained the same, there is now
more emphasis on the students reading and analyzing infor-
mation prior to class. This information is generally in the form
of Harvard Business School (HBS) Cases and Notes. The
result of this approach is more in-depth discussion in class.
I built the course syllabus around the HBS Cases and Notes.
Harvard Business School Publishing"1 offers an Index of
Cases and Notes available for purchase. I suggest one HBS


The objective of the course was to
increase student awareness of the non-
technical competencies they should pos-
sess in order to succeed in
the work world.

Case and two HBS Notes per week, requiring about nine hours
of homework (reading and writing a summary) per week.
Lectures to reinforce and elaborate upon the major themes of
the course are strongly recommended. We have found that
many of these should be given by outside speakers from busi-
ness and government in order to emphasize the broad appli-
cability of the concepts being discussed. Finally, additional
reading material can be used to round out the course.

COURSE STRATEGY
AND TEACHING METHOD
I developed the syllabus to follow the chronological order
of the professional and business career of an engineering
graduate. Selecting the first employer is the starting point,
followed by early career assignments and culminating with
the complex organizational, personal, and business challenges
of a senior manager. HBS Cases provide a well-written plat-


Copyright ChE Division of ASEE 2002


Chemical Engineering Education


Ramon L. Espino received his BS degree from
Louisiana State University in 1964 and his Doc-
tor of Science degree from the Massachusetts
Institute of Technology in 1968, both in chemi-
cal engineering. Hejoined the facultyat the Uni-
versity of Virginia in 1999 after twenty-six years
with Exxon Mobil. His research interests are in
fuel cell technology and methane conversion to
clean fuels and chemicals.











[ Graduate Education )


SIMILARITY BETWEEN TWO-MODE MODELS
OF HOMOGENEOUS REACTORS AND
TWO-PHASE MODELS OF
CATALYTIC REACTORS

A striking structural similarity between the two-mode mod-
els for homogeneous reactors and two-phase models for het-
erogeneous catalytic reactors exists. This could be seen more
clearly when Eqs. (24) and (25) are rewritten as

dC C (C) R((C))
(U) dx t -ix

with Cm=Cmin @x=0 (34)

The two-phase model for a heterogeneous wall-catalyzed re-
action in a tubular reactor is given by


(U1) dCm Cm Cs R(Cs)
dx tTP
with Cm = Cm,in @ x = 0 (35)

It may be noticed that the spatially averaged concentration
(C) of the TMM (in Eq. 34) is replaced by the surface (wall)
concentration Cs in the two-phase model (Eq. 35), while the
local mixing time tm. of the TMM is replaced in the two-
phase model by a characteristic mass transfer time between
the two phases typ, which is given by

tTP = PTptD= 61 (36)
Sh,,T Dm

where tD is the transverse diffusion time scale and Sh T(=l/
PTP) is the two-phase dimensionlesss mass) transfer coeffi-
cient (asymptotic Sherwood number) that depends on the
velocity profile and tube geometry. For the case of fully de-
veloped laminar flow in a circular tube, Sh T = 48/11 = 4.36,
while its analogue in the TMM (comparing Eqs. 26 and 36)
is Sh E = 1/P1 = 48 (the dimensionless mass exchange coef-
ficient in the TMMs).
As illustrated in the next section, just as the two-phase
models can capture the mass-transfer limited asymptote in
heterogeneous reactions (which is missed by the pseudo-
homogeneous models), so can the two-mode models capture
the mixing-limited asymptote in homogeneous reactions,
which is rendered inaccessible by the traditional one-mode
models. Thus, there exists the following one-to-one corre-
spondence between two-phase models of catalytic reactors
and two-mode models of homogeneous reactors: two-phase
transfer time (tTP) -> local mixing time (tm), two-phase trans-
fer coefficient (Sh, ) -> two-mode exchange coefficient
(ShE), surface (wall) concentration Cs -> spatially averaged
concentration (C), and mass-transfer limited reaction mix-
ing-limited reaction.

Fall 2002


APPLICATIONS OF TWO-MODE MODELS

Bimolecular Second-Order Reactions

Second-order reactions provide the simplest example of
nonlinear kinetics, where micromixing limitations have sig-
nificant effects on reactant conversion. We use the TMM to
determine micromixing effects on conversion of a typical
bimolecular second-order reaction of the type

A+B- P with rate= kCACB
occurring in a CSTR, where k is the reaction rate constant.
For the case of stoichiometric feeding (i.e., CA,n=CB,n=C n),
the conversion (X) obtained by using the TMM is given by

1 4 Da(1+)+ + 1 (37)
X= (37)
1+1 2 Da(1+ 1)2

where 1 (=tmj Z) is the dimensionless local mixing time,
and Da(=kCn Tc) is the DamkOhler number. Figure 1 shows
the variation of conversion X with Da for different values of
the dimensionless local mixing time 1. The case of 11 = 0
corresponds to the ideal CSTR. For 1 > 0 and Da --> the
local concentrations (Ci)(i=A,B) approach zero, while the
mixing-cup concentrations approach a mixing limited asymp-
tote, given by


(CA)=(CB)= 0 CAm=CBm
1 +1l


x=
1+1-


As mentioned in the previous section, this rtii, r1 ;--,l;, ii. .


0.01 0.1 1 10 100
Da
Figure 1. Variation of exit conversion with Damkoihler
number, Da, for a second order reaction in a CSTR, for
different values of dimensionless local mixing time, 1r.


o00


80
so


S60


g 40










your reference. Further, the following is a brief summary of
the survey paper. It's appearance would be a fitting finale to
the effort that started with the initial publication of our letter
in your journal.

Summary
A recent survey of the current use of Inherently Safer Design
(ISD) concepts attracted responses from 63 people in 11 coun-
tries. These included industrialists, consultants, regulators,
and academics. The salient results of the survey are noted
below in bullet form to focus attention, followed by recom-
mendations to expedite the adoption and spread of ISD.
Almost everyone responding knows of ISD. Their
knowledge stems from specialized lectures, short
courses, books, conferences, and training videos.
ISD has been practiced by some for decades, whereas
others started only recently.
ISD is used in almost all stages of chemical process
development, design, and operation.
ISD is used during the manufacture of a whole range of
products.
Almost all hazards have been targeted, both on-shore
and off-shore.
The above attests to the universality of ISD applica-
tions.
There is a favorable impact on balance sheets.
It is important to use "Management of Change" when
implementing ISD to avoid introducing any new
hazards.
There is very little additional cost if implemented early.
Payback is fast.
Some applications/practitioners have won awards.
ISD is included in lectures at several institutions. More
will do so now.
Many are not familiar with the current Inherent Safety
(IS) indices. Those familiar with them have used them
sparingly. A simple, realistic index is needed that also
shows economic benefits. Detailed examples of use at
different stages of process development are necessary.
ISD concepts can influence R&D in various areas of
chemical engineering and chemistry.
ISD should encompass inherent safety, health, and
environment (ISHE).
ISD concepts, suitably modified, can be used for other
branches of engineering such as mining, construction,
transport, etc.
Current regulations do not force the use of ISD.

Recommendations
The sad truth is that ISD is applied when an ISD enthusiast is
on the team and not otherwise. Implementation of the recom-


mendations below might encourage the uptake of ISD.
Every chemist and chemical engineer should be trained
in ISD. Academics and professional bodies should lead
in this.
Other scientists and engineers should be given intro-
ductory lectures in ISD with examples from different
industries.
IChemE should make ISD a part of its approved degree
syllabus. Subsequently, it should persuade other
engineering and science accrediting societies to do
likewise.
There is a need to teach IS to management and finan-
cial people also since their role is crucial in encourag-
ing applications of ISD.
Dedicated funding by government and industry for
research and teaching in ISD will encourage many
academics to take it up.
Incentives by the government to cost share demonstra-
tion plants and provide tax breaks for ISD.
Expand ISD to encompass ISHE since the environment
and occupational health are day-to-day concerns. It
may eventually be extended to ISHEQ (Q for Quality)
since improvements in SHE will decisively impact
quality of product.
Companies should provide examples of ISD use in
various situations and the economic benefits reaped in
order to convince other industries, regulators, govern-
ment, the media, the public, academics, R&D funding
agencies, etc.
Involve the mainstream print and audiovisual media to
favorably impact public opinion.
Amend regulations to enforce the use of ISD.
Insistence by international agencies to include ISD in
projects that they fund in the same way that the World
Bank now insists on environmental impact assessment
studies in projects funded by it.
Some expected results
Tall columns of chemical plants will be reduced to one-
or two-story heights. This will improve the image of the
chemical industry.
Increased investment in process industry.
Less restrictive regulations.
Greater enrolments in UG and PG courses.
Significantly enhanced funding for R&D.
Adoption of ISD by other engineering disciplines,
especially the more accident-prone ones such as
construction, mining, transportation, etc.
J.P. Gupta
David W. Edwards
Loughborough University


Fall 2002















A SIMULATED CARBON CYCLE
SI


r4!--
toat a'
retorbst ao A
reforelsatiosr
raze gegCly
( soils & deLritus (PgC)
114al ;155


fossil fuel
supply (PgC)


25-:
-

**


manual


atmosphere (ppmv)
l354 562
1 '990 simulation year


atmospheric C02 (ppmv)
75
700
2x 1850 level
(576 ppmv) so60 ____ _
with IS92a soo.
this simulation
400:
1850 level 300
(288 ppmv) 25S
1990 2100


I surce er(PgC)
|i i -;91B


to amraspnere
(rrac on)


z100
simulation
year ;


emissions (PgC/y)
with IS92a 2-
scenano 20
total
fossil fuels s-
deforestation
with manually -
adjusted -
scenario 1990 2100







dw can waer (P)
I -"fc


( BGequa9traL.orl IngS
*r o t .A


Figure 5.

The user's panel
for LabVIEW
simulations.
The elements
with black
arrows are for
user inputs,
adjustable as the
simulation
proceeds.

The number to
the left in each
reservoir box is
the initial value
given in Table 2;
that on the right,
the current value.

The two surface
water boxes of
Figure 1 are
combined into
one for these
simulations.


Additional Work

Using Mathcad and LabVIEW simulations, students obvi-
ously can be involved in examining all sorts of questions,
model variations, and parameter effects. Here is a partial list
of exercises that I have used, some of which require consult-
ing outside references.

- Extend simulations beyond 2100 to address a number of
questions raised about the ultimate steady state. (Actu-
ally, I ask the students to use the steady-state forms of
the equations to address some of these.) What would that
ultimate state be if emissions were halted immediately?




950 --- --
o reported data to 2000 ,93
850 ------for lS92e scenario from 1990 i-
E -- IS92a
750 IS92c
S/ ,702
s - Kyoto
o 650

550
499
S450 -- 472
450

S350 -

250
1850 1900 1950 2000 2050 2100
year

Figure 6. Atmospheric carbon dioxide levels; reported
historical data and model predictions.


What would it be if all carbon in the fossil fuel reservoir
were eventually used? How long will it take to approach
a steady state if carbon emissions to the atmosphere are
halted at a certain time?

- Carry out simulations to clarify, if necessary, the roles
and effects of kd, kr, and M8-or to test entirely different
forms of F15, the rate of photosynthetic uptake of car-
bon.

- What is a realistic mathematical description for the dis-
turbance, Fr, if reforestation begins with new trees that
require a number of years for maturation?

- Examine the predicted changes in the strengths of the
terrestrial and oceanic sinks (or sources?) of atmospheric
carbon over the 21"s century.

- It is sometimes suggested that the most realistic goal that
can be achieved regarding the control of atmospheric CO2
is to "stabilize" it at twice the pre-industrial level by the
year 2100. Try to achieve that goal by manipulating the
emissions (or by fabricating an emissions scenario) in
such a way that atmospheric CO2 lines out at about 1224
PgC (572 ppmv) by the year 2100. (This is an ideal exer-
cise-even an entertaining one-for the LabVIEW simu-
lator. In fact, the data shown on the digital displays and
charts in Figure 5 are the end states of this exercise.)
Notice that the difference between the emissions level
so achieved in 2100 and that dictated by the IS92a sce-

Continued on page 309.


Fall 2002


M*"ic- ..---
5086" 1











closely related to phase equilibrium have a higher proportion
of graphs than the text as a whole, as indicated by the num-
bers in parentheses in Table 4.
Furthermore, many students have a visual learning style.
These students may struggle with equations and textual in-
formation, especially in an abstract context, and it is crucial
that they see data presented graphically and also learn how to
prepare data in a format that is most comprehensible to them.
Hence, students need to make the connection between calcu-
lations and equations discussed in class and graphical pre-
sentation of phase equilibrium data. To assure they are ca-
pable of both understanding and generating graphical data, I
assign a significant number of computer problems requiring
this, as explained in further detail later in this article. Com-
puter spreadsheets have been previously ,i i -.c -.lcd 1 for use
in solving phase equilibrium and equation-of-state calcula-
tions, and they are well suited both for the calcula-
tions and for subsequent graphical presentation. One
recent text191 includes a number of example spread-
sheets that may be used for applications similar to those 2
described in this article, although I prefer to have stu-


dents write their own spreadsheets.

DETAILS OF
PHASE DIAGRAM
COMPUTER ASSIGNMENT
As an illustration of such assignments, consider the
construction of a binary Pxy diagram for an ideal so-
lution at some constant temperature. Figure 1 is an
example generated by repetitive dew point pressure
and bubble point pressure calculations. Taking liquid
mole fraction x1 as the independent variable, and as-
suming component vapor pressures Plat and Psat are
known, Eqs. (1-3) allow calculation of all dependent
variables in the problem. To generate the diagram, al-
low x1 to vary over the range 0.0 to 1.0. These calcu-
lations are easily done using computer spreadsheet
software.


X2 = 1 X1

P = xPsat + x2P2at

xYPisat
Y1 P
P


Figure 2 shows the general organization of this spread-
sheet. The upper rows contain headings and constants
such as the vapor pressures. The middle rows are used
for calculations. The leftmost column is initially filled
with values between 0 and 1 at intervals of 0.01, or a
suitable small increment. (This should be done using
spreadsheet commands or formulas; occasionally, a
student will attempt to enter the numbers manually
and become frustrated that using the computer appar-


ently makes solving the problem too time-consuming.) Fill
the remaining three columns in the middle rows of the spread-
sheet with formulas given by Eqs. (1-3). If these formulas
are entered correctly in the first of the middle rows, a single
copy/paste command generates the entire table through the
remaining middle rows.
There may be one complication in producing a graph from
these results. In a conventional Pxy diagram, pressure is taken
as the vertical coordinate twice. With liquid composition as
the horizontal coordinate, a bubble point curve is produced,
then with vapor composition as the horizontal coordinate, a
dew point curve is produced. To do this on the spreadsheet, a
single y-coordinate must be paired with two different x-co-
ordinates. At one time, few spreadsheet packages included
this capability, but many recent versions (including Microsoft
Excel) now allow it. If using an older package without this


goo



900




600
0 01 02 03 04 05 06 07 08 09
xl, yl


Figure 1. Pxy diagram prepared using spreadsheet.



and
Constants
(xi values)
0.00
0.01
0.02
x2 values P values yl values (Blank)

0.99
1.00



Copy of (Blank) Copy of
yl values P values





Figure 2. General structure of spreadsheet for Pxy diagram.


Chemical Engineering Education


P x y Dagram at T = 100 deg C
Methyl sopropyl ketone (1) Dethyl ketone(2)





PAGE 1

Fall 2002 249 Chemical Engineering Education Volume 36 Number 4Fall 2002 CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the Chemical Engineering Division, American Society for Engineering Education, and is edited at the University of Florida. Correspondence regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical Engineering Department, University of Florida, Gainesville, FL 32611-6005. Copyright 2002 by the Chemical Engineering Division, American Society for Engineering Education. The statements and opinions expressed in this periodical are those of the writers and not necessarily those of the ChE Division, ASEE, which body assumes no responsibility for them. Defective copies replaced if notified within 120 days of publication. Write for information on subscription costs and for back copy costs and availability. POSTMASTER: Send address changes to Chemical Engineering Education, Chemical Engineering Department., University of Florida, Gainesville, FL 32611-6005. Periodicals Postage Paid at Gainesville, Florida and additional post offices. EDITORIAL AND BUSINESS ADDRESS:Chemical Engineering Education Department of Chemical Engineering University of Florida Gainesville, FL 32611PHONE and FAX : 352-392-0861 e-mail: cee@che.ufl.eduEDITOR Tim Anderson ASSOCIATE EDITOR Phillip C. Wankat MANAGING EDITOR Carole Yocum PROBLEM EDITOR James O. Wilkes, U. Michigan LEARNING IN INDUSTRY EDITOR William J. Koros, Georgia Institute of Technology CHAIRMAN E. Dendy Sloan, Jr. Colorado School of Mines MEMBERS Pablo Debenedetti Princeton University Dianne Dorland Rowan University Thomas F. Edgar University of Texas at Austin Richard M. Felder North Carolina State University Bruce A. Finlayson University of Washington H. Scott Fogler University of Michigan William J. Koros Georgia Institute of Technology David F. Ollis North Carolina State University Ronald W. Rousseau Georgia Institute of Technology Stanley I. Sandler University of Delaware Richard C. Seagrave Iowa State University C. Stewart Slater Rowan University James E. Stice University of Texas at Austin Donald R. Woods McMaster University GRADUATE EDUCATION 250 A Novel Approach for Describing Micromixing Effects in Homogeneous Reactors, V emuri Balakotaiah, Saikat Chakraborty 258 Introducing Moleculr Biology to Environmental Engineers Through Development of a New Course, Daniel B. Oerther CLASSROOM 264 A New Approach to Teaching Turbulent Thermal Convection, Stuart W. Churchill 278 Gas Station Pricing Game: A Lesson in Engineering Economics and Business Strategies, Aaron Sin, Alfred M. Center 284 Making Phase Equilibrium More User-Friendly, Michael J. Misovich CURRICULUM 272 Novel Concepts for Teaching Particle Technology, Wo lfgang Peukert, Hans-Joachim Schmid 296 The Earth's Carbon Cycle: Chemical Engineering Course Material, Roger A. Schmitz 316 Aspects of Engineering Practice: Examining Value and Behaviors in Organizations, Ramon L. Espino RANDOM THOUGHTS 282 Speaking of EducationIII, Richard M. Felder LABORATORY 288 Chem-E-Car Downunder, Martin Rhodes 292 On Improving "Thought with Hands," G.K. Sureshkumar, K.C. Khilar 304 Determining the Flow Characteristics of a Power Law Liquid, James R. Hillier, Dale Ting, Lisa L. Kopplin, Margaret Koch, Santosh K. Gupta ASSESSMENT 310 Portfolio Assessment in Introductory ChE Courses, Surita R. Bhatia 257, 263, 270 Letter to the Editor 281 Announcements 320 Index for Graduate Education Advertisements PUBLICATIONS BOARD

PAGE 2

250 Chemical Engineering Education A Novel Approach for DescribingMICROMIXING EFFECTS IN HOMOGENEOUS REACTORSVEMURI BALAKOTAIAH, SAIKAT CHAKRABORTYUniversity of Houston Houston, TX 77204-4004Ve muri Balakotaiah is Professor of Chemical Engineering at the University of Houston. He received his BTech from the Indian Institute of T echnology (Madras) in 1978 and his PhD from the University of Houston in 1982, both in chemical engineering. His teaching and research interests are in the areas of chemical reaction engineering, multiphase flows, and applied mathematics. Saikat Chakraborty is a PhD candidate in the Department of Chemical Engineering at the University of Houston. He received his BTech from Jadavpur University in 1997 and his MS from the Indian Institute of Science (Bangalore) in 1999, both in chemical engineering. His research interests are in the areas of chemical reaction engineering and granular materials.Reacting flow systems are hierarchical in nature, i.e., they are characterized by multiple length (or time) scales. Scale separation exists in most reactors, however, and these disparate scales are typically characterized by three representative ones, namely, micro (molecular), meso (catalyst particle or tube diameter), and macro (reactor or process) scales. In most cases of practical interest, a strong nonlinear coupling exists bet ween reaction and transport at micro and meso scales, and the reactor performance at the macro scale. As a result, transport limitations at the smaller scales significantly influence the reactor and hence the process performance. Such effects could be quantified by numerically solving the convection-diffusion-reaction (CDR) equation from the macro down to the micro scale. But the solution of the CDR equation from the reactor (macro) scale down to the local diffusional (micro) scale, using computational fluid dynamics (CFD), is prohibitive in terms of numerical effort and impractical for the purpose of reactor control and optimization. Moreover, even with today's computational power, it is impractical to explore the different types of bifurcation features and spatio-temporal behaviors that exist in the multidimensional parameter space, using CFD codes. In such cases, low dimensional models are a natural alternative. Historically, chemical engineers have derived low dimensional models for reactors using a top-down approach, which is based on a priori assumptions on the length and time scales of convection, diffusion, and reaction. The classical ideal reactor (CSTR and PFR) models are examples of such lowdimensional models obtained on the basis of simplified (or oversimplified) assumptions. These assumptions are usually not justified since justification requires comparison of the solution obtained from the simplified models with that obtained from the CDR model. In order to account for experimental observations that could not be explained by these ideal reactor models, the latter have been modified by introducing the concepts of dispersion coefficients[1-5] and residence time distribution[3,6,7] to account for macroand micro-mixing effects. Several other reactive mixing models followed in the next forty years: the twoand three-environment model,[8.9] the coalescence-redispersion model,[10] interaction by exchange with mean model,[11] engulfment-deformation-diffusion model,[12] and CFD models using probability density functions (PDF) and direct numerical simulation (DNS). This article presents an alternative (bottom-up) approach and an elementary treatment of mixing effects on reactor performance. We will present a brief historical review of homogeneous reactor models before discussing this new approach.BRIEF HISTORY OF HOMOGENEOUS REACTOR MODELSThe most widely used homogeneous reactor models are the three classical ideal reactor models: the plug-flow reactor (PFR) model, the continuous stirred tank reactor (CSTR) model, and the batch reactor (BR) model. While the BR model and the PFR model (which are identical for constant density systems with time replaced by space time or dimensionless distance along the tube) have existed since the late eighteenth century. A conceptual leap came in the form of the CSTR model through the work of Bodenstein and Wohlgast in 1908.[13] Unlike the PFR model, which assumes no gradients in the radial direction and no mixing in the axial direction, Copyright ChE Division of ASEE 2002 Graduate Education

PAGE 3

Fall 2002 251 the CSTR model assumes complete mixing at all scales. For constant density systems, the three classical reactor models are described by PFR u dC dx RCw ithCCxin=Š()==()@01 BR dC dt RCw ithCCtin=Š()==()@02 CSTR CC RCin CŠ =Š()() 3where C is the spatially (or cross-sectional) averaged reactant concentration, Cin is the mean inlet concentration of the reactant, RC() is the sink term due to the presence of homogeneous reaction, x is the coordinate along the length of the PFR, u is the mean fluid velocity in the reactor, t is the time, and C is the total residence time in the reactor. Irving Langmuir[1] first replaced the assumption of no axial mixing of the PFR model with finite axial mixing and the accompanying Dirichlet boundary condition ( C = Cin @ x = 0) by a flux-type boundary condition D dC dx uCCxmin=Š[]=()@04where Dm is the molecular diffusivity of the species. The above boundary condition was rediscovered several times in the years that followed: first by Fšrster and Geib[6], which was quoted and applied by Damkšhler,[2] and then, later, by Danckwerts.[3] Since then it has been known as the "Danckwerts" boundary condition. In his paper, Langmuir dealt with both the limiting cases of "mixing nearly complete" and "only slight mixing." Thirty years later, Gerhard Damkšhler in his historic paper, summarized various reactor models and formulated the two-dimensional CDR model for tubular reactors in complete generality, allowing for finite mixing both in the radial and the axial directions. In his paper, Damkšhler used the fluxtype boundary condition at the inlet and also replaced the assumption of plug flow with parabolic velocity profile, which is typical of laminar flow in tubes. Fšrster and Geib first introduced the concept of residence time distribution (RTD) to study the case of longitudinal dispersion in tubes. Twenty years later, Danckwerts, in his much celebrated paper,[3] devised a generalized treatment of RTD and introduced the concepts of "holdback" and "segregation." Following this, it was Zweitering,[7] who quantified the degrees of mixing with the ideas of "complete segregation" and "maximum mixedness" and brought forth the concept of micromixing or mixing at the molecular scale in homogeneous reactions. In the last forty years, a wide range of micromixing models for homogeneous reactors have been formulated. While most of these low-dimensional mixing models are phenomenological in nature, the rigorously derived CFD models are high-dimensional and therefore numerically very expensive, especially for the case of multiple reactions with fast/nonisothermal kinetics. As a result, in spite of the simplifying assumptions present, the century-old ideal classical reactor models (Eqs. 1-3) are still the most popular choices among chemical engineering practitioners (and teachers). The classical ideal reactor models, which are easy-to-solve ordinary differential or algebraic equations with no adjustable parameter, are particularly preferred over the full CDR models (which are partial differential equations in more than one dimension) in case of multiple reactions with complex kinetics.SPATIAL AVERAGING OF CONVECTION-DIFFUSION-REACTION EQUATIONThe main goal of this article is to illustrate a new approach for deriving low-dimensional homogeneous reactor models, capable of predicting mixing effects. These models are derived through rigorous spatial averaging of the three-dimensional CDR equations over local length scales by using the Liapunov-Schmidt (L-S) technique of classical bifurcation theory. We illustrate this spatial averaging technique using the simple case of laminar flow in a tube with homogeneous reaction. The scalar concentration Crxt ,,, () in a tubular reactor is assumed to obey the CDR equation +() = + + Š()()C t ur C x rr Dr C r r D C x D C x RCx11 52 with accompanying initial and boundary conditions, given by CrxtC C r ra CrxtCrxt D C x urCrxtCx C x xLxin,,,@ ,,,,,, ,,,@ @ =()= == ()=+ () =()()Š[]= ==()00 2 0 060 where D and Dx are the transverse and axial diffusivities, respectively; rx ,, are the radial, azimuthal, and axial coor-Graduate Education

PAGE 4

252 Chemical Engineering Educationdinates, respectively; and u(r) is the fluid velocity profile. We take a (radius of the pipe) and L (length of the pipe) to be the characteristic lengths in the radial and axial directions, respectively; u is the cross-sectional average velocity; and CR is a reference concentration. Then, we obtain four timescales in the system associated with convection (C), radial diffusion (tD), axial diffusion (tx), and reaction (tR) tttDx x CR R Ra D L D L u C RC====()()227,,, and the ratios of these time scales give rise to the dimensionless parameters: p (transverse Peclet number), Pe (axial Peclet number), Da (Damkšhler number), and 2 (local Damkšhler number), given by pPeDa pDaau LD t uL D t LRC uCt aRC DC t tD Cx x C R R C R R xR D R====== ===()()2 2 2 In dimensionless form, Eq. (5) for the case of constant species diffusivities, can be rearranged as =+= Š +() +() ()()2 2 2 2 2 211 1 8c ppgccc c tPe c z u c z Darc with initial and boundary conditions being cc cc uzzzt c ztzt Pe c z cc c zin ,,, ,,,,,,@ @@=() ()+() ()Š[] ()=== = ====0 2 1 9001 001where tzu crtr a x L u u C C c RC RCC RR==== ==()()()() 10The form of the CDR equation (Eq. 8) clearly illustrates that a scale separation exists in the system, with p being the ratio of the local to the global scale (when Pe and Da are of order unity), and spatial averaging over the local scales is possible. It can be seen from Eqs. (8) and (9) that in the limit ofpc 020 and transverse (or small scale) concentration gradients vanish, in which case the equations simplify to the classical one-mode axial dispersion model. If local diffusion time is small but finite compared to convection, reaction, and axial diffusion time, local (transverse) gradients remain small and we can write ccztcztzt ,,,,,,,()()()()=+ 11 where c is the transverse averaged concentration and c is the fluctuation about this average, and casp 00. (Also, by definition =c0 .) Multiplying Eq. (11) by the local velocity profile, uuu ()=+ and averaging over the cross-section gives cmcuc=+()12 where cm is the mixing-cup (velocity weighted) concentration. Similarly, transverse averaging of Eq. (8) over the crosssection gives ()()Š++== = = =c tPe c z c z rcmDadd1 132 2 0 1 0 20 For the case of a tubular reactor, the spatial (transverse) average and mixing-cup concentrations are defined by c cxtdd dd== = = = = = = = ()() 0 1 0 2 0 1 0 214 ,,, and cmucxtdd udd== = = = = = = = ()()()() 0 1 0 2 0 1 0 215 ,,, It may be noted that in all flow reactors, cm is the experimentally measured variable. We refer to c and cm as the two modes of the system and our spatially averaged reactor models as T wo-Mode Models (TMMs). Equation 13 is called the global equation while Eq. (12) is called the local equation. The local equation shows that the difference between cm and c depends on the local velocity gradients ()u and the local concentration gradients ()c caused by molecular diffusion and reaction at the local scales. Micromixing is captured by the local equation as an exchange between the two modes (scales), cm and c. In order to determine c (and hence the term uc or the difference between cm and c), we substitute Eq. (11) in Eq (8) to obtain =+ ()()216cpgcc Graduate Education

PAGE 5

Fall 2002 253The L-S technique solves Eq. (16) for c by expanding it in the parameter p as == ()cpci i i117and by using the Fredholm Alternative ( i.e., t he fact c lies in the function space orthogonal to which c resides). Such an expansion (Eq. 17) is possible, since for p = 0, the transverse diffusion operator in Eq. (8) has a zero eigenvalue with a constant eigenfunction. Thus, uc could be determined to any order in p, i.e., closure of the local equation could be accomplished to any desired accuracy. In practice, the leading term (that is of order p) is sufficient to retain all the qualitative features of the full CDR equation. For example, for the case of azimuthally symmetric feeding, we have =Š Š+ +()()cp c z Op 1 1248 1824 2Substituting Eq. (18) into Eqs. (12) and (13) gives the twomode model to O(p) as + Š +()+()=()Š= +()= +()()c t c zPe c z DarcOp ccp c z Op p c z Opm m m1 019 202 2 2 1 2 1 2 with boundary and initial conditions given by 1 021 0122 0230Pe c z ccz c z z cctmmin m =Š=() ==()==(),@ @ @where 11/ is called the exchange coefficient, which depends on the local shear rates. For the case of fully developed laminar flows, DDDxm == (molecular diffusivity of the species), and 1=1/48. We refer to this model as the two-mode axial dispersion model. (Further details of the spatial averaging procedure using the L-S technique can be found in Chakraborty and Balakotaiah.[14,15]) It should be noted that the spatially averaged CDR equation (Eqs. 19 and 20) retains all the parameters (p, Pe, Da) of the three-dimensional CDR equation (Eq. 8) and hence all the qualitative features of the latter. It should also be mentioned that this model is capable of capturing macromixing effects through the axial Peclet number Pe in the global equation (Eq. 19), as well as micromixing effects through the exchange coefficient 1 1 Š and transverse Peclet number p in the local equation (Eq. 20). In fact, the L-S technique guarantees that the solution of the averaged model (Eqs. 19-23) agrees w ith th e exact solution of the three-dimensional CDR equation to O(p). [Three decimal accuracy is obtained for a second-order reaction for the case of Pe if 2 < 1 (see ref. 14).] Using the spatial averaging technique illustrated above, accurate low-dimensional models could be obtained for different types of reactors and flow profiles. For example, the two-mode model for a tubular reactor with fully developed turbulent flow is the same as Eqs (19) through (23), whereD is the effective turbulent diffusivity and 1 is a function of Reynolds number (Re) and friction factor f. This model is obtained by starting with the time-smoothed (Reynolds averaged) CDR equation, where the reaction rate R(C) in Eq. (5) is replaced by the Reynolds averaged reaction rate (after closure) Rav(C). Spatial averaging by the L-S technique is then performed on the timeaveraged CDR equation ( i.e., spatial averaging follows time averaging) to obtain the two-mode model (see ref. 15 for details). In the next section, we will present the two-mode models for other types of homogeneous reactors.TWO-MODE MODELS FOR HOMOGENEOUS REACTORS T ubular ReactorsThe steady-state two-mode model for a tubular reactor for the case of Pe ( i.e., no macromixing present) may be obtained from Eqs. (19) through (21). In dimensional form, it is given by u dC dx RCw ithCxC CCtu dC dx tRCm mmin mmix m mix=Š()=()=()Š=Š=()()024 25, where the local mixing time tmix (in the local Eq. 25 describing micromixing effects) is given by t a Dmix=()1 226 where a is the local diffusional length scale over which spatial averaging is performed, D is the local diffusion coeffici en t, and 1 1 Š is the exchange coefficient. In the limit of complete micromixing ( i.e., tmix 0 ), the two-mode convection model reduces to the ideal one-mode zero-parameter PFR model. Loop and Recycle ReactorsIn a loop reactor of length L, a flow rate of qin, and with an average velocity of uin, enters and leaves the reactor at points x = 0 and x = l respectively (where x is the length coordinate along the loop). The total flow rate in the loop is Q + qin between points x = 0 and x = l and is Q between Graduate Education

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254 Chemical Engineering Educationpoints x = l and x = L, due to a recycle rate of Q. The recycle ratio is the ratio of the volume of fluid returned to the reactor entrance per unit time to the volume of fluid leaving the system per unit time, and is given by = Q/qin. The twomode model for such a loop reactor can be obtained as u dC dx RCx RCxL CCin m mmixCtRxL = Š=<Š +()< Š() ()()()1 1 0 1 27 280 l lwith boundary conditions Cm minmx CCxL CxCx =()+=()+ =()=()()= =Š+0 1 29, llFor the special case when no reaction occurs between x = l and x = L, i.e., Cm(x= l ) = Cm(x=L), the loop reactor reduces to a recycle reactor of length l the two-mode model for which is given by u dC dx C x CCx CCin m m minm mmixR withC CtR =Š = Š=<+()=()+=()+()()()1 1 0 1 30 310 ,lxlThe two-mode loop and recycle reactor models, like the two-mode axial dispersion model, are two-parameter twomode models. Here, the two parameters are the recycle ratio, and the local mixing time tmix, which describe macroand micro-mixing effects in the system, respectively. T ank Reactors (CSTRs)It is well known that as the recycle ratio of a recycle reactor is increased, the behavior shifts from a PFR at = 0 (no macromixing) to a CSTR as = ( perfect macromixing). We use this idea to obtain the two-mode model for a perfectly macromixed CSTR, by integrating Eq. (30) along the length of the reactor x and simplifying the resulting equation for > > 1. This gives the two-mode model for a perfectly macromixed CSTR as CC t CC CCm mix minm C mmixCtRŠ Š()()()= Š=, 32 33where C(=V/qin) is the total residence time in the reactor, and tmix is the characteristic local mixing time, which captures micromixing effects. In the limit of complete micromixing ( i.e., tmix 0), the TMM for a CSTR reduces to the ideal one-mode zero-parameter CSTR model. It should be pointed out that the local equation (eqs. 25, 28, 31, 33) is the same for all reactor types. This is an important observation, which shows that scale separation exists in all types of homogeneous reactors.PHYSICAL INTERPRETATION OF TWO-MODE MODELSUsing the example of a tank reactor, we present a physical interpretation of the two-mode models. The physical system equivalent to the two-mode model of a CSTR is a tank reactor consisting of two zones, each of size V, namely, a nonreacting convection zone (A), represented by Cm, and a reaction zone (B), represented by C. Thus, Cm is representative of the convection scale of the system and C is representative of the reaction scale of the system. The interaction between the two scales (or the two zones A and B) is quantified by an exchange of materials at a rate of qE. This exchange occurs only through local diffusion, and tmix(=V/qE), which is the characteristic time scale for this exchange, therefore depends on the local shear rate and diffusion coefficient. Equations (32) and (33) represent the steady-state material balances for zone B and zone A, respectively. In general, any infinitesimal volume dV inside the tank could be so imagined to consist of two zones/scales, and a corresponding two-mode model could be written (Eqs. 3233) for the volume dV. If macromixing in the tank is complete, the two-mode model for any control volume dV could be integrated over the entire volume of the tank to generate a single two-mode model (Eqs. 32-33) for the whole tank. Macromixing effects are often not negligible in real tanks, however, and are influenced by several factors including the type and speed of impellers (turbines) and the manner of feed distribution. Several macromixing models are available in the literature, e.g., the two-compartment model, recycle model, tanks-in-series model, exchange-with-stagnant-zone model, any of which could be suitably coupled with the TMM to describe both macroand micro-mixing in tanks. However, if micromixing effects are dominant compared to macromixing ones (as in well-stirred tanks), it could be shown by using L-S reduction in finite dimensions, that these models ( i.e., the two-mode n-compartment model, etc.) could be reduced to Eqs. (32) and (33), where the local mixing time tmix is replaced by an effective mixing time tM, which captures both macroand micro-mixing effects. This effective mixing time tM now not only depends on the local diffusion time and local shear rates, but also intricately on the tank geometry, type and number of impellers, baffle positions, and power dissipation in the system. Graduate Education

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Fall 2002 255SIMILARITY BETWEEN TWO-MODE MODELS OF HOMOGENEOUS REACTORS AND TWO-PHASE MODELS OF CATALYTIC REACTORSA striking structural similarity between the two-mode models for homogeneous reactors and two-phase models for heterogeneous catalytic reactors exists. This could be seen more clearly when Eqs. (24) and (25) are rewritten as u dC dx CC t Cx m m mix mminR withCCx =Š=Š ==Š()(),@034The two-phase model for a heterogeneous wall-catalyzed reaction in a tubular reactor is given by u dC dx CC t Cx m mS TP S mminR withCCx =Š=Š ==Š()(),@035It may be noticed that the spatially averaged concentration C of the TMM (in Eq. 34) is replaced by the surface (wall) concentration CS in the two-phase model (Eq. 35), while the local mixing time tmix of the TMM is replaced in the twophase model by a characteristic mass transfer time between the two phases tTP, which is given by ttTPTPD TmSh a D==()1 362 ,where tD is the transverse diffusion time scale and Sh ,T(=1/TP) is the two-phase (dimensionless mass) transfer coefficient (asymptotic Sherwood number) that depends on the velocity profile and tube geometry. For the case of fully developed laminar flow in a circular tube, Sh ,T = 48/11 = 4.36, while its analogue in the TMM (comparing Eqs. 26 and 36) is Sh ,E = 1/1 = 48 (the dimensionless mass exchange coefficient in the TMMs). As illustrated in the next section, just as the two-phase models can capture the mass-transfer limited asymptote in heterogeneous reactions (which is missed by the pseudohomogeneous models), so can the two-mode models capture the mixing-limited asymptote in homogeneous reactions, which is rendered inaccessible by the traditional one-mode models. Thus, there exists the following one-to-one correspondence between two-phase models of catalytic reactors and two-mode models of homogeneous reactors: two-phase transfer time (tTP) local mixing time (tmix), two-phase transfer coefficient (Sh ,T) two-mode exchange coefficient (Sh E), surface (wall) concentration CS spatially averaged concentration C, and mass-transfer limited reaction mixing-limited reaction.APPLICATIONS OF TWO-MODE MODELS Bimolecular Second-Order ReactionsSecond-order reactions provide the simplest example of nonlinear kinetics, where micromixing limitations have significant effects on reactant conversion. We use the TMM to determine micromixing effects on conversion of a typical bimolecular second-order reaction of the typeAB P withratekCCk AB+=" "occurring in a CSTR, where k is the reaction rate constant. For the case of stoichiometric feeding ( i.e., CA,in=CB,in=Cin), the conversion (X) obtained by using the TMM is given by XDa Da=Š+ +()+Š +()()1 1 4111 21 372# # # where #(=tmix/C) is the dimensionless local mixing time, and Da(=kCinC) is the Damkšhler number. Figure 1 shows the variation of conversion X with Da for different values of the dimensionless local mixing time #. The case of # = 0 corresponds to the ideal CSTR. For # > 0 and Da the local concentrations Ci(i=A,B) approach zero, while the mixing-cup concentrations approach a mixing limited asymptote, given by CCABAmBmCCX =====++()01 1 1 38,,# ## As mentioned in the previous section, this mixing-limited Figure 1. Variation of exit conversion with Damkšhler number, Da, for a second order reaction in a CSTR, for different values of dimensionless local mixing time, #. Graduate Education

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256 Chemical Engineering Educationasymptote for homogeneous reactions is analogous to the mass-transfer limited asymptote for wall-catalyzed reactions. Just as the wall (surface) concentrations approach zero for the case of infinitely fast surface reactions (while the bulk/ mixing-cup concentrations remain finite), so do the local concentrations Ci for infinitely fast homogeneous reactions (i=A,B). Unlike in catalytic reactions, where exchange between the phases occurs at the solid-fluid boundary, the exchange between modes (scales) in homogeneous reactors occurs over the entire domain. Competitive-Consecutive ReactionsCompetitive-consecutive reactions of the typeABC andBCDkk++" "" "12are prototype of many multistep reactions such as nitration of benzene and toluene, diazo coupling, bromination reactions, etc. Experimental observations[16] show that if the first reaction is infinitely fast as compared to the second one ( i.e., k1/k2 ), under perfectly mixed conditions B is completely consumed by the first reaction and the yield of D is zero (if A and B are fed in stoichiometric amounts). But it was observed that if the mixing of A and B is not attained down to the molecular scale, the first reaction is not complete and there remains a local excess of B, which can then react with C to produce D. The yield of D increases monotonically as the rate of the second reaction increases, finally attaining a mixing-limited asymptote. We use the TMM for a CSTR to verify this observation. Figure 2 shows the increase in the yield of D, YD, with Damkšhler number of the second reaction, Da2, where YD = 2CDm/(CCm+2CDm), and Da2 = k2CinC. The figure corresponds to the case when the first reaction is infinitely fast ( i.e., k1/k2 ), and A and B are fed in stoichiometric amounts ( i.e., CB,in = CA,in=Cin and CC,in = CD,in= 0). While no D is formed for the case of # = 0 (ideal CSTR), a significant increase in yield of D is obtained if finite micromixing limitations are present in the system. The maximum yield of D, obtained when the mixing limited asymptote is attained also for the second reaction, is YDfor for,max=+ + > ()2 12 1 2 12 1 39 # # # # #Thus, in this case, an optimal yield of D is obtained for # = 1.CONCLUSIONSIn the hierarchy of homogeneous reactor models, the classical ideal reactor models stand at one end as the simplest, while the generalized convective-diffusion-reaction (CDR) Figure 2. V ariation of the yield of D with Damkšhler number for a competitive-consecutive reaction scheme A+BC, B+CD, when the first reaction is infinitely fast, for different values of the dimensionless local mixing time, #.model stands at the other end as the most detailed one. While the former cannot capture the mixing effects due to local velocity gradients, molecular diffusion and reaction, the latter requires extensive computations, especially for large Schmidt and/or Damkšhler numbers, and for multiple reactions with large number of species. The Two-Mode Models (TMMs) proposed here bridge the gap between the two extreme cases of reactor models and provide a practical approach for describing mixing effects on reactor performance. They retain all the parameters present in the full CDR model and therefore all the qualitative features of the latter, and yet their solution requires a numerical effort comparable to that of the classical ideal reactor models. The analogy between the two-mode models of homogeneous reactors and two-phase models of catalytic reactors could be carried further by noting that for all cases of welldefined flow-fields, where two-phase mass-transfer coefficients (ShT) can be estimated theoretically, the exchange coefficient (ShE) or the local mixing time (tmix) of the TMMs could also be estimated. For more complex flow-fields ( e.g., packed beds), the local mixing time, like the mass-transfer coefficient, could be correlated to Re, Sc, and the geometrical characteristics of the system. Thus, the two-mode models of homogeneous reactors are as general as the two-phase models of catalytic reactors and have a similar range of applicability. (In fact, the classical two-phase models are also two-mode models, the modes being the cup-mixing and the surface (or solid-phase) concentrations. Thus, the two-mode/ Graduate Education

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Fall 2002 257two-scale approach may be used to present a unified theory of homogeneous and heterogeneous reactors!) To summarize, the two-mode models are the minimal models that provide a low-dimensional description of mixing, by coupling the interaction between chemical reaction, diffusion, and velocity gradients at the local scales to the macro-scale reactor variables. Due to their simplicity and generality, it is hoped that they will find applications in the preliminary design and optimization of homogeneous chemical reactors, as well as provide an alternative method for teaching micromixing effects in homogeneous reactors.ACKNOWLEDGMENTSThis work was supported by grants from the Robert A. We lch Foundation, the Texas Advanced Technology Program, and the Dow Chemical Company. We thank David West of Dow Chemical, Dr. Grigorios Kolios of the University of Stuttgart and Prof. Dan Luss of the University of Houston for their help in locating and translation of the articles by Bodenstein and Wolgast and Fšrster and Geib.REFERENCES1.Langmuir, I., "The Velocity of Reactions in Gases Moving Through Heated Vessels and the Effect of Convection and Diffusion," J. Am. Ceram. Soc., 30 656 (1908) 2. Damkšhler, G., "EinflŸsse der Stršmung, Diffusion und WŠrmeŸberganges auf die Leistung von Reaktionsšfen. II Die Isotherme, RaumbestŠndige, Homogene Reaktion Ester Ordnung," Z. Elektrochem., 43 1 (1937) 3.Danckwerts, P.V., "Continuous Flow Systems: Distribution of Residence Times," Chem. Eng. Sci. 2 1 (1953) 4.Taylor, G.I., "Dispersion of Soluble Matter in Solvent Flowing Slowly Through a Tube," Proc. Roy. Soc. Lond. A, 219 186 (1953) 5.Aris, R., "On the Dispersion of a Solute in a Fluid Flowing Through a T ube," Proc. Roy. Soc. Lond. A, 235 67 (1956) 6. Fšrster, V.T., and K.H. Geib, "Die Theorietische Behandlung Chemischer Reaktionen in Stršmenden Systemen," Annalen. der Physik, 5 250 (1934) 7.Zwietering, T.N., "The Degree of Mixing in Continuous Flow Systems," Chem. Eng. Sci., 11 1 (1959) 8.Ng, D.Y.C., and D.W. T. Rippin, "The Effect of Incomplete Mixing on Conversion in Homogeneous Reactions," Chem. Eng. Sci., 22 65 (1965) 9.Miyawaki, O., H. Tsujikawa, and Y. Uraguchi, "Chemical Reactions Under Incomplete Mixing," J. Chem. Eng. Japan, 8 63 (1975) 10.Harada, M., "Micromixing in a Continuous Flow Reactor (Coalescence and Redispersion Models)," The Memoirs of the Faculty of Engineering, Kyoto Univ., 24 431 (1962) 11 .V illermaux, J., and J.C. Devillon, "ReprŽsentation de la Coalescence et de la Redispersion des Domaines de SŽgrŽgation dans un Fluide per ModŽle d'Interaction PhŽnomŽnologique," Proc. 2nd Ind. Symp. Chem. React. Eng., Amsterdam, B1 (1972) 12.Baldyga, J., and J.R. Bourne, "Mixing and Fast Chemical ReactionVIII. Initial Deformation of Material Elements in Isotropic Homogeneous Turbulence," Chem. Eng. Sci., 39 329 (1984) 13. Bodenstein, M., and K. Wolgast, "Reaktionsgeschwindigkeit in Stršmenden Gasen," Ztschr. Phys. Chem., 61 422 (1908) 14.Chakraborty, S., and V. Balakotaiah, "Low Dimensional Models for Describing Mixing Effects in Laminar Flow Tubular Reactors," Chem. Eng. Sci., 57 2545 (2002) 15.Chakrabory, S., and V. Balakotaiah, "Two-Mode Models for Describing Mixing Effects in Homogeneous Reactors," AIChE J., in review (2002) 16.Li, K.T., and H.L. Toor, "Turbulent Reactive Mixing with a SeriesParallel Reaction-Effect of Mixing on Yield," AIChE J., 32 1312 (1986) ChEletter to the editorDear Editor: I recently used the illustration below to explain the benefits of countercurrent flow to students in a separation processes subject that I teach. I've never heard this illustration used before and it seems to be a good one, so I thought it would be good to put it in the public domain for the benefit of other lecturers. However, it is very short and does not warrant being a "peer-reviewed" paper. Explaining Why Counter-Current is More Efficient than Co-Current While washing the dishes one night, I realized that this activity provides a useful everyday illustration of why countercurrent mass and heat transfer processes are more efficient than co-current ones. I asked the students in my class what would be the best way to clean a pile of dirty dishes if they had at their disposal one basin of dirty wash water and one basin of clean wash water. The class quickly reached the consensus that it would be best to first use the dirty water to clean off as much of the dirt as possible and then use the clean water to perform a second-stage clean. The dirty water would remove the bulk of the dirt, minimizing the contamination of the clean water and leaving it in better condition to clean off any remaining stubborn dirt. Putting the dirty dishes straight into the clean water would quickly dilute and waste its cleaning ability. This is equivalent to having the countercurrent flow of streams in a liquid-liquid extraction or gas-liquid absorption column. The clean sol vent is best used to perform the final stage of cleaning, while the used solvent is still able to perform some cleaning of the raw feed stream as it enters the column. Students seemed to intuitively understand this illustration, and it provides a non-graphical complement to the usual method of explaining the benefits of countercurrent flow, which involves showing how the average concentration (or temperature) difference driving force differs between coand countercurrent flows. Simon IvesonUniversity of Newcastle Callaghan NSW 2308, Australia cgsmi@cc.newcastle.edu.au Graduate Education

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258 Chemical Engineering EducationINTRODUCING MOLECULAR BIOLOGY TO ENVIRONMENTAL ENGINEERSThrough Development of a New CourseDANIEL B. OERTHERUniversity of Cincinnati Cincinnati, OH 45221-0071Historically, applications of biology in chemical and environmental engineering have been approached from different perspectives with different goals. For example, chemical engineering optimizes biochemical reactions of pure cultures of microorganisms in highly controlled bioreactors used for manufacturing ( e.g., fermentation), whereas environmental engineering employs mixed microbial communities with minimum controls as least-cost processes for meeting regulatory requirements ( e.g., sewage treatment). Although chemical and environmental engineering education often incorporates formal training in biology, the motivation for course selection can be very different. Incremental advances in biological knowledge that can be used to increase manufacturing capability or improve efficiency are useful in chemical engineering practice, and their integration into chemical engineering education is justified. The same principle does not hold for environmental engineering, however. Once minimum regulatory requirements are met, incremental advances in biological knowledge do not offer the significant cost savings for environmental biological unit operations that are needed to encourage the adoption and integration of the new knowledge into environmental engineering education. Recently, development of 16S ribosomal ribonucleic acid (16S rRNA)-targeted technology provided researchers in environmental engineering with new tools to identify micoorganisms and to study micoorganisms in bioreactor environments. As compared to classical techniques for identification and enumeration, 16S rRNA-targeted technology allows in situ examination of the structure ( i.e., who is present?) and function ( i.e., what are they doing?) of microbial communities without a prerequisite for isolating pure cultures.[1] For researchers in environmental engineering, 16S rRNA-targeted technology has been extensively tested, and current research activities have moved beyond the "proofof-concept" state to widespread applications.[2,3] In contrast, integration of 16S rRNA-targeted technology within the environmental engineering curriculum remains to be fully developed. At the University of Cincinnati, the author has developed and pilot tested a "proof-of-concept" course titled "Molecular Methods in Environmental Engineering." The course was designed to teach limited fundamentals of molecular biology in the context of quantitative engineering design and practice. During its first offering, fifteen graduate students in environmental engineering were exposed to "stateof-the-art" technology, including hands-on laboratory exercises following the "full-cycle 16S rRNA approach."[1] Students learned the importance of detailed understanding of microbial communities and microbial-mediated biochemical networks in biological unit operations, natural biological systems, and the global biosphere. The format of the course included a weekly lecture as well as a semester-long series of hands-on laboratory exercises designed to teach students to develop scientific questions, learn appropriate methodology, conduct careful experimentation, analyze data, and draw conclusions worthy of presentation to peers. Thus the final outcome of the course included preparation of peer-review quality manuscripts by each team of students as well as one-on-one interviews with the instructor.FULL-CYCLE 16S rRNA APPROACHTr aditionally, the identification of microorganisms in environmental samples has relied upon semi-selective culturing or direct microscopic examination. These techniques have led to a rudimentary understanding of the role of microorganisms in the global biosphere as well as the importance of microorganisms in public health and biocatalysis. Recently, the techniques for determinative microbiology have been dramatically expanded to include cultivation-and-morphologicindependent identification and enumeration of microorgan- Copyright ChE Division of ASEE 2002 Daniel B. Oerther joined the Department of Civil and Environmental Engineering at the University of Cincinnati in 2000. For ten years, he has been adapting methods from molecular biology to identify, enumerate, and measure the physiology of microorganisms in biotechnology processes including wastewater treatment and bioremediation. His research links the results of novel molecular biology assays with mechanistic modeling of bioreactor performance. Graduate Education

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Fall 2002 259isms in environmental samples. Arguably, one of the most widespread families of new techniques for determinative microbiology targets rRNA. Comparative studies of rRNA nucleotide sequences collected from a variety of microorganisms led to the development of a universal phylogenetic framework for understanding the evolutionary history of microorganisms.[4,5] Subsequently, these comparative approaches were coupled with oligonucleotide probe hybridizations to study microorganisms in situ without prerequisite culturing.[1,6]The "full-cycle 16S rRNA approach" refers to the process of obtaining genomic information directly from an environmental sample and then employing molecular methods to assay the abundance of nucleotide sequences directly within an environmental sample. The steps of the cycle, as applied in my course, are briefly described and outlined in Figure 1. Genomic deoxyribonucleic acid (DNA) is extracted from an environmental sample using chemical and physical disruption of the microorganisms. Subsequently, a polymerase chain reaction (PCR) is used to selectively "grow-up" target genes from the heterogeneous pool of genetic material. In our case, the target genes are 16S rRNA. The target genes, amplified in the PCR, are cloned into bacterial vectors and transformed into competent cells of Escherichia coli The recombinant clones are cultured and plasmid DNA is extracted. The results from commercial dideoxy terminal sequencing are used to design an oligonucleotide hybridization probe purchased from a commercial vendor. The fluorescently labeled probe is hybridized to a "fixed" sample, and individual microbial cells are identified using an epifluorescence microscope. For my class, commercially available kits were used to the extent possible to minimize the time spent by students and the teaching assistant in preparing reagents. Genomic DNA was extracted using an UltraClean Soil DNA Isolation Kit.[7]PCR was conducted using a model 2400 thermal cycler[8] and the Takara Ex Taq kit.[9] Cloning of the PCR products was accomplished with the TOPO TA Cloning kit version K2,[10]and plasmid DNA was prepared using PerfectPrep Plasmid Mini preps.[11] Throughout the exercises a variety of equipment was used including an ultra low temperature freezer,[12]a Mini Beadbeater-8,[13] a system for agarose gel electrophoresis,[14] a Genesys 10uv,[15] a constant-temperature rotary shaker,[16] and an epifluorescence microscope.[17]FORMAT FOR LABORATORY EXERCISES Step 1 Students arranged themselves into teams of three. The selection of teammates was based both on a common interest in one environmental sample and on an effort to spread previous experience and expertise in molecular biology among the groups. Step 2 Teams identified, evaluated, and proposed an appropriate environmental system for study. Each system seFigure 1. Schematic of the principal steps in the "full-cycle 16S rRNA approach." Genetic material is isolated directly from an environmental sample and the 16S rDNA genes are amplified in a PCR. The product of the PCR is cloned, and recombinants are isolated for extraction of plasmid DNA. Automated sequencing is used to provide the primary nucleotide structure of the clones, and probe design is accomplished using semi-automated procedures and readily available software. Finally, individual microbial cells are visualized through fluorescence in situ hybridization (FISH) with fluorescently labeled 16S rRNA-targeted oligonucleotide probes. Graduate Education

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260 Chemical Engineering Education. . we plan to expand the enrollment [in this course] to include undergraduate environmental engineering students as well as graduate and undergraduate students from related disciplines, including chemical engineering and biomedical engineering. lected for the course was novel for the field of environmental engineering and possessed the capacity to stimulate a more extensive research question ( e.g., supplemented a research question in an existing/developing MS or PhD degree, or promoted a novel research direction generally underexplored.) A sample was obtained from the selected system. In all cases, preference was placed on samples that were a part of a developing/ongoing research project with significant supplementary information generated from advanced process engineering and chemical/physical analyses ( e.g., sample(s) from a novel bioreactor configuration or a bioreactor treating a novel waste stream). Step 3 Each team generated 16S rDNA sequence information from their sample(s). Genomic DNA was extracted using an UltraClean Soil DNA Isolation Kit[7] according to the manufacturer's instructions. Mechanical lysis of the samples was performed for one minute at the maximum setting of a Mini Beadbeater-8.[13] Genomic DNA was quantified using a Genesys 10uv[15] spectrophotometer assuming that an absorbance reading of 1.0 at a wavelength of 260 nm corresponded to a concentration of 50 mg DNA/l. The 16S rDNA genes of bacteria present in the sample were amplified by PCR using primer set S-D-Bact-0011-a-S-17 (5' to 3' sequence = gTT TgA TCC Tgg CTC Ag) and S-DBact-1492-a-A-21 (5' to 3' sequence = ACg gYT ACC TTg TTA CgA CTT).[18] The conditions for PCR included: 5 min. at 94 C; 30 cycles of 0.5 min. at 94 C, 0.5 min. at 55 C, and 0.5 min. at 72 C; 7 min at 72 C; and hold at 4 C. Each reaction tube contained: 1.25 U Takara Ex Taq polymerase,[9] 1x T akara Ex Taq reaction buffer, 200M of each deoxy ribonucleotide triphosphate (dNTP), 0.2M of each primer, and 500 ng of genomic DNA. PCR was conducted using a model 2400 thermal cycler.[8]Agarose gel electrophoresis was used to check the quality of the PCR product. A 1% (wt./vol.) agarose gel was prepared in 1 x tris buffered EDTA (1 x TBE is 90mM tris borate and 2 mM ethylenediamine-tetraacetic acid [EDTA]) according to the manufacturer's instructions.[19] Electrophoresis was conducted for two hours using a setting of 100 V for the power supply. DNA fragments were visualized with a hand-held UV lamp after staining the agarose gel for ten minutes at room temperature with 50 mg/l of ethidium bromide. The PCR products were cloned into component cells of E. coli using the TOPO TA cloning kit, version K2[10] according to the manufacturer's instructions. The blue/white screen with x-gal was used to detect the presence of insert in each plasmid, and the antibiotic ampicillin was used to screen for the presence of plasmids in colony-forming units of competent cells. Ten clones were selected for each team of students, and plasmid DNA was prepared using Perfectprep Plasmid Mini preps[11] according to the manufacturer's instructions. Purified plasmid DNA was subjected to endonuclease restriction analysis using EcoR I.[20] Digested plasmid DNA was electrophoresed on 2% (wt./vol.) agarose gels and visualized using ethidium bromide staining and a hand-held UV lamp as described above. T wo clones from each team were selected for commercial, automated dideoxy terminal sequencing by the DNA Core Facility at the University of Cincinnati. Sequencing primers included M13(-20) forward and M13 reverse[10] as well as S*-Bact-0343-a-A-15 (5' TAC ggg Agg CAg CAg 3'), S-*0519-a-S-18 (5'gTA TTA CCg Cgg CTg CTg 3'), S-*-Bact0907-a-A-20 (5' AAA CTC AAA TgA ATT gAC gg 3'), and S-*-Bact-a-S-16 (5' Agg gTT gCg CTC gTT g 3').[18] Step 4 An initial phylogenetic analysis was conducted, and the results were used to design oligonucleotide hybridization probes for fluorescence in situ hybridization (FISH). Assembled sequences were compared to the Ribosome Database Project (RDP) (available at rdp.cme.msu.edu) using Chimera Check and Probe Match. Preliminary phylogenetic affiliation was confirmed using a BLAST (Basic Local Alignment Search Tool) search of GenBank (available at www.ncbi.nlm.nih.gov, follow the links to BLAST). The fluorescently labeled oligonucleotide probes were ordered from a commercial vendor. Step 5 Each team conducted fluorescence in situ hybridization (FISH) analysis of their original samples. Aliquots of the original sample were chemically "fixed" for one hour at room temperature with 4% (wt./vol.) paraformaldehyde prepared in 1 x phosphate buffered saline (1 x PBS is 130 mM NaCl and 10 mM sodium phosphate buffer). The samples were subsequently stored at -20 C in a 50% (vol./vol.) mixture of ethanol and 1 x PBS. The fixed samples were applied in a sample well on a Heavy Teflon Coated microscope slide[21]and air-dried. FISH was performed as previously described.[22]Briefly, each microscope slide was dehydrated in an increasing ethanol series (50, 80, and 95% [vol./vol.] ethanol, one minute each), each sample well was covered with 9 l of Graduate Education

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Fall 2002 261Figure 2. Demographic of students enrolled in the pilot course as determined by an anonymous, in-class survey.hybridization buffer (20% [vol./vol.] formamide, 0.9 M NaCl, 100 mM Tris HCl [pH 7.0], 0.1% SDS), and fluorescently labeled oligonucleotide probe, 1 l (50 ng), was added to each sample well. Hybridizations were conducted in a moisture chamber for two hours, in the dark, at 46 C. The slides were washed for 30 minutes at 48 C with 50 ml of prewarmed wash solution (215 mM NaCl, 20 mM Tris HCl [pH 7.0], 0.1% SDS, and 5 mM EDTA). Fixed, hybridized cells were mounted with Cargille immersion oil[23] and a cover slip. Probe-conferred fluorescence was visualized with a model E600 upright epifluorescence microscope,[24] and digital images were captured using a Spot-2 charge coupled device (CCD) camera.[25] The results of the FISH analysis included determining the abundance and spatial organization of phylogentically defined microbial populations identified by unique oligonucleotide hybridization probes. The students learned the procedures for the laboratory exercises through a video series produced specifically for this course. They were given a laboratory manual at the start of the class, and videos of the laboratory exercises were distributed biweekly in VHS format. The manual outlined all of the procedures for the laboratory and provided step-by-step instructions to complete each exercise. The videos gave the students an opportunity to view the instructor completing all of the steps of each exercise. The laboratory exercises were completed independently by the three-student teams according to a schedule arranged at the start of the class. Approximately the first fifteen minutes of the weekly lectures were dedicated to reviewing the progress of each team toward meeting the schedule for completion of the laboratory exercises.TOPICS FOR THE LECTURESEach week, approximately two hours were spent in a lecture discussion format with the entire class. The nine topics that were covered in the pilot course included:Overview of methods including the value of different methods and an answer to the question, "Why do Environmental Engineers need to learn molecular biology?"Measuring microbial community structureMeasuring microbial community functionQuantitative molecular biology for Environmental Engineering versus qualitative molecular biology for Environmental ScienceTr oubleshooting the laboratory exercises to improve the course for the subsequent yearWhat is this "phylogeny stuff" anyway?Historical development of molecular tools in Environmental Science and EngineeringSuccess stories for molecular tools in Environmental Science and EngineeringPrinciples of microscopic examinationSTUDENT FEEDBACKFigure 2 summarizes the results of students' responses to a demographic survey. Thirteen of the fifteen students enrolled in the course responded to the survey. The class was divided almost equally between male and female students with a median age of 27-30 years old. Five of the students had received significant formal training in biology, previously participating in more than ten biology courses. The majority of the students had already completed their MS degree (eight out of thirteen), but more than 50% of the students had received their degree outside of environmental engineering or environmental science. Most students spent less than six hours per week on the course, but some students spent significantly more time. Overall, the students enrolled in the pilot test of "Molecular Methods in Environmental Engineering" could be categorized as mature students ( i.e., in their late twenties working toward their doctoral degrees). Furthermore, the class contained a significant number of students with extensive previous experience in biology. Thus, the students enrolled in the pilot course were well prepared in maturity and previous biology experience to actively participate in this novel course. As the course continues to be offered, I plan to track the success of the course in relationship to the demographics of the enrolled students. In addition to collecting demographic information, at the end of the class the students were asked to respond to three open-ended questions. In response to the question, "In your opinion, were the objectives of the course met?" students responded: The course met some of the objectives, but some students Graduate Education

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262 Chemical Engineering Educationare not convinced why we use molecular biology to id en tify microorganisms in systems that have been proved or have been operating successfully. Y es. I am equipped with knowledge about this approach, and I can interpret research results and publications from this developing field.In response to the question, "What was the best aspect of this course?" students responded: Most of the procedures are basic/universal operations in molecular biology which means that we understand how to study biology and biotechnology at the molecular level. Experimental workbecause it is through applications that a student gets a tight grip on ideas and concepts. In addition, the challenging experiments and the value of the final result make the work more interesting. The lectures were interesting and informative. I learned a great deal, and my ideas about environmental engineering and science have been positively affected by the knowledge I have gained. Y our perspective. We will never see "cutting edge" developments in a book. The whole structure of the course is similar to a research project. The best aspect was carrying the concepts from the classroom to the lab in a manner relevant to our field. Also, having a class that is new gives a fresh perspective into the future of environmental engineering.In response to the question, "What part of the course would you suggest improving?" students responded: More theoretical basis, especially for the background of molecular biology methods.From their responses to the open-ended questions, it is apparent that the students felt the pilot course was a success. It is interesting to note that the students appreciated that the pilot course represented an effort to integrate research into the classroom. One of the greatest difficulties for developing a role for molecular biology in an engineering curriculum is discovering a mechanism for moving these "state-of-the-art" research skills into a classroom setting. In the future, we plan to expand the enrollment for "Molecular Methods in Environmental Engineering" to include undergraduate environmental engineering students as well as graduate and undergraduate students from related disciplines, including chemical engineering and biomedical engineering.CONCLUSIONSTo address the growing national need for integrating genomics and molecular biology into the engineering curriculum, the author developed and pilot tested a new course, "Molecular Methods in Environmental Engineering." Fifteen graduate students were successfully introduced to molecular biology through lectures and hands-on laboratory exercises following the "full-cycle 16S rRNA approach." Although the pilot course can be considered a success, future offerings of this course must be modified to reduce the difficulty of comprehending molecular biology by inexperienced engineering students. One of the most daunting challenges for this type of "state-of-the-art" course is providing a supportive, yet independent learning environment. For highly motivated graduate students, the author demonstrated that the format for this course is successful. To offer this course to undergraduate students or poorly prepared graduate students represents a future challenge. In upcoming course offerings, the author plans to open enrollment for "Molecular Methods in Environmental Engineering" to undergraduate students in environmental engineering as well as students in chemical engineering and biomedical engineering. As genomics and molecular biology become as common to an engineering curriculum as chemistry and physics, engineering faculty need to take the lead in developing courses that introduce these topics from an engineering perspective with a focus upon quantitative approaches and the application of science to find cost-effective solutions to society's problems.ACKNOWLEDGMENTSThis laboratory course would not have been possible without the commitment of significant resources from the Department of Civil and Environmental Engineering of the University of Cincinnati. For the success of the pilot test, the author is grateful to the Department.REFERENCES1.Amann, R., W. Ludwig, and K.H. Schleifer, "Phylogentic Identification and In Situ Detection of Individual Microbial Cells without Cultivation," Microbiol. Rev. (59) p. 143, (1995) 2. Rittman, B. "Editorial: Molecular Understanding," Wa ter Environ. Res., (70) p. 1107, (1998) 3. Stensel, H.D., 2001, "Editorial: Probing the Black Boxes, Water Environ Res., (73) p. 259, (2001) 4. W oese, C.R., "Bacterial Evolution," Microbiol. Rev. (51) p. 221, (1987) 5. W oese, C.R., "There Must be a Prokaryote Somewhere: Microbiology's Search for Itself," Microbiol. Rev. (58) p. 1, (1994) 6.Hugenholtz, P., B.M. Goebel, and N.R. Pace, "Impact of Culture-Independent Studies on the Emerging Phylogenetic View of Bacterial Diversity," J. Bact. (180) p. 4765, (1998) 7.Catalog # 12800-100, MoBio, Solano Beach, CA 8.Applied Biosystems, Foster City, CA 9.PanVera Corp., Madison, WI 10.Invitrogen Corp., Carlsbad, CA 11 Eppendorf Scientific, Westbury, NY 12.Model Ultima II, Revco, Inc., Asheville, NC 13.Biospec Products, Bartlesville, OK 14.Catalog # CSSU1214 and EC105, E-C Apparatus Corp., Holbrook, NY 15.Spectronic Unicam, Rochester, NY 16.Model C24, New Brunswick Scientific, Edison, NJ 17.Model E600, Nikon, Inc. Melville, NY Graduate Education

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Fall 2002 263 18.de los Reyes, M.F., F.L. de los Reyes, M. Hernandez, and L. Raskin, Quantification of Gordona amarae Strains in Foaming Activated Sludge and Anaerobic Digester Systems with Oligonucleotide Hybridization Probes, Appl. Environ. Microbiol. (64) p. 2503, (1998) 19.E-C Apparatus Corp., Holbrook, NY 20.Promega, Inc., Madison, WI 21.Cel-Line Associates, New Field, NJ 22.Oerther, D.B., J. Pernthaler, A. Schramm, R. Amann, and L. Raskin, Monitoring Precursor 16S rRNA of Acinetobacter spp. in Activated Sludge Wastewater Treatment Systems, Appl. Environ. Microbiol., (66) p. 2154 (2000) 23.Type FF, Cedar Grove, NJ 24.Nikon Instruments, Inc., Melville, NY 25.Diagnostic Instruments, Inc. Sterling Heights, MI

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264 Chemical Engineering Education A New Approach to TeachingTURBULENT THERMAL CONVECTIONSTUART W. CHURCHILLUniversity of Pennsylvania Philadelphia, PA 19104-6393At AIChE's annual meeting in 2000, I gave an oral presentation of an early version of a pair of new expressions, completely free of explicit empiricism, for the prediction of fully developed turbulent thermal convection in all channels and for all thermal boundary conditions. At the same venue, In 2001 I also presented a greatly improved version, although at the expense of a smidgen of empiricism. Both presentations prompted the same question from participants: "Is this approach being taught to current students, and if not, why not?" I explained in both instances that this material is very new and is not in any textbooks, and furthermore, that it may not appear in textbooks for some time to come since the authors of transport textbooks must first become aware of the concept and its results, and then be convinced of its educational (as well as predictive superiority) over the method they are currently teaching. Also, as Anderson[1] has noted, textbooks in chemical engineering seem to have a unique longevity, and the more successful of them are replaced or revised only after long intervals of time. Undoubtedly with these textbook characteristics in mind, my mentor and departmental chairman, Donald L. Katz, long ago made the suggestion (which to a young assistant professor was virtually an order) that every year I replace at least 20% of the graduate transport course content by embracing new developments in the literature. Throughout my career, that suggestion led to my use of notes incorporating these new segments, together with using a book or books as a supplement rather than the other way around. I conclude, a full half-century later, that this process of annual supplementation and revision has, by virtue of the associated forced self-study and self-learning in the fields of my teaching, more than compensated me (and perhaps my students) for the efforts, and that it is a worthy complement of the new materials most of us introduce periodically from our own research and consulting. I am here taking advantage of the platform provided by Chemical Engineering Education to encourage and assist the process of supplementation for transport teachers with respect to a new approach for the description and prediction of turbulent thermal convection. In a previous CEE article,[2] I presented a new approach to the description and teaching of turbulent flow with the same objective. For that simpler and more restricted topic, it was possible to include in the presentation a virtually complete set of supplementary notes for direct use by any interested faculty member. For the much more complex process of turbulent thermal convection and the much more complex process of development of the new model, however, the presentation of a working set of supplemental notes in this format is simply not feasible. Rather, this article has the more limited objective of outlining the new approach with the hope that faculty members who teach transport will be inspired to study the more complete documentation in the key references and make the effort to formulate their own supplemental notes. Perhaps I will eventually find the time and motivation to prepare a monograph on this topic, but I do not recommend that anyone procrastinate with that as the excuse. When an analogue of the approach that was so simple, Copyright ChE Division of ASEE 2002 ChEclassroom Stuart W. Churchill is the Carl V.S. Patterson Professor Emeritus at the University of Pennsylvania, where he has been since 1967. His BSE degrees (in ChE and Math), MSE, and PhD were all obtained at the University of Michigan, where he also taught from 1950 to 1967. Since his formal retirement in 1990, he has continued to teach and carry out research on heat transfer and combustion. He is also currently completing books on turbulent flow and correlation.

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Fall 2002 265straightforward, and successful for turbulent flow was first attempted for the closely related topic of turbulent thermal convection, I anticipated that the path of development would closely parallel the previous one. While convection is inherently more complex than flow in several respects, it is also simpler in the sense that it merely consists of the superposition of a scalar quantity, the temperature, on the flow. The path of development that emerged after considerable trial and error proved to reflect the greater complexity that had been anticipated, and the final results proved to reflect the anticipated greater simplicity. The predictive equations for turbulent thermal convection that are described in this paper are, by a significant margin, more accurate, fundamentally sound, and general than any prior ones. They also provide better insight into the relationship between flow and convection and a better conception of thermal convection itself that more than compensates for the greater detail. This new material should therefore, as suggested by audience members at the AIChE presentations, be given serious consideration for inclusion in the final portfolios of both our undergraduate and graduate students. Apart from the merit of the predictive equations for turbulent thermal convection that emerged, the path of their development appears to have merit itself in an educational sense. On the one hand, it provides insight into a creative process of correlation that is within the capabilities of our students. On the other hand, it provides a perspective within which the strengths and weaknesses of all forms of correlation can be evaluated, not only in flow and convection but also in every aspect of chemical enginee ring. Our students should be made to realize that whatever career they follow after graduation, they will spend considerable time using and/ or formulating correlations. I have a predilection for presentations in narrative and historical contexts under the presumption that the personal characteristics, as well as the triumphs and failures, of our predecessors not only stimulate interest but also provide a mnemonic for students. In this instance, a description of the serendipitous and irregular path of development of a completely new formulation in a relatively mature field may serve a similar role. Teachers who prefer a more orderly and skeletal approach are welcome to eliminate such diversionary material. Many details concerning origins, proofs, uncertainties, and limitations are deferred to the references, and in particular to Churchill and Zajic.[3] It is, however, essential that the teacher present these details, or perhaps in the instance of graduate students, assign key references as required collateral reading. In either event, students should be encouraged to question the validity of the many assertions and simplifications in this article rather than accept them "on faith." Undergraduate students may require more guidance than do graduate students with respect to the new approach, but they have the counterbalancing advantage of less to unlearn.THE NEW APPROACH FOR TURBULENT FLOWA thorough understanding by students and faculty alike of the new approach for the description and teaching of turbulent flow, as previously described[2], is an essential prerequisite for the complementary new approach presented here for turbulent thermal convection. Because of space limitations, however, only those results that are directly applied or adapted for thermal convection will be reproduced here. The time-averaged, once-integrated differential equation of conservation for momentum in the radial (negative-y) direction in steady-on-the-mean, full developed flow of a fluid of invariant density and viscosity through a round tube can be represented by $wy a du dy uv 11 Š =Š () Here, w is the shear stress on the wall, y is the distance from the wall, a is the radius of the pipe, u is the time-averaged velocity, and u and v are the fluctuating components of the velocity in the x and y directions, respectively. The superbar designates the time-average of their product, while and $ are the dynamic viscosity and specific density of the fluid. ( Aside to teachers : The origin of this expression and the physical meaning of the several variables and terms, including the signs of the latter, should be described or reviewed as appropriate. Any uneasiness of the students in this regard can be expected to persist in what follows. Of course, this warning applies to some extent to subsequent details as well.) Equation (1) can be rewritten in terms of the dimensionless "wall" variables of Prandtl, namelyuu yy aaw w w + + +=()=()=()$ $ $ / / // / / 12 12 12and one new variable, namely the fraction of the transport of momentum (or the total shear stress) due to the turbulent fluctuations ()=Š ++uvuv $ / as 112 Š Š =()+ + ++ + +y a uv du dy Equation (1), with y+/a+ replaced by 1-R, can be integrated formally to obtain the following expression for the radial distribution of the time-averaged velocity: u a uvdRR + + ++=Š () ()2 132 12

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266 Chemical Engineering EducationThe velocity distribution can in turn be integrated over the cross-section to obtain, after utilizing integration by parts, the following integral expression for the mixed-mean velocity and thereby the Fanning friction factor: 2 4 1412 2 0 1 4 0 1f uudR a uvdRm =%=Š () ()++ + ++/Equations (1) through (4) are exact insofar as the restrictions mentioned above with respect to Eq. (1) are fulfilled. In order to implement Eqs. (3) and (4), an expression is required for ()++uvin terms of y+ and a+. For this purpose, Churchill[4]proposed the following semi-empirical expression: () = + Š & Š+ ()++ Š + Š ++ + + Šuv y ya y a87 3 87 8707 10 1 0 436 1 0 436 1 695 5/ / /. exp .. .It is essential for the students to be aware of the origins and uncertainties of Eq. (5) since this expression has a critical role, both numerically and functionally, in all of the developments that follow for both flow and convection. The thirdpower dependence on y+ for small values of y+ was originally postulated on the basis of asymptotic analyses, but has since been confirmed by direct numerical simulations, which have also produced a theoretical value of approximately 7 x 10-4for the numerical coefficient. The exponential term for moderate values of y+, as well as the deductive term for ya +were both derived by speculative analysis, but the coefficients of 0.436 and 6.95 were determined from recent, improved experimental data for the time-averaged velocity distribution. The power-mean form of Eq. (5) is arbitrary and the combining exponent of -8/7 is based on experimental data for uv. (See Churchill and Zajic[3] for further details, including complete references.) Numerical integration of Eqs. (3) and (4) using ()++uvfrom Eq. (5) results in almost exact values of u+ and um + owing to the smoothing associated with integration. Such values of um +may be represented with a high degree of accuracy for a+ > 300 by the following expression that invokes no additional empiricism beyond that of Eq. (5): 2 32 227501 0 436 612 2f u aa nam ==Š+ +{}()+ ++ + /. lEquations (1) through (6) are the only ones for flow that will be referred to directly in the developments that follow for convection. It may occur to teachers and graduate students at this point that the relevant consideration of turbulent flow has been completed without any mention of the eddy viscosity or the mixing length. One merit of the new approach, which carries over to thermal convection, is that the need to introduce such heuristic quantities is avoided completely by the more direct and simple development in terms of ()++uv.AN ASIDE ON A GENERIC CORRELATING EQUATIONEquation (5) is a particular application of the generic correlating equation proposed by Churchill and Usagi[5] for two regions, namely yyybbb=+() 07 Here, y = y{x}, y0 = {x0}, y = y{x }, and b is an arbitrary exponent. Either y0 or y or both are necessarily functions of x rather than fixed values. For three regions, Eq. (7) can be extended either directly as yyyybqb i b q bq=+()+() 08 or in staggered form as yyyyybb q i bq bb qŠ()=+Š()() 009 Here, yi is an intermediate asymptote and q is a second arbitrary exponent. The reverse order of combination of y0, yi, and y leads to equally valid and, in general, fundamentally different representations. Equations (7) through (9) have been introduced here to avoid interrupting the continuity of the development in which they are used.DEVELOPMENT OF A NEW FORMULATION FOR TURBULENT CONVECTIONThe analogue of Eq. (1), with the additional idealization of negligible viscous dissipation, is jk T y cTv =Š + ()$ 10 and that of Eq. (2) is j j Tv T yw111 Š () = ()++ + + Here, j is the heat flux density in the y-direction, T is the temperature of the fluid, jw and Tw are their values at the wall,TkTTjwww +=()Š()$12 //, Tv is the time-averaged product of these fluctuating quantities, ()= ++TvcTvj $ / is the fraction of the radial heat flux density due to the turbulent fluctuations, and k is the thermal conductivity of the fluid. The terms j/jw and ()++Tv in Eq. (11) depend on two parameters, namely the Prandtl number Pr = c /k and the mode of heating at the wall, as well as on y+ and a+.

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Fall 2002 267From an energy balance over an inner cylindrical segment of the fluid stream, it follows that j jR u u Tx Tx dRwmm R= ()1 122 02/ /Here, Tm is the mixed-mean temperature of the fluid stream. As contrasted with /w, which may be inferred from Eq. (1) to vary linearly with R, j/jw varies non-linearly because of its dependence on the velocity distribution and in some instances on the temperature distribution as well. Also, as can be inferred from Eq. (12), T varies with x as well as with y, even in fully developed thermal convection, whereas u varies only with y in fully developed flow. Fully developed thermal convection is ordinarily defined by two criteria, namely Š Š , x TT TT and h xw wm00where h = jw/(Tw Tm) is the local heat transfer coefficient. Equation (11) can be put in a more tractable form for both formal and numerical solution by introducing new variablesand Prt defined as follows, in place of j/jw and ()++Tv 1 1 132 2 02+= == ()j j j jR R u u Tx Tx dRw w wmm R/ /and Pr Pr PrtTv uv uv Tv % Š ()Š () ()()()++ ++ ++ ++1 1 14The result is 1 1 1 15 +()+ ()Š () =()++ ++ + +R uv uv dT dytPr PrThe use of -, the perturbation of the heat flux density distribution from that of the shear stress distribution, was suggested by Reichardt.[6] The variable Prt was originally introduced in connection with modeling in terms of the eddy viscosity and eddy conductivity, and accordingly, by analogy with the corresponding ratio of molecular quantities, was called the turbulent Prandtl number. Although the redefinition of Prt in terms of ()++uv and ()++Tv avoids these heuristic variables, the traditional name and symbol for this quantity are retained herein out of respect for its historical origin. It should be noted that Prt is not necessarily proportional to Pr since ()++Tv is, in general, a function of Pr. Equation -=R can be integrated formally to obtain T a dR uv uvt R + + ++ ++= +()+ ()Š () ()2 1 1 1 162 12Pr Pr Then T+, weighted by uum ++/, can be integrated over the cross section to obtain Nua Tm dR uv uv u u dRt R m%=+ + ++ +++()+ Š () () 2 4 1 1 1 172 1 2 0 12Pr PrFor uniform heating at the wall, it follows from the criteria for fully developed thermal convection that= TxTxm//. It then follows from the correspondingly reduced form of Eq. (13), together with Eqs. (3) and (4), thatis a function only of y+ and a+. Equation (17) can then by virtue of the same considerations, be integrated by parts to obtain NudR uv uvt=+()+ ()Š () ()++ ++8 1 1 1 182 4 0 1Pr PrEquation (18) can be reduced for three special cases. For Pr = 0, it can be expressed as NuNudRmR 0 2 4 0 1 208181194%==+()=+()(){Pr} --while for Prt = Pr, it can be reduced by virtue of Eq. (4) to NuNutuvdR uvdR uvdR uvdR1 2 4 0 1 4 0 1 4 0 1 2 4 0 18 11 8 1 1 11===={}+()Š () Š () Š () Š () +() ++ ++ ++ ++ PrPr +()()=+ +2 1 2042a um wmR-

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268 Chemical Engineering Education Here, as can be inferred, 142+()-mR designates the integratedmean value over R4, and 142+()-wmR the integrated-mean value weighted by 1 ()++uv. Both quantities may readily be evaluated numerically, using Eqs. (3), (4), and (5), and the reduced form of Eq. (13). For Pr the temperature field develops almost completely very near the wall where ()++uvcan be approximated by 0.7 (y+/10)3 and can be neglected. Equation (16) can then be integrated in closed form to obtainNuNua ft t +={}=()()=()()()Pr.Pr/Pr/ .Re/Pr/Pr/ / / / /30 0007 0 0734322132 13 13 12 13For uniform wall temperature, the criteria for fully developed convection require that()(),++TxTxTTmm////Integration of Eq. (17) by parts is no longer possible, but from the limiting form of Eq. (16) for R = 0, it follows that NuTTcm mR 0 041222=()+()()++/ -and Nu u u T T fm c c m wmR 1 14 2 1 232= ()+()()+ + + +Re -Here, Tc is the temperature at the axis of the pipe. Equation (21) remains applicable as is. The determination of numerical values of -, Tc +, and Tm + from Eqs. (13), (16), and (17) now requires iteration, but the functional forms of Eqs. (22) and (23) are adequate for the development herein. On the basis of the previous experiences with various aspects of turbulent flow, I anticipated that Eqs. (19) through (23) could be combined in appropriate pairings in the form of Eq. (7) to construct satisfactory correlating equations for Pr Prt and for Pr Prt, or alternatively, in appropriate triplets in the form of Eq. (8). All such attempts failed, however. I then found (somewhat serendipitously) that a successful correlating equation for turbulent thermal convection could be devised by using a particular analogy between momentum and energy transfer in which the exact solutions for three particular values of Pr occur in the form of Eq. (9). Accordingly, a brief and very selective review of such analogies is appropriate at this point.SELECTIVE ANALOGIESReynolds[7] postulated that the transport of both momentum and energy between a turbulent stream and its confining surface occurred wholly by means of a mass flux of eddies and thereby derived the equivalent ofNuf =()()PrRe/224Prandtl[8] improved upon the Reynolds analogy by postulating an added resistance due to linear molecular diffusion of momentum and energy across a viscous boundary layer of thickness / in series with transport by the eddies of Reynolds in the turbulent core, thereby obtaining the equivalent of Nu f f =()+Š()()()+PrRe/ Pr//2 112 2512/ Equation (25), just as Eq. (24), is inapplicable for Pr < 1, owing to neglect of thermal conduction in the turbulent core, and also for Pr >> 1, owing to neglect of eddy transport within the viscous boundary layer. Even so, it represents a great advance in that it correctly predicts a coupled, non-power dependence on both Pr and Re, in the latter case by virtue of the dependence of f on Re. Of the many analogies that have been proposed to eliminate the deficiencies of the Prandtl analogy for large and small values of Pr (see, for example, Churchill[9]), only two need to be examined here. Reichardt[6] eliminated dy+ between the equivalents of Eqs. (2) and (15) and made several ingenious approximations that allowed him to integrate the resulting combined equation in closed form. Churchill[9] assembled the fragments of this solution into a single expression for Nu and corrected the erroneous expression used by Reichardt for the shear stress near the wall, thereby obtaining 1 1 2 1362 2 12612 13Nuf T T u u f T Tmu m c c m t m c tt= +()() +() Š ()++ + + + + +Re/ Pr Pr Re/ Pr Pr Pr Pr/ / Equation (26) is limited in applicability to Pr Prt by virtue of one of the simplifications made by Reichardt in order to be able to integrate analytically. Churchill[10] (also Churchill and Zajic[3]) followed a completely different path to derive an expression, which for Pr Prt, is exactly equivalent to Eq. (26) except for replacement of the term 1 Prt/Pr by 1 (Prt/Pr)2/3. In retrospect, the difference in these expressions is a consequence of the approximation of Reichardt of du+ by dy+ in the differential term leading to the right-most term of Eq. (26).FINAL FORMSThe final predictive expressions for turbulent thermal convection emerged from the various expressions above by means of the following lengthy series of insights, postulates, and inferences, all of which were essential. 1 Churchill, et al.,[11] recognized that Eq. (26) was equivalent, with TTmc ++/ evaluated at the limiting conditions, to

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Fall 2002 269 11 1 1 271NuNuNutt= +Š ()Pr Pr Pr Pr 2 They further recognized that when Eq. (17) was rearranged as NuNu NuNu Nu Nut tŠ Š =+ Š () 1 111128 Pr PrPrit had the form of Eq. (9), with bq yNu yNu y Nu Nu NuNui t=Š= = = =Š()Š 1 101 1 1Pr PrThe staggered independent variable, Pr/Prt 1, has the essential role of converting Nu1 from a particular value to an asymptote. According to Eq. (28), Nu goes through a sigmoidal transition from Nu1 to N, a nuance of behavior that had previously been overlooked. In retrospect, correlation in terms of Eq. (7), that is, direct interpolation between Nu1 and Nu, was doomed to fail. The relationship provided by the Reichardt analogy was essential to the derivation of Eq. (27). 3 The identification of Eq. (28) with Eq. (9) suggested that the analogue of Eq. (28) in terms of Nu0 and Nu1 might be applicable for Pr Prt. That concept led to an expression with a discrete step in the derivative of Nu with respect to Pr/ Prt at Pr = Prt, but elimination of this discontinuity by means of an arbitrary but ultimately vanishing coefficient resulted in NuNu NuNu Nu Nu NuNu NuNutŠ Š =+ Š Š Š () 0 10 1 1 1 1 101129 PrPr Prwhere NuNuft =={}=()1 120 073432 PrPr.Re//. 4 The absence of any allusion to geometry or to the thermal boundary condition suggested that Eqs. (28) and (29) might be applicable for all geometries and all thermal boundary conditions. Plots of numerically computed values of Nu versus Pr/Prt for round tubes with uniform heating and uniform wall temperature, and for parallel-plate channels with equal uniform heating and with unequal uniform temperatures, confirmed the validity of this speculation. 5 These plots in logarithmic coordinates appeared to provide an excellent overall representation for all values of Pr/ Prt, for all values of a+ or b+ (where b is the half-spacing of the parallel plates) greater than 145, which is the lower limit for the existence of fully turbulent flow, for all geometries, and for all thermal boundary conditions. The more critical test provided by arithmetic plots, however, reveal errors in Nu of up to 20% for both Pr/Prt = 0{10} and Pr/Prt = 0{0.01}. After many attempted correctives, substitution of the analogy of Churchill for that of Reichardt to obtain 11 1 1 301 23NuNuNutt= +Š ()Pr Pr Pr Pr/ was found to result in an almost perfect representation for the dependence of Nu on Pr/Prt. 6 The analogue of Eq. (30) for Pr Prt, corrected as was Eq. (29) to remove the singularity in the derivative, and with the arbitrary inclusion of the empirical factor (Prt/Pr)1/8, is NuNu NuNu NuNuNu NuNuNut tŠ Š =+ Š Š ()Š() () 0 10 1 11 18 10 111 1 2 3 31 Pr Pr Pr/Pr/This expression results in almost exact representations for Pr < Prt for all of the previously mentioned conditions thereby it is a complement in every respect to Eq. (30).IMPLEMENTATIONThe numerical calculation of values of Nu for specified values of Re and Pr and for particular geometries and boundary conditions requires numerical values or expressions for f, Nu0, Nu1, and Prt. For a round tube, values of f of sufficient accuracy can be determined from Eq. (6) by noting that Re =++2aum. Values of Nu0 and Nu1 can be calculated from Eqs. (19) and (20), but an array of such values has already been calculated for representative values of a+, and correlating equations have been devised for interpolation. The slight inaccuracy associated with Eq. (5) is totally negligible when it is used in conjunction with Eqs. (19) and (20). Equivalent expressions for f, and values and expressions for Nu0 and Nu1 are also available or can readily be derived and calculated for other geometries and thermal boundary conditions. Equation (21) is directly applicable as an asymptote for large values of Pr for all geometries and conditions. Current correlative and predictive equations for Prt are quite uncertain (see, for example, Kays[12] or Churchill[13]). However, Nu as predicted by Eqs. (30) and (31) is fortuitously insensitive to the expression used for Prt, and the following purely empirical equation Pr. Prt=+()085 0 015 32 appears to be adequate for that purpose. The dividing value

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270 Chemical Engineering Educationof Pr with respect to the use of Eq. (30) or (31), that is, the value of Pr for which Pr = Prt, is 0.867 according to Eq. (32). Other correlating equations for Prt give only slightly different numerical values for this pivotal value of Pr. Either Eq. (30) or Eq. (31) can be used without serious error for 0.45 < Pr < 1.7, which suggests that Eq. (30) is a sufficient expression for all fluids other than liquid metals.SUMMARYEquations (30) and (31), together with Eq. (32), predict values of Nu within 1% or 2% of numerically calculated values for all geometries and conditions in the fully turbulent regime. This is to be compared with deviations of 10% to 40% on the mean for all expressions in current use, many of which are greatly restricted with respect to range and conditions (see Churchill and Zajic[3]). The remarkable improvement in accuracy for Pr Prt, as provided by Eq. (27), is a consequence of using the Reichardt analogy, which is free of any explicit empiricism. This expression fails in exactness only due to some minor mathematical simplifications made in its derivation. This slight inaccuracy is in turn virtually eliminated by use of the analogy of Churchill. On the other hand, the greatly improved accuracy of Eq. (31) for Pr Prtis a consequence of the identification of the structure of the analogy of Reichardt with that of the generic correlating equation of Churchill and Usagi for three regimes in staggered form, together with a minor empiricism. This same identification revealed a virtual regime and a point of inflection for Pr Prt, and another such pair that had never before been recognized for Pr > Prt. The existence of these virtual regimes explains the numerical and functional failures of most prior correlating equations. The generality of the new expressions for all geometries and thermal boundary conditions is a consequence of the recognition that the analogy of Reichardt could be expressed in terms of Nu0, Nu1, Nu, and Pr/Prt. The supplementary expressions for Nu0, Nu1, and Nu, which are exact insofar as Prt is independent of y+, follow directly from formulation of the equations of conservation in terms of the fraction of the transport due to the turbulent fluctuations. They could have been derived using eddy diffusional models, but not so simply. Implementation of the new expressions for specified values of Re and Pr, and for particular geometries and thermal boundary conditions, is not onerous since the entire calculation can be preprogrammed. The path of development leading to Eqs. (30) and (31) could now be streamlined, but the description of the irregular path that was actually followed has educational value in that all students and practicing engineers should be concerned with the evaluation if not the construction of correlating equations. Although the process of derivation of the new relationships for thermal convection is much more complicated, and the relationships themselves are slightly more complicated to employ, these deficiencies appear to be a small price to pay for their greater accuracy, sounder rationale, and broader applicability. Students should be pr ompted to question any of the assertions and non-obvious steps that were made in the abbreviated development herein and not expanded upon by the teacher. Justifications may generally be found in the references.REFERENCES1.Anderson, T.J., "Chemical Processing of Electrons and Holes," Chem. Eng. Ed., 24 (1), 26 (1990) 2. Churchill, S.W., "A New Approach to Teaching Turbulent Flow," Chem. Eng. Ed., 32 (2), 142 (1999) 3.Churchill, S.W., and S.C. Zajic, "The Prediction of Turbulent Convection with Minimal Explicit Empiricism," AIChE J., 48, 927 (2002) 4.Churchill, S.W., "New Simplified Models and Formulations for Turbulent Flow and Convection," AIChE J., 42 1125 (1997) 5.Churchill, S.W., and R. Usagi, "A General Expression for the Correlation of Rates of Transfer and Other Phenomena," AIChE J., 18 1121 (1972) 6. Reichardt, H., "Die Grundlagen des Turbulenten WŠrmeŸbertraganges," Archiv ges. WŠrmetechn., 2 129 (1951): English translation, "The Principles of Turbulent Transfer," Nat. Advisory Comm. Aeronaut., TM 1408, Washington, DC (1957) 7.Reynolds, O., "On the Extent and Action of the Heating Surface of Steam Boilers," Proc. Lit. Soc., Manchester, 14 7 (1874) 8. Prandtl, L., "Ein Beziehung zwischen WŠrmeaustaush und Stršmungswiderstand der FlŸssigkeiten," Phys. Z., 11 1072 (1910) 9.Churchill, S.W., "Critique of the Classical Algebraic Analogies between Heat, Mass, and Momentum Transfer," Ind. Eng. Chem. Res., 36 3878 (1987) 10.Churchill, S.W., "New Wine in New Bottles: Unexpected Findings in Heat Transfer. Part III. The Prediction of Turbulent Convection with Minimal Explicit Empiricism," Thermal Sci. Eng., 5 (3), 13 (1997) 11 Churchill, S.W., M. Shinoda, and N. Arai, "A New Concept of Correlation for Turbulent Convection," Thermal Sci. Eng., 8 (4), 49 (2000) 12.Kays, W.M., "Turbulent Prandtl Number: Where are We?" J. Heat T ransfer, Trans ASME, 116 234 (1994) 13.Churchill, S.W., "A Reinterpretation of the Turbulent Prandtl Number," Ind. Eng. Chem. Res., in press Dear Editor: Late last year, you published our Letter to the Editor regarding a survey we were carrying out on the use of Inherently Safer Design (ISD), meant to make the process industry a lot safer. Several of your readers downloaded our questionnaire and sent their responses to us. We got responses from eleven countries world wide. The findings of the survey have just been published under the title "Inherently Safer Design: Present and Future" in the Tr ansactions of the Institution of Chemical Engineers, Process Safety and Environmental Progress, 80 Part B, May 2002. We are pleased to enclose a copy of the publication for ChEletter to the editor

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Fall 2002 271your reference. Further, the following is a brief summary of the survey paper. It's appearance would be a fitting finale to the effort that started with the initial publication of our letter in your journal. SummaryA recent survey of the current use of Inherently Safer Design (ISD) concepts attracted responses from 63 people in 11 countries. These included industrialists, consultants, regulators, and academics. The salient results of the survey are noted below in bullet form to focus attention, followed by recommendations to expedite the adoption and spread of ISD. A lmost everyone responding knows of ISD. Their knowledge stems from specialized lectures, short courses, books, conferences, and training videos. I SD has been practiced by some for decades, whereas others started only recently. I SD is used in almost all stages of chemical process development, design, and operation. I SD is used during the manufacture of a whole range of products. A lmost all hazards have been targeted, both on-shore and off-shore. The above attests to the universality of ISD applications. There is a favorable impact on balance sheets. It is important to use "Management of Change" when implementing ISD to avoid introducing any new hazards. There is very little additional cost if implemented early. Payback is fast. Some applications/practitioners have won awards. I SD is included in lectures at several institutions. More will do so now. Many are not familiar with the current Inherent Safety (IS) indices. Those familiar with them have used them sparingly. A simple, realistic index is needed that also shows economic benefits. Detailed examples of use at different stages of process development are necessary. I SD concepts can influence R&D in various areas of chemical engineering and chemistry. I SD should encompass inherent safety, health, and environment (ISHE). I SD concepts, suitably modified, can be used for other branches of engineering such as mining, construction, transport, etc. Current regulations do not force the use of ISD. RecommendationsThe sad truth is that ISD is applied when an ISD enthusiast is on the team and not otherwise. Implementation of the recommendations below might encourage the uptake of ISD. Every chemist and chemical engineer should be trained in ISD. Academics and professional bodies should lead in this. O ther scientists and engineers should be given introductory lectures in ISD with examples from different industries. I ChemE should make ISD a part of its approved degree syllabus. Subsequently, it should persuade other engineering and science accrediting societies to do likewise. There is a need to teach IS to management and financial people also since their role is crucial in encouraging applications of ISD. Dedicated funding by government and industry for research and teaching in ISD will encourage many academics to take it up. I ncentives by the government to cost share demonstration plants and provide tax breaks for ISD. Expand ISD to encompass ISHE since the environment and occupational health are day-to-day concerns. It may eventually be extended to ISHEQ (Q for Quality) since improvements in SHE will decisively impact quality of product. Companies should provide examples of ISD use in various situations and the economic benefits reaped in order to convince other industries, regulators, government, the media, the public, academics, R&D funding agencies, etc. I nvolve the mainstream print and audiovisual media to favorably impact public opinion. Amend regulations to enforce the use of ISD. I nsistence by international agencies to include ISD in projects that they fund in the same way that the World Bank now insists on environmental impact assessment studies in projects funded by it. Some expected resultsT all columns of chemical plants will be reduced to oneor two-story heights. This will improve the image of the chemical industry. I ncreased investment in process industry. L ess restrictive regulations. G reater enrolments in UG and PG courses. S ignificantly enhanced funding for R&D. Adoption of ISD by other engineering disciplines, especially the more accident-prone ones such as construction, mining, transportation, etc. J.P. Gupta David W. EdwardsLoughborough University

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272 Chemical Engineering Education NOVEL CONCEPTS FOR TEACHING P ARTICLE TECHNOLOGY Copyright ChE Division of ASEE 2002 ChEcurriculumWOLFGANG PEUKERT, HANS-JOACHIM SCHMIDMunich University of Technology 85748 Garching, GermanyParticle technology is an interdisciplinary subject dealing with disperse systems, including all types of solid particles (aerosols, suspensions), liquid particles (droplets, emulsions), and gaseous particles (bubbles). The main focus of our current research and curriculum, however, is on solid particles. The goal of particle technology is producing and handling disperse materials under economical and ecological constraints. The materials are produced due to a surplus value of the product properties. Typical examples for these properties are the taste of chocolate, the color of pigments, the strength of concrete, or the electrical properties of semiconductors. Consequently, this is also a key point in our curriculum. In order to prepare a young engineer for his possible tasks in industry and research, we have organized the curriculum to reflect the structure of the field (see Figure 1). The field can be structured generally in four levels. The first and most fundamental level covers the elementary processes, i.e., the physical fundamentals. They include the statistical foundations of particle technology, multiphase flow, bulk mechanics and powder flow, interfacial phenomena, and the interactions of dispersed matter with electromagnetic radiation. On the second level, we apply the fundamentals to machines and unit operations. In our curriculum, we concentrate on separation processes, further strengthening students' capabilities in multiphase flow phenomena. The third level considers whole pr oce sse s. Here, we teach the concept of product engineering, i.e. how to tailor product properties. Consequently, we have a close link to the applications, which are actually very broad: Materials science ( e.g. all ceramics manufacturing is in fact applied particle technology) L ife science ( e.g., proteins may be treated as small particles in some respects, drug delivery) Information technology ( e.g., quantum dots, clean room technology, chemical mechanical polishing) Environmental engineering ( e.g. particle separation)Tr aditionally, chemical engineering has been taught in Germany using the unit-operations concept. In most universities, teaching particle technology has followed the concept of Hans Rumpf, who stressed the physical fundamentals in the basic course, which is followed by courses in agglomeration, solid-liquid separation, or particle characterization, to name just a few. Unfortunately, in the USA particle technology is taught extensively in only a few universities. Students learn how to design machines and processes that either keep the particle size constant ( i.e. separation, mixing) or change the particle size ( i.e. size reduction and size enlargement). In the past, only mechanical means to produce and handle par-Wo lfgang Peukert got his diploma degree in Chemical Engineering (1984) and PhD (1990) at Karlsruhe University. In 1998 he became a full professor at Munich University of Technology. He is the chair of solids and interface process technology. He also leads the particle technology research group and teaches particle technology. Hans-Joachim Schmid got his diploma degree in chemical engineering (1993) and PhD in mechanical process engineering (1998) from the University of Karlsruhe. He is a research assistant in the particle technology group at MUT. His main research interests are multiphase flows and particle characterization. How can the new areas be included in the curriculum without disregarding the conventional ones? In our opinion, the only answer is that teaching the fundamentals is even more important, but the examples given to the students should change.

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Fall 2002 273 Figure 1. Structure of particle technology curriculum and courses offered at Munich University of Technology.ticles were considered; therefore, particles larger than approximately 1 m were mainly dealt with while the non-mechanical methods of particle synthesis ( e.g. crystallization, gas phase processes) that lead to submicron particles were neglected. By introducing product properties, we address the overall goal of a chemical process, i.e. the production of well-defined product properties under economical and ecological constraints. The concept of product engineering transcends educational traditions and recognizes the end value of dealFigure 2. Property functions of a typical pigment.ing with process technology, i.e. the product property. Although this point of view is not new, it is largely neglected in the curriculum. Rumpf[1] coined the expression "property function" for the end-product qualities as well as handling characteristics. The property function is defined asProduct property = F(disperse properties and microstructure, chemical composition)Disperse properties are particle-size distribution, particle shape, particle morphology, and particle-surface characteristics. As an example, Figure 2 shows the product quality of a pigment (in this case the color strength per unit mass of pigments) that improves with decreasing particle diameter. The yield stress of the powder, as an important handling property, also increases with smaller particles, indicating prohibitive high resistance against powder flow. Obviously, there exists an optimum where both product and handling quality are acceptable. One solution to this problem may be to optimize powder formulation allowing both high product quality and acceptable handling properties. Of course, there are many other end-product qualities, such as taste ( e.g. of chocolate), strength ( e.g. of concrete), activity ( e.g. of a catalyst or a drug), or the band gap ( e.g. of a nanocrystalline semiconductor). Typical handling characteristics are flowability, dust development, filtration resistance, risk of explosion, and abrasiveness, to name only a few. Polke and Krekel[2] introduced the term "process function" to relate the disperse properties of the product to the production process and the eductsDisperse properties = F(process parameters, educts)Process parameters include the types of machines and unit operations as well as their interconnection, the operational parameters. The art of chemical engineering in this context involves designing the best process for producing the correct dispersed properties, leading to the desired product quality with a minimum of co sts, including environmental costs. This way, the product would achieve the highest profit since it is the most competitive. Our point of view includes both the economical aspects and a global perspective of environmental responsibility.EDUCATION IN PARTICLE TECHNOLOGY AT TU MUNICHT eaching Concept and New Topics The particle technology courses are a part of the chemical engineering and process engineering ("Verfahrenstechnik" in German) curricula at the Munich University of Technology. On one hand, the traditional education of chemical engineers prepares students for well-known applications such as the design of cyclones or heat exchangers, but many of the traditional applications have reached the point where their economic success is decreasing. On the other hand, new opportunities are evolving in areas that are less familiar to engineers, e.g. information technology or various aspects of maFigure 3. T eaching concept and new topics (gray).

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274 Chemical Engineering EducationFigure 4. Fundamentals of Particle Technology course (particle characterization included in separate course). Figure 5. Particle Separation course. Figure 6. Product Engineering course. terials science. The question is: How can the new areas be included in the curriculum without disregarding the conventional ones? In our opinion, the only answer is that teaching the fundamentals is even more important, but the examples given to the students should change.[3,4]In Figure 3, our approach is shown schematically. We explain the whole picture to the students by showing them the progression from molecular precursors to the whole process, which actually covers many orders of magnitude in both geometrical dimensions and time scale. In other words, we pave the way from feed materials to end-product propertiesthis is the horizontal line. In the vertical, depth is gained by explaining certain aspects in a detailed way. By reflecting the first three levels of Figure 1, we stress particulate interfaces (fundamental level) since we believe that this aspect has not been sufficiently covered in the past. Moreover, with the advent of nanotechnology, interfacial aspects have become increasingly important. The second level, comprising unit operations, is handled in a more-or-less traditional way, although new aspects such as CFD modeling are included. On the process level, disperse systems have to be treated mathematically by means of population balance equations, which have so far not been covered in traditional particle technology curricula.CoursesThe courses are organized into three levels. The first and most fundamental level comprises a two-semester course in "Fundamentals of Particle Technology" (see Figure 4). In this course, the important foundations (ranging from statistics, motion of particles in fluids, fracture mechanics, to dimensional analysis) and their implication in mechanical process engineering are covered. In addition, new elements such as population balances (which are increasingly used in industry) and interfacial phenomena are introduced. The latter comprise the fundamentals of interactions between molecules and particles, characterization of particulate interfaces and aspects of nanoparticle technology ( e.g. coagulation and stabilization of colloidal suspensions). The second level stresses unit operations. Here, we concentrate on "Particle Separation" (see Figure 5). This course is principally organized in the traditional way, focusing on separation of particles from gases as well as solid-liquid separation. Different unit operations in gassolid separation are introduced systematically by focusing on common principles, i.e. on transport mechanisms of particles to the collecting surfaces of the respective separators. In this way, various unit operations are treated very efficiently, which allows for introduction of new, modern methods such as CFD and its use for optimizing such apparatuses. We also offer a complementary course

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Fall 2002 275Figure 7. Particle Characterization course. Figure 8. Methodological approach. Figure 9. Integrated approach of university education. dealing with "Downstream Processing of Biotechnological Products" that focuses primarily on different unit operations for separation, disintegration, and purification of bioproducts as well as their interactions in the whole production process. In several aspects, bioproducts such as proteins can be regarded as nanoparticles, although the limits of this point of view should be kept in mind. A completely new course is being offered in product engineering (see Figure 6). The key question is how to produce the physical properties that define the product property, from the point of view of both handling and application. Examples for property functions are presented together with various methods for producing the particles ( e.g. comminution and classification, gas phase synthesis of nanoparticles, crystallization, and precipitation). Handling and formulation topics round out this course. The students learn key concepts for formation of structured solids, product design, and powder processing systems. In this context, the systems engineering approach is important. There is also a course in particle characterization that teaches the main principles in characterizing particle properties, e.g. concentration, size, shape, surface, and zeta potential (see Figure 7). The purpose of this course is to enable the students to choose an appropriate setup for arbitrary particle characterization tasks. This is accomplished by emphasizing the basic aspects of a measuring technique ( e.g. physical principle, signal recording, conditioning, and evaluation) as well as a complete measurement system (including sampling, transport, and preconditioning). These principles are explained in conjunction with a choice of the most important measurement techniques. Whereas Fundamentals of Particle Technology I and II are mandatory for all chemical engineering students, Particle Separation is one of a group of three courses (together with Process and Plant Design and Design of Thermal Processes) from which the students must choose two. The remaining courses are elective.Methodology and DidacticsThe course in particle technology follows several guidelines: The key item is the product property approach, i.e. particles have physical properties such as particle size distribution, particle shape, or particle morphology that are closely related to product properties. A lthough it is difficult to describe complete process chains, we enhance the student's awareness of the complete process.From a methodological point of view, we believe that teaching should follow a double-tracked approach. On one hand, the teacher should stress the important physical foundations, since excellent skills in the fundamental principles will be essential for the students throughout their studies and their professional lives. This implies that a large num-

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276 Chemical Engineering Educationber of facts have to be taught, thus assigning an important role to the teacher. On the other hand, to promote the students' understanding of the underlying principles as well as to sharpen their view of the complete process, active learning appears to be a key issue.[3,5,6] We try to support this active learning in different ways (see Figure 8). Lab and virtual experiments are conducted so that students can apply and transfer their acquired knowledge and get involved with more realistic problems. This is accomplished by a mandatory lab course (one semester) as well as lab components that are integrated into the courses described above. The lab experiments include a wide field of exemplary tasks that include, for example, dust separation in cyclones, filtration, mixing, and particle characterization by laser diffraction as well as the investigation of the stability of colloidal suspensions by dynamic light scattering. Furthermore, a completely new virtual lab is currently being established in the course Product Engineering, with computer simulations of disperse systems ( e.g. crystallization, comminution) based on population balances using commercial software ( e.g. LabView and Parsival). We also encourage the students to take an active role throughout the courses wherever it is appropriate, for example, in the particle characterization course. After introducing the basic principles and the important characteristics of a measurement systems ( e.g. assessed equivalent particle size, signal recording, conditioning and evaluation, necessary sample preparation, etc.) as well as discussing their application to the most important measurement techniques, the students are arranged in small groups. Each group is then assigned the task of analyzing one measurement technique that is so far unknown to them. They also have to prepare a presentation of their results that will relay the most important facts to their fellow students. The groups are supposed to work autonomously, with the teacher playing a more passive role and only giving guidelines or help when asked. In this way, several goals can be achieved. The students work and access information autonomously, e.g. from literature in a foreign language. The group work necessitates that students find their roles in a group and work together productively.[7]F inally, the students are given the chance to prepare and give a presentation. Even listening and assessing the presentation of other groups increases their ability in this respect. This is a capability that is not practiced enough.[8]By actively preparing a small part of the course, the students not only acquire valuable technical knowledge, but they also get a chance to increase their "soft skills." Personal development is often neglected in a university education. Students should concentrate on both their technical skills and their personal growth (see Figure 9). This includes an ability for self-organization and focusing on defined targets, intrinsic motivation to reach goals, and an ability to communicate results. On a deeper level, internal self-reflection is indispen sab le fo r accepting personal strengths and weaknesses as well as those of others. This is a precondition for all social skills.CONCLUSIONSParticle technology is a much wider field than many people realize since it also comprises biochemical, chemical, and thermal processes dealing with particles. Hence, it is not only of the utmost importance in the chemical industry, where about 60-70% of all products are fabricated in dispersed form, but also for a number of other fields, such as materials science and information technology. Product properties and the subsequently developed product engineering approach is at the center of our considerations. With a continuously growing number of applications for disp ersed systems, we feel a need to stress the fundamental aspects even more. With the generally observed trend toward finer particle sizes, new topics such as particle interactions and population dynamics have been included in order to prepare our students for newly developing areas such as nanotechnology. The technical courses are complemented by various activities to strengthen the soft skills of the students. Recently, suggestions have been made by Cussler, et al. ,[9]on how to change chemical engineering curriculae. Considering the shift in industrial practice from large-scale processes producing commodities toward more specialized product design, we feel that particle technology and particle design methods deserve a prominent place in the curriculum.ACKNOWLEDGMENTSThe authors would like to thank Professor Helmar Schubert from the University of Karlsruhe for very valuable discussions.REFERENCES1. Rumpf, H. †ber die Eigenschaft von NutzstŠuben, Stab-Reinhaltung der Luft 27 (1), p. 3 (1967) 2. Polke, R. and J. Krekel, "QualitŠtssicherung bei der V erfahrensentwicklung," Chem. Ing. Tech., 64 (6), p. 528 (1992) 3.J.L. Cano, Garces, A., and Saenz, M.J. "Oral Presentations of Students in Product Engineering Lectures." Int. J. Engg. Ed., 13 (3), p. 175 (1997) 4.Cussler, E.L. "Do Changes in the Chemical Industry Imply Changes in the Curriculum?" Chem. Eng. Ed. 33 (1), p. 12 (1999) 5.Davis, R.H. "Helpful Hints for Effective Teaching," Chem. Eng. Ed. 32 (1), p. 36 (1998) 6.Felder, R.M., D.R. Woods, J.E. Stice, and A. Rugarcia. "The Future of Engineering Education Part 2: Teaching Methods that Work." Chem. Eng. Ed. 34 (1), p. 26 (2000) 7.Humphreys, P., V. Lo, F. Chan, and G. Duggan, "Developing Transferable Groupwork Skills for Engineering Students," Int. J. Engg. Ed. 17 (1), p. 59 (2001) 8.Brostow, W., "Instruction in Materials Science and Engineering: Modern Technology and the New Role of the Teacher," Mat. Sci. and Eng ., A302 p. 181 (2001) 9.Cussler, E.L., D.W. Savage, A.P.J. Middelberg, and M. Kind. "Refocusing Chemical Engineering," Chem. Eng. Progr. 98 (1), p. 26S (2002)

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Fall 2002 277 Figure 2. Residual plot for Example 5 in Fahidy paper.[1]Figure 3. Residual plot for vapor pressure data from Reference 3. Regression model: log P = 7.6380342-1622.8666/Tb=8.5164364 1.5315505; the error variance s2=0.467503; and correlation coefficient R2=0.953603. Professor Fahidy advises not to put too much faith in the linear regression model, in spite of the relatively large R2 value, because of the extremely wide confidence intervals on the parameter a. The fairly random distribution of the residuals (see Figure 2) suggests, however, that the linear model may be the correct one. Furthermore, both physical considerations (fuel consumption should be zero for a zero mass vehicle) and the wide confidence intervals on the free parameter a, indicate that the model can be improved by setting the free parameter at zero. Indeed, carrying out the regression while setting a=0 yields: b=7.892916 0.3599903; s2=0.4641509, and R2=0.9481781. Thus, this model is now acceptable, even with respect to the confidence interval values. One of Professor Fahidy's objectives in presenting this example was to warn against accepting relatively large R2 values as proof of good linear relationship between the dependent and independent variables. The limitations of the R2 statistics in this respect can be most strikingly demonstrated using residual plots. Shacham, et al.,[3] for example, fitted vapor pressure data of 1-propanol with the two-parameter Clapeyron equation. This regression yields the values: R2=0.9998818 and s2=1.659E-05 (based on log P). Such a high value of R2 can be interpreted as a perfect fit. But the residual plot (seen in Figure 3) shows that the vapor pressure data set exhibits a curvature, which is not predicted by the Clapeyron equation. Indeed, using the four-parameter Riedel equation for representation of the same data yields: R2=1; s2=1.327E-09 and randomly distributed residuals. The last example, given in the Appendix of the article deals with a linear model for representing coded effectiveness indicators versus catalysts containing various coded platinum mass units. Analysis of this example shows that if the free parameter, a, is set at zero (as suggested by the wide confidence intervals on a and physical considerations) the linear model is appropriate to represent the data with §=1.6437659 0.0845917, R2=0.8860414, and s2=0.8508906. We can conclude that teaching statistical analysis of data and regression models is very important, but interpretation of numeric statistical indicators must be complemented by graphical analysis and consideration of the physical nature of the model in order to arrive at the correct conclusions. Mordechai ShachamBen-Gurion University of the NegevNeima BraunerTe l-Aviv University Refer ences 1.T.Z., "An Undergraduate Course in Applied Probability and Statistics," Chem. Eng. Ed., 36 (2), 170 (2002) 2.Fahidy, T.Z., Personal communication (2002) 3. Shacham, M., N. Brauner, and M.B. Cutlip, "Replacing the Graph Paper with Interactive Software in Modeling and Analysis of Experimental Data," Comp. Appl. Eng. Ed., 4 (1), 241 (1996) Author s ResponseI am delighted at Professor Shacham's interest in my paper. I also fully concur with the argument that the residual plots are an important and integral part of regression analysis. This is now standard textbook material, and I do routinely discuss this subject in my course. Although my intention was to keep the article from being too long, in retrospect I should have spent a paragraph or two on residual analysis, and I regret the omission. In Example 4 it was stated that the reaction mechanism was firstorder irreversible, but perhaps not strongly enough to imply an a priori knowledge of non-statistical origin, so that 0th and 2nd order models are beyond consideration. With limited data and given a physically correct model, the method that provides regression parameters relating data to model with the smallest error variance may be acceptable in l ack of something better, even if the residual plot does not show randomness of a desired degree. The quest for additional measurements is almost universal in the case of limited-size data. My views about R2 versus confidence intervals for true regression parameters do not fully coincide with the respondents', but may I point out the redundancy of seven-digit values, computer printouts notwithstanding. An R2=0.8860414 is not more meaningful than R2=0.89 Thomas Z. FahidyLetter to the EditorContinued from page 262.

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278 Chemical Engineering EducationGAS STATION PRICING GAMEA Lesson in Engineering Economics and Business StrategiesAARON SIN, ALFRED M. CENTERCornell University Ithaca, NY 14850The School of Chemical Engineering at Cornell University recently undertook an evaluation of its Masters of Engineering program to assess the curriculum and the amount of value added to the student's education by their participation in the program. One conclusion that we reached was that students in a professional masters program were most likely to go on, at least initially, to some kind of a position in a corporate environment. To increase the likelihood of their success in those early years on the job, we felt that some level of knowledge of how a business unit works and how an engineer fits into such a unit would be of significant importance to their careers. W ith this in mind we added a requirement that all M. Eng. Candidates take a course that would give them some insight into these areas. While there are a number of different courses at Cornell that deal with related topics, there was no one course that covered all of the areas that we thought were relevant. This led to the development of a new course, primarily for Masters of Engineering students, titled "Managing New Business Development." The course is an attempt to explain the business development process as it is likely to be carried out in a major corporation. It deals with concept development, feasibility assessment, front-end analysis to select the best implementation strategy, tactics to take the concept forward, implementation of the selected strategy, and ongoing improvement of the process once it is implemented to either increase or maintain profitability. The students are exposed to a number of different concepts. As the course advances, they are asked to demonstrate their knowledge through several case studies. The first case study involves producing plans for executing a feasibility study to introduce a new line of cosmetics in a newly opened overseas market. The second involves maximizing value from a feedstock that contains a number of different components. One of the concepts we found particularly difficult to get across to the students was pricing strategy. To provide a means for hands-on experience with this concept, we developed what we call the "gas station game." Unlike most games in business schools that generally involve multiple inputs and focuses at sitewide or businesswide optimization in a qualitative manner, this is a quantitative pricing game that aims at illustrating market forces at work. Since most people in the U.S. regularly deal with the fluctuation of gas prices, it is easy for the students to relate to it. We play this game every time the class meets.THE GAS STATION GAMEIn the game, students are divided into four groups, with each of them managing a gas station. Operating under different restrictions ("mom and pop" versus "big chain"), students are asked to decide on their business goals and facility sizes, which in turn lead to pricing structure and marketing tactics. We found that it is generally effective to have students per Copyright ChE Division of ASEE 2002Aaron Sin received his B.ChE. in 1998 from the University of Delaware, where he was trained to become a practical engineer. At Cornell, he used this knowledge to design microfluidic devices for pharmaceutical testing with his research advisor. Aaron is completing his Ph.D. thesis and considering a career in academia. Alfred Center is a registered professional engineer with over thirty years of experience in the petroleum industry. He is now a senior lecturer in chemical engineering at Cornell, teaching classes in unit operations laboratory, senior design, project management process control, and business development strategies. ChEclassroom

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Fall 2002 279form cash flow analyses for different scenarios. (The project assignment is shown in Appendix A.) The cost parameters are approximated and tested to produce realistic profit figures in the end. Capital costs include the storage tank material and installation, gas pumps, land requirement, engineering costs, etc. The operating costs are estimated as 10% of the capital investment, assuming a ten-year project lifetime. When the students are ready for the actual price bidding, a simulation is used to determine the demand in each station, based on the four stated prices (see Figure 1). The simulation is modified from the Monte Carlo Gillespie algorithm from reaction kinetics. Simply, the probability of customers visiting each gas station is inversely proportional to the price difference between that particular station and the minimum bidder. The simulation then u ses a random number generator to determine the exact demand for each station. An extra station with a fixed price is added to model gas stations from outside this town. To account for different levels of service provided by each station ( e.g. method of payment that is accepted), the prices are adjusted before the probabilities are calculated. These adjustment amounts are based on polls conducted among students regarding their own consumer preferences. The simulation also includes some proportion of cars that stop at the first gas station in sight instead of comparing prices, which again is determined using a Gillespie algorithm with a predetermined probability. The profit of each company is calculated based on the number of gallons sold minus operating costs of the gas station. As mentioned before, each group decides in advance what the suitable underground storage capacity will be, which gives rise to certain capital costs and operating costs. In the event that the gas station sells more gas than its capacity allows, it will have to obtain extra gas at 115% of the maximum price among the four gas stations. In this way, each gas station is equally profitable if the right price relative to each other is found.RESULTS AND DISCUSSIONSThe results of the game are quite encouraging. We are trying to teach the concepts of customer perception of product value, convenience, and price differentiation based on those perceptions. We are also trying to show that the strategy ofFigure 1. The gas station game simulation in action.

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280 Chemical Engineering Education T ABLE 1Differences between Mom/Pop Operations and Chain CompaniesInvestmentSupply CostPersonnelServiceMom/Pop$300,000$1.45/gal1 @ $5/hr12 hr ChainUnlimited$1.47/gal2 @ $5/hrSpeed pass T ABLE 2Gas Station Configurations and CostsCapacities20,000 gal25,000 gal30,000 gal40,000 galCapital Cost$200,000$300,000$400,000$500,000 Operating Cost$56/day$84/day$111/day$138/day maximizing an individual player's revenue did not necessarily mean defeating the others. And, in fact, the most favorable revenue picture is one in which all participants were able to share the market in some fashion. We found that within approximately ten iterations, the students were able to arrive at the conclusion that a shared market created more revenue and that cutthroat competition was unlikely to succeed. With this realization, the students go on to develop pricing strateg ies that allow each of them to sell close to their facility's capacity and to maximize their individual revenues. Figure 2 shows a typical adjustment process based on rootmean-squared deviations in prices and revenues, as compared to values at the last iteration. At around the tenth iteration, prices begin to converge to the range where a reasonable profit is sustained among all stations. The revenues continue to fluctuate, on the other hand, since students often react to price ch a ng es of th e ot h er st ations after their demands have changed, instead of anticipating the behavior of the others. These fluctuations are likely to stabilize if we carry the game further.CONCLUSIONWe think this game provides an easy way to teach pricing strategy in a fairly simplistic business model, and we are happy to pass along this game for your interest and use.APPENDIX AAssignment Sheet for the Gas Station Pricing GameThere are four gas stations on Rt. 13, coming into Ithaca. They are about a block apart, as indicated in the figure below. IIIIV Rt. 13 to Ithaca IIIFigure 1A: Map of the four gas stationsPreliminary market research indicates a demand of about 120 cars/hr in the day and 20 cars/hr at night, at 10 gals/car. While some percentage of the drivers go to the first gas station in sight, most make that decision based on things such as price, convenience (credit card/speed pass), and brand name. They also have the choice of getting gas from the next town if they feel prices are too high. Y our first task is to decide on the amount of investment, level of service, and pricing strategy for your gas station. Your decision will depend on the nature of your company (mom/ pop vs. chain), as listed in Table 1. Table 2 lists the available gas station configurations. The supply trucks come every seven days to refill the underground gas tanks. If you sell more gas than your designed capacity, the extra gas will be available at 115% x Max gas price in Ithaca. The goal of this exercise is to achieve the highest return on investment a mong all groups, with a minimum acceptable ROI at 12% per year. You will be able to change your prices (and only prices) every week, depending on the market situation. Figure 2. The adjustment process: root mean squared deviation in prices relative to final average price (left axis) and root mean squared deviation in revenues (right axis) plotted against iteration number.

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Fall 2002 281CONFERENCETEACHING ENTREPRENEURIAL ENGINEERING Monterey, California January 13-16, 2003 Engineering educators have done a great job of teaching students engineering science and engineering design. In addition, engineering schools are beginning to address the development of "soft skills" such as communications, teamwork, and ethics. In the current environment, it is increasingly important for the engineering education system to also find ways of teaching entrepreneurship and motivating students toward such activities. This conference will set the stage for a continuing and fruitful dialog between engineering educators and the business community. The conference will assemble entrepreneurs, engineering educators, and business school faculty to discuss What are the attributes of successful entrepreneurs? What are models of successful programs teaching entrepreneurship to engineers? What is the culture at a university that fosters a spirit of innovation and entrepreneurship? How can engineering faculty become role models of innovation and entrepreneurship? The outcomes of the conference will be a set of recommendations to engineering faculty, curricular integration options, model programs available for replication, and contacts between academic and business that will be published in the journals of various professional societies. The Chairs of the Conference are Eleanor Baum of The Cooper Union and Carl McHargue of the University of Tennessee. Additional information about this Conference, and a registration form, can be found at the Conference's web site: Engineering Conferences International offices are located at 6 MetroTech Center, Brooklyn, NY 11201 Te lephone at 212-591-8144 Fax at 212-591-8145 e-mail at bhconf@poly.edu web at www.engconfintl.org. ChEannouncementsCONFERENCEENHANCEMENT OF THE GLOBAL PERSPECTIVE FOR ENGINEERING STUDENTS BY PROVIDING AN INTERNATIONAL EXPERIENCE T omar, Portugal April 6-11, 2003 This conference will provide a forum for exchange of ideas on methods of enhancing the global perspective of engineering students, identify the key obstacles, and discuss progress toward eliminating the obstacles. The conference is jointly sponsored by Engineering Conferences International, Ordem des Engenheiros, Portugal, and E4 (Enhancing Engineering Education in Europe). Thematic Network is financed by the European Commission under SOCRATES II and co-financed by the University of Florence. Contact for more information or go to . The conference will focus on the recognition that exposure to other cultures brings personal enrichment to individuals and can be an important component of the educational experience. With the increased globalization of economies, the need extends beyond personal enrichment and has become an important asset to student mobility. Among the issues that must be addressed are compatibility of degree systems, accreditation of courses and/or degrees, quality assurance, an accepted credit system, language of instruction, and legal and social issues such as visas, taxation, and financial suport. The Chairs of the Conference are Carl McHargue of the University of Tennessee and Eleanor Baum of The Cooper Union (New York, NY). The Co-Chairs are Antonio Salgado Baros of the Orem dos Engenheiros (Portugal), G. Augusti of the University of Rome (LaSapienza, Italy), and C. Borri of the University of Florence (Italy). Additional information about this conference, and a registration form, can be found at the Conference's web site Engineering Conferences International (ECI) is the successor to the United Engineering Foundation Conferences. ECI offices are located at 6 MetroTech Center, Brooklyn, NY 11201 Te lephone at 212-591-8144,Fax at 212-591-8145 e-mail at bhconf@poly.edu web at www.engconfintl.org.

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282 Chemical Engineering Education There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened. ( Douglas Adams ) A lecture is a process by which the notes of the professor become the notes of the students without passing through the minds of either. ( R.K. Rathbun ) A teacher who is attempting to teach without inspiring the pupil with a desire to learn is hammering on a cold iron. ( Horace Mann ) T eachers who cannot keep students involved and excited for several hours in the classroom should not be there. ( John Roueche )SPEAKING OF EDUCATION IIIIf a professor can be replaced by a CD-ROM, he/she should be. ( Jack Wilson ) I'm sure the reason such young nitwits are produced in our schools is because they have no contact with anything of any use in everyday life. ( Petronius, d. ~66 AD ) Ti mes are bad. Children no longer obey their parents, and everyone is writing a book. ( Cicero ) What's on your mind, if you'll forgive the overstatement? ( Fred Allen ) Everything should be made as simple as possible, but not simpler. ( Albert Einstein ) In theory, there is no difference between theory and practice; in practice, there is. ( Chuck Reid ) Copyright ChE Division of ASEE 2002 Random Thoughts . .RICHARD M. FELDERNorth Carolina State University Raleigh, NC 27695 Richard M. Felder is Hoechst Celanese Professor Emeritus of Chemical Engineering at North Carolina State University. He received his BChE from City College of CUNY and his PhD from Princeton. He is coauthor of the textElementary Principles of Chemical Processes(Wiley, 2000) and codirector of the ASEE National Effective Teaching Institute

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Fall 2002 283To state a theorem and then to show examples of it is literally to teach backwards. ( E. Kim Nebeuts ) Setting an example is not the main means of influencing another, it is the only means. ( Albert Einstein ) Education is what happens to the other person, not what comes out of the mouth of the educator. ( Miles Horton ) Education is the ability to listen to almost anything without losing your temper or your self-confidence. ( Robert Frost ) Lack of education is an extraordinary handicap when one is being offensive. ( Josephine Tey ) Education is one of the few things a person is willing to pay for and not get. ( W illiam Lowe Bryan ) Education is what survives when what has been learned has been forgotten. ( B.F. Skinner ) A graduation ceremony is an event where the commencement speaker tells thousands of students dressed in identical caps and gowns that individuality is the key to success. ( Robert Orben ) There is a legend that the difference between classes of freshmen and post-graduates is that if you say "Good Morning" to the first, they reply "Good Morning." But the graduate students write it down. ( Donald Bligh ) I used to keep my college roommate from reading my personal mail by hiding it in her textbooks. ( Joan Welsh ) Predicting the future is easy. It's trying to figure out what's going on now that's hard. ( Fritz Dressler ) If I knew what I was looking for, it wouldn't be research, would it? ( Richard Feynmann ) If I accept you as you are, I will make you worse; however if I treat you as though you are what you are capable of becoming, I help you become that. ( Goethe ) T eaching is the greatest act of optimism. ( Colleen Wilcox ) T ry not to have a good timethis is supposed to be educational. ( Charles Schulz )All of the Random Thoughts columns are now available on the World Wide Web at http://www.ncsu.edu/effective_teaching and at http://che.ufl.edu/~cee/

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284 Chemical Engineering Education MAKING PHASE EQUILIBRIUM MORE USER-FRIENDLYMICHAEL J. MISOVICHRose-Hulman Institute of Technology Terre Haute, IN 47803I believe phase equilibrium thermodynamics is the most conceptually difficult undergraduate chemical engineer ing class. Even students who perform calculations satisfactorily seem confused over the meaning of what they have learned. Phase equilibrium is the single undergraduate chemical engineering class in which abstract concepts are presented to the near exclusion of practical applications. Table 1 gives examples of practical or physically intuitive subject matter found in classes that students typically consider abstract, theoretical, or mathematical. These actually contain some balance of theory and practice, giving students a point of reference to physical processes and equipment. Calculations such as bubble and dew points are needed for practical design, of course, but most phase equilibrium courses do not connect these to real processes or equipment. Practical applications of the material are taught as part of unit operations, mass transfer, or distillation courses. Students frequently have more intuition about the physical meaning of abstract quantities in classes other than phase equilibrium. Heat transfer students could define the Prandtl number as Ckp /, give a physical interpretation for all three variables, and potentially recognize related facts. For example, "The Prandtl number could be derived by applying the Buckingham Pi theorem to a heat transfer problem," or "Larger Prandtl numbers result in larger convective heat transfer coefficients." They know that the Prandtl number for liquid water at 100 atm and 150 C is unlikely to be 100 or 0.01. When phase equilibrium students define chemical potential, it is typically in terms of other abstract conceptsfree energy, standard states, fugacity, and activity. They are unlikely to know whether a certain chemical potential is positive or negative, nor what practical significance its sign would have. Without doing a calculation, how many phase equilibrium students know whether the fugacity of liquid water atT ABLE 1Content of "Theoretical" ChE Classes Class Theor etical Concepts Practical Concepts Fluid MechanicsShear stress tensor,Pumps, Valves, Piping Dimensional Analysis Mass TransferFluxes of all sortsPacked absorption towers T ransport PhenomenaPartial differentialViscometers, Heat transfer equations, Dimensionlesswith free convection, Greek variablesWetted wall columns Phase EquilibriumChemical potentialBubble and Dew Points, fugacity, activityFlash, Solubilities 100 atm and 150 C is closest to 5 atm, 50 atm, or 500 atm? Most are at a complete loss when asked to apply abstract quantities such as activity coefficients to practical questions, e.g. "Is ethanol more likely to form an azeotrope with nhexane or n-octane?" Lacking qu alitative understanding, their only approach for answering this question is detailed quantitative calculation.STRATEGIES FOR BUILDING INTUITIONPrausnitz, et al.,[1] describes the phase equilibrium problem as a three-step process. First, a real problem is translated into an abstract mathematical problem. Second, the mathematical problem is solved. In the final step, the mathematical solution is translated back into physically meaningful Copyright ChE Division of ASEE 2002 Michael Misovich will be Associate Professor in the Physics and Engineering Department of Hope College in August, 2002. His research interests include thermodynamic property predictions from equations of state, physical chemistry of polymer solutions, chemical engineering education, and its assessment. ChEclassroom

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Fall 2002 285T ABLE 2Common Intuition about Chemical Engineering DataH igh moleclar weight compounds have high boiling points A substance with a density order of magnitude less than water is probably a gas A Reynolds number in the laminar range for flow of water in typical process piping is not typical Convective heat transfer coefficients are very low for gases as compared to liquids T ABLE 3Uncommon Intuition about Phase Equilibrium Data The fugacity of a liquid is approximately its vapor pressure, as long as the pressure is not extremely high The fugacity of a component in an ideal gas mixture is its partial pressure Substances we consider noncondensible gases have fugacity coefficients larger than one; liquids and condensible vapors have fugacity coefficients smaller than one Substances with large differences in boiling points are unlikely to form azeotropes; substances with very close boiling points are almost certain to form them A ctivity coefficients larger than approximately seven indicate that liquid-liquid phase separation is possible The dilute component in either of two nearly immiscible phases obeys Henry's Law up to its solubility limit T ABLE 4Comparison of Graphical Figure Use in ChE TextbooksNon-graphGraphs perPercent Graph T extbook Graph Figur es Figur es Pagesb 100 pages Figur es Introduction to Chemical Engineering Thermodynamics[2]107445681971 (Chapters 10-15)(57)(11)(199)(29)(84) Chemical and Process Thermodynamics[3]11660 5412166 (Chapters 9-13)(62)(6)(253)(25)(91) T ransport Phenomena[4]691057111040 Elementary Principles of Chemical Processes[5]1715587353 (Chapter 6)(8) (0)(71)(11)(100) Momentum, Heat, and Mass Tr ansfer[6]1591067732160 (Chapters 35, 37-40)(63)(19)(143)(44)(77) aGraph figures include all twoand three-dimensional coordinate plots and nomographs. Any figure that included both graphical and nongraphical information was treated as a graph figure. Only numbered, captioned figures in text and examples were counted; figures with problems and in appendices were excluded.bPages include all text, examples, questions, and problems but exclude appendices.terms. Typically, this step consists of transforming highly abstract variables into physically significant ones.Chemical Potential Fugacity Activity CompositionEach transformation results in a less abstract variable than the previous step. Students do not seem to recognize this, perhaps because we do not teach it explicitly. Instead, they see chemical potential, fugacity, and activity as equally nebulous and abstract concepts upon which a rote series of mathematical operations will hopefully produce a physically meaningful variable such as composition, pressure, or t emperature. One of my principal goals in teaching phase equilibrium thermodynamics is to help students develop an intuitive understanding of the topic. I point out to them in the beginning that this class deals with techniques for generating data to use in other classes to the nearly total exclusion of applications. Since students will not be able to rely on processes or equipment to provide intuition, I em phasize understanding the data and its significance. This type of intuition about data, rather than equipment, occurs in other classes as the Prandtl number example above and as similar examples in Table 2 indicate. To promote this, I emphasize calculation and use of data having an obvious physical interpretation, e.g., temperature, pressure, volume, vapor pressure, composition, and enthalpy. When concepts such as free energy, chemical potential, fugacity, and activity are presented, the focus is partly on their use in solving for the more physical variables. Whenever possible, I encourage students to examine how the abstract variables affect the physical variables, and thus to develop some intuition about the significance of the abstract variables. Examples are given in Table 3; these are sometimes present, but not frequently emphasized, in phase equilibrium texts. More so than in many chemical engineering classes, phase equilibrium data are most useful and understandable when presented graphically. This is evident from observations given in Table 4 of how frequently graphical material is presented in textbooks. Thermodynamics and unit operations texts contain more graphs and a higher proportion of figures that are graphs, as opposed to schematic diagrams and other drawings. Within each text, the chapters more

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286 Chemical Engineering EducationFigure 2. General structure of spreadsheet for Pxy diagram. Figure 1. Pxy diagram prepared using spreadsheet. closely related to phase equilibrium have a higher proportion of graphs than the text as a whole, as indicated by the numbers in parentheses in Table 4. Furthermore, many students have a visual learning style. These students may struggle with equations and textual information, especially in an abstract context, and it is crucial that they see data presented graphically and also learn how to prepare data in a format that is most comprehensible to them. Hence, students need to make the connection between calculations and equations discussed in class and graphical presentation of phase equilibrium data. To assure they are capable of both understanding and generating graphical data, I assign a significant number of computer problems requiring this, as explained in further detail later in this article. Computer spreadsheets have been previously suggested[7,8] for use in solving phase equilibrium and equation-of-state calculations, and they are well suited both for the calculations and for subsequent graphical presentation. One recent text[9] includes a number of example spreadsheets that may be used for applications similar to those described in this article, although I prefer to have students write their own spreadsheets.DETAILS OF PHASE DIAGRAM COMPUTER ASSIGNMENTAs an illustration of such assignments, consider the construction of a binary Pxy diagram for an ideal solution at some constant temperature. Figure 1 is an example generated by repetitive dew point pressure and bubble point pressure calculations. Taking liquid mole fraction x1 as the independent variable, and assuming component vapor pressures Psat 1 and Psat 2 are known, Eqs. (1-3) allow calculation of all dependent variables in the problem. To generate the diagram, allow x1 to vary over the range 0.0 to 1.0. These calculations are easily done using computer spreadsheet software. xx PxPxP y xP Psatsat sat 21 1122 1 1111 2 3 =Š()=+()=()Figure 2 shows the general organization of this spreadsheet. The upper rows contain headings and constants such as the vapor pressures. The middle rows are used for calculations. The leftmost column is initially filled with values between 0 and 1 at intervals of 0.01, or a suitable small increment. (This should be done using spreadsheet commands or formulas; occasionally, a student will attempt to enter the numbers manually and become frustrated that using the computer apparently makes solving the problem too time-consuming.) Fill the remaining three columns in the middle rows of the spreadsheet with formulas given by Eqs. (1-3). If these formulas are entered correctly in the first of the middle rows, a single copy/paste command generates the entire table through the remaining middle rows. There may be one complication in producing a graph from these results. In a conventional Pxy diagram, pressure is taken as the vertical coordinate twice. With liquid composition as the horizontal coordinate, a bubble point curve is produced, then with vapor composition as the horizontal coordinate, a dew point curve is produced. To do this on the spreadsheet, a single y-coordinate must be paired with two different x-coordinates. At one time, few spreadsheet packages included this capability, but many recent versions (including Microsoft Excel) now allow it. If using an older package without this

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Fall 2002 287T ABLE 5Graphs Prepared Using Spreadsheets for Phase Equilibrium ClassBinary phase diagrams for ideal solutions Pxya TxybxyaFugacity versus pressure N umerical integration of PV databG eneralized viral coefficientb Redlich-Kwong equation of statebV olumetric properties of binary nonideal solutions Excess volumea Partial molar excess volumesaActivity coefficients in binary solutions versus composition Mar gulesaV an LaarbWil sonaInfinite dilution activity versus temperature Wil sonaPhase diagram for nonideal azeotrope forming binary mixture Pxyb TxybxyaExcess free energy of homogeneous azeotrope forming binary mixture versus composition Experimental dataaM argules equation (fit to azeotrope data)aM argules equation (best fit to VLE data)aW ilson equation (literature constants)bExcess free energy of heterogeneous azeotrope forming binary mixture versus composition Experimental dataaM argules equation (best fit to VLE data)aM argules equation (best fit to LLE solubility data)a aPrepared by students as homework assignmentbPrepared by instructor for class discussion capability, set up the lower rows of Figure 2 as shown, then define the first column as the x-coordinate for graphing and each of the two columns containing pressure values as separate y-coordinates. The lower rows of Figure 2 can be omitted when using current versions of Excel and other spreadsheets that allow multiple xy pairs to be graphed.ADDITIONAL COMPUTER ASSIGNMENTST able 5 lists other thermodynamic data graphs prepared using computer spreadsheets. A very brief discussion of each follows. Many were prepared by students as homework assignments using techniques similar to those outlined for the Pxy diagram. Copies of these assignments are available upon request. Some graphs were not assigned but were generated by the instructor and presented during class discussion. The same spreadsheet data used to produce a Pxy diagram as described above could be used to plot an xy diagram at constant temperature. Pxy and Txy are the predominant representations of VLE data in phase equilibrium classes, but xy is probably the most frequently used format of the phase equilibrium data in other classes, e.g., distillation, absorption, mass transfer. Using the method described above, generating Pxy data for an ideal binary system at constant temperature does not require trial and error. Calculation of a single Txy datum for an ideal binary system at constant pressure requires iteration or trial and error since the vapor pressures are functions of temperature. But generating a Txy diagram for such a system the locus of dew and bubble point temperatures for all possible compositions does not require trial and error. Taking temperature as the independent variable rather than liquid composition, all other variables can be calculated directly by Eqs. (1-3). Selecting a range of temperatures in increments between the pure-component boiling points generates the diagram. Plotting y versus x instead of T versus y and T versus x produces an xy diagram at constant pressure from the same data. For nonideal binary mixtures, activity coefficients are functions of liquid composition and possibly temperature. Pxy and xy diagrams at constant temperature are generated in a straightforward fashion without iteration since temperature is fixed and liquid composition is taken as the independent variable for generating the table as described above. Iteration cannot be avoided when generating Txy and xy diagrams at constant pressure for nonideal binaries. To find activity coefficients and vapor pressures, liquid composition and temperature are needed. Only one can be assumed. Direct calculation of liquid composition from vapor pressure, as in the ideal case, is not possible. If temperature is used as the independent variable, as suggested for the ideal case, a unique composition may not result because azeotropes are possible. I recommend using liquid mole fraction as the independent variable ranging from 0 to 1, as in the Pxy diagrams. Iteration can be performed by circular recalculation on the spreadsheet. Unfortunately, spreadsheets vary significantly in their implementation of circular recalculation, even from version to version, and it is difficult to give a "recipe" that works in all cases. Often, particular rearrangements of equations or ordering of the columns is necessary. No matter what package was being used, however, I have always been able to find some method that eventually worked. Thermodynamics textbooks commonly contain graphs of excess and partial excess properties such as volume and enthalpy for binary solutions. In the volumetric properties assignment, students generate similar graphs for ethanol-water using density data as a function of composition taken fromContinued on page 291.

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288 Chemical Engineering Education CHEM-E-CAR DOWNUNDERMARTIN RHODESMonash University Melbourne, Victoria 3800 Australia Copyright ChE Division of ASEE 2002 ChElaboratoryThe Chem-E-Car competition has been run for undergraduates by the AIChE for the past three years with finals at the AIChE annual meetings. The idea is for teams of undergraduate students to design and build a small car powered by a chemical reaction. The objective is for the car to travel a certain distance and then stop. The distance to be traveled and the weight to be carried by the car are not announced until the day of the competition. The emphasis is on control of a chemical reaction, with a keen eye on safety and the environmental impact of the design. The winner is the team whose car stops nearest to the required distance. In addition to designing and building the car, each team must make a poster that describes the car's operation and include a safety and environmental assessment. Having witnessed the enthusiasm of the participating students and spectators at the AIChE Chem-E-Car Competition finals held in Dallas and Los Angeles, I decided to organize a Chem-E-Car competition here in Australia. Early in 2001, I contacted all chemical engineering departments in Australia and New Zealand, sent them copies of the rules (for the AIChE competition), and invited them to join. Six departments responded enthusiastically, and within a couple of months teams of students were working away. The original plan was to have local competitions within each department, with these competitions generating finalists for the grand Australasian final. University work and the difficulty of the Chem-E-Car task took its toll, however. Several teams fell by the wayside, including the team from my department. As time went on, it Martin Rhodes is Professor in the Department of Chemical Engineering at Monash University in Melbourne, Australia. He has a keen interest in chemical engineering education and specializes in particle technology, a subject on which he has written an undergraduate textbook. His research interests include fluidization, gas-particle flows, interparticle forces, and particle mixing. 1a 1bFigure 1. The NUS car (a) with bodywork removed to reveal the inner detail and (b) in motion. Figure 2. The UNSW car drifting through its selfgenerated mist.became clear that the grand final would be a fight between five teamsfour from Australia and one from the National University of Singapore, who, upon hearing about the competition, asked if they could take part. The grand final was held on day three of the World Congress of Chemical Engi-

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Fall 2002 289 Figure 3. The Sydney University three-wheeled, two-cell car. Figure 4. The Newcastle One team car experiencing terminal technical problems. 5a 5bFigure 5. The Newcastle Two team's car a) running without its sparkler timing device and b) in full sparkling glory. neering at the Melbourne Exhibition Centre in late September.THE TEAMS AND THE CARSNational University of Singapore (NUS)The NUS car (Figure 1) used the decomposition of 15% hydrogen peroxide solution with dilute potassium permanganate solution as a catalyst to generate oxygen, which was stored in the stainless steel reactor. Opening the ball valve at the rear of the reactor released the contents in short order, propelling the car along. The car was stopped by friction. The distance traveled was controlled by adjusting the quantities of reactant used and the time for reaction. During the test runs prior to the competition, this car announced itself with a loud bang and blew away the plastic sheeting that had been specially erected as a splashguard behind the start line. Race helpers hurriedly modified and reerected the splashguard. The valve on the rear of the reactor was equipped with a lengthened handle. Starting the car involved swinging an oversized pair of laboratory tongs, golfiron style, to hit the handle and swiftly open the valve. The swipe with the tongs only happened at the precise time, dictated by the reaction countdown. On its first official competition run, the team member wielding the tongs was either a little too enthusiastic or had poor aim; the result was that the car turned onto its side within a few meters of the start line.University of New South Wales (UNSW)The UNSW car, named "Cold Power," was powered by a 1.5-3V electric motor running from an electrochemical cell. The cell used solutions zinc sulfate and copper sulfate with zinc and copper electrodes. The electrodes were made from 1mm sheet, totaling around 200cm2 for each metal. The distance was controlled using a switch that involved measuring the speed of sublimation of solid carbon. A quantity of solid carbon dioxide was placed in a container on one side of a pulley. On the other side were a number of counterweights such that the solid carbon dioxide container rested on a metal electrode, which completed the circuit. As the solid carbon dioxide vaporized, the weight on that side of the pulley decreased until it was outweighed by the counterweights. Once this occurred, the solid carbon dioxide container lifted off the electrode and cut the power to the motor. The amount of solid carbon dioxide initially placed in the container (anywhere from 20g to 50g) was determined by the distance to be traveled. The UNSW car was interesting to observe as it glided along in a white cloud generated by the subliming carbon dioxide (see Figure 2).Sydney UniversityThe Sydney University car (see Figure 3) was designed and built by a team of first-year engineering students (mechanical and chemical). It was driven by an electric motor powered by an electrochemical cell comprised of 1.8M sulfuric acid and potassium dichromate solution (1g/100ml) with zinc electrodes. This car had three wheels and a low center of gravity. It

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290 Chemical Engineering Education Figure 6. The winning poster of the Newcastle Two team. was able to travel well in a straight line. The inventory of acid was only 5ml, and the cell was enclosed to minimize spillage problems in the event of a crash. The first run of the Sydney team was good, but unfortunately, it started without the required weight.Newcastle University Team OneThe Newcastle Team One car was driven by a small 3.5V 1A motor and powered by a zinc/copper copper sulfate battery, using 1M copper sulfate solution and 1M sulfuric acid. This car made a promising start, getting third closest to the line on its first run. Technical problems (a broken electrical connection to the motor), however, prevented it from leaving the starting line on its second run (see Figure 4).Newcastle University Team TwoThe Newcastle Team Two car (see Figure 5) was driven by a 3V electric motor via a six-speed gearbox. The motor was powered by a battery of four cells each producing 1.45V-two cells in series with another two cells in series. The cell used was an alkaline battery, very similar in chemistry to commercial batteries. A ch ildren's sparkler was used as a timing fuse to stop the car. When the sparkler burned to the end, it melted through a section of solder wire incorporated into the cell wiring and disconnected the power supply from the car motor. The length of the sparkler determined the running time of the car and was decided according to the results of previous trials. Sparklers were found to be remarkably consistent and had a burning rate of around 0.28 cm/s. Extensive safety testing had been carried out on sparklers used indoors to ensure minimum smoking or sparking. W ith the sparkler burning away as the car rolled along, it was pleasing to the eye. In practice on home turf, it had managed to consistently stop only a few centimeters from the desired distance. On this day it was the most consistent car and eventually achieved second place.THE RESULTT eam Newcastle Two won the poster competition with a concise, informative display (see Figure 6). The performance competition winner was the team from the National University of Singapore; after a crash on its first run, their car stopped only 135cm short of the 20m designated distance on its second and final attempt. Team Newcastle Two took second place when their car stopped 180cm after the line. The trophy, a polished Plexiglas CSTR on wheels, was made by the workshop staff at Monash University and is now in the hands of the NUS team. Reports from faculty involved in supervising the local department competitions suggested that the students benefited greatly from the experience. To get to the start line with a car that was competitive and worked according to the rules, each team had to solve the series of specific engineering problems. Several teams went beyond mere functionality and considered aesthetics. The concentration and enthusiasm of the participants was palpable, and I was privileged to witness it. It is not often that our students engage in something that is fun and also a great learning exercise. The Chem-E-Car Competition was this and more. The Chem-E-Car Competition will be held again next year with the grand final in Christchurch, New Zealand, at the CHEMECA 2002, the annual conference of chemical engineers in Australia and New Zealand.

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Fall 2002 291handbooks.[10,11] By doing this assignment, students can develop a better intuitive understanding of the meaning of such excess property data because they see where the data came fr om. Add iti ona lly, the magnitude of the variation of activity coefficient with pressure is related to the partial molar excess volume. Using these results, students can prove to themselves why activity coefficients are typically assumed pressure-independent. Before using activity coefficients in VLE calculations, students prepare a few plots of activity coefficient versus composition or of infinite dilution activity coefficient versus temperature. When they produce graphs similar to those in the textbook, students reinforce their concept of what "shape" these functions should have. Also, by plotting results from several different equations on one graph, students see that it makes little difference which correlation is chosen in most cases. For subsequent VLE and LLE calculations, they typically use the Margules equation because it is the most simple mathematically. In conjunction with VLE phase diagrams, students produce plots of excess free energy functions. These plots can be used to determine constants in an activity coefficient correlation. For example, a plot of GE/RTx1x2 versus x1 can be used to determine Margules equation parameters by a straight-line fit. When constants determined by several methods are used to plot an xy diagram, students learn the fit of the data is as important as which equation is used. Phase separation and LLE are analyzed with graphs of free energy of mixing versus liquid composition. For LLE, it is the shape of these curvesconvex or concavethat is the determining factor in phase stability. As with the VLE data, students generate plots of these functions from experimental data points and, by fitting activity coefficient correlations in various ways, compare the results. Phase equilibrium and chemical reaction equilibrium are often taught in one course. I have also successfully used computer spreadsheet assignments or demonstrations for class discussion in the reaction equilibrium portion of the course. It is a fundamental belief of mine that students will choose to use the computer and specific software in cases where it makes a problem easier to solve. When I assigned these problems, I did not require the use of specific software. (In fact, I did not require the use of a computer at all, but with the availability of computing resources and the students' general familiarity with computers, no hand-plotted solutions have been submitted in about ten years!) I typically discussed how to structure a spreadsheet for the assignment and frequently had the students work through a hand calculation for a single data point as an in-class exercise. The majority of students "follow the path of least resistance" and complete the assignment using the standard spreadsheet package, currently Microsoft Excel. The specific choice of spreadsheet has little effect. Students have solved the problems using Quattro Pro, Lotus 1-2-3, SuperCalc, and the Smart Spreadsheet in past years. Moreover, it is unnecessary to use a spreadsheet, as a few students have demonstrated by solving the problems using programming languages (FORTRAN, C), graphics packages, and math solvers (Mathcad, Maple). All students eventually gravitated to spreadsheets by the end of the class, however. The only warning I give to students who use nonstandard computer software is that I may not be able to assist them with computer-related problems if they are using a package with which I am unfamiliar.CONCLUSIONSIn teaching phase equilibrium thermodynamics, I have attempted to promote understanding and intuition of the course material. Initial explanation that the goals of the class relate mainly to data handling and generation, unlike other chemical engineering classes, prevents confusing expectations from developing. Meaning and consequences of data are emphasized, particularly for abstract quantities such as activity coefficients for which interpretation is not necessarily explicit. Wi despread presentation and students' use of graphical data is made convenient using computer spreadsheet software.ACKNOWLEDGMENTSThese computer assignments were developed over a series of courses taught at Michigan State University and Villanova University.REFERENCES1.Prausnitz, J.M., R.N. Lichtenthaler, and E.G. de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed., Prentice-Hall Inc., Englewood Cliffs, NJ, p. 4 (1986) 2.Smith, J.M., H.C. Van Ness, and M.M. Abbott, Introduction to Chemical Engineering Thermodynamics 5th ed., McGraw-Hill, New York (1996) 3. Kyle, B.G., Chemical and Process Thermodynamics 2nd ed., PrenticeHall, Englewood Cliffs, NJ (1992) 4.Bird, R.B., W.E. Stewart, and E.N. Lightfoot, T ransport Phenomena John Wiley & Sons, New York (1960) 5.Felder, R.M., and R.W. Rousseau, Elementary Principles of Chemical Processes John Wiley & Sons, New York (1986) 6.Bennett, C.O., and J.E. Myers, Momentum, Heat, and Mass Transfer McGraw-Hill, New York (1985) 7.Savage, Phillip E., "Spreadsheets for Thermodynamics Instruction," Chem. Eng. Ed. 29 (4), p. 262 (1995) 8.Pratt, R.M., "Thermodynamic Properties Involving Derivatives: Using the Peng-Robinson Equation of State," Chem. Eng. Ed. 35 (2), p. 1 12 (2001) 9.Elliott, J.R., and C.T. Lira, Introductory Chemical Engineering Thermodynamics, Prentice Hall PTR (1999) 10.Green. D.W., and J.O. Maloney, eds, Perry's Chemical Engineers' Handbook, 7th ed., McGraw-Hill, New York, NY (1997) 11 .W east, R.C., ed., CRC Handbook of Chemistry and Physics, 60th ed., CRC Press, Boca Raton, FL, D-227 (1979) User-Friendly Phase EquilibriumContinued from page 287.

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292 Chemical Engineering Education ON IMPROVING "THOUGHT WITH HANDS" Copyright ChE Division of ASEE 2002 ChElaboratoryG.K. SURESHKUMAR, K.C. KHILARIndian Institute of Technology, Bombay India 400 076Laboratory exercises are essential[1,2] toward the development of a good chemical engineering graduate with desirable skills such as independent learning, interdependent learning, problem solving, critical thinking, creative thinking, interpersonal skills, teamwork, leadership, integration, communication, and change management.[3] The standard laboratory exercise in chemical engineering, however, revolves around an apparatus that remains unchanged for several years and can lead to unethical practices among students[1,4] such as submission of data/reports from previous years. Moreover, the application of thought, which is crucial for laboratory work and developing the skills mentioned above, is almost nonexistent in the standard laboratory exercise. From an instructional-objectives viewpoint,[5] most laboratory exercises are designed to be at Bloom level 2 (comprehension) out of the possible six levels. This leads to severe resentment toward laboratory work among students and professors alike. Students consider lab courses as a formality to be completed, while faculty treat them as poor cousins of theory courses, relegating the entire responsibility for lab courses to lab supervisors or teaching assistants. We believe that if students are challenged to think critically on laboratory exercises and encouraged to be creative, their interest in and respect for laboratory work would improve, and in turn, the faculty would be further motivated to offer better laboratory courses/projects. With this belief, a laboratory course consisting of both dual-step laboratory exercises and a recommendation/innovation exercise was conceived and assigned to third-year (junior) undergraduate students taking the fluid mechanics laboratory at the Indian Institute of Technology, Bombay. Our laboratory guidelines state that the overall aim of this laboratory course is to inspire students to appreciate the underlying themes of the experimental aspects/approaches to engineering/science with fluid-flow aspects as a model subject. The goal is to develop students' abilities to "think with their hands." Another purpose of this course is to improve understanding of fluid-flow principles, to develop a physical feel for some fluid-flow situations, to develop a familiarity with some commonly used fluid-flow equipment, to inculcate a concern for safety, to improve communication of experimental results, to improve the quality of analysis and inquiry, and to kindle the spirit of discovery in students. Further, we expect the exercise to develop some of the abovementioned skills in a chemical engineering graduate.THE LABORATORY EXERCISESThe activities for the laboratory consisted of dual-step laboratory experiments (p erformed by student groups) and a recommendations report (an individual activity). The Dual-Step Laboratory Exercise Each laboratory experiment was conducted over two lab sessions. During the first session, student groups were expected to follow the procedures given in the manual to carry out the experiment. Students were expected to become comfortable with the equipment and the experiment, and the firstsession experiments were designed accordingly. After the first session, students were required (as homewor k) to analyze the data t aken during the lab session based on the theoretical principles in the lab manual/fluid mechanics textbook/notes and examine whether the results obtained were asG.K. Sureshkumar (G.K.) is currently Associate Professor in the Chemical Engineering Department at Indian Institute of Technology, Bombay. He received his BTech. in Chemical Engineering from Indian Institute of Technology, Madras, and his PhD from Drexel University. His research interest is free radical-based improvements in the productivity of bioreactors. He can be reached at Kartic C. Khilar is currently Professor in the Chemical Engineering Department at Indian Institute of Technology, Bombay. He earned his BTech degree in Chemical Engineering from Indian Institute of Technology, Kharagpur, and his PhD from University of Michigan. He and his students work in nanoparticle production and colloid-associated contaminants transport in porous media.

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Fall 2002 293expected. The following ensued:a)If the experimental results matched the expected results, students were expected to think of additional experiments, preferably new ones, that could be done with the same (or slightly modified) setup. But the additional experiments need to be done within the time frame of the second lab session. We believe that working with these practical constraints would help students acquire "street smarts," which are useful in handling real-world problems. b)If the experimental results did not match the expected results, students were required to form hypotheses based on the results and design ways to experimentally (with certain calculations) prove or disprove their various hypotheses in the second lab session. The emphasis was on the technical/scientific rigor in proofs. The students were also warned that their theories could be proved false by their experiments and that it was acceptable to admit they did not understand the reasons for disagreement within the time available to them and therefore, additional study would be required.After the second lab session, each student group was expected to submit a single report in the regular format, i.e., (a) Aim and Objectives, (b) Methodology, (c) Results and Discussion (which was required to be significant), (d) Conclusions, and (e) the original data sheets. The reports were graded on the following bases: If the actual results matched the expected results: Ability to follow procedures10% Data analysis (1st session)15% D iscussion (1st session)15% Creativity/originality aspects (2nd session)20% Data analysis (2nd session)15% D iscussion (2nd session)15% Presentation (mainly communication)10%Reports that addressed novel aspects to study in their second session were rewarded handsomely in grading the creativity/originality criterion (see the student examples presented later). If the actual results did not match the expected results: Ability to follow procedures10% Data analysis (1st session)15% D iscussion15% C larity in thought and situation/problem analysis (2nd session)20% R igor (2nd session)15% D iscussion (2nd session)15% Presentation (mainly communication)10%Reports that were well developed on both the possible reasons for the disagreement between actual and expected data and the experiments to prove or disprove them were given high marks for the clarity-in-thought criterion. The difficulty level in problem analysis was also recognized in that criterionreports that fully analyzed a difficult situation received higher marks than those that, as a matter of chance, analyzed a simple, easy-to-identify situation. Also, reports that unequivocally proved or disproved their points received high marks for the rigor criterion. Other criteria, such as data analysis, discussion, and presentation, carry their usual weight. The Recommendations Report Over the duration of the course, each student was expected to think about an experiment or a set of experiments that could be done in the fluid mechanics lab. Students were encouraged to be as creative as possible. Near the end of the course (a week before the last day of classes), each student was expected to submit a detailed report on this experiment (or set of experiments) and the equipment and instruments needed. The reports were evaluated on the following bases:C reativity/originality aspects30% C larity in thought20% Detail30% D oability10% Presentation (mainly communication)10%The dual-step exercises evaluated through the reports carried a 70% weight, and the recommendation report carried a 30% weight toward the final grade.IMPLEMENTATION OF DETAILS /RATIONALEIn the beginning of the semester before the experiments began, the instructor met the class and discussed the exercises and recommended strategies. In addition to experimental details for the first session, the laboratory manual carried information on safety procedures for the lab, error analysis, technical writing, and the unacceptability of academic dishonesty, all of which were seriously discussed in the initial meeting. The instructor also emphasized the need for safety procedures whenever he observed lapses during the lab sessions. Student groups were asked to select their own leaders who would assign duties for the group members and be generally responsible for the group's activities. This ensured that an avenue for the development of teamwork and leadership skills existed. Also, on many occasions, the instructor communicated to the groups through their leaders. Before the start of the first session, the groups were advised to familiarize themselves with the details for each experiment using the lab manual and the textbook. The firstsession experiments were designed as shorter versions of the experiments given in the usual lab course, and students were encouraged to spend the additional time becoming comfortable with the setup and the various equipment used. For example, the instructor encouraged the students to raise questions regarding the equipment or the reasoning behind the various experimental steps, which the students normally took for granted. The students took the first session seriously because they knew they had to consider the setup, the experimental methods, and the underlying theory in order to have an interesting second session. During the experiment (both sessions), groups were advised to record the data in duplicate

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294 Chemical Engineering Education . the overall aim is . to improve the quality of analysis and inquiry, and to kindle the spirit of discovery in students.using a carbon sheet, and the members were asked to sign each data sheet. The duplicate copy was submitted to the instructor at the end of each session, and nonsubmission would result in a grade of zero for that session. The instructor has never had to give a zero over the past two years for this reason. After the data analysis for the first session, the groups were required to meet the instructor to discuss their plans for the second session. This meeting was not to guide the students on what they could do in the second session, but for the instructor to listen and comment on the possibility of doing the experiments. This meeting was normally scheduled a few days before the second session, primarily to address any special requirements for the experiment that needed to be communicated to the lab superintendent. Also, this meeting helped the instructor ensure that the secondsession experiments were of proper scope (neither too large nor too small) and reasonably well thought out, especially if the actual data matched the expected data in the first session. In addition, it was communicated to the students at the beginning of the semester that no complete dismantling of the set-ups would be allowed, except in rare cases. This encouraged the students to think of "non-invasive" means for testing their theories. Also, this precaution was necessary because some piping networks in our lab had packings to prevent leaks that would be difficult for an inexperienced person to reassemble. The lab reports for the dual-step exercises were due before the start of the next experiment; the instructor graded them and offered constructive criticism and feedback within a week of submission. Students appreciated the timely feedback. The grading of the recommendations report was time consuming (three to four consecutive, full days). As long as grades are important, some students may cheat to get the best grade;[6,7] t herefore, a significant amount of time was spent establishing the originality of submitted reports. This was achieved through one-on-one interviews with students who had submitted "doubtful" reports. During an interview, it was easy to ascertain whether cheating had taken place by asking relevant questions, most of which were on the experiment submitted. All experiments were run on existing equipment; therefore, this dual-step exercise does not require additional funds for equipment. It can be run anywhere, even in the face of fund crunches. It also provides a greater probability for disagreement between actual and expected data, and thus helps students develop lateral-thinking abilities while forming hypotheses for the disagreement. Therefore, the dual-step laboratory exercise provides a way to turn a seeming disadvantage in running an existing laboratory course into an advantage of improving thought in students.SAMPLES FROM STUDENT EXERCISES Samples from the Dual-Step Laboratory Exercises Agreement Between Actual and Expected Data An experiment for the lab involved studying the relationship between Power number and Reynolds number in an agitated system. One of the groups found good agreement between actual and expected data and therefore had to think of additional experiments to do on the same setup. They decided to compare the relationship between Power and Reynolds numbers for an aqueous system with and without a surfactant. They found that the Power number for the corresponding Reynolds number was lower for the system with surfactant than for plain water. Therefore, they concluded that the power requirements for an aqueous system with surfactant are lower than that for plain water. They also provided qualitative explanations for the observed results from a molecular viewpoint. Another experiment involved studying twophase flow characteristics in a vertical transparent tube such as the relationships between slug length and slug velocity and between pressure drop and void fraction, etc. The group that obtained results as expected decided to study the relationship between the radius of curvature of the slug's leading edge and its length. They developed a theory based on geometrical considerations for the variation of the leading-edge curvature with slug length; they also showed correspondence between the theoretically expected results and measured data. Disagreement Between Actual and Expected Data Another experiment involved a piping network with various types of pipes, fittings, and valves. The objectives for the first session included determination of the frictional losses across the pipe fittings and valves. The experiment required recording readings from manometers att ached to the pressure taps across relevant fittings or valves and determining the water flow rate using the pressure difference measured across the orifice meter. The first group that worked on the experiment found that the friction loss constants obtained for the various fittings on the network were higher by almost an order of magnitude than literature values. Therefore, the group first postulated that scale formation led to higher loss constants. To test the postulate, they arranged for the network to be cleaned thoroughly and repeated the experiment in the second session. This did not yield significantly different loss constants, thereby partly disproving the postulate that the scale formation alone resulted in the discrepancy. Students in one of the other groups that worked on the experiment postulated that the water-flow rate measurements using the calibration curve for the orifice meter may not have been correct; they noticed

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Fall 2002 295a discrepancy between flow rates measured using a measuring jar/stop watch arrangement and the orifice meter readings. So, the students prepared a fresh calibration graph for the orifice meter and found it to be different from the existi ng, e rroneous calibration chart. They also proved that the friction loss constants obtained using the new calibration graph were comparable to the values found in the literature. Samples from the Recommendations Report A student named Nikhil Agarwal suggested an inexpensive, simple method for determining the viscosity of a solution by allowing it to flow over a smooth, inclined flat plate from a reservoir and taking measurements. Using suitable balances, Nikhil expressed the viscosity as a function of measurable parameters (with origins from the thickness of the liquid layer[8]) as: $/ = g Q33 coswhere $ is the fluid density, g is the acceleration due to gravity, / is the film thickness, is the angle between the plate and the vertical, and Q is the flow rate. He carefully considered the details and limitations of the experimental procedure and suggested a method to study the variation of viscosity with temperature using the same setup. Another student, Sikander Siraj, using input from a friend in electrical engineering, suggested a photoelectric diodebased (PED) device for the measurement of slug lengths in the two-phase flow experiment. The idea had its origins in the burglar alarm principle. For the measurement, he used the deviation caused by the refraction of the infrared beam when it passes through media of different refractive indices.STUDENT AND STAFF FEEDBACKThe students were asked to send their comments through e-mail to their class representative, who removed details pertaining to the authors of the comments, compiled without editing, and forwarded the comments as a single file to the instructor. For the improved version of the lab, comments from 82 out of 83 students were received, and all except nine explicitly stated that the lab was useful to them. They said that their learning included fluid-mechanics principles, application of thought to a lab, leadership qualities, thinking creatively, and working in a group. Some positive comments over the past two years include, "Due to this lab alone, I can say that I know some chemical engineering,'" and "This is the first time I feel what a lab course is all about." Also, many students suggested minor changes in equipment, etc., to improve the lab. Of the nine students who did not state their liking for the lab, seven were neutral, and the other two said that the lab was not useful to them. The staff associated with the lab were enthusiastic about fulfilling the re quirements of the lab. They also said that they enjoyed setting up the various experiments although it involved additional time.INITIAL CHALLENGESThe first time it was offered, almost all students expressed that the lab demanded a lot of their time. We believe this was because students compared it with previous editions of the same course. In addition, the same experiments that were given in previous editions were packaged into a two-session (dual-step) format, significantly increasing the work. Therefore, in the next edition of the course, the experiments were consolidated into half the original number, with all other details unchanged. Afterwards, there were very few comments (3 out of 83) that there was too much work. The first time the course was offered, the groups were assigned according to student roll numbers, which the students hated. The next time, the students were asked to form their own groups with the average cumulative performance index (CPI) of the group members being close to the class average CPI; this incorporates cooperative learning elements. Complaints about unsuitable groups were almost eliminated. The remaining challenge is group size. Six students in a group is nonideal and should be reduced. We intend to reduce the number by running the experiments more frequently in the future. The logistics constraint needs to be addressed first, however. In short, a focus on developing the critical thought process in students made the laboratory course interesting to both students and instructors and also developed students' respect for experimental work.ACKNOWLEDGMENTSWe would like to thank the students of CL333 for their enthusiastic participation in the exercise as well as O.S. Sawarkar, V.B.V. Nair, V. Ramachandran, and A.D. Kadam for their contributions.REFERENCES1.Middleberg, A.P.J., "Laboratory Projects: Should Students Do Them or Design Them?" Chem. Eng. Ed. 29 (1), p. 34, (1995) 2.Jones, W.E., "Basic Chemical Engineering Experiments," Chem. Eng. Ed., 27 (1), p. 188, (1993) 3.Rugarcia, A., R.M. Felder, D.R. Woods, and J.E. Stice, "The Future of Engineering Education. I. A Vision for a New Century," Chem. Eng. Ed. 34 (1), p. 16, (2000) 4.Macias-Machin, A., G. Zhang, and O. Levenspiel, "The Unstructured Student-Designed Research Type of Laboratory Experiment," Chem. Eng. Ed., 24 (2), p. 78, (1990) 5.Felder, R.M., D.R. Woods, J.E. Stice, and A. Rugarcia, "The Future of Engineering Education. II. Teaching Methods that Work," Chem. Eng. Ed., 34 (1), p. 26, (2000) 6.Felder, R.M., "Cheating: An Ounce of Prevention...Or the Tragic Tale of the Dying Grandmother," Chem. Eng. Ed. 19 (1), p. 12 (2000) 7.Sureshkumar, G.K., "A Choose-Focus-Analyze Exercise in ChE Undergraduate Courses," Chem. Eng. Ed. 35 (1), p. 80, (2001) 8.McCabe, W.L., J.C. Smith, and P. Harriott, Unit Operations of Chemical Engineering, McGraw-Hill, Singapore, 6th ed., (2000)

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296 Chemical Engineering Education THE EARTH'S CARBON CYCLEChemical Engineering Course MaterialROGER A. SCHMITZUniversity of Notre Dame Notre Dame, IN 46556On three occasions in recent years, I have taught an elective course at the University of Notre Dame for chemical engineering seniors titled "Topics on Ecology and the Environment." I developed the course because I felt it was important for our students (and myself as well) to have a greater appreciationfrom a chemical engineer's perspectivefor the workings of Earth's natural processes, both biotic and abiotic, and a knowledge of how human and industrial activities are disturbing or might disturb them. One of the significant components is a module on the carbon cyclethe subject of this article. In gathering and developing material for this module and others in the course, I was struck by these observations: Many of the Earth's processes, including the carbon cycle, though fundamentally very complex in detail, can be represented by simple models that are useful for study purposes and even for quantitative estimates, at least as a first approximation. The development, analysis, and application of models are well within the scope of an undergraduate chemical engineering curriculum. The subject matter, or bits and pieces of it, can be integrated advantageously, straightforwardly, and nearly seamlessly into core chemical engineering courses.My objectives in this article are to demonstrate all of this, using the carbon cycle as the means, and to provide convenient material for others who may be persuaded by my third observation. Of the biogeochemical cycles of the six major "life" elements, C, N, P, S, O, and H, the carbon cycle receives the lion's share of the attention in the literature. That's no surprise inasmuch as most of our energy needs are met by the burning of carbon-based fuels and inasmuch as the consequent increasing level of atmospheric carbon dioxide and its potential effect on the Earth's climate is a frequent focus of attention in technical and nontechnical publications. What's more, chemical engineers will have opportunities to play a prominent role in any steps taken to moderate that level, whether those steps be toward alternate energy sources or toward sequestering or otherwise preventing emissions directly into the atmosphere.THE CONCEPTUAL MODELCarbon is found in all of Earth's compartments or reservoirsin the biota and in the atmosphere, hydrosphere, and lithosphere. Mathematical models describing the cycle account for the movement of carbon among and within those reservoirs and for anthropogenic disturbances, which are principally due to fossil fuel burning and deforestation ( i.e. mainly burning of removed trees) for land use changes. Figure 1 presents a schematic diagram of a conceptual model of the carbon cycle consisting of six reservoirs, numbered one through six. (A seventh reservoir for fossil fuels enters dynamically into the model later only as a disturbance to the six-reservoir natural cycle.) Other reservoirs, including sediments, marine biota, and lakes, rivers, and streams, are omitted for reasons given later. In one way or another, all models are based on this starting picture, which is sometimes ChEcurriculum Copyright ChE Division of ASEE 2002Roger Schmitz is the Keating-Crawford Professor of Chemical Engineering at the University of Notre Dame. He received his bachelor's degree from the University of Illinois and his PhD from the University of Minnesota, both in Chemical Engineering. His current interests are in the modeling and analysis of environmental and ecosystem dynamics.

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Fall 2002 297Figure 1. Schematic diagram of a six-box model of the carbon cycle. Values shown for reservoir masses (Mi, in PgC) and fluxes (Fij, in PgC/y) are representative of the pre-industrial steady state (~1850).modified to include one or more of the omitted reservoirs. Models differ primarily in the extent of detail and correspondingly in the objectives of the modeler. For example, highly detailed climate studies employ general circulation models based on fundamental transport equations to describe processes in the atmosphere and/or ocean reservoirs and several types of vegetation to describe the atmosphere-biota exchange.[1] At the other extreme, so-called "box" (or "compartment" or "lumped") models that are intended to give estimates of global averages of carbon in major reservoirs, are based on spatially aggregated descriptions, often with no more detail, sometimes even less, than that shown in Figure 1.[2-7] Except to allude to the structure of high-end models and their purposes (and sometimes to compare results), I choose to work with simple box models in the course. In short, as tools for study, they have suited my purposes. Further, if properly calibrated and tuned, they have proven useful for quantitative purposes so long as the principal interest is in global averages, particularly in atmospheric carbon dioxide levels. The conceptual model represented in Figure 1 and the mathematical description to follow are amalgamations of several box models that I have studied and used in the course. The version presented here is closely patterned after, but not identical to, that described in a recent publication by Lenton.[3]I usually have the students go through the development of other models as complementary outside work.THE REFERENCE PRE-INDUSTRIAL STATEThe quantities shown in parentheses in the boxes in Figure 1 represent estimates of the "pre-industrial" distribution of carbon ( i.e. the mass of element C in all of its compounds) in petagrams (PgC, 1 Pg = 1015g.) These are typical reference values presumed to rep resent the balanced (steady-state) conditions around the year 1850early in the industrial revolution when there was little or no observable change from year to year. The numbers in parentheses beside the arrows in Figure 1 represent estimates, in petagrams of carbon per year (PgC/ y), of the transport (commonly termed "fluxes" in the relevant literature) of carbon between reservoirs. Such fluxes are estimates, adjusted so that each box is balanced at a steady state, where it would remain unless disturbed. There is no common agreement on the values of the reference pre-industrial masses and fluxes, or even on the reference year (generally between 1800 and 1860), but the variation from one reference source to another is of little significance. The values shown in Figure 1 are in line with those used in the references cited above. M1, the mass of carbon in the atmosphere reservoir can be taken to be entirely in the form of CO2. The 612 PgC in that reservoir corresponds to a CO2concentration of 286 ppmv (parts per million by volume) the concentration unit used in most illustrations to follow. (The conversion factor of 2.128 PgC/ppmv is based on a total atmosphere mass of 5.14 x 106 with a molecular weight of 29.) Notice the notation in Figure 1. Mi stands for the mass of carbon in box i; Fijfor the flux of carbon from box i to box j. The anthropogenic disturbance flux Ff moves carbon from a nonrenewable fossil fuel reservoir to the atmosphere.* The other anthropogenic disturbances, Fdand Fr, take carbon from the renewable terrestrial biota reservoir to the atmosphere (deforestation) and from the atmosphere to the terrestrial biota (reforestation), respectively. (There is increasing interest in sequestering part of Ffby redirecting it to cavities in the lithosphere and/or to the deep ocean.[8,9] Those slight but interesting variations to the model will be mentioned in suggested exercises near the end.) The following list gives a succinct description of the other fluxes:*Actually, Ff accounts for all carbon emissions to the atmosphere except those due to deforestation. It is commonly termed "emissions due to fossil fuel burning"a term that I shall use throughout. Other industrial sources, such as cement manufacturing, account for only a few percent of the total.

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298 Chemical Engineering Education F12, F21, F13, and F31 are simply mass transfer rates for the exchange of carbon (as carbon dioxide in this case since nearly all atmospheric carbon is in that form) between the atmosphere and the ocean waters. Basically, the rates are described by the product of a mass transfer coefficient and a concentration driving force, but the nuances involved in using that description warrant further attention later. F23 represents the advective flow of carbon from the warm to cool surface ocean reservoirs. This flow, which accounts for most of the ocean mixing, results from the downflow of cool surface water at high latitudes and the corresponding upwelling to the warmer surfaces at low latitudes. There is also an eddy-mixing component contained in the fluxes between the surface and deep ocean waters. The model could be further simplified without affecting results noticeably by lumping boxes 2 and 3 into a single box. F15 is the rate of photosynthetic uptake of carbon from the atmosphere by terrestrial vegetation. This flux, assumed often in models of this type to be describable by a single overall rate expression, gets special attention later. M5 is the total carbon in terrestrial biota, but we might think of it as being the mass of vegetation since about 90% of it is in forests. F56 is the flux of carbon in litter fallmostly dead leaves and the like, but generally including all dead and waste products from the terrestrial biota. F51 and F61 are the fluxes of carbon, mostly as carbon dioxide with small amounts as methane and other compounds, to the atmosphere by biotic respiration.As mentioned above, a more complete box structure would include additional elements for aquatic biota; sediments; and rivers, streams, and lakes. Such additions are more suited for discussions and assigned work than for incorporation into a working model for the following reasons: The inventory of carbon in aquatic biota and in rivers, streams, and lakes is negligibly small; sediments, the largest of all reservoirs with a total carbon mass of about 108 PgC, are the most sluggish by far; the small fluxes (~0.3 PgC/y) into and out of the sediments lead to a first-order time constant of the order of several hundred million years! For the reservoirs represented in Figure 1, first-order time constants, calculated as the ratio of the mass of carbon in a reservoir to the flux of carbon out of it, range from 1.19 years for the cool surface waters in box 3 to 330 years for the deep ocean waters in box 4. For the atmosphere, box 1, it's 3.48 years. The illustrations in simulations to come will cover time spans up to 250 years, over which time the sediment reservoirs are virtually steady.THE EQUATIONSThe mathematical description of the box model of Figure 1 consists of a set of carbon balance equations. For the atmosphere, box 1, for example dM dt FFFFFFFFFFfdr 1 21123113 5115 611 = Š+Š+Š+++Š()()In general dM dt FFi jiij jji=Š()+()=0disturbances1 62If a particular Fij does not appear in Figure 1, its value in Eq. (2) is zero. The disturbances, as represented in Figure 1, appear only in the balances for boxes 1 and 5. To keep account of the fossil fuel supply, a seventh box is added, an out-of-cycle, nonrenewable reservoir of the carbon in fossil fuels. The following balance describes the depletion of that reservoir: dM dt Ff 73 =Š()All terms in these equations have units of petagrams of carbon per year (PgC/y). The initial conditions are the reference pre-industrial reservoir levels in 1850. I use 5300 PgC for the initial value of M7, somewhat arbitrarily, but based on rather common statemen ts t hat wh ile t he to ta l carbon stored in fossil fuels is about 10,000 PgC, only about half of it can actually be recovered for use. Since most of the reservoirs undergo relatively small changes over periods of interest, as later simulations will show, the fluxes can be related to the reservoir masses by first-order processes. That isFkMijiji=()4Such relationships are frequently employed in box models of the biogeochemical cycles, including the carbon cycle, with three exceptions: F15, F21, and F31. For the others, the numerical value of kij can be obtained readily from the reference data given in Figure 1. If the carbon in the ocean were present simply as carbon dioxide in aqueous solution, we would expect all four of the F's connecting the ocean surface waters to the atmosphere to be describable by Eq. (4)under the safe assumption that Henry's law applies to the dilute CO2 solution. The situation is complicated, however, by the fact that CO2 in aqueous solution enters into equilibrium chemical reactions involving carbonate and bicarbonate forms. Therefore, while the fluxes F21 and F31 can be related linearly to aqueous CO2, they are not linearly related to the total C; that is, to M2 a nd M3. The relationship to the total carbon in solution is complicated. It is affected by all of the factors that affect acid-base equilibrium in ocean watertotal alkalinity, salinity, temperature, and dissolved salts of weak bases, such as boron. A rigorous treatment requires linking a set of equations for ocean chem-

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Fall 2002 299istry dynamics to the above set. Some studies[3,5] have followed that procedure, as have I in some instances. Others[2,4,7]have opted for a simpler empirical approach that uses the following relationships:FkMFkM2121 2 3131 32 35 ==() Va lues of the exponents 2and 3, called buffer factors or Revelle factors, can be obtained from charts of the type given in the book by Butcher, et al .[10] They can also be obtained by delving into the intricacies of ocean chemistry dynamics and correlating results of calculations. I used the latter approach to obtain the values shown later, but to save space and to stay on track, I shall spare further detail. My testing has shown that results of computations using constant values of the 's hardly differ from those obtained by appending detailed ocean dynamics to the model, so long as changes in M2 and M3 are relatively small, generally less than 5%. The numerical values of range between 9 and 15; the nonlinearity is surprisingly strong. Notice that with values of 2 and 3 given, numerical values of the rate constants k21 and k31 can be determined from the reference conditions given in Figure 1. The rate of photosynthetic uptake, F15, of carbon from the atmosphere cannot be represented realistically as a linear function of M1. The basic reason is that the function should account for a saturation effect with regard to the nutrient CO2. That is, the rate increases with increasing CO2 but approaches a limit. For small changes in M1, the function may be approximated by a linear relationship, but as a later illustration will show, changes in M1 ar e large over the periods of interest. There seems to be no clear consensus as to what form to use for F15 in models of this type. Whatever the specific form, a common feature is a dependence on atmospheric carbon that suggests an ultimate saturation. The particular one chosen does not seem to be a critical matter so long as the constants are calibrated or tuned to fit existing data. Nevertheless, this is a fertile item for classroom discussion, debate, and outside work. Here I shall use the form employed by Lenton[3] F kM M M forM forM15 15 8 1 1 10 6 = Š + > ()1whereis the threshold value of M1 (I used Lenton's value of 62 PgC.) 1 is a saturation parameter (Lenton used it as a tuning parameter and arrived at a value of 194 PgC. By methods described later, I arrived at a value of 198 PgC.) k15 is a rate coefficient to be calculated from the reference state. M8 is a function that depends on the disturbances Fr and Fd as explained and described below. In short, it accounts for changes in the Earth's capacity for terrestrial biota.The role of the function M8 is important but not obvious at first glance, and definitions and explanations do not come easily. Let me first define it by way of the following equation and then offer brief explanations. Mt kFkFdt Mrrdd ref t 8 5 185017()=+ Š()(),wherekd is the fraction of forested area or mass (or forest capacity) that cannot be reforested (is not available for regrowth) following deforestation activitiesfor example, forest areas cleared for urban development. kr is that fraction of the reforested area or mass that increases the Earth's capacity for terrestrial biota. (This is sometimes termed "aforestation" as opposed to "reforestation" that directly renews deforested areas. M5,ref is a normalizing factor inserted arbitrarily to make M8 dimensionless. I take it to be the initial value of M5.Lenton used this form but did not include kr and Fr explicitly in his formulation. Reforestation can be accounted for without those factors if Fd is allowed to have negative values. I prefer to show Fr and Fd separately for clarity in simulations later. Simply stated, the integral in Eq. (7) accounts for permanent effects of the disturbances Fd and Fr. Were that integral not included, the model equations would lead to the following illogical conclusion, among others: If Ff % 0, and if Fdand Fr eventually settle to zero, the ultimate steady state of carbon in the reservoirs would be identical to the starting reference state; the effects of the temporary nonzero values of the disturbances would die away, according to the model. But obviously the effects of some land use changes must persistfor example, if forest areas are cleared and urbanized with no offsetting reforestation. With the integral included in M8 w ith kd 0 0 and Fr % 0, such land use change would permanently affect the distribution of carbon, not its total amount. Other illustrations can be given to justify the form of M8, but perhaps further explanation, if needed, is better sought in student exercises later. An alternate form of the integral equation above is this differential equation: dM dt kFkF M withinitialconditionMrrdd ref 8 5 8185018 = Š()=(),The numerical value of the coefficient k15 in Eq. (6) can be calculated from the reference values shown in Figure 1, given values for 1 and and taking M8 = 1 (its initial state). W ith Eq. (8) added to the material balance equations, the complete mathematical model consists of the following set of eight ordinary differential equations:

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300 Chemical Engineering Education Figure 2. Historical record of carbon emissions to the atmosphere. Symbols represent reported data;[11,12] solid curves are empirical fits.T ABLE 1Numerical Values and Units for Model Constants symbol value units k120.0931y-1k130.0311y-1k15147y-1k2158( 7302 Š )PgCy1 2 1 Š()Š k230.0781y-1k240.0164y-1k3118( 1403 Š )PgCy1 3 1 Š()Š k340.714y-1k420.00189y-1k430.00114y-1k510.0862y-1k560.0862y-1k610.0333y-129.4310.2-62.0PgC1198PgC kd0.230 kr1.0 dM dt kkMkM M M kM kMkM kMFtFtFt dM dt kMkkMkMkM dM dt kMkMkMfdr 1 12131 15 8 1 1 21 2 31 3 515 616 2 1212324221 2 424 3 131232342 3 2=Š+()Š Š + + ++++()+()Š()=Š+()Š+ =+Š 1 3 331 3 434 4 24234342434 5 15 8 1 1 51565 6 565 616 7 83Š+ =+Š+()= Š + Š+()Š()+()=Š =Š()= Š()Š kMkM dM dt kMkMkkM dM dt kM M M kkMFtFt dM dt kMkM dM dt Ft dM dt kFtkFtdr f ddrr 1 ( ()[]& ()Mref 59,Numerical values for the constants are given in Table 1. Determining the values of the k's, as described earlier, calibrates the model to the data for the reference year 1850. The value for is taken from Lenton's model. The value for kd is somewhat arbitrary and could be adjusted by tuning the model, but I have taken it to be constant throughout at 0.23. (Lenton used a value of 0.27.) I have arbitrarily chosen a value of unity for kr. My method for determining the value for 1, the only tuning parameter, will be described in the next section. The values for 2 and 3 were determined as described earlier. Implicit in this development is the assumption that the carbon cycle is independent of all other state variables, or that all others are constant, such as temperature, moisture, and other nutrient levels. That assumption is frequently invoked, but it may be an oversimplification if the model results are to be applied to global climate dynamics, for example. In the aforementioned work of Lenton[3] the carbon cycle is coupled to the Earth's energy balance, and in that of Ver et al .[7] to other nutrient cycles.TUNING AND TESTING WITH HISTORICAL DATAExtensive historical records are available for testing and tuning the model. Figure 2 shows data on emissions due to fossil fuel consumption, Ff, taken from Marland et al.,[11] and deforestation, Fd, taken from Houghton and Hackler,[12] as well as the total of the two over the period 1850 through 1990. (I used 1990 as the endpoint because the deforestation data given by Houghton and Hackler are not tabulated beyond that year. We can safely assume that reforestation, Fr, has been negligibly small in the past.) The dramatic increase in fossil fuel emissions since the middle of the twentieth century is evident. The solid curves in Figure 2 show my empirical fit of the r epo rt ed d ata In or der to get a rather precise representation I used separate functions over four segments of Ffand over six segments of Fd. This detailed fitting may seem to be overkill. I simply wanted to eliminate an inaccurate

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Fall 2002 301 Figure 3. Reported and model-calculated records of atmospheric carbon dioxide since 1850.T ABLE 2Model Computed Quantities for 1990iMi *1 753 2 744 3 143 4 37071 5 577 6 1489 7 5086 8 0.952*Units of Mi are PgC, except M8, which has no units. The list given in the References section is only a small sample. The interested reader will be led to a much larger assortment of models and r elated subjects simply by entering the keyword "carbon" on a web browser. representation of the disturbance record as an explanation for any model failure. W ith this representation of the historical disturbances and the model constants in Table 1, the system of ordinary differential equations in Eq. (10) can be solved readily, by numerical routines available in a number of software packages, to obtain a model-generated record of carbon in the reservoirs from 1850 through 1990. (I used Mathcad for this particular exercise and extensively throughout the course.) The solid curve of Figure 3 shows the result for atmospheric CO2; the data points are reported estimates or measurements from the Wo rldwatch Institute database.[13] The good agreement between model results and reported data was assured over a portion of the curve, at least by my method of determining the value of 1. Its value of 198 PgC, as given in Table 1, was determined by an iterative search aimed at minimizing the total squared difference between model results and reported data over the period 1980-1990. Admittedly, the good agreement over the early years was also virtually assured because model constants were calculated to give a perfect fit of the reference data of 1850. Over the other years, the maximum disagreement, which occurs around 1925, is less than 1.3%. All such things considered, this test of the model lends legitimacy to its use in predicting carbon distributions through some years ahead. T able 2 lists the calculated 1990 levels of carbon for all reservoirs. Notice that changes in the five of the six reservoirs have been relatively small over the 140-year period, according to the model. The terrestrial biota in box 5 increased only from 577 to 580 PgC owing to the offsetting effects of decreases by deforestation and increases by atmospheric CO2fertilization. The atmospheric reservoir increased by 23% by 1990 and is obviously destined to go higher, but changes in others have amounted to about 2% or less. A total of 214 petagrams of new carbon was injected into the cycle from the fossil fuel reservoir and distributed among the other reservoirs over the period 1850 through 1990. Eventually most of that will reside in the deep oceans, box 4, but by 1990 that reservoir has increased by only 71 petagrams. Atmospheric carbon increased by 141 petagrams. Some of that redistribution of carbon, but not any of the increase in the total, is due to deforestation with a nonzero value of kd. In the simulations to follow, the ending values of the M's for 1990, given in Table 2, are used as the initial state.SIMULATIONSThe simulations described in this section engage the students in the use of the model and exhort them to learn about current trends, issues, and possible future actionsand to become informed about likely consequences regarding future disturbances to the carbon cycle. The principal interest is in the prediction of atmospheric carbon dioxide levels through the 21st century. Such predictions, based on models of varying degrees of complexity, have been reported in a number of recent studies.[1,3,5,7,14]*Disturbance ScenariosPostulated scenarios for future carbon emissions over a century of time when human activities, worldwide economies, and international politics are involved are naturally laden with uncertainty, the effects of which, in fact, probably overshadow the effects of the assumptions and simplifications in the model itself. Notwithstanding such, predictions through simulations require inserting the disturbance functions Ff, Fd, and Fr into the model equations. The most commonly employed scenarios for carbon emissions are those in a set of five that were suggested in a 1992 report to the International Panel on Climate Change, IPCC.[3,15]

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302 Chemical Engineering Education *I modified the IS92 scenarios for both the fossil fuel and deforestation components in order to bring the 1990 values of the scenarios in agreement with the data actually reported for that year.[11,12] This amounted to adding 0.1 PgC to all of the IS92 fossil fuel quantities and increasing all of the deforestation values by about 50%. These modifications are more for refinement and fastidiousness than for any significant effect on calculations. **LabVIEW, developed by the National Instruments Corporation in Austin, Texas, is graphical programming software developed mainly for data acquisition and instrument control. It also serves as a powerful tool for constructing virtual laboratories. Figure 4. Carbon emissions to the atmosphere; historical data and possible future scenarios.Known by the names IS92a, IS92b, . .IS92e, they are based on likely or possible trends in population changes, economic growth, energy supplies, etc. in developed and developing countries. There is also a Kyoto protocol, which, if enacted according to Article 3 of the agreement, would call for a worldwide decrease in emissions to 95% of the 1990 level by the year 2012.[16]Shown in Figure 4 are slightly modified versions of three of the IS92 scenarios for total carbon emissions for 1990 onward, including the most pessimistic (IS92e) and the most optimistic (IS92c) cases, and what's usually referred to as the "business-as-usual" scenario (IS92a).* The latter is the most commonly used version, and as its description implies, is based on the assumption that carbon emissions can be predicted from current trends with no major changes in policies and practices. Also shown in Figure 4 is a representation of the scenario for the Kyoto protocol, based on the assumption that emissions would be held constant after 2012. (Ver, et al. used a similar representation.[7]) The IS92 scenarios break down the anticipated emissions into fossil fuel use and deforestation. All of them use the same deforestation pattern, which declines to zero by 2100. A curve showing the modified deforestation scenario is also included in Figure 4. The differences between that curve and the others in the figure are the fossil fuel components. Reforestation is not included in the scenarios as a separate disturbance.Some ResultsI use two different approaches for simulations, each having certain advantages over the other. One is a straightforward numerical solution of the differential equations using Mathcadbasically similar to the method used to generate the historical curve in Figure 3. It's the workhorse that I incorporate into classroom presentations and the major tool used by the students for assigned work. I constructed the other using LabVIEW¨** to give a convenient user interface, a virtual laboratory, for certain classroom demonstrations and student experiments. It provides the user with hands-on control of the disturbances during a simulation, showing effects of manipulations "live" on virtual strip-chart recorders and digital displays. (Actually, I've used the LabVIEW simulation for classroom demonstration at the very beginning of the module because it is illustrative and serves to introduce goals and whet the appetite for learning about model development and simulations.) Space limitations prohibit a full description of the LabVIEW simulator and its operation here, but the gist of it is shown in the photo of the user's panel in Figure 5 and the brief description in the caption. Notice that those features afford the user an option of sequestering carbon by reforestation and by capturing a fraction of emissions, Ff, in the deep ocean and geologic reservoirs. Figure 6 presents an example of the results of Mathcad simulations using the four scenarios of Figure 4. (For those simulations, I used linear interpolation between the data points shown in Figure 4 for the period 1990-2100.) The results in Fi gur e 6 are bas ed on the parameters listed in Table I except that here the values used for 2 a nd 3 are 11.0 and 12.3, respectively. (As I mentioned above, those values depend on the total carbon in the surface ocean reservoirs. I used the 1990 values of M2 a nd M3 given in Table 2 as a basis for the new values for the period 1990-2100.) Fris taken to be zero. Notice that the model predicts atmospheric CO2 would increase to 702 ppmv by the year 2100 if the IS92a businessas-usual scenario were followed. Based on that scenario, predictions by models used by others[1,3,14] range between 697 and 724 ppmv. Over the entire 110-year period, the maximum difference in atmospheric CO2 between any two of the four models (the three cited above and the present one) is about 4%, an observation that buttresses confidence in discussions of quantitative results from the model at hand. Notice the wide range of predicted CO2 levels in 2100 resulting from the different scenarios for carbon emissions. The highest is nearly twice the lowest; both are probably unrealistic extremes. Business-as-usual would result in nearly doubling the 1990 CO2 level by the year 2100, according to the model prediction.

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Fall 2002 303 Figure 5. The user's panel for LabVIEW simulations. The elements with black arrows are for user inputs, adjustable as the simulation proceeds. The number to the left in each reservoir box is the initial value given in Table 2; that on the right, the current value. The two surface water boxes of Figure 1 are combined into one for these simulations. Figure 6. Atmospheric carbon dioxide levels; reported historical data and model predictions.Additional WorkUsing Mathcad and LabVIEW simulations, students obviously can be involved in examining all sorts of questions, model variations, and parameter effects. Here is a partial list of exercises that I have used, some of which require consulting outside references. Extend simulations beyond 2100 to address a number of questions raised about the ultimate steady state. (Actually, I ask the students to use the steady-state forms of the equations to address some of these.) What would that ultimate state be if emissions were halted immediately? What would it be if all carbon in the fossil fuel reservoir were eventually used? How long will it take to approach a steady state if carbon emissions to the atmosphere are halted at a certain time? Carry out simulations to clarify, if necessary, the roles and effects of kd, kr, and M8or to test entirely different forms of F15, the rate of photosynthetic uptake of carbon. What is a realistic mathematical description for the disturbance, Fr, if reforestation begins with new trees that require a number of years for maturation? Examine the predicted changes in the strengths of the terrestrial and oceanic sinks (or sources?) of atmospheric carbon over the 21st century. It is sometimes suggested that the most realistic goal that can be achieved regarding the control of atmospheric CO2is to "stabilize" it at twice the pre-industrial level by the year 2100. Try to achieve that goal by manipulating the emissions (or by fabricating an emissions scenario) in such a way that atmospheric CO2 lines out at about 1224 PgC (572 ppmv) by the year 2100. (This is an ideal exerciseeven an entertaining onefor the LabVIEW simulator. In fact, the data shown on the digital displays and charts in Figure 5 are the end states of this exercise.) Notice that the difference between the emissions level so achieved in 2100 and that dictated by the IS92a sce-Continued on page 309.

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304 Chemical Engineering EducationDETERMINING THE FLOW CHARACTERISTICS OF A POWER LAW LIQUIDJAMES R. HILLIER, DALE TING, LISA L. KOPPLIN, MARGARET KOCH, SANTOSH K. GUPTAUniversity of Wisconsin Madison, WI 53706Non-Newtonian liquids present unique problems with respect to their flow behavior. These problems are seldom addressed in undergraduate courses in chemical/mechanical engineering and are possibly covered only through a single experiment in one of the laboratory courses. Tjahjadi and Gupta[1] extended the work of Walawender and Chen[2] and developed an experimental scheme that illustrates how the apparent viscosity,#, of a pseudoplastic liquid (dilute aqueous solution of Na-CMC) decreases with increasing shear rate, -. They also s uggested performing additional experiments after adding some sodium chloride to the CMC solution, to observe a dramatic decrease in # and relate it to the contraction of the polyelectrolyte molecules in an ionic medium. Although the results had considerable educational value, the equations used w ere quite complex and cumbersome to use, with the result that a student obtained little insight into the method of analysisthis limits the value of their experiment. In the present work (developed as part of the "informal" experiments[3] at the Summer 2000-I laboratory at the University of Wisconsin-Madison), a much simpler experiment has been developed that uses the easily understood macroscopic energy balance (the engineering Bernoulli equation[4]) to obtain experimental results. A 0.07% (by weight) solution of a sodium salt of carboxymethyl cellulose (Na-CMC; weight average molecular weight = 7 x 105; DS = 0.9; Aldrich Chemicals, Milwaukee, WI) in deionized water was used for our study. CMC was selected because of its pseudoplastic nature over a range (1 105 s-1) of shear rates. In addition, CMC is an inexpensive, nontoxic, biodegradable, water-soluble polymer, commonly used in mining applications, food thickeners, adhesives, and textiles. The results obtained could also be compared to existing values in the literature[1] for consistency.EXPERIMENTAL SET-UPThe experimental set-up is similar to that used for studying the flow characteristics of Newtonian liquids, as described by Crosby.[5] Flush-mounted glass capillaries (in one case, a copper tube) of different diameters and lengths are used with a drain tank,[5] as shown in Figure 1. Two different kinds of experimental units were made so as to vary the shear rate over a reasonable range. The detailed dimensions are provided in Table 1.PROCEDUREThe CMC solution to be used in all the experimental runs was prepared using laboratory-grade carboxymethyl cellulose powder. A solution of 0.07 wt% CMC in deionized wa-James R. Hillier received his BS degrees from the University of Wisconsin-Madison in Chemical Engineering (2000), Biochemistry (2000), and Molecular Biology (2000). He is currently the Plant Engineer for Equistar Chemicals in Fairport Harbor, OH, while working on a master's degree in polymer engineering and a diploma in disaster management. Dale Ting received his BS in Chemical Engineering from the University of W isconsin-Madison in 2000. He is currently working in process development at The Procter and Gamble Co. in Cincinnati, OH. Lisa Kopplin received a BS in Chemical Engineering from the University of Wisconsin-Madison (2000). She is currently serving as a Project Engineer for General Mills, Inc., in their West Chicago manufacturing facility. Margaret R. Koch graduated from the University of Wisconsin-Madison with a BS in Chemical Engineering in 2000. She is currently working in Process Development at S.C. Johnson & Son, Racine, WI. Santosh K. Gupta received his BTech (1968) from I.I.T., Kanpur, and his PhD (1972) from the University of Pennsylvania-Philadelphia. He has been on the faculty of I.I.T., Kanpur, since 1973, and has also been a Visiting Professor at the University of Notre Dame, National University of Singapore, and the University of Wisconsin-Madison. His research interests include polymerization engineering and optimization using AI techniques. Copyright ChE Division of ASEE 2002 ChElaboratory

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Fall 2002 305 T ABLE 1Details of the Experimental RunsSet-UpApprox RunUsed103 (2ro)h (t=0)Range ofK++No.(Fig. No)m+L, m+m+ -, s-1n++Pa-sn11 a 0.5320.5410.070569-1220.8090.054 21 a 1.0400.2050.20288-5520.6400.0884 31 a 1.0400.2050.20268-4360.8580.7913 41 a 1.0400.1200.20347-7330.860.04755 51 a 1.0400.1010.20377-10130.620.1048 61 a 1.0400.1010.20358-8570.700.06653 71 a 1.0400.0550.20535-16190.7010.06599 81 a 1.0400.0550.20518-16080.6850.07466 91 a 1.0400.0550.46515-56280.6390.100 101a1.0400.0550.46530-59240.6330.1018 11 1b1.5361.2160.565318-4830.8390.031 121b1.5361.2160.57312-4421.000.012 131c (glass)*2.2001.2790.57513-5630.3110.791 141c (glass)*2.7201.2790.0705658-6830.8570.026 151c (glass)*2.7202.2790.0705892-9650.3550.611 161c (Cu)*3.1760.6100.06521098-12160.5070.229* Glass capillary or Cu tube used + See Figures 1 a-c ++ See Eq. (2) Figure 1. Experimental set-ups for Phases 1 and 2. a and b, 50 ml graduated tube (buret with lower end cut) connected to aligned glass capillaries, flush-mounted to minimize entrance losses. c, 5 lit SS tank (diameter 0.158 m) with sight glass to measure h, used. Glass or Cu capillaries/tubes used. Details provided in T able 1.ter was prepared well in advance to guarantee the homogeneity of the solutions.[1] The solution was heated to 30-50 C for about 4 to 8 hours and stirred for over 24 hours. Hom ogeneity of the solution was confirmed by observing its clarity against a very bright light source.[1,6]In each experimental run, a specified amount of polymer solution was added to the holding tank. The initial values, ho, of the level of solution in the tank (see Figure 1) are given for the different experimental runs (Table 1). Flow was started, and data on h was recorded over time, t, starting at the calibration mark. This allowed flow patterns to establish so that data would not be a lte r ed by flow development. Experimental runs were stopped prior to complete efflux of the liquid from the tank, so as to reduce the significance of end effects.THEORYSince CMC solutions behave like pseudoplastics, their apparent viscosities, #, decrease with increasing shear rates, -. The general dependence of # on is quite complex, but over small ranges of the shear rate, -, the following power law model[4,6,7] is followed quite well:=()Kn 1where is the shear stress. In Eq. (1), the constant, K, is referred to as the consistency index, and the exponent, n, is the power law index. The apparent viscosity is then given by # %=()Š Kn12A macroscopic (mechanical energy balance for this system[7, Eq. 5.20] leads to (see Appendix 1 for details) $ gLhKL n n v rn n n+()= + ()+2 31 30 1In Eq. (3), $ is the density of the solution, ro and L are the (inner) radius and length of the capillary (Figure 1), h is the height of the solution above the capillary entrance at time, t, g is the acceleration due to gravity, and v is the mass-average velocity inside the capillary at time t. The mass-average velocity of the solution inside the capillary can be obtained using the continuity equation v R r dh dto= Š ()24where R is the inner radius of the drain tank. A second

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306 Chemical Engineering Education Figure 2. Apparent viscosity vs. shear rate for a 0.07 wt% Na-CMC aqueous solution, assuming power law behavior of the liquid. Phase 1 results shown with Runs indicated. Results from Ref. 11 also shown for comparison. Temperature = 23C.or third degree polynomial can be fitted to data on h(t). This gives excellent values of the coefficient-of-determination of about 0.999 and higher. This polynomial is then used with Eq. (4) to obtain v. Eqs. (3) and (4) can be combined and integrated for Newtonian fluids (n = 1) to give the standard[4]equation for the efflux time for a vertical tank-pipe assembly under laminar-flow conditio ns. The students find these derivations easier to comprehend (in fact, they can make the derivations themselves) than the equations described by Tjahjadi and Gupta.[1]The validity of the assumption of laminar flow should be confirmed by calculating the Reynolds number for the pseudoplastic liquid using[7; Eq 5.50] Re = + ()Š Š2 31 53 2 n n nnn n Dv K $For pseudoplastic flows present in the laminar region, as in this study, the sudden contraction/entrance losses are expected to be negligible.[1,2] In the more general case where the entrance losses are important, the Bagley correction[8,9] can be used. This could be a possible avenue of further study for a student. Equation (3) can be rewritten as logloglog $ gLh KL r n n nvn n+()[]= + +()()+231 60 1An appropriate log-log plot of Eq. (6) gives n (= slope). K can then be obtained using n and the intercept, 2, using K r L n nn n= + ()+exp 20 1231 7Once values are obtained for both n and K, the shear rate (at the wall of the tube, r = ro) can be evaluated using[4,7; App 1] /$ = +() ()gLhr LKo n2 81The apparent viscosity, #, can then be evaluated (at this wall shear rate) using Eq. (2). Equation (8) assumes that the power law dependence is valid, and so the value of obtained is inferred from the data-fitting procedure. Unfortunately, use of the power law assumption, though helpful in simplifying the experiment at the undergraduate level, can give a false idea of the complexity of the method of analysis routinely used by professional, non-Newtonian rheologists (who commonly use the Rabinowitsch technique[6,9]). An alternative procedure of data analysis that is not as difficult and that can be attempted by an undergraduate student, is the use of the Schummer approximation[10] (described in Appendix 2). Such an analysis preserves, to some extent, the physics of mechanical energy balance and closely follows the steps that would be employed in the professional rheological evaluation of non-Newtonian viscosity. One set of experimental data generated herein is analyzed later to compare the results using the power law and the Schummer approaches.RESULTS AND DISCUSSIONDetails of the several experimental set-ups and runs are given in Table 1. These experiments were designed and performed in two phasesRuns 1 and 11 through 16 in Table 1 comprising the first phase, followed by Runs 2-10. The results of the first phase were analyzed and used to help improve the designs for Phase 2. Figure 2 shows data from Phase 1. It demonstrates the decrease of the apparent viscosity with increasing shear rates. Although the viscosity vs. shear rate diagram is incomplete, the shear-thinning effect characteristic of pseudoplastic fluids is quite evident. The straight-line segments on this log-log plot confirm the validity of the power-law model over small ranges of shear rate. The data overlap in some regions, which confirms the accuracy of the results. The value of the power law index varies from about 0.3 to 1.0 (see Table 1). The range of shear rates covered extends over almost two decades, and the data appears to fallThe primary advantage of the present study is that analysis of the raw data can be performed using equations that are easily understood by juniors in chemical engineering, and standard computer packages can be used .

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Fall 2002 307 Figure 3. Results for Phase 2, assuming power law behavior of the liquid. Run Nos. 2,3, x; 4, ; 5, -; 6, --; 7, o; 8, +; 9, ; 10 ; Temperature = 23 C. Figure 4. Comparison of # vs obtained assuming power law behavior of the liquid with that using the Schummer correction. Set 9 (Table 1) data used. on a smooth curve over this range. The data is also found to be consistent with some earlier work[11] performed using the same solution, using a stainless steel tank with a copper tube, similar to that used in Run No. 16. Our data is also consistent with the earlier data[1] on a 0.07 wt% Na-CMC solution having a slightly larger weight-average molecular weight of 7.5 x 105 (the apparent viscosity at 1000 s-1 was about 7 cP earlier, and is about the same in Figure 2). The replicability of our results was found to be excellent. It should be mentioned here that an interesting activity would be to confirm the experimental results obtained here with those using more sophisti cated capillary-flow or Couette viscometers available in research laboratories. Use of the former would also illustrate the use of the more exact Rabinowitsch technique of analysis.[1,9]The experimental results shown in Figure 2 were then used to design a few additional experiments (Phase 2) so as to extend the range of shear rates. The corresponding plot for the apparent viscosity vs. shear rate for these runs is given in Figure 3, and the values of K and n in Table 1. It was found that the data for the two sets of experimental runs, in the range of shear rates of about 300 to 1000 s-1, superposed very well (these have not been shown since the data points get too cluttered). It is interesting to observe that Runs 9 and 10 give data over a very large range of shear rate, and one could as well use just one or both of these set-ups for a routine laboratory experiment. It should be emphasized that Eq. (3) is applicable only over small ranges of shear rate (and so over a small range of t, as the meniscus falls). A log-log plot of this equation does not show straight lines for some cases, and one must exercise some judgment to fit the points. Moreover, the viscosity of CMC (a polyelectrolyte) solutions in deionized water is very sensitive to the concentration of small amounts of salts that may be present.[1] The addition of small quantities of NaCl to the solution could help improve the reproducibility of the results substantially, and would help if one were to compare the results obtained by different groups of students taken over several weeks. Figure 4 shows one set of data (Run 9, Table 1) that has been analyzed using both the power law assumption for the solution as well as the more accurate Schummer technique. The results superpose quite well, but a shift in the curves is quite evident, as discussed in Ref. 10.CONCLUSIONSA simple experimental set-up was developed to study the decrease of the apparent viscosity of a 0.07% (by weight) aqueous solution of Na-CMC with increasing shear rate. Two experimental units were found that covered a reasonably large range of shear rates of 500 to 6000 s-1. The primary advantage of the present study is that analysis of the raw data can be performed using equations that are easily understood by juniors in chemical engineering, and standard computer packages ( e.g., Excel¨, etc.) can be used for this purpose. Additional experimental data can easily be taken after adding sodium choride to the CMC solution, to study the effect of molecular contraction of the polyelectrolyte.[1] The results obtained using the power law assumption are compared to more elaborate methods of analysis, and a few additional experiments have been suggested for the more enterprising student.APPENDIX 1Details of the Derivation of Eqs. (3) and (8) The macroscopic mechanical energy balance[4] is applied

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308 Chemical Engineering Education between points 1 and 2 (Figure 1a) with the following assumptions: The column is vertical The kinetic energies of the liquid at 1 and 2 are negligible E ntrance or other losses are negligible, and the only losses are due to viscous effects in the capillary This leads to gLh P r Acapillary o+()= =() $ 2 110.where 0 is the shear stress at the capillary wall, r = ro, and ( P)capillary is the pressure drop across the length, L, of the capillary. A force balance over a control volume of radius, r, and having a differential length, dz, gives[4] Š()=dP dzr A 2 12 .or Š ()==dP dz P Lr Acapillary o 2 130 .Equations (A1.2) and (A1.3) give 014= ()r r Ao.Using the following variation of Eq. (1) =Š ()Kdu dr An15 .where u is the axial velocity at location, r, in Eq. (A1.4), we obtain / /.r du drrK An nr()Š ()%=0 0 1 116This can be integrated from r = r0 ( =0) to r = r ( =) to give ur Kr rr n An nn() Š +()=++0 0 1 0 11111 1 17/ //.Equation (A1.7) can easily be integrated over 0 r r0 to give the mass average velocity, v, as vrK n An= +()0 0 11 3 1 18 /.which can be rearranged (and Eq. A1.1 used) to give 0 0 031 2 19==+ ()Kv r n n r P L An n n capillary Equation (A1.9) can be combined with Eq. (A1.1) to give Eq. (3). Equation (A1.6) can be simplified to give / /.$ r r Kr gLh LK rAn n() +() ()=0 0 1 12 110 which leads to Eq. (8) (with r = r0).APPENDIX 2Details of the Schummer Approximation[10]The apparent shear rate -ap, and the apparent viscosity,#ap, are defined[10] by .# $ap ap apv r Q r a rgLh vL bA== %=()+()()()44 8 210 0 3 0 0 2 Schummer states that the "true" shear rate, -, corresponding to -ap (at which the viscosity is equal to #ap) is given by . .-==()083332 220 apv r A The experimental data can be used to give the average velocity, v, in the capillary, as a function of time. This can be used with Eqs. (A2.1b) and (A2.2) to evaluate #ap and the "true" (or the corresponding) shear rate, -, to give a more accurate plot of # vs -.REFERENCES1.Tjahjadi, M., and S.K. Gupta, Chem. Eng. Ed., 20 84 (1986) 2.Walawender, W.P., and T.Y. Chen, Chem. Eng. Ed., 9 10 (1975) 3.Sather, G.A., and J. Coca, Chem. Eng. Ed. 22 140 (1988) 4.Bird, R.B., W.E. Stewart, and E.N. Lightfoot, T ransport Phenomena, 2nd ed., John Wiley and Sons, New York, NY (2001) 5.Crosby, E.J., Experiments in Transport Phenomena, Department of Chemical Engineering, University of Wisconsin, Madison, WI (1961) 6.Kumar, A., and S.K. Gupta, Fundamentals of Polymer Science and Engineering, T ata McGraw Hill, New Delhi, India (1978) 7.McCabe, W.L., J.C. Smith, and P. Harriot, Unit Operations of Chemical Engineering, 5th ed., McGraw Hill, New York, NY (1993) 8.Bagley, E.B., J. Appl. Phys., 28 624 (1957) 9. McKelvey, J.M., Polymer Processing, John Wiley and Sons, New York, NY (1962) 10.Dealy, J.M., and K.F. Wisbrun, Melt Rheology and Its Role in Plastics Processing, van Nostrand Reinhold, New York, NY (1990) 11 Zhang, J., J. Jenkins, B. Linden, and A. Kristopeit, UW-Madison Transport Lab Memo, Madison, WI (2000)

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Fall 2002 309nario ( i.e., the difference between the end points of curves of the lower strip chart of Figure 5) is the amount of carbon that would have to be replaced by an equivalent energy source. Follow-up questions for consideration and/or further simulations: What alternate sources of energy might fill the gap? Could it be filled by sequestering carbon in the terrestrial biota (reforestation activities)? ...in geologic storage? ...in the deep ocean waters? Would those possibilities lead to a permanent stabilization? What is the trend of the fabricated emissions curve in 2100? What is its ultimate fate if atmospheric CO2 is to stay level at 572 ppmv? Start from the beginning with an alternative model that presumably improves on this one ( e.g., by adding layers to the ocean or atmosphere, a spatial variation to the terrestrial reservoirs). Calibrate, tune, and test the model against the results shown here.CONCLUDING COMMENTSMany of the Earth's biogeochemical processes can be studied and modeled within the context of the usual chemical engineering curricular material. The carbon cycle, the focus of this article, is a particularly apt example because, though basically complex, it can be usefully described by a simple mathematical model. Additionally, it is being disturbed and altered by human activities, possibly to the extent of causing global warming and other climate changes, and is therefore a subject of current interest and concern. Aside from students learning about this particular subject, important and timely as it is, in my view another worthwhile outcome is that they gain confidence in their ability to analyze physical situations that may not be on their usual bill-offare and to apply their chemical engineering tools to the formation of a mathematical description. Never mind that the description is soaked with simplifications and assumptions such as perfectly mixed boxes for oceans, single-rate expressions for all of the Earth's photosynthesis, and so on. A great deal is learned by pondering, investigating, and debating the bases for such simplifications and assumptions. This article describes my coverage of the subject in a course devoted to topics on ecology and the environment. The coverage is scalabledownward to a brief treatment and selected homework assignments integrated into some of the usual core course offerings, or upward to the development of more sophisticated models and the application of more advanced descriptions of the rate processes, mathematical analysis, and computational methods. Whatever the scope, students benefit from the broadening experience of applying their chemical engineering tools in a quantitative way to an important subject outside the mainstream. Readers who would like to have an electronic copy of this module, which consists of a slide show with links to spreadsheets, simulations, etc., including the LabVIEW simulator, should contact me at .ACKNOWLEDGMENTDevelopment of the material for this article was part of a project supported by the CRCD program (Grant EEC9700537-CRCD) of the National Science Foundation.REFERENCES1.Cox, P.M., R.A. Betts, C.D. Jones, S.A. Spall, and I.J. Totterdell, "Acceleration of Global Warming Due to Carbon-Cycle Feedbacks in a Coupled Climate Model," Nature, 408 184 (2000) 2.Chameides, W.L., and E.M. Perdue, Biogeochemical Cycles: A Computer-Interactive Study of Earth System Science and Global Change, Oxford University Press (1997) 3.Lenton, T.M., "Land and Ocean Carbon Cycle Feedback Effects on Global Warming in a Simple Earth System Model," T ellus 52B 1159 (2000) 4.Rodhe, H., and A. Bjorkstrom, "Some Consequences of Non-Proportionality Between Fluxes and Reservoir Contents in Natural Systems," T ellus, 31 269 (1979) 5.Schnoor, J.L., Environmental Modeling: Fate and Transport of Pollutants in Water, Air, and Soil, John Wiley & Sons (1996) 6.Siegenthaler, U., and F. Joos, "Use of a Simple Model for Studying Oceanic Tracer Distributions and the Global Carbon Cycle," T ellus 44B 186 (1992) 7.Ver, L.M.B., F.T. Mackenzie, and A. Lerman, "Biogeochemical Responses of the Carbon Cycle to Natural and Human Perturbations: Past, Present, and Future," Am. J. of Sci., 299 762 (1999) 8.Herzog, H., B. Eliasson, and O. Kaarstad, "Capturing Greenhouse Gases," Sci. Am., February 2000, 72 (2000) 9.Kane, R.L., and D.E. Klein, "Carbon Sequestration: An Option for Mitigating Global Climate Change," Chem. Eng. Prog., June 2001, 44 (2001) 10.Butcher, S.S., R.J. Charlson, G.H. Orians, and G.V. Wolfe (eds), Global Biogeochemical Cycles, Academic Press (1992) 11 .M arland, G., T.A. Boden, R.J. Andres, A.L. Brenkert, and C.A. Johnston, Tr ends: A Compendium of Data on Global Change, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN (1998) 12.Houghton, R.A., and J.L. Hackler, Tr ends: A Compendium of Data on Global Change, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN (1998) 13.Worldwatch CD-ROM, Worldwatch Institute, Washington, DC (2001) (This CD-ROM and downloadable datasets are available at 14. Houghton, J.T., L.G. Meira Filho, B.A. Callander, N. Harris, A. Kattenberg, and K. Maskell (eds), Climate Change 1995: The Science of Climate Change, Contribution of Working Group I to the Second Assessment Report of the Intergovernmental Panel on Climate Change, See Figure 5 of Technical Summary (Published for the Intergovernmental Panel on Climate Change, IPCC), Cambridge University Press (1995) (This and other reports of the IPCC are available online at 15.Leggett, J., W.J. Pepper, and R.J. Swart, "Emissions Scenarios of the IPCC: An Update," Climate Change 1992: The Supplementary Report to the IPCC Scientific Assessment (J.T. Houghton, B.A. Callander, and S.K. Varney, eds), p. 69-95, Cambridge University Press (1992) 16.United Nations Framework Convention on Climate Change, COP 3 Report, Document FCCC/CP/1997/7/Add.1. (The full text of this report is available at The Earth's Carbon CycleContinued from page 303.

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310 Chemical Engineering Education PORTFOLIO ASSESSMENTIn Introductory ChE CoursesSURITA R. BHATIAUniversity of Massachusetts Amherst, MA 01003-9303As defined by Feuer and Fulton,[1] performance-based assessment refers to assessment techniques that require students to create a final product, such as a written report, oral presentation, or portfolio of their work, as opposed to the more conventional assessment techniques of written quizzes or exams. Performance assessment can also be defined as an assessment method that evaluates a student's ability to perform a specific procedure or task;[2] in this context, the assessment must contain a performance task, a student-response format, and a scoring system. Examples would include judging a student's ability to manipulate laboratory equipment or respond to an open-ended problem.[2] Slater suggests designing a performance task that is "somewhat undefined, complex, and has multiple entry and exit points;" that is, a task that has more than one correct so lution path.[2]The advantages of performance-based assessment techniques have been documented by several studies in the educational literature.[1-6] Many studies emphasize the "realworld" nature of performance assessment;[3] student work is evaluated in a manner that is much closer to what will be encountered in the work environment. Perhaps most importantly, research has shown that alternative assessment helps in the evaluation of students with various learning styles and educational backgrounds, promoting excellence among a more diverse student population.[4]These "alternative assessment" techniques[3] are not new to engineering education. Traditional performance-based assessment is often used (although not often acknowledged as such) in juniorand senior-level courses in the form of laboratory experiments, written lab reports, design projects, and oral presentations; and the ABET EC 2000 guidelines have brought increased attention to outcomes-based assessment.[7,8]But alternative assessment is not widely used in the fresh- Copyright ChE Division of ASEE 2002 Surita R. Bhatia is an assistant professor in the ChE Department at the University of Massachusetts. She received her BChE from the University of Delaware, her PhD from Princeton University, and held a postdoctoral position at the CNRS/Rhodia Complex Fluids Laboratory. Her research interests are associative polymers, rheology, shear-induced structure, and structured cell encapsulation materials. She has taught mass balances and heat transfer at the undergraduate level and coteaches a graduate course on colloidal dispersions. manand sophomore-level courses for a variety of reasons. Educators may worry that freshmen and sophomores do not have the depth and breadth of knowledge to complete a design project or written paper, or that there is simply not enough class time to have students give oral p resentations...after all, there is barely enough class time to teach these students mass and energy balances and thermodynamics. There is another means of implementing performancebased assessment in these courses, howeverone that has remained largely under-used in engineering education: student portfolios.WHAT IS A PORTFOLIO?Portfolios are collections of student work, typically selected according to guidelines set forth by the instructor.[3] These guidelines may have a one-to-one correspondence with the course objectives, or an instructor may choose to highlight particular course objectives. An example of required items from the freshman chemical engineering course at UMass, which I will discuss in more detail below, is given in Table 1. Along with each item, students are asked to submit a statement of why the item was chosen. This element of self-analysis or self-reflection is crucial if portfolios are to be more than just "student folders."[9] For comparison, the course obChEassessment

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Fall 2002 311T ABLE 1Required Portfolio Entries for Freshman Course in Chemical Engineering Fundamentals1.A problem with a "nonroutine" solution, where students had to employ new strategies or methods of solution 2.A homework problem that involved teamwork or group work 3.A problem that gave the student a good sense of real-world applications 4.A problem involving data analysis or data fitting 5.A problem involving the use of MathCAD 6.A problem involving the use of Microsoft Excel 7.A self-analysis of the student's strengths and weaknesses with regards to concepts learned in class 8.Reflections on chemical engineering, this class, and any thoughts on career choicesT ABLE 2Course Objectives for Freshman Course in Chemical Engineering Fundamentals At the end of this course, students should Understand concepts of engineering calculations, including significant figures and dimensional analysis, and be able to perform unit conversions Understand process flowsheets, know how to draw and label a flowsheet, and be able to clearly define subsystems within processes to set up conservation equations Understand conservation of mass and be able to solve material balances on steady processes Understand thermodynamic quantities such as internal energy, enthalpy, and heat capacity Understand the concept behind distillation and be able to perform simple vapor-liquid equilibria calculations using Raoult's Law and Henry's Law Understand conservation of energy and be able to set up simple energy balances Be able to use software packages (for instance, Microsoft Excel or MathCAD) to set up and solve engineering calculations and aid in data analysis Be able to use the principles and tools learned in this course to solve problems not covered in detail as part of the course and to continue learning related material as needed in the future. jectives are listed in Table 2. A widely cited benefit of portfolio assessment is an improvement in communication skills and creative-thinking skills, particularly in mathematics and science, two disciplines where students often have dif ficulty communicating their results.[3,4,9] These assessment techniques also promote student self-assessment and reflection. This allows students to become better at selecting and presenting their best work, which helps them gain confidence in their abilities.[4]Studies in college physics classes[6] have shown that portfolios may serve to help students organize work and internalize concepts; however, preliminary studies of portfolio use in undergraduate chemistry courses[10] i ndicate that there is a disconnect between student performance on exams and in portfolio entries with regard to specific course objectives. Educators in chemical engineering may feel uncomfortable with the concept of "student self-reflection"; after all, we are here to teach students, not to ask them how they "feel" about engineering, right? We prefer hard numbers and are more accustomed to quantitative asses sment methods. But the utility of portfolios has been demonstrated in several science, mathematics, and engineering courses.[4,6,10-16] Many states require use of portfolios in all s ubject areas for grades four through twelve,[4,5] and portfolios have been successfully used in undergraduate physics, chemistry, and geology courses.[6,9]The chemical engineering program at the Colorado School of Mines has relied heavily on portfolio assessment for over a decade, and Olds and Miller[14] give an excellent description of the use of portfolios in the ChE curriculum. Both Alverno College[15] and Rose-Hulman Institute of Technology[16] have implemented an electronic portfolio system for all students. Preliminary results from the Rose-Hulman project indicate that students find the electronic portfolio system easy to use, and that use of a web-based system reduced some of the disadvantages of conventional portfolios, including storage, user access, and availability.[16]It is important to keep in mind the difficulties and limitations associated with portfolio assessment. Portfolios are not appropriate for assessing factual knowledge or recall abilities; thus, they should be used in conjunction with conventional, quantitative assessment techniques.[9] Portfolios can be difficult to manage and time-consuming to grade, which Many studies emphasize the "real-world" nature of performance assessment; student work is evaluated in a manner that is much closer to what will be encountered in the work environment.

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312 Chemical Engineering EducationT ABLE 3Questions for Student Self-Analysis in Portfolio Entries What concept or topic was involved with this problem? What skills did you use in solving it? How did this problem help you learn something new? Did you learn anything about yourself, your thought process, or your strengths and weaknesses as a result of this activity? What strategies did you use? What were you thinking as you worked the problem? W ould you do anything differently if you had more time? Can you describe any connections between the activity and other concepts, subject areas, or real-life situations? Does the problem represent a special achievement for you, a sense of accomplishment at having learned a particular concept, or a sense of improvement over time? Perhaps most importantly, research has shown that alternative assessment helps in the evaluation of students with various learning styles and educational backgrounds, promoting excellence among a more diverse student population.makes them easiest to implement in courses with small to medium enrollments. Slater[9] and Wink[10] have reported techniques to extend the use of portfolios to large lecture courses, however. Although there has been an emphasis on the use of portfolios in upper-level "capstone" courses, such as senior design and the unit operations laboratory,[14] I focus on their use in introductory chemical engineering courses. I believe portfolio assessment has unique benefits to beginning engineering students, as described further in the following paragraphs.GRADING PORTFOLIOSImplementing innovative assessment is all well and good, but how are we going to evaluate and grade student portfolios? Since the portfolio entries have presumably been graded as part of a homework assignment or exam earlier in the semester, it does not seem fair to me to place the students in "double jeopardy" by basing the portfolio grade on whether or not the problems are correct. I chose to grade portfolios by giving equal weight to three criteria: Completeness and organization Quality and style of writing Level of thought, analysis, and reflection in each entry The first two criteria are easy to evaluate. The first refers to whether students have all the required items, including a table of contents and page numbers. The second criterion refers to writing style and grammar, again fairly straightforward to evaluate. The third criterion is a little more subjective and requires some planning on the part of the instructor. I evaluated the level of thought and analysis by judging the extent to which each entry addressed two to three "thought questions," which are listed in Table 3. Students were given these questions at the start of the semester to help guide them through the selfanalysis process. Slater[9] recommends developing a "scoring rubric," whereby the portfolio grade is based on the extent to which students demonstrate mastery of the required number of objectives. For example, you may require students to have at least eight entries, each of which is related to a specific course objective. A simple scoring rubric could then be an "A" grade for demonstrating adequate mastery in seven or more objectives (as evidenced by the portfolio entries), a "B" grade in five or more objectives, and so on. More detailed examples, developed for a unit operations course, are given by Olds and Miller;[14] see also the examples given by Slater.[9]EXAMPLEPortfolios in the Introductory ChE Course In the spring of the freshman year, students at UMass take a course titled Chemical Engineering Fundamentals. The course content covers units and dimensions, mass balances, simple reactive systems ( i.e., CSTRs and PFRs), and forms of energy. The typical enrollment is 40-50 students, most of whom are engineering majors with an inte rest in chemical engineering. After completing the freshman year requirements, students can apply for admission into the chemical engineering major. Thus, many students in the ChE Fundamentals course are still unsure of their choice of major. I chose to implement portfolio assessment in this course as an optional assignment. The portfolio assignment could be used to replace a low grade on either of two midterm exams or a low homework grade, but not the final exam. Many instructors give students the option of "dropping" one low grade, so I did not feel that the use of portfolios would cause grade

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Fall 2002 313T ABLE 4Student Evaluation Survey0.Did you complete the optional portfolio assignment for this class? 1.(If "Yes" to the first question) I enjoyed completing the portfolio assignment. 2.(If "Yes" to the first question) I felt that I learned more about myself and my strengths and weaknesses in chemical engineering and problem solving as a result of completing the portfolio. 3.(If "Yes" to the first question) My written communication skills have improved as a result of completing the portfolio assignment. 4.I feel that the use of both qualitative ( e.g., written reports, oral reports, and portfolios) and quantitative ( e.g., exams and homework) methods of assessment were appropriate for this class. 5.I dislike qualitative methods of assessment ( e.g., written reports, oral reports, and portfolios) because I feel that they are subjective. 6.I feel that quantitative methods of assessment ( e.g., exams and homework) are most appropriate for engineering and science classes. 7.I would like to see qualitative methods of assessment ( e.g., written reports, oral reports, and portfolios) incorporated into other science and engineering classes. Figure 1. Results from student surveys after completing course. Responses to questions are as follows: 1 Strongly agree; 2 Agree; 3 No strong opinion; 4 Disagree; 5 Strongly disagree. Columns and error bars represent the average and standard deviation for each question, from a sample size of 13 surveys for questions 1-3 and 28 surveys for questions 4-7. Question numbers correspond to those given in Table 4. inflation. On t he first day of class, I gave students a handout describing the portfolio assignment, including the information in Tables 1 through 3, and a summary of the grading protocol for portfolios. I also held a short class discussion on what portfolios are and why they were being used for this course. Students were required to have at least eight portfolio entries, which are listed in Table 1. Six of these entries were related to course objectives or outcomes, with a focus on objectives that are difficult to assess using conventional exam techniques ( i.e., the use of Microsoft Excel, data-fitting techniques, etc.). These entries were expected to be copies of problems, either from the homework or exams. Students were required to attach a copy of their solution to the problem and a short (one paragraph to one page) explanation of why the problem was chosen. In addition, two one-page essays (the last two items in Table 1) were required. I also handed out a list of questions to keep in mind as they wrote their portfolio entries (listed in Table 3). Finally, students were asked to organize their entries, number each page, and include a table of contents in the portfolio. Periodically throughout the semester, I reminded students to work on the portfolio assignment and to come see me if they had questions on the assignment.RESULTSStudent Feedback and Assessment Survey The class enrollment was 41 students. Forty-one percent of the students (17 students) completed the portfolio assignment. Grades on the portfolios were roughly in the low "C" to high "A" range. For most students, the portfolio grade was used to replace a low homework grade, but the difference in the final grade for the course with and without the portfolio was never more than a letter grade. I was somewhat distressed to find that several students counted on the portfolio to bring up their low homework grade and thus did not spend as much time on the homework assignments throughout the semester as I would have liked. I have since altered the portfolio guidelines to allow students to replace a low midterm exam grade, but not the final exam or a low homework grade. I found that grading of the portfolios was time consuming, but I did not feel that it took longer than grading exams. The time commitment is similar to that required for evaluating written reports, and I made comments on all portfolios regarding grammar and writing style. Students were asked to complete a survey upon completion of the course, and the survey questions and student responses are given in Table 4 and Figure 1, respectively.

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314 Chemical Engineering Education Portfolios can be particularly useful for beginning chemical engineering students, who often do not have class projects that require them to synthesize concepts and present their results in a written format.These are preliminary results; obviously, data need to be taken on a larger sample size before conclusions can be drawn. The results also may be biased due to wording of the survey questions. This needs to be addressed before definitive conclusions can be reached, and I am currently updating and redesigning the survey questions for future classes. On the whole, the response from students was quite positive. The strongest and most uniform response was to Questions 2 and 4; 86% of students who completed a portfolio strongly agreed or agreed that the portfolio helped them to learn more about themselves and their strengths and weaknesses in chemical engin eering and problem solving, and 89% of all students felt that the use of both quantitative and qualitative assessment methods were appropriate in the course. It remains unclear whether or not the portfolio assignment helped students improve their written communication skills. Several of the written comments that accompanied portfolio entries were quite encouraging, and I have listed some of the more memorable comments in Table 5. There were also comments both positive and negative, that were useful to me as an educator. Students were very honest about components of the class that they liked and disliked. Most of these comments were made in response to Item 8, Table 1, reflections on chemical engineering and the class. Examples of these comments are also given in Table 5.CONCLUSIONS AND RECOMMENDATIONSPortfolios can be particularly useful for beginning chemical engineering students, who often do not have class projects that require them to synthesize concepts and present their results in a written format. Interestingly, students did not feel as though the assignment improved their written communication skills, but the portfolio assignment did seem to give these incoming students an opportunity to reflect on their abilities and their choice of major. Portfolios can also be used to assess course objectives that are difficult to evaluate using traditional techniques. Based on my experience, I have some guidelines and recommendations for implementation of portfolios: Be prepared to read up on assessment techniques. Several of the references listed contain excellent examples of student entries and grading schemes.[4,5,9,11] I found the National Institute of Science Education Field-Tested Learning Assessment Guide website particularly useful. (Found at .) Be clear about expectations for portfolios at the start of the semester. You may want to give students sample entries. Remind students that they should be saving homework sets and collecting problems for entries in their portfolio. This is extremely important for freshman-level students who are still learning how to organize their coursework. If you allow students to use a portfolio grade as a replacement, make sure their expectations are realistic. One fabulous portfolio assignment will not pull a final "D" grade up to an "A"as I mentioned above, the overall effect on the final grades in the course was never more than a letter grade. It is worth noting that implementing portfolios as a "replacement" for a poor exam could allow a student to bring a failing grade up to a "D." Instructors need to decide for themselves whether this is permissible and to develop their own guidelines accordingly. For example, I specified that if students received a zero grade on an exam or homework due to academic dishonesty, this grade could not be "replaced" under any circumstances. One could imagine extending this rule to any failing grade to prevent the above scenario. Finally, I found that it was problematic to allow students to replace a low homework average with the portfolio grade. Create a grading scheme that places emphasis on what you think is most important, whether this is good writing, clear organization, self-reflection,

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Fall 2002 315T ABLE 5Sample Comments from Student Portfolios New Strategies of Problem Solving (Item 1) and Self-Analysis (Item 7) "I now have more confidence knowing that if I can't solve a problem using the accepted method of solution, I will be able to come up with a new method, perhaps something nonroutine, in order to solve the problem." "This problem showed me that I should have more confidence in my ability to find a solution when it doesn't simply present itself after a series of steps." "I could apply things I had learned in a completely different context to other situations. This is actually quite comforting, as I've always wondered if I'll be able to use the things I learn now later on in life when I might actually need them." "I've had trouble [with] time management, as I have usually been able to understand the problems but have not left myself enough time to gather it all in a presentable format." " My weakness is that every time I hit a wall, I tend not to do anything about it. I can only blame myself for not attempting, [but] I already made my choice in staying in this major and it is all up to me in keeping that choice." Reflections on Chemical Engineering and The Fundamentals Course (Item 8) " All in all I enjoyed the class, I enjoy being a chemical engineering student, and I look forward to the day when I am employed as a fabulous chemical engineer." "I dislike computers and I dreaded using them for this class. I probably would have stuck with this major if it were not for MathCAD and Excel. I do not think being taught [MathCAD] for one class period is enough class time." "Since the class is almost over, I feel a real sense of accomplishment. I know that it is only a freshman level class, but I put a great deal of effort and time into the class...It makes me proud to say that I'm a chemical engineering major when people ask me." "I feel like I've gotten a much better idea about what chemical engineers do through the various assignments and from the oral presentations of my peers." "I feel that we did not [spend] much time on using the computer." "Before taking this class I wasn't positive that chemical engineering was the right major for me. I felt that perhaps I would not be able to handle the workload or grasp all of the material that I needed to know. However, I now feel that I am actually capable of becoming an engineer." "I love going to my chemical engineering classes, they are the only ones that I don't purposely skip." " As a result of this class I am much more confident about my choice of major and the preparation it will give me to succeed in the career I want to pursue." or assessment of a specific course objective. Make sure your grading scheme is clear to the students at the start of the semester.ACKNOWLEDGMENTSI would like to acknowledge my Chemical Engineering Fundamentals students for participating in this work. Professor Donald Wink (Chemistry, University of Illinois at Chicago) provided me with a copy of his recent ACS presentation on portfolio assessment and suggested several of the works cited in this article, which was greatly appreciated. The manuscript reviewers, particularly Reviewer #3, made several useful and constructive comments. Mrs. Kanak Bhatia (Ed.D. candidate, University of Delaware) also suggested several helpful references and made comments on the manuscript.REFERENCES1.Feuer, M.J., and K. Fulton, "The Many Faces of Performance Assessment," Phi Delta Kappan, 74 473 (1993) 2.Slater, T.F., "Performance Assessment," in Field-Tested Learning Assessment Guide, National Institute of Science Education (2000) (accessed 6/6/02) 3.Herman, J.L., P.R. Ashbach, and L. Winters, A Practical Guide to Alternative Assessment, Association for Supervision and Curriculum Development, Alexandria, VA (1992) 4.Lambin, D.V., and V.L. Walker, "Planning for Classroom Portfolio Assessment," Arithmetic Teacher, 41 318 (1994) 5.Abruscato, J., "Early Results and Tentative Implications from the V ermont Portfolio Project," Phi Delta Kappan, 74 474 (1993) 6. Slater, T.F., "The Effectiveness of Portfolio Assessments in Science," J. Coll. Sci. Teach., 26 315 (1997) 7. Shaeiwitz, J.A., "Outcomes Assessment: Its Time Has Come," Chem. Eng. Ed., 33 (2), 102 (1999) 8.DiBiasio, D.A., "Outcomes Assessment: An Unstable Process?" Chem. Eng. Ed., 33 (2), 116 (1999) 9. Slater, T.F., "Portfolios," in Field-Tested Learning Assessment Guide, National Institute of Science Education (2000) (accessed 2/15/02) 10.Wink, D.J., "Portfolio Assessment in Large Lecture Class," Abstracts of Papers of the ACS, 220 49 (2000) 11 Johnson, J.M., "Portfolio Assessment in Mathematics: Lessons from the Field," The Computing Teacher, 21 22 (1994) 12. Adamchik, Jr., C.F., "The Design and Assessment of Chemistry Portfolios," J. Chem. Ed., 73 528 (1996) 13.Phelps, A.J., M.M. LaPorte, and A. Mahood, "Portfolio Assessment in High School Chemistry: One Teacher's Guidelines," J. Chem. Ed., 74 528 (1997) 14.Olds, B.M., and R.L. Miller, "Using Portfolios to Assess a ChE Program," Chem. Eng. Ed., 33 (2), 110 (1999) 15."Alverno's Diagnostic Digital Portfolio," (accessed 6/6/02) 16. Rogers, G.M., and J. Williams, "Building a Better Portfolio," PRISM 8 (1999)

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316 Chemical Engineering Education ASPECTS OF ENGINEERING PRACTICEExamining Value and Behaviors in OrganizationsRAMON L. ESPINOUniversity of Virginia Charlottesville, VA 22904-4741Ramon L. Espino received his BS degree from Louisiana State University in 1964 and his Doctor of Science degree from the Massachusetts Institute of Technology in 1968, both in chemical engineering. He joined the faculty at the University of Virginia in 1999 after twenty-six years with Exxon Mobil. His research interests are in fuel cell technology and methane conversion to clean fuels and chemicals. Copyright ChE Division of ASEE 2002 Since 1995, the School of Engineering and Applied Sciences at the University of Virginia has offered an elective course that examines human values and practices in engineering organizations. The course is available to all fourth-year engineering students and is taken by 40 to 50 students each year. It is taught by the Brenton S. Halsey Visiting Professor of Chemical Engineering, who is selected annually from individuals with high-level experience in industry. Support for the Chair comes from a generous endowment by The James River Corporation in honor of its founding CEO, Brenton Halsey. Previous Halsey Professors and their affiliations are given in Table 1. The details of the course content and execution are left to the discretion of the Halsey Professor, but its core objective is to provide engineering students with significant insight into the professional and nontechnical aspects of engineering practice. The intention is to better prepare the University of Virginia engineering graduates to succeed in the business and technical world that they will be entering after graduation. This paper describes the course materials, assignments, and assessments for the spring semester of 2001, which is representative of recent offerings.DEVELOPING THE COURSEThe teaching experiences of previous Halsey Professors contributed significantly to the current course content. Although the objectives have remained the same, there is now more emphasis on the students reading and analyzing information prior to class. This information is generally in the form of Harvard Business School (HBS) Cases and Notes. The result of this approach is more in-depth discussion in class. I built the course syllabus around the HBS Cases and Notes. Harvard Business School Publishing[1] offers an Index of Cases and Notes available for purchase. I suggest one HBS Case and two HBS Notes per week, requiring about nine hours of homework (reading and writing a summary) per week. Lectures to reinforce and elaborate upon the major themes of the course are strongly recommended. We have found that many of these should be given by outside speakers from business and government in order to emphasize the broad applicability of the concepts being discussed. Finally, additional reading material can be used to round out the course.COURSE STRATEGY AND TEACHING METHODI developed the syllabus to follow the chronological order of the professional and business career of an engineering graduate. Selecting the first employer is the starting point, followed by early career assignments and culminating with the complex organizational, personal, and business challenges of a senior manager. HBS Cases provide a well-written platChEcurriculum The objective of the course was to increase student awareness of the nontechnical competencies they should possess in order to succeed in the work world.

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Fall 2002 317T ABLE 1Halsey Professors at the University of VirginiaY earName Company/Position 1995N.H. PraterMobay/CEO 1996J.M. Trice, Jr.Monsanto/Director-HR 1997R.A. Moore, Jr.International Paper/VP 1998D.L. AshcraftTemple-Island/VP 1999J.D. SteinBASF/CEO 2000V.A. RussoScott Paper/VP 2001R.L. EspinoExxon/R&D Manager 2002A.R. HirsigARCO Chemical/CEO form that describes specific situations with no direct answers or outcomes. The additional reading assignment consisted mainly of HBS Notes, which provided a conceptual framework for the students to analyze the cases with some knowledge of basic concepts on business practices, interpersonal behavior, and human values. The students were all expected to read two books: Getting to Yes[2[ and The Seven Habits of Highly Effective People.[3]The classes were designed to be highly interactive, with the bulk of the time spent discussing the HBS Cases and Notes. In addition, there were lectures on S tyles of communicating and interacting I ndividual competenciesT ABLE 2HBS CasesT itleTopic Kevin SimpsonInterviewing and selecting your employer Elizabeth FisherDual career decisions Lisa BentonConflicts in your first assignment Amelia RodgersFirst group-leader assignment Anne LivingstonChanging jobs and new leadership role T ech Transfer at...Conflict between development and production Thurgood Marshall...Leader of middle-level managers Conflict in a diverse...Harassment and social conflict David FletcherHiring your ideal business team MOD IV Product...Effective teamwork PPG-Developing...Risks and rewards of empowerment John Smithers at SigtekLeading a quality process initiative Jenssen ShoesManaging a diversity conflict Corning Glass WorksLeadership during a business downturn Conflict management T eams and team performance S trategic planning Developing a personal career plan Six outside speakers led discussions on various aspects of their business careers. These included Managing family and business life How to improve leadership skills Conflict management and negotiation W orking with consulting companies A ttending business school Reinforcing organizational values A detailed outline of the course is presented in Table 3 (next page). The two 75-minute class periods each week allowed adequate time for discussion of the Case and the Notes, as well as for the lectures given by the Halsey Professor or by invited speakers.LEARNING THROUGH THE HBS CASESThe "Case Method" is based on real-life situations that represent the kind of challenges that engineers and managers are likely to face during their work life. The cases helped students sharpen their analytical skills, their ability to communicate clearly and forcefully, and most importantly, helped them to develop their problem-solving abilities. Table 2 indicates the topic being discussed in each case. The students were assigned the HBS Case a week in advance. They were required to write a 3-to-4-page summary of their assessment of the situation and their proposed solution(s). They were also asked to document the key learnings they had derived from the case. It was gratifying to observe their increasing sophistication in analysis and problem solving during the course of the semester. There were a number of interesting observations that resulted from discussion of the HBS Cases. The students paid a lot of attention to the interpersonal style of the protagonists and were quite sensitive to antisocial behavior. They were, to my surprise, expecting to experience such behavior in the workplace. This applied even to harassment situations. Another class-wide attitude was to view most conflicts as rooted in poor communication, and it took a lot of discussion for them to see poor communication simply as the external manifestation of a more profound conflict.LEARNING KEY CONCEPTS THROUGH THE HBS NOTESThe course provides an introduction to a number of critical competencies engineers need in order to succeed in organizations. These were provided mainly through reading and discussion of HBS Notes. The Notes were also given to the students a week in advance of the class discussion. There

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318 Chemical Engineering Education W eek 1 Homework/Class Discussion HBS Notes on "Learning by the case method" and "How to choose a leadership pattern" Lecture Individual and team competencies W eek 2 Homework/Class Discussion HBS Notes on "Understanding context" and "Conflicting responsibilities" HBS Case "Kevin Simpson" Lecture Styles of communicating and interacting W eek 3 Homework/Class Discussion HBS Notes on "Managing your career" HBS Case "Elizabeth Fisher" Lecture Invited SpeakerManaging family and business life W eek 4 Homework/Class Discussion HBS Notes on "Power dynamics in organizations" HBS Case "Lisa Benton" Lecture The seven habits of highly effective people W eek 5 Homework/Class Discussion HBS Notes on "Managing your boss" and "Exercising influence" HBS Case "Amelia Rodgers" Lecture Invited SpeakerImproving your leadership skills W eek 6 Homework/Class Discussion HBS Notes on "Evaluating an action plan" and "Understanding communications in one-to-one relationships" HBS Case "Ann Livingston and Power Max Systems" Lecture The seven habits of highly effective people W eek 7 Homework/Class Discussion HBS Notes on "Beyond the myth of a perfect mentor" and "Managing networks" HBS Case "Technology transfer at a defense contractor" Lecture Invited SpeakerConflict management and negotiation W eek 8 Homework/Class Discussion HBS Notes on "Power dependence and effective management" and "Influence tactics" HBS case "Thurgood Marshall High School" Lecture Conflict management styles W eek 9 Homework/Class Discussion HBS Notes on "Integrity management" and "Managing a task-force" HBS Case "Managing conflict in a diverse environment" Lecture Invited SpeakerWorking in a consulting company W eek 10 Homework/Class Discussion HBS Notes on "Barriers and gateways to communications" and "On good communications" HBS Case "David Fletcher" Lecture Invited SpeakerShould you get an MBA? W eek 1 1 Homework/Class Discussion HBS Notes on "The power of talk" and "The discipline of teams" HBS case "Mod IV product development team" Lecture Getting to Yes W eek 12 Homework/Class Discussion HBS Notes on "The challenge of comitment" and "A note on high-commitment work systems" HBS Case "PPGDeveloping a self-directed workforce" Lecture Strategic planning W eek 13 Homework/Class Discussion HBS Notes on "Organization structure," "Organization effectiveness," and "The challenge of change" HBS Case "John Smithers at Sigtek" Lecture Invited SpeakerReinforcing organizational values W eek 14 Homework/Class Discussion HBS Notes on "Business ethics: the view from the trenches," "Ethics without a sermon," and "Ways of thinking about and across differences" HBS Case "Jenssen Shoes" Lecture Developing a personal career plan W eek 15 Final Homework: A personal career plan Analysis of the "Most admired company..." Group report of HBS Case "Corning Glass Works"T ABLE 3Course Outline was a close coupling between the teachings in the Notes and the Case being discussed in parallel. This worked well, as confirmed by the frequent references to concepts presented in the Notes in the students' analyses of Cases. It is unrealistic to expect the students to fully master all the concepts, but it was clear that they became very aware of their importance. The hope is that when they are confronted with similar situations, they will refer to these Notes for guidance. We discussed the differences between management and leadership and the many complex and ambiguous issues that most managers face. We spent very productive time on the influence of culture and history on subtle but important differences in managers' behavior in the USA, Europe, Japan, India, China, and Latin America. Having some students from outside the USA gave immediacy to these discussions. As expected, issues of business ethics grabbed the students' attention and elicited strong and quite varied opinions. In fact, I was surprised at the diversity of viewpoints, how strongly they were held, and that there was no correlation with gender, race, or economic background.

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Fall 2002 319T ABLE 4Course AssessmentNot Useful12345678Very Useful February %-----254530 March %----3295018 April %----3253735 I was disappointed in the students' lack of interest in learning about team building, task-force management, and building commitment in the workplace. The students felt that they knew about these topics and that they were already proficient. I do not believe I ever convinced them there was a lot for them to learn and that success in these areas requires skills they actually did not possess.OTHER FEATURES OF THE COURSEThe students were given a three-part final homework assignment. One element was a personal mission statement with an associated five-year career development plan. The plan could also include other facets of their life, such as family, health, religion, community involvement, etc. For each of the elements they were encouraged to follow a disciplined approach that included short-term (6 months), midterm (2-3 years), and long-term (5 years) plans. For each time period, they were asked to state goals and specific objectives and to define strategies and action steps. They were initially unenthusiastic about this task, but the final product indicates that they thought hard about it and put together a realistic and credible plan. The second element of the final homework was a team project. Groups of four students were asked to analyze a fairly complex HBS Case of a Corning Glass Works Division undergoing a change in management during a business downturn. They were asked to devise strategies and specific action plans for the division as well as a self-assessment of their team performance. The reports indicated a wide range of team performance, with the key problems being an inability to agree on an action plan, finding time to work together, and uneven participation by team members. This assignment came at the very end of the semester, which was too late to refute their earlier assertions that "teamwork was something they knew how to handle." The third element of the final homework was an analysis of a company's performance during the last four years. Each student selected a company from those reviewed by Fortune Magazine in its annual publication of "America's Most Admired Companies."[4,5] They were asked to analyze the performance of the company they chose, to identify reasons for any change in rankings during the four-year period, and to forecast future trends. The objective of this exercise was to allow the students to apply to a specific company-wide situation what they had learned about effective management, leadership, and managing change. The companies chosen reflected the students' wide range of career interests and included, among others, entertainment, communications, financial, computer technology, oil and chemicals, consumer products. They were asked to suggest the future direction the company needed to take to improve performance. A majority suggested expanding global reach and more technology investment, while only a few focused on improving cost competitiveness.STUDENT ASSESSMENT AND FEEDBACKDuring the semester, the students were asked to provide feedback on course content and to assess its effectiveness. The data are summarized in Table 4 and show that the majority of the class found the course very useful. They rated the discussions of HBS Cases and Notes, my work experiences and personal stories, and the outside speakers the highest. They were less enthusiastic about the other reading material, perhaps because they were not used to this amount of reading in an engineering course.SUMMARYThe objective of the course was to increase student awareness of the nontechnical competencies they should possess in order to succeed in the work world. It is unrealistic to expect that at the end of a semester they would have mastered all these competencies, but it was evident that they were much more sensitive to the importance of such skills and had grasped the essentials. Also, they were left with an excellent collection of HBS Cases and Notes that could serve them well when confronted with similar situations. As I frequently indicated to them, I wished that I had such a learning experience in my engineering schooling and early career. The main reason for writing this article is to encourage other colleges and universities to consider offering a course along the general outline that I have described. I also encourage experienced business practitioners to teach such a course. The Halsey Professors are unanimous: it was an exciting and gratifying experience to share what you have learned with the next generation of engineering and business leaders.REFERENCES1.Harvard Business School Publishing, 60 Harvard Way, Boston MA 02163 2.Fisher, R., W. Ury, and B. Patton, Getting to Yes, 2nd ed., Penguin Books 3. Covey, S.R., The 7 Habits of Highly Effective People Simon and Schuster 4. Fortune Magazine, March 6, 1997 5. Fortune Magazine, February 21, 2001

PAGE 72

320 Chemical Engineering Education Akron, University of.....................................321 Alabama, University of................................322 Alabama, Huntsville; University of..............323 Alberta, University of...................................324 Arizona, University of..................................325 Arizona State University..............................326 Auburn University........................................327 Brigham Young University...........................427 British Columbia, University of...................427 Brown University.........................................441 Bucknell University......................................428 Calgary, University of..................................328 California, Berkeley; University of..............329 California, Davis; University of...................330 California, Irvine; University of...................331 California, Los Angeles; University of.........332 California, Riverside, University of.............333 California, Santa Barbara; University of......334 California Institute of Technology................335 Carnegie-Mellon University.........................336 Case Western Reserve University.................337 Cincinnati, University of..............................338 City College of New York............................339 Cleveland State University...........................340 Colorado, Boulder; University of.................341 Colorado School of Mines............................342 Colorado State University............................343 Columbia University....................................428 Connecticut, University of...........................344 Cornell University........................................345 Dartmouth College.......................................346 Delaware, University of...............................347 Drexel University.........................................348 ƒcole Polytechnique MontrŽal.....................349 Engineering Research Center.......................429 Florida, University of...................................350 Florida A&M/Florida State University.........351 Florida Institute of Technology....................352 Georgia Institute of Technology...................353 Houston, University of.................................354 Howard University.......................................355 Idaho, University of......................................429 Illinois, Chicago; University of....................356 Illinois, Urbana-Champaign; University of..357 Illinois Institute of Technology....................358 Iowa, University of.......................................359 Iowa State University...................................360 Johns Hopkins University............................361 Kansas, University of...................................362 Kansas State University................................363 Kentucky, University of...............................364 Lamar University..........................................430 Laval UniversitŽ...........................................365 Lehigh University.........................................366 Louisiana, Lafayette: University of..............367 Louisiana State University...........................368 Louisiana Tech University............................430 Louisville, University of...............................431 Manhattan College.......................................369 Maryland, University of...............................370 Maryland, Baltimore County; University of371 Massachusetts, Lowell; University of..........441 Massachusetts, Amherst; University of........372 Massachusetts Institute of Technology.........373 McGill University.........................................431 McMaster University....................................374 Michigan, University of...............................375 Michigan State University............................376 Michigan Technological University.............432 Minnesota, University of..............................377 Mississippi State University.........................378 Missouri, Columbia; University of...............379 Missouri, Rolla; University of......................380 Monash University.......................................432 Montana State University.............................433 Nebraska, University of................................381 Nevada, Reno; University of........................433 New Jersey Institute of Technology.............382 New Mexico, University of..........................383 New Mexico State University......................384 New South Wales, University of..................434 North Carolina State University...................385 North Dakota, University of.........................434 Northeastern University...............................386 Northwestern University..............................387 Notre Dame, University of...........................388 Ohio State University...................................389 Ohio University............................................390 Oklahoma, University of..............................391 Oklahoma State University..........................392 Oregon State University...............................393 Pennsylvania, University of.........................394 Pensylvania State University........................395 Pittsburgh, University of..............................396 Polytechnic University.................................397 Princeton University.....................................398 Purdue University.........................................399 Rensselaer Polytechnic Institute...................400 Rhode Island, University of..........................435 Rice University.............................................401 Rochester, University of...............................402 Rose Hulman Institute of Technology..........435 Rowan University.........................................403 Rutgers University........................................404 Saskatchewan, University of........................436 Singapore, National University of................405 South Carolina, University of.......................406 South Florida, University of.........................437 Southern California, University of...............436 State University of New York.......................407 Stevens Institute...........................................408 Sydney, University of...................................437 Syracuse, University of................................438 T ennessee, University of..............................409 T exas, University of.....................................410 T exas A&M University................................411 T exas A&M University, Kingsville..............438 T oledo, University of....................................412 T ufts University............................................413 T ulane University.........................................414 T ulsa, University of......................................415 Utah, University of.......................................439 V anderbilt University...................................416 V illanova University.....................................439 Vi r ginia, University of..................................417 Vi r ginia Tech................................................418 W ashington, University of............................419 W ashington State University........................420 W ashington University.................................421 W aterloo, University of................................440 W ayne State University................................422 W est Virginia University..............................423 W isconsin, University of..............................424 W orcester Polytechnic Institute....................425 W yoming, University of...............................440 Y ale University.............................................426I N D E XGRADUATE EDUCATION ADVERTISEMENTS











Letter to the Editor
Continued from page 262.
b=8.5164364+1.5315505; the error variance
s2=0.467503; and correlation coefficient R2=0.953603.
Professor Fahidy advises not to put too much faith in the
linear regression model, in spite of the relatively large
R2 value, because of the extremely wide confidence in-
tervals on the parameter a. The fairly random distribu-
tion of the residuals (see Figure 2) suggests, however,
that the linear model may be the correct one. Further-
more, both physical considerations (fuel consumption
should be zero for a zero mass vehicle) and the wide
confidence intervals on the free parameter a, indicate that
the model can be improved by setting the free parameter
at zero. Indeed, carrying out the regression while setting
a=0 yields: b=7.8929160.3599903; s2=0.4641509, and
R2=0.9481781. Thus, this model is now acceptable, even
with respect to the confidence interval values.
One of Professor Fahidy's objectives in presenting this
example was to warn against accepting relatively large
R2 values as proof of good linear relationship between
the dependent and independent variables. The limitations
of the R2 statistics in this respect can be most strikingly
demonstrated using residual plots. Shacham, et al.,E3' for
example, fitted vapor pressure data of 1-propanol with
the two-parameter Clapeyron equation. This regression
yields the values: R2=0.9998818 and s2=1.659E-05
(based on log P). Such a high value of R2 can be inter-












Figure 2. Residual plot for Example 5 in Fahidy
paper.!












Figure 3. Residual plot for vapor pressure data from
Reference 3.
Regression model: log P = 7.6380342-1622.8666/T

Fall 2002


preted as a perfect fit. But the residual plot (seen in Figure 3) shows
that the vapor pressure data set exhibits a curvature, which is not
predicted by the Clapeyron equation. Indeed, using the four-param-
eter Riedel equation for representation of the same data yields: R= 1;
s2=1.327E-09 and randomly distributed residuals.
The last example, given in the Appendix of the article deals with a
linear model for representing coded effectiveness indicators versus
catalysts containing various coded platinum mass units. Analysis of
this example shows that if the free parameter, a, is set at zero (as
suggested by the wide confidence intervals on a and physical con-
siderations) the linear model is appropriate to represent the data with
1=1.64376590.0845917, R2=0.8860414, and s2=0.8508906.
We can conclude that teaching statistical analysis of data and re-
gression models is very important, but interpretation of numeric sta-
tistical indicators must be complemented by graphical analysis and
consideration of the physical nature of the model in order to arrive
at the correct conclusions.
Mordechai Shacham
Ben-Gurion University of the Negev
Neima Brauner
Tel-Aviv University
References
1. T.Z., "An Undergraduate Course in Applied Probability and Sta-
tistics," Chem. Eng. Ed., 36(2), 170 (2002)
2. Fahidy, T.Z., Personal communication (2002)
3. Shacham, M., N. Brauner, and M.B. Cutlip, Rcpl.c-lilg the Graph
Paper with Interactive Software in Modeling and Analysis of Ex-
perimental Data," Comp. Appl. Eng. Ed., 4(1), 241 (1996) 1


Author's Response
I am delighted at Professor Shacham's interest in my paper. I also
fully concur with the argument that the residual plots are an impor-
tant and integral part of regression analysis. This is now standard
textbook material, and I do routinely discuss this subject in my course.
Although my intention was to keep the article from being too long,
in retrospect I should have spent a paragraph or two on residual
analysis, and I regret the omission.
In Example 4 it was stated that the reaction mechanism was first-
order irreversible, but perhaps not strongly enough to imply an a
priori knowledge of non-statistical origin, so that 0th and 2nd order
models are beyond consideration. With limited data and given a
physically correct model, the method that provides regression pa-
rameters relating data to model with the smallest error variance may
be acceptable in lack of something better, even if the residual plot
does not show randomness of a desired degree. The quest for addi-
tional measurements is almost universal in the case of limited-size data.
My views about R2 versus confidence intervals for true regression
parameters do not fully coincide with the respondents', but may I point
out the redundancy of seven-digit values, computer printouts notwith-
standing. An R2=0.8860414 is not more meaningful than R2=0.89
Thomas Z. Fahidy











I
the CSTR model assumes complete mixing at all scales. For
constant density systems, the three classical reactor models
are described by


PFR

(u) dC)
dx


d(C)
dt


-R((C)) with (C)= Cin @ x = 0



R((C)) with (C)= Cin @t = 0


CSTR

C) C -R((C)) (3)
'c
where (C) is the spatially (or cross-sectional) averaged reac-
tant concentration, C, is the mean inlet concentration of the
reactant, R((C)) is the sink term due to the presence of ho-
mogeneous reaction, x is the coordinate along the length of
the PFR, (u) is the mean fluid velocity in the reactor, t is the
time, and Tc is the total residence time in the reactor.
Irving LangmuirM11 first replaced the assumption of no axial
mixing of the PFR model with finite axial mixing and the
accompanying Dirichlet boundary condition ((C) = Cl @ x
= 0) by a flux-type boundary condition

Dm dx=(u)[(C)-Cin] @ x=0 (4)

where Dm is the molecular diffusivity of the species. The above
boundary condition was rediscovered several times in the
years that followed: first by Firster and Geib[6], which was
quoted and applied by DamkOhler,[2] and then, later, by
Danckwerts.[3] Since then it has been known as the
"Danckwerts" boundary condition. In his paper, Langmuir
dealt with both the limiting cases of iil'iili nearly com-
plete" and "only slight mixing."
Thirty years later, Gerhard Damkohler in his historic pa-
per, summarized various reactor models and formulated the
two-dimensional CDR model for tubular reactors in complete
generality, allowing for finite mixing both in the radial and
the axial directions. In his paper, Damkohler used the flux-
type boundary condition at the inlet and also replaced the
assumption of plug flow with parabolic velocity profile, which
is typical of laminar flow in tubes.
Firster and Geib first introduced the concept of residence
time distribution (RTD) to study the case of longitudinal dis-
persion in tubes. Twenty years later, Danckwerts, in his much
celebrated paper,[3] devised a generalized treatment of RTD
and introduced the concepts of holdbackk" and ,cI l c o.II "
Following this, it was Zweitering,[7] who quantified the de-
grees of mixing with the ideas of "complete segregation" and


Graduate Education J

"maximum mixedness" and brought forth the concept of
i,,; ..; i; in:. or mixing at the molecular scale in homoge-
neous reactions.
In the last forty years, a wide range of micromixing mod-
els for homogeneous reactors have been formulated. While
most of these low-dimensional mixing models are phenom-
enological in nature, the rigorously derived CFD models are
high-dimensional and therefore numerically very expensive,
especially for the case of multiple reactions with fast/non-
isothermal kinetics. As a result, in spite of the simplifying
assumptions present, the century-old ideal classical reactor
models (Eqs. 1-3) are still the most popular choices among
chemical engineering practitioners (and teachers). The clas-
sical ideal reactor models, which are easy-to-solve ordinary
differential or algebraic equations with no adjustable param-
eter, are particularly preferred over the full CDR models
(which are partial differential equations in more than one di-
mension) in case of multiple reactions with complex kinetics.

SPATIAL AVERAGING OF
CONVECTION-DIFFUSION-REACTION
EQUATION
The main goal of this article is to illustrate a new approach
for deriving low-dimensional homogeneous reactor models,
capable of predicting mixing effects. These models are de-
rived through rigorous spatial averaging of the three-dimen-
sional CDR equations over local length scales by using the
Liapunov-Schmidt (L-S) technique of classical bifurcation
theory. We illustrate this spatial averaging technique using
the simple case of laminar flow in a tube with homogeneous
reaction. The scalar concentration C(r, 0, x, t') in a tubular
reactor is assumed to obey the CDR equation

aC ac
atu(r ax
1 D ac 1 a ac
r _rD r + 1 L2 D + (D OC-R(C) (5)
with accompanying initial and boundary conditions, given by
with accompanying initial and boundary conditions, given by


C(r,0,x,t'=0)=C0


@C
--=0 @ r=a
ar


C(r, x, t')= C(r,0 + 2r, x,t')
ac
Dx- = u(r)[C(r,O,x,t')-Ci] @ x=0
ax
-=0 @ x=L


where DI and Dx are the transverse and axial diffusivities,
respectively; r, 0, x are the radial, azimuthal, and axial coor-


Fall 2002










[ Graduate Education I


INTRODUCING MOLECULAR BIOLOGY

TO ENVIRONMENTAL ENGINEERS

Through Development of a New Course


DANIEL B. OERTHER
University of Cincinnati Cincinnati, OH 45221-0071
historically, applications of biology in chemical and
environmental engineering have been approached
from different perspectives with different goals. For
example, chemical engineering optimizes biochemical reac-
tions of pure cultures of microorganisms in highly controlled
bioreactors used for manufacturing (e.g., fermentation),
whereas environmental engineering employs mixed micro-
bial communities with minimum controls as least-cost pro-
cesses for meeting regulatory requirements (e.g., sewage treat-
ment). Although chemical and environmental engineering
education often incorporates formal training in biology, the
motivation for course selection can be very different. Incre-
mental advances in biological knowledge that can be used to
increase manufacturing capability or improve efficiency are
useful in chemical engineering practice, and their integration
into chemical engineering education is justified.
The same principle does not hold for environmental engi-
neering, however. Once minimum regulatory requirements
are met, incremental advances in biological knowledge do
not offer the significant cost savings for environmental bio-
logical unit operations that are needed to encourage the adop-
tion and integration of the new knowledge into environmen-
tal engineering education.
Recently, development of 16S ribosomal ribonucleic acid
(16S rRNA)-targeted tchlin ,ii-li provided researchers in en-
vironmental engineering with new tools to identify
microorganisms and to study microorganisms in bioreactor
environments. As compared to classical techniques for iden-
tification and enumeration, 16S rRNA-targeted tcolt il%4 .,-
allows in situ examination of the structure (i.e., who is
present?) and function (i.e., what are they doing?) of micro-
bial communities without a prerequisite for isolating pure cul-
tures.'1 For researchers in environmental engineering, 16S
rRNA-targeted tcl iiili .1, has been extensively tested, and
current research activities have moved beyond the "proof-
of-concept" state to widespread applications.E2,3] In contrast,
integration of 16S rRNA-targeted tclin li 1-.1, within the en-
vironmental engineering curriculum remains to be fully de-


veloped. At the University of Cincinnati, the author has de-
veloped and pilot tested a "proof-of-concept" course titled
"Molecular Methods in Environmental Engineering."
The course was designed to teach limited fundamentals of
molecular biology in the context of quantitative engineering
design and practice. During its first offering, fifteen graduate
students in environmental engineering were exposed to "state-
of-the-art" technology, including hands-on laboratory exer-
cises following the "full-cycle 16S rRNA approach."E'1 Stu-
dents learned the importance of detailed understanding of
microbial communities and microbial-mediated biochemical
networks in biological unit operations, natural biological sys-
tems, and the global biosphere. The format of the course in-
cluded a weekly lecture as well as a semester-long series of
hands-on laboratory exercises designed to teach students to
develop scientific questions, learn appropriate methodology,
conduct careful experimentation, analyze data, and draw con-
clusions worthy of presentation to peers. Thus the final out-
come of the course included preparation of peer-review quality
manuscripts by each team of students as well as one-on-one
interviews with the instructor.

FULL-CYCLE 16S rRNA APPROACH
Traditionally, the identification of microorganisms in en-
vironmental samples has relied upon semi-selective cultur-
ing or direct microscopic examination. These techniques have
led to a rudimentary understanding of the role of microor-
ganisms in the global biosphere as well as the importance of
microorganisms in public health and biocatalysis. Recently,
the techniques for determinative microbiology have been dra-
matically expanded to include cultivation-and-morphologic-
independent identification and enumeration of microorgan-
Daniel B. Oertherjoined the Department of Civil and Environmental Engi-
neering at the University of Cincinnati in 2000. For ten years, he has been
adapting methods from molecular biology to identify, enumerate, and mea-
sure the physiology of microorganisms in biotechnology processes includ-
ing wastewater treatment and bioremediation. His research links the re-
sults of novel molecular biology assays with mechanistic modeling of
bioreactor performance.
Copyright ChE Division of ASEE 2002


Chemical Engineering Education










(Prt 1 + Pr t 1
P r Nu1 1 Pr Nuw


(27)


SThey further recognized that when Eq. (17) was rear-
ranged as

Nu Nu Nu, Prt
Nu, Nul Nu1 Pr- Prt

it had the form of Eq. (9), with

b=-q=l
Yo = Nul
y, = Nu-

y Nu (Nu -Nu) r-1
Nu, Prt

The staggered independent variable, Pr/Prt 1, has the essen-
tial role of converting Nu, from a particular value to an as-
ymptote. According to Eq. (28), Nu goes through a sigmoi-
dal transition from Nu, to N_, a nuance of behavior that had
previously been overlooked. In retrospect, correlation in terms
of Eq. (7), that is, direct interpolation between Nu, and Nu_,
was doomed to fail. The relationship provided by the
Rci'li.iid1i .iII.il -., was essential to the derivation of Eq. (27).


O The identification of Eq. (28) with Eq. (9) suggested
that the analogue of Eq. (28) in terms of Nu0 and Nu, might
be applicable for Pr < Prt. That concept led to an expression
with a discrete step in the derivative of Nu with respect to Pr/
Prt at Pr = Prt, but elimination of this discontinuity by means
of an arbitrary but ultimately vanishing coefficient resulted
in

Nu-Nu /I+ Nul Nu Nu Prt Pr
Nu1 -Nu N uL Nu1 Nuo ) PrJ (29)

where Nu = Nu {Pr = Prt } = 0.07343 Re (f / 2)12.


(4 The absence of any allusion to geometry or to the ther-
ma boundary condition suggested that Eqs. (28) and (29)
might be applicable for all geometries and all thermal bound-
ary conditions. Plots of numerically computed values of Nu
versus Pr/Prt for round tubes with uniform heating and uni-
form wall temperature, and for parallel-plate channels with
equal uniform heating and with unequal uniform tempera-
tures, confirmed the validity of this speculation.


SThese plots in logarithmic coordinates appeared to pro-
vide an excellent overall representation for all values of Pr/


Prt, for all values of a+ or b+ (where b is the half-spacing of
the parallel plates) greater than 145, which is the lower limit
for the existence of fully turbulent flow, for all geometries,
and for all thermal boundary conditions. The more critical
test provided by arithmetic plots, however, reveal errors in
Nu of up to 20% for both Pr/Prt = 0 {10) and Pr/Prt = 0 0.01).
After many attempted correctives, substitution of the anal-
ogy of Churchill for that of Reichardt to obtain

= -+1-f Nr- (30)
1 (Pr< 1 ( prt )/] 1 (30)
Nu lPr Nu1 L --Pr) jNu-

was found to result in an almost perfect representation for
the dependence of Nu on Pr/Prt.
Q The analogue of Eq. (30) for Pr < Prt, corrected as was
Eq. (29) to remove the singularity in the derivative, and with
the arbitrary inclusion of the empirical factor (Pr/Pr)18, is

Prt P Nu- 2Nul Nu

Nu1 -Nu (Prt/Pr)l/(Nul Nu)Nul


This expression results in almost exact representations for
Pr < Pr, for all of the previously mentioned conditions-
thereby it is a complement in every respect to Eq. (30).


IMPLEMENTATION
The numerical calculation of values of Nu for specified
values of Re and Pr and for particular geometries and
boundary conditions requires numerical values or expres-
sions for f, Nu0, Nu1, and Prt. For a round tube, values of
f of sufficient accuracy can be determined from Eq. (6)
by noting that Re = 2 a+u,. Values of Nu, and Nu, can be
calculated from Eqs. (19) and (20), but an array of such val-
ues has already been calculated for representative values of
a+, and correlating equations have been devised for interpo-
lation. The slight inaccuracy associated with Eq. (5) is totally
negligible when it is used in conjunction with Eqs. (19) and
(20). Equivalent expressions for f, and values and expres-
sions for Nu0 and Nu, are also available or can readily be
derived and calculated for other geometries and thermal
boundary conditions. Equation (21) is directly applicable as
an asymptote for large values of Pr for all geometries and
conditions. Current correlative and predictive equations for
Prt are quite uncertain (see, for example, KaysE121 or
Churchill"131). However, Nu as predicted by Eqs. (30) and (31)
is fortuitously insensitive to the expression used for Prt, and
the following purely empirical equation
0.015
Prt = 0.85 + (32)
Pr
appears to be adequate for that purpose. The dividing value


Fall 2002











[ Graduate Education I


asymptote for i,. ir. i:. i. reactions is analogous to the
mass-transfer limited asymptote for wall-catalyzed reactions.
Just as the wall (surface) concentrations approach zero for
the case of infinitely fast surface reactions (while the bulk/
mixing-cup concentrations remain finite), so do the local con-
centrations (Ci) for infinitely fast homogeneous reactions
(i=A,B). Unlike in catalytic reactions, where exchange be-
tween the phases occurs at the solid-fluid boundary, the ex-
change between modes (scales) in homogeneous reactors
occurs over the entire domain.


Competitive-Consecutive Reactions
Competitive-consecutive reactions of the type

A+B -C and B+C ~D
are prototype of many multistep reactions such as nitration
of benzene and toluene, diazo coupling, bromination reac-
tions, etc. Experimental observations"16 show that if the first
reaction is infinitely fast as compared to the second one (i.e.,
k /k -> -), under perfectly mixed conditions B is completely
consumed by the first reaction and the yield of D is zero (if A
and B are fed in stoichiometric amounts). But it was observed
that if the mixing of A and B is not attained down to the mo-
lecular scale, the first reaction is not complete and there re-
mains a local excess of B, which can then react with C to
produce D. The yield of D increases monotonically as the
rate of the second reaction increases, finally attaining a mix-
ing-limited asymptote. We use the TMM for a CSTR to verify
this observation. Figure 2 shows the increase in the yield of
D, YD, with Damkohler number of the second reaction, Da2,
where YD = 2CDm/(Cm+2CDm), and Da, = k 2Cn Zc. The figure
corresponds to the case when the first reaction is infinitely
fast (i.e., kl/k2 -> -), and A and B are fed in stoichiometric
amounts (i.e., CBln = CA,n=C and Cln = CDln= 0). While no
D is formed for the case of 1 = 0 (ideal CSTR), a significant
increase in yield of D is obtained if finite micromixing limi-
tations are present in the system. The maximum yield of D,
obtained when the mixing limited asymptote is attained also
for the second reaction, is


-21 for 1 1+21j
1D,max 2
S- for q>1
1+2T1


Thus, in this case, an optimal yield of D is obtained for r = 1.

CONCLUSIONS

In the hierarchy of homogeneous reactor models, the clas-
sical ideal reactor models stand at one end as the simplest,
while the generalized convective-diffusion-reaction (CDR)


model stands at the other end as the most detailed one. While
the former cannot capture the mixing effects due to local ve-
locity gradients, molecular diffusion and reaction, the latter
requires extensive computations, especially for large Schmidt
and/or Damkohler numbers, and for multiple reactions with
large number of species. The Two-Mode Models (TMMs)
proposed here bridge the gap between the two extreme cases
of reactor models and provide a practical approach for de-
scribing mixing effects on reactor performance. They retain
all the parameters present in the full CDR model and there-
fore all the qualitative features of the latter, and yet their so-
lution requires a numerical effort comparable to that of the
classical ideal reactor models.
The ; -i.lI, between the two-mode models of homoge-
neous reactors and two-phase models of catalytic reactors
could be carried further by noting that for all cases of well-
defined flow-fields, where two-phase mass-transfer coeffi-
cients (ShT) can be estimated theoretically, the exchange co-
efficient (hi ) or the local mixing time (tm) of the TMMs
could also be estimated. For more complex flow-fields (e.g.,
packed beds), the local mixing time, like the mass-transfer
coefficient, could be correlated to Re, Sc, and the geometri-
cal characteristics of the system. Thus, the two-mode models
of i,. .*.. ,.. wr. reactors are as general as the two-phase
models of catalytic reactors and have a similar range of ap-
plicability. (In fact, the classical two-phase models are also
two-mode models, the modes being the cup-mixing and the
surface (or solid-phase) concentrations. Thus, the two-mode/


Figure 2. Variation of the yield ofD with Damkohler num-
ber for a competitive-consecutive reaction scheme
A+B- C, B+C- D, when the first reaction is infinitely
fast, for different values of the dimensionless local mixing
time, 1r.


Chemical Engineering Education











ber of facts have to be taught, thus assigning an important
role to the teacher. On the other hand, to promote the stu-
dents' understanding of the underlying principles as well as
to sharpen their view of the complete process, active learn-
ing appears to be a key issue. E3,561 We try to support this ac-
tive learning in different ways (see Figure 8).
Lab and virtual experiments are conducted so that students
can apply and transfer their acquired knowledge and get in-
volved with more realistic problems. This is accomplished
by a mandatory lab course (one semester) as well as lab com-
ponents that are integrated into the courses described above.
The lab experiments include a wide field of exemplary tasks
that include, for example, dust separation in cyclones, filtra-
tion, mixing, and particle characterization by laser diffrac-
tion as well as the investigation of the stability of colloidal
suspensions by dynamic light scattering. Furthermore, a com-
pletely new virtual lab is currently being established in the
course Product Engineering, with computer simulations of
disperse systems (e.g., crystallization, comminution) based
on population balances using commercial software (e.g.,
LabView and Parsival).
We also encourage the students to take an active role
throughout the courses wherever it is appropriate, for example,
in the particle characterization course. After introducing the
basic principles and the important characteristics of a mea-
surement systems (e.g., assessed equivalent particle size, sig-
nal recording, conditioning and evaluation, necessary sample
preparation, etc.) as well as discussing their application to
the most important measurement techniques, the students are
arranged in small groups. Each group is then assigned the
task of analyzing one measurement technique that is so far
unknown to them. They also have to prepare a presentation
of their results that will relay the most important facts to their
fellow students. The groups are supposed to work autono-
mously, with the teacher playing a more passive role and only
giving guidelines or help when asked. In this way, several
goals can be achieved.

The students work and access information autonomously,
e.g., from literature in a foreign language.
The group work necessitates that students find their roles
in a group and work together productively.[7
Finally, the students are given the chance to prepare and
give a presentation. Even listening and assessing the
presentation of other groups increases their ability in this
respect. This is a capability that is not practiced
enough.[]

By actively preparing a small part of the course, the stu-
dents not only acquire valuable technical knowledge, but they
also get a chance to increase their "soft skills." Personal de-
velopment is often neglected in a university education. Stu-
dents should concentrate on both their technical skills and
their personal growth (see Figure 9). This includes an ability
for self-organization and focusing on defined targets, intrin-


sic motivation to reach goals, and an ability to communicate
results. On a deeper level, internal self-reflection is indis-
pensable for accepting personal strengths and weaknesses as
well as those of others. This is a precondition for all social skills.

CONCLUSIONS
Particle tc'liin -1 -:, is a much wider field than many people
realize since it also comprises biochemical, chemical, and
thermal processes dealing with particles. Hence, it is not only
of the utmost importance in the chemical industry, where about
60-70% of all products are fabricated in dispersed form, but
also for a number of other fields, such as materials science
and information tLchliii in .;,. Product properties and the sub-
sequently developed product engineering approach is at the
center of our considerations. With a continuously growing
number of applications for dispersed systems, we feel a need
to stress the fundamental aspects even more. With the gen-
erally observed trend toward finer particle sizes, new topics
such as particle interactions and population dynamics have
been included in order to prepare our students for newly de-
veloping areas such a, Ii.lin ic'liin 'I *-.,. The technical courses
are complemented by various activities to strengthen the soft
skills of the students.
Recently, suggestions have been made by Cussler, et al.,19
on how to change chemical engineering curriculae. Consid-
ering the shift in industrial practice from large-scale processes
producing commodities toward more specialized product
design, we feel that particle tcclii ,li ,--:, and particle design
methods deserve a prominent place in the curriculum.

ACKNOWLEDGMENTS
The authors would like to thank Professor Helmar Schubert
from the University of Karlsruhe for very valuable discussions.

REFERENCES
1. Rumpf, H. Uber die Eigenschaft von Nutzstauben, Stab-Reinhaltung
der Luft, 27(1), p. 3 (1967)
2. Polke, R. and J. Krekel, "Qualitatssicherung bei der
Verfahrensentwicklung," Chem. Ing. Tech., 64(6), p. 528 (1992)
3. J.L. Cano, Garces, A., and Saenz, M.J. "Oral Presentations of Stu-
dents in Product Engineering Lectures." Int. J. Engg. Ed., 13(3), p.
175 (1997)
4. Cussler, E.L. "Do Changes in the Chemical Industry Imply Changes
in the Curriculum?" Chem. Eng. Ed., 33(1), p. 12 (1999)
5. Davis, R.H. "Helpful Hints for Effective Teaching," Chem. Eng.
Ed., 32(1), p. 36 (1998)
6. Felder, R.M., D.R. Woods, J.E. Stice, and A. Rugarcia. "The Future
of Engineering Education Part 2: Teaching Methods that Work."
Chem. Eng. Ed., 34(1), p. 26 (2000)
7. Humphreys, P, V. Lo, F. Chan, and G. Duggan, "Developing Trans-
ferable Groupwork Skills for Engineering Students," Int. J. Engg.
Ed., 17(1), p. 59 (2001)
8. Brostow, W., "Instruction in Materials Science and Engineering:
Modern Technology and the New Role of the Teacher," Mat. Sci.
and Eng., A302, p. 181 (2001)
9. Cussler, E.L., D.W. Savage, A.P.J. Middelberg, and M. Kind. "Re-
focusing Chemical Engineering," Chem. Eng. Progr., 98(1), p. 26S
(2002) 1


Chemical Engineering Education












Perhaps most importantly, research has shown that alternative assessment
helps in the evaluation of students with various learning styles and
educational backgrounds, promoting excellence
among a more diverse student population.


makes them easiest to implement in courses with small to
medium enrollments. SlaterE91 and Winko101 have reported tech-
niques to extend the use of portfolios to large lecture courses,
however.
Although there has been an emphasis on the use of portfo-
lios in upper-level "capstone" courses, such as senior design
and the unit operations laboratory,141 I focus on their use in
introductory chemical engineering courses. I believe portfo-
lio assessment has unique benefits to beginning engineering
students, as described further in the following paragraphs.

GRADING PORTFOLIOS
Implementing innovative assessment is all well and good,
but how are we going to evaluate and grade student portfo-
lios? Since the portfolio entries have presumably been graded
as part of a homework assignment or exam earlier in the se-
mester, it does not seem fair to me to place the students in
"double jeopardy" by basing the portfolio grade on whether
or not the problems are correct. I chose to grade portfolios by
giving equal weight to three criteria:

Completeness and ., *.,,,:.i;..,,
Quality and style <.fin i, ;i;li
Level cr.t i, .r...i,t analysis, and reflection in each entry

The first two criteria are easy to evaluate. The first refers to
whether students have all the required items, including a table
of contents and page numbers. The second criterion refers to
writing style and grammar, again fairly straightforward to
evaluate.
The third criterion is a little more subjective and requires
some planning on the part of the instructor. I evaluated the
level of thought and analysis by judging the extent to which
each entry addressed two to three i n i'ii questions," which
are listed in Table 3. Students were given these questions at
the start of the semester to help guide them through the self-
analysis process.
SlaterE91 recommends developing a l'I Illn rubric,"
whereby the portfolio grade is based on the extent to which
students demonstrate mastery of the required number of ob-
jectives. For example, you may require students to have at
least eight entries, each of which is related to a specific course
objective. A simple scoring rubric could then be an "A" grade
for demonstrating adequate mastery in seven or more objec-


tives (as evidenced by the portfolio entries), a "B" grade in
five or more objectives, and so on. More detailed examples,
developed for a unit operations course, are given by Olds
and Miller;[141 see also the examples given by Slater.[9]

EXAMPLE
Portfolios in the Introductory ChE Course
In the spring of the freshman year, students at UMass take
a course titled Chemical Engineering Fundamentals. The
course content covers units and dimensions, mass balances,
simple reactive systems (i.e., CSTRs and PFRs), and forms
of energy. The typical enrollment is 40-50 students, most of
whom are engineering majors with an interest in chemical
engineering. After completing the freshman year require-
ments, students can apply for admission into the chemi-
cal engineering major. Thus, many students in the ChE
Fundamentals course are still unsure of their choice of
major.
I chose to implement portfolio assessment in this course as
an optional assignment. The portfolio assignment could be
used to replace a low grade on either of two midterm exams
or a low homework grade, but not the final exam. Many in-
structors give students the option of "dropping" one low grade,
so I did not feel that the use of portfolios would cause grade


TABLE 3
Questions for Student Self-Analysis
in Portfolio Entries

[ What concept or topic was involved with this problem? What
skills did you use in solving it?
I How did this problem help you learn something new?
[ Did you learn anything about yourself, your thought process, or
your strengths and weaknesses as a result of this activity?
I What strategies did you use? What were you thinking as you
worked the problem?
[ Would you do anything differently if you had more time?
I Can you describe any connections between the activity and other
concepts, subject areas, or real-life situations?
[ Does the problem represent a special achievement for you, a
sense of accomplishment at having learned a particular concept,
or a sense of improvement over time?


Chemical Engineering Education











[I n= laboratory


CHEM-E-CAR

DOWNUNDER



MARTIN RHODES
Monash University Melbourne, Victoria 3800 Australia


he Chem-E-Car competition has been run for under-
graduates by the AIChE for the past three years with
finals at the AIChE annual meetings. The idea is for
teams of undergraduate students to design and build a small
car powered by a chemical reaction. The objective is for the
car to travel a certain distance and then stop. The distance to
be traveled and the weight to be carried by the car are not
announced until the day of the competition. The emphasis is
on control of a chemical reaction, with a keen eye on safety
and the environmental impact of the design. The winner is
the team whose car stops nearest to the required distance. In
addition to designing and building the car, each team must
make a poster that describes the car's operation and include a
safety and environmental assessment.
Having witnessed the enthusiasm of the participating stu-
dents and spectators at the AIChE Chem-E-Car Competition
finals held in Dallas and Los Angeles, I decided to organize a
Chem-E-Car competition here in Australia. Early in 2001, I
contacted all chemical engineering departments in Australia
and New Zealand, sent them copies of the rules (for the AIChE
competition), and invited them to join. Six departments re-
sponded enthusiastically, and within a couple of months teams
of students were working away. The original plan was to have
local competitions within each department, with these com-
petitions generating finalists for the grand Australasian final.
University work and the difficulty of the Chem-E-Car task
took its toll, however. Several teams fell by the wayside, in-
cluding the team from my department. As time went on, it


Martin Rhodes is Professor in the Depart-
ment of Chemical Engineering at Monash
University in Melbourne, Australia. He has a
keen interest in chemical engineering educa-
tion and specializes in particle technology, a
subject on which he has written an under-
graduate textbook. His research interests in-
clude fluidization, gas-particle flows, interpar-
ticle forces, and particle mixing.


@ Copyright ChE Division of ASEE 2002


became clear that the grand final would be a fight between
five teams-four from Australia and one from the National
University of Singapore, who, upon hearing about the com-
petition, asked if they could take part. The grand final was
held on day three of the World Congress of Chemical Engi-


Figure 1. The NUS car (a) with bodywork removed to
reveal the inner detail and (b) in motion.


Figure 2. The UNSW car drifting through its self-
generated mist.


Chemical Engineering Education











I was disappointed in the students' lack of interest in learn-
ing about team building, task-force management, and build-
ing commitment in the workplace. The students felt that they
knew about these topics and that they were already profi-
cient. I do not believe I ever convinced them there was a lot
for them to learn and that success in these areas requires skills
they actually did not possess.

OTHER FEATURES OF THE COURSE

The students were given a three-part final homework as-
signment. One element was a personal mission statement with
an associated five-year career development plan. The plan
could also include other facets of their life, such as family,
health, religion, community involvement, etc. For each of
the elements they were encour-
aged to follow a disciplined ap-
proach that included short-term
(6 months), midterm (2-3 TA
years), and long-term (5 years) Cours
plans. For each time period,
Not Useful 1 2
they were asked to state goals
and specific objectives and to February %
define strategies and action March %
steps. They were initially unen- April %
thusiastic about this task, but
the final product indicates that
they thought hard about it and
put together a realistic and credible plan.
The second element of the final homework was a team
project. Groups of four students were asked to analyze a fairly
complex HBS Case of a Coming Glass Works Division un-
dergoing a change in management during a business down-
turn. They were asked to devise strategies and specific action
plans for the division as well as a self-assessment of their
team performance. The reports indicated a wide range of team
performance, with the key problems being an inability to agree
on an action plan, finding time to work together, and uneven
participation by team members. This assignment came at the
very end of the semester, which was too late to refute their
earlier assertions that "teamwork was something they knew
how to handle."
The third element of the final homework was an analysis
of a company's performance during the last four years. Each
student selected a company from those reviewed by Fortune
-I, .:,,i,-. in its annual publication of "America's Most Ad-
mired Companies."14,51 They were asked to analyze the per-
formance of the company they chose, to identify reasons for
any change in rankings during the four-year period, and to
forecast future trends.
The objective of this exercise was to allow the students to
apply to a specific company-wide situation what they had
learned about effective management, leadership, and manag-


ing change. The companies chosen reflected the students' wide
range of career interests and included, among others, enter-
tainment, communications, financial, computer tc'Ll iiii .:,,
oil and chemicals, consumer products. They were asked to
suggest the future direction the company needed to take to
improve performance. A majority suggested expanding glo-
bal reach and more tcclhin l. \ investment, while only a few
focused on improving cost competitiveness.

STUDENT ASSESSMENT AND FEEDBACK
During the semester, the students were asked to provide
feedback on course content and to assess its effectiveness.
The data are summarized in Table 4 and show that the major-
ity of the class found the course very useful. They rated the
discussions of HBS Cases and Notes, my work experiences
and personal stories, and the
outside speakers the highest.
E 4 They were less enthusiastic
essment about the other reading mate-
rial, perhaps because they
5 6 7 8 Very Useful were not used to this amount
25 45 30 of reading in an engineering
3 29 50 18 course.
3 25 37 35 SUMMARY

The objective of the course
was to increase student aware-
ness of the nontechnical competencies they should possess
in order to succeed in the work world. It is unrealistic to ex-
pect that at the end of a semester they would have mastered
all these competencies, but it was evident that they were much
more sensitive to the importance of such skills and had grasped
the essentials. Also, they were left with an excellent collec-
tion of HBS Cases and Notes that could serve them well when
confronted with similar situations. As I frequently indicated
to them, I wished that I had such a learning experience in my
engineering schooling and early career.
The main reason for writing this article is to encourage other
colleges and universities to consider offering a course along
the general outline that I have described. I also encourage
experienced business practitioners to teach such a course. The
Halsey Professors are unanimous: it was an exciting and grati-
fying experience to share what you have learned with the
next generation of engineering and business leaders.

REFERENCES
1. Harvard Business School Publishing, 60 Harvard Way, Boston MA
02163
2. Fisher, R., W. Ury, and B. Patton, Getting to Yes, 2nd ed., Penguin
Books
3. Covey, S.R., The 7 Habits of Highly Effective People Simon and
Schuster
4. Fortune Magazine, March 6, 1997
5. Fortune Magazine, February 21, 2001 1


Fall 2002


.BL
eAss

3 4










Graduate Education


... we plan to expand the enrollment [in this course] to include undergraduate envi-
ronmental engineering students as well as graduate and undergraduate students from
related disciplines, including chemical engineering and biomedical engineering.


elected for the course was novel for the field of environmental
engineering and possessed the capacity to stimulate a more
extensive research question (e.g., supplemented a research
question in an existing/developing MS or PhD degree, or pro-
moted a novel research direction generally underexplored.)
A sample was obtained from the selected system. In all cases,
preference was placed on samples that were a part of a devel-
oping/ongoing research project with significant supplemen-
tary information generated from advanced process engineer-
ing and chemical/physical analyses (e.g., samples) from a
novel bioreactor configuration or a bioreactor treating a novel
waste stream).

Step 3 Each team generated 16S rDNA sequence infor-
mation from their sampless. Genomic DNA was extracted
using an UltraClean Soil DNA Isolation KitE7 according to
the manufacturer's instructions. Mechanical lysis of the
samples was performed for one minute at the maximum set-
ting of a Mini Beadbeater-8.J13 Genomic DNA was quanti-
fied using a Genesys 10uvE151 spectrophotometer assuming
that an absorbance reading of 1.0 at a wavelength of 260 nm
corresponded to a concentration of 50 mg DNA/1.
The 16S rDNA genes of bacteria present in the sample were
amplified by PCR using primer set S-D-Bact-0011-a-S-17
(5' to 3' sequence = gTT TgA TCC Tgg CTC Ag) and S-D-
Bact-1492-a-A-21 (5' to 3' sequence = ACg gYT ACC TTg
TTA CgA CTT).E181 The conditions for PCR included: 5 min.
at 940C; 30 cycles of 0.5 min. at 940C, 0.5 min. at 550C, and
0.5 min. at 720C; 7 min at 720C; and hold at 40C. Each reac-
tion tube contained: 1.25 U Takara Ex Taq polymerase,E91 lx
Takara Ex Taq reaction buffer, 200 M of each deoxy ribo-
nucleotide triphosphate (dNTP), 0.2 pM of each primer, and
500 ng of genomic DNA. PCR was conducted using a model
2400 thermal cycler.E8]
Agarose gel electrophoresis was used to check the quality
of the PCR product. A 1% (wt./vol.) agarose gel was pre-
pared in 1 x tris buffered EDTA (1 x TBE is 90mM tris borate
and 2 mM ethylenediamine-tetraacetic acid [EDTA]) accord-
ing to the manufacturer's instructions.191 Electrophoresis was
conducted for two hours using a setting of 100 V for the power
supply. DNA fragments were visualized with a hand-held UV
lamp after staining the agarose gel for ten minutes at room
temperature with 50 mg/1 of ethidium bromide.
The PCR products were cloned into component cells of E.
coli using the TOPO TA cloning kit, version K2E101 according


to the manufacturer's instructions. The blue/white screen with
x-gal was used to detect the presence of insert in each plas-
mid, and the antibiotic ampicillin was used to screen for the
presence of plasmids in colony-forming units of competent
cells. Ten clones were selected for each team of students, and
plasmid DNA was prepared using Perfectprep Plasmid Mini
preps[11 according to the manufacturer's instructions. Puri-
fied plasmid DNA was subjected to endonuclease restriction
analysis using EcoRI.E201 Digested plasmid DNA was electro-
phoresed on 2% (wt./vol.) agarose gels and visualized using
ethidium bromide staining and a hand-held UV lamp as de-
scribed above.
Two clones from each team were selected for commercial,
automated dideoxy terminal sequencing by the DNA Core
Facility at the University of Cincinnati. Sequencing primers
included M13(-20) forward and M13 reversel101 as well as S-
*-Bact-0343-a-A-15 (5' TAC ggg Agg CAg CAg 3'), S-*-
0519-a-S-18 (5'gTATTACCg Cgg CTg CTg 3'), S-*-Bact-
0907-a-A-20 (5' AAACTC AAA TgAATT gAC gg 3'), and
S-*-Bact-a-S-16 (5' Agg gTT gCg CTC gTT g 3').[18]

Step 4 An initial phylogenetic analysis was conducted,
and the results were used to design oligonucleotide hybrid-
ization probes for fluorescence in situ hybridization (FISH).
Assembled sequences were compared to the Ribosome Da-
tabase Project (RDP) (available at rdp.cme.msu.edu) using
Chimera Check and Probe Match. Preliminary phylogenetic
affiliation was confirmed using a BLAST (Basic Local Align-
ment Search Tool) search of GenBank (available at
www.ncbi.nlm.nih.gov, follow the links to BLAST). The
fluorescently labeled oligonucleotide probes were ordered
from a commercial vendor.
Step 5 Each team conducted fluorescence in situ hybrid-
ization (FISH) analysis of their original samples. Aliquots of
the original sample were chemically "fixed" for one hour at
room temperature with 4% (wt./vol.) paraformaldehyde pre-
pared in 1 x phosphate buffered saline (1 x PBS is 130 mM
NaCl and 10 mM sodium phosphate buffer). The samples
were subsequently stored at -200C in a 50% (vol./vol.) mix-
ture of ethanol and 1 x PBS. The fixed samples were applied
in a sample well on a Heavy Teflon Coated microscope slideE211
and air-dried. FISH was performed as previously described.E22"
Briefly, each microscope slide was dehydrated in an increas-
ing ethanol series (50, 80, and 95% [vol./vol.] ethanol, one
minute each), each sample well was covered with 9 pl of


Chemical Engineering Education











[IRn= laboratory


ON IMPROVING "THOUGHT WITH HANDS"



G.K. SURESHKUMAR, K.C. KHILAR
Indian Institute of Technology, Bombay India 400 076


Laboratory exercises are essentialE1 ,2 toward the devel-
opment of a good chemical engineering graduate with
desirable skills such as independent learning, inter-
dependent learning, problem solving, critical iliiikiir-. cre-
ative iliiikiik-. interpersonal skills, teamwork, leadership,
integration, communication, and change management.J31 The
standard laboratory exercise in chemical engineering, how-
ever, revolves around an apparatus that remains unchanged
for several years and can lead to unethical practices among
studentsE14' such as submission of data/reports from previous
years. Moreover, the application of thought, which is crucial
for laboratory work and developing the skills mentioned
above, is almost nonexistent in the standard laboratory exer-
cise. From an instructional-objectives viewpoint,E15 most labo-
ratory exercises are designed to be at Bloom level 2 (com-
prehension) out of the possible six levels. This leads to se-
vere resentment toward laboratory work among students and
professors alike. Students consider lab courses as a formality
to be completed, while faculty treat them as poor cousins of
theory courses, relegating the entire responsibility for lab
courses to lab supervisors or teaching assistants.
We believe that if students are challenged to think criti-
cally on laboratory exercises and encouraged to be creative,
their interest in and respect for laboratory work would im-
prove, and in turn, the faculty would be further motivated to
offer better laboratory courses/projects. With this belief, a
laboratory course consisting of both dual-step laboratory ex-
ercises and a recommendation/innovation exercise was con-
ceived and assigned to third-year (junior) undergraduate stu-
dents taking the fluid mechanics laboratory at the Indian In-
stitute of Tc'liii h i- .1,, Bombay.
Our laboratory guidelines state that the overall aim of this
laboratory course is to inspire students to appreciate the un-
derlying themes of the experimental aspects/approaches to
engineering/science with fluid-flow aspects as a model sub-
ject. The goal is to develop students' abilities to "think with
their hands." Another purpose of this course is to improve
understanding of fluid-flow principles, to develop a physical
feel for some fluid-flow situations, to develop a familiarity


with some commonly used fluid-flow equipment, to incul-
cate a concern for safety, to improve communication of ex-
perimental results, to improve the quality of analysis and in-
quiry, and to kindle the spirit of discovery in students. Fur-
ther, we expect the exercise to develop some of the above-
mentioned skills in a chemical engineering graduate.

THE LABORATORY EXERCISES
The activities for the laboratory consisted of dual-step labo-
ratory experiments (performed by student groups) and a
recommendations report (an individual activity).
The Dual-Step Laboratory Exercise
Each laboratory experiment was conducted over two lab
sessions. During the first session, student groups were ex-
pected to follow the procedures given in the manual to carry
out the experiment. Students were expected to become com-
fortable with the equipment and the experiment, and the first-
session experiments were designed accordingly.
After the first session, students were required (as home-
work) to analyze the data taken during the lab session based on
the theoretical principles in the lab manual/fluid mechanics text-
book/notes and examine whether the results obtained were as


ate Professor in the Chemical Engineering De-
partment at Indian Institute of Technology,
Bombay. He received his BTech. in Chemical
Engineering from Indian Institute of Technol-
ogy, Madras, and his PhD from Drexel Univer-
sity. His research interest is free radical-based
improvements in the productivity of bioreactors.
He can be reached at


Kartic C. Khilar is currently Professor in the
Chemical Engineering Department at Indian
Institute of Technology, Bombay. He earned
his BTech degree in Chemical Engineering
from Indian Institute of Technology, Kharagpur
and his PhD from University of Michigan. He
and his students work in nanoparticle produc-
tion and colloid-associated contaminants
transport in porous media.


Copyright ChE Division ofASEE 2002
Chemical Engineering Education










straightforward, and successful for turbulent flow was first
attempted for the closely related topic of turbulent thermal
convection, I anticipated that the path of development would
closely parallel the previous one. While convection is inher-
ently more complex than flow in several respects, it is also
simpler in the sense that it merely consists of the superposi-
tion of a scalar quantity, the temperature, on the flow. The
path of development that emerged after considerable trial and
error proved to reflect the greater complexity that had been
anticipated, and the final results proved to reflect the antici-
pated greater simplicity.
The predictive equations for turbulent thermal convection
that are described in this paper are, by a significant margin,
more accurate, fundamentally sound, and general than any
prior ones. They also provide better insight into the relation-
ship between flow and convection and a better conception of
thermal convection itself that more than compensates for the
greater detail. This new material should therefore, as sug-
gested by audience members at the AIChE presentations, be
given serious consideration for inclusion in the final portfo-
lios of both our undergraduate and graduate students.
Apart from the merit of the predictive equations for turbu-
lent thermal convection that emerged, the path of their devel-
opment appears to have merit itself in an educational sense.
On the one hand, it provides insight into a creative process of
correlation that is within the capabilities of our students. On
the other hand, it provides a perspective within which the
strengths and weaknesses of all forms of correlation can be
evaluated, not only in flow and convection but also in every
aspect of chemical engineering. Our students should be
made to realize that whatever career they follow after
graduation, they will spend considerable time using and/
or formulating correlations.
I have a predilection for presentations in narrative and his-
torical contexts under the presumption that the personal char-
acteristics, as well as the triumphs and failures, of our prede-
cessors not only stimulate interest but also provide a mne-
monic for students. In this instance, a description of the ser-
endipitous and irregular path of development of a completely
new formulation in a relatively mature field may serve a simi-
lar role. Teachers who prefer a more orderly and skeletal ap-
proach are welcome to eliminate such diversionary material.
Many details concerning origins, proofs, uncertainties, and
limitations are deferred to the references, and in particular to
Churchill and Zajic.J31 It is, however, essential that the teacher
present these details, or perhaps in the instance of graduate
students, assign key references as required collateral read-
ing. In either event, students should be encouraged to ques-
tion the validity of the many assertions and simplifications in
this article rather than accept them "on faith." Undergradu-
ate students may require more guidance than do graduate stu-
dents with respect to the new approach, but they have the


counterbalancing advantage of less to unlearn.


THE NEW APPROACH
FOR TURBULENT FLOW
A thorough understanding by students and faculty alike of
the new approach for the description and teaching of turbu-
lent flow, as previously described[2], is an essential prereq-
uisite for the complementary new approach presented here
for turbulent thermal convection. Because of space limita-
tions, however, only those results that are directly applied or
adapted for thermal convection will be reproduced here.
The time-averaged, once-integrated differential equation
of conservation for momentum in the radial (negative-y) di-
rection in steady-on-the-mean, full developed flow of a fluid
of invariant density and viscosity through a round tube can
be represented by

w(_yL)= du ,1)
a dy
Here, tw is the shear stress on the wall, y is the distance
from the wall, a is the radius of the pipe, u is the time-aver-
aged velocity, and u' and v' are the fluctuating components
of the velocity in the x and y directions, respectively. The
superbar designates the time-average of their product, while
p and p are the dynamic viscosity and specific density of
the fluid. (Aside to teachers: The origin of this expression
and the physical meaning of the several variables and terms,
including the signs of the latter, should be described or reviewed
as appropriate. Any uneasiness of