Chemical engineering education

Material Information

Chemical engineering education
Alternate Title:
Abbreviated Title:
Chem. eng. educ.
American Society for Engineering Education -- Chemical Engineering Division
Place of Publication:
Storrs, Conn
Chemical Engineering Division, American Society for Engineering Education
Publication Date:
Annual[ FORMER 1960-1961]
Physical Description:
v. : ill. ; 22-28 cm.


Subjects / Keywords:
Chemical engineering -- Study and teaching -- Periodicals ( lcsh )
periodical ( marcgt )
serial ( sobekcm )


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

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
01151209 ( OCLC )
70013732 ( LCCN )
0009-2479 ( ISSN )
TP165 .C18 ( lcc )
660/.2/071 ( ddc )

UFDC Membership

Chemical Engineering Documents


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Phili Morris

A high technology development
and process manufacturing
The technology that is required to produce such well-known tobacco
products as Marlboro, Merit, Benson & Hedges and Virginia Slims
ranks among the most sophisticated to be found in industry.
Advanced process control systems, process development, state-of-
the-art drying and blending operations and environmental controls
are vital functions that play a major role in our growth.
To the Chemical Engineer who wants to contribute, be recognized
and rewarded, Philip Morris U.S.A. is a company you should explore.
You can find out more about us by sending a letter or resume, or
complete the back side of this page.
More About Us
.. Philip Morris U.S.A.
Attn: Jim Hardin, Dept. 065
P.O. Box 26603
Richmond, VA 23261
An Equal Opportunity Employer M/F/H
Tum Page

Tell us a little about yourself and
we'll tell you a lot about us. Mail to:
Jim Hardin, Dept. 065 Philip
Morris, U.S.A., PO Box 26603
Richmond, VA 23261

Name: Please PRINT or TYPE Last Name, First Initial ahd Middle Initial


Home Phone No. Business Phone No.

Type of Position

Date Available Salary Desired

College Location Degree/Major

Present Employer Position Dates of Employment


Previous Employer Position Dates of Employment


MaH This Cnfidentia

Department of Chemical Engineering
University of Florida
Gainesville, Florida 32611
Editor: Ray Fahien
Associate Editor: Mack Tyner
Editorial & Business Assistant:
Carole C. Yocum (904) 392-0861
Publications Board and Regional
Advertising Representatives:
Klaus D. Timmerhaus
University of Colorado
Vice Chairman:
Lee C. Eagleton
Pennsylvania State University
Homer F. Johnson
University of Tennessee
Vincent W. Uhl
University of Virginia
CENTRAL: Leslie E. Lahti
University of Toledo
Camden A. Coberly
University of Wisconsin
Darsh T. Wasan
Illinois Institute of Technology
WEST: R. W. Tock
Texas Tech University
William H. Corcoran
California Institute of Technology
William B. Krantz
University of Colorado
C. Judson King
University of California Berkeley
NORTH: J. J. Martin
University of Michigan
Edward B. Stuart
University of Pittsburgh
NORTHEAST: Angelo J. Perna
New Jersey Institute of Technology
NORTHWEST: Charles Sleicher
University of Washington
Charles E. Wicks
Oregon State University
Thomas W. Weber
State University of New York
D. R. Coughanowr
Drexel University
Stuart W. Churchill
University of Pennsylvania
James H. Hand
N.S.F., Washington, D.C.
FALL 1979

Chemical Engineering Education

156 1978 f4awad .ecae
The Dynamics of Runaway Systems,
Theodore Vermeulen
155 Class and Home Problems
The Mirror Fog Problem, R. L. Kabel

160 The Integration of Real-Time Computing
into Process Control Teaching, M. Morari
and W. H. Ray
164 Heterogeneous Catalysis, M. A. Vannice
168 Doctoral Level Chemical Engineering Eco-
nomics, Oran L. Culberson
172 Functional Analysis for Chemical Engineers,
D. Ramkrishna
176 Colloidal Phenomena, William B. Russel,
Dudley A. Saville, David F. Ollis, and
William R. Schowalter
180 Coal Liquefaction Processes, T. F. Yen
184 Mathematical Methods in Chemical Engi-
neering, Arvind Varma
190 Courses in Polymer Science,
Curtis W. Frank
194 The Structure of the Chemical Processing
Industries, T. W. F. Russell
198 Introduction to the Molecular Theory of
Thermodynamics, H. Ted Davis
170 Book Reviews
179 Errata
188, 197 Books Received
197 Positions Available
203 ChE News
204 Memorium
209 Stirred Pots

CHEMICAL ENGINEERING EDUCATION is published quarterly by the Chemical
Engineering Division, American Society for Engineering Education. The publication
is edited at the Chemical Engineering Department, University of Florida. Second-class
postage is paid at Gainesville, Florida, and at DeLeon Springs, Florida. Correspondence
regarding editorial matter, circulation and changes of address should be addressed
to the Editor at Gainesville, Florida 32611. Advertising rates and information are
available from the advertising representatives. Plates and other advertising material
may be sent directly to the printer: E. O. Painter Printing Co., P. O. Box 877,
DeLeon Springs, Florida 32028. Subscription rate U.S., Canada, and Mexico is $15 per
year, $10 per year mailed to members of AIChE and of the ChE Division of ASEE.
Bulk subscription rates to ChE faculty on request Write for prices on individual
back copies. Copyright 1979 Chemical Engineering Division of 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 of the ASEE
which body assumes no responsibility for them. Defective copies replaced if notified
within 120 days.
The International Organization for Standardization has assigned the code US ISSN
0009-2479 for the identification of this periodical.



Carbon is part of every living
thing, and of everything that ever
lived. Union Carbide makes this
basic material into products es-
sential to the way we live: every-
thingfrom space-age fibers to
giant steel-making electrodes.
The steel industry's
electric are fur- I.
:aces feed dec- -
tric p(t er
electrodes .lL
eight feet .- ,
tall that

amperes .
of cur-
rent. These'
furnaces make new steel from
scrap, so they help clean up the
countryside and cut pollution
while they save energy.

Many electric motors share a
basic priblciri: hli% t(o co-nduct
electric current bettweenl mo\ inig
and stationary parts. The solu-
tion, for motors as diverse as
your electric mixer and this giant
diesel electric engine. is a piece
of manufactured carbon called
a brush. No substitute can do
the job as ell. .

Soon, space shuttles like this
will carry satellites and scientific
cargo into orbit.The shuttle's
60-foot cargo doors are made of
Union Carbide's Thornel carbon
fiber- amazingly light, yet so
strong it will stand up to re-
peated launches and reentries.
For a more down-to-earth appli-
cation, cars with Thornel carbon
fiber parts will weigh less and
use less gas than
today~" models.


Union Carbide Corporation, 270 Park Avenue, NewYork, N.Y. 10017

A Letter to Chemical Engineering Seniors
This is the 11th Graduate Issue to be published by CEE
and distributed to chemical engineering seniors interested
in and qualified for graduate school. As in our previous
issues we include articles on graduate courses that are
taught at various universities and ads of departments on
their graduate programs. In order for you to obtain a
broad idea of the nature of graduate course work, we
encourage you to read not only the articles in this issue,
but also those in previous issues. A list of these follows. If
you would like a copy of a previous Fall issue, please write



Butt & Peterson




Carbonell &



Blanch, Russell

Bailey & Ollis



Ray Fahien, Editor CEE
Fall 1978
"Horses of Other Colors-Some Notes
on Seminars in a ChE Department'
"Chemical Reactor Engineering"
"Influential Papers in Chemical Re-
action Engineering"
"A Graduate Course in Polymer Pro-
"Reactor Design From a Stability
"The Dynamics of Hydrocolloidal
"Coal Science and Technology"
"Transport Phenomena in Multicom-
ponent, Multiphase, Reacting
Fall 1977
"Fundamental Concepts in Surface In-
"Electrochemical Engineering"
"Chemical Reaction Engineering Sci-
"Biochemical Engineering"
"Polymer Science and Engineering"
Fall 1976
"Electrochemical Engineering"
"Biochemical Engr. Fundamentals"
"Food Engineering"
"Distillation Dynamics & Control"
"Fusion Reactor Technology"
"Environmental Courses"
"Ad Bubble Separation Methods"
"Intro. Polymer Science & Tech."
"The Engineer as Entrepeneur"
"Energy, Mass and Momentum Trans-
Fall 1975
"Modern Thermodynamics"
"Heterogeneous Catalysis"
"Dynamical Syst. & Multivar. Control"
"Digital Computations for ChE's"
"Industrial Pollution Control"
"Separation Process"
"Enzyme Catalysis"
Fall 1974
"Digital Computer Control of Process"

Gates, et al.
Melnyk & Prober
Hamrin, et. al

Locke & Daniels



Chao &

Curl & Kadlee

Kelleher & Kafes
Douglas &

"Solid-State Materials and Devices"
"Multivariable Control and Est."
"Chemistry of Catalytic Process"
"Advanced Thermodynamics"
"Wastewater Engineering for ChE's"
"Enzyme and Biochemical Engr."
"Synthetic & Biological Polymers"
"Energy Engineering"
Fall 1973
"Applied Chemical Kinetics"
"Corrosion Control
"Digital Computer Process Control"
"Economics of Chem. Processing Indus-
"Polymers, Surfactants and Colloidal
"Polymer Processing"
"Staged Separations"
Fall 1972
"Process Heat Transfer"
"Equilibrium Theory of Fluids"

"Biological Transport Pnenomena and
Biomedical Engineering"
"Applied Surface Chemistry"
"Momentum, Energy and Mass Trans-
"Process and Plant Design Project"
"Engineering Entrepeneurship"

Fall 1971
Reid & Modell "Thermo: Theory & Applications"
Theofanous "Transport Phenomena"
Weller "Heterogeneous Catalysis"
Westerberg "Computer Aided Process Design"
Kabel "Mathematical Modeling..."
Wen "Noncatalytic Heterogeneous Reaction
Beamer "Statistical Analysis and Simulation"
Himmelblau "Optimization of Large Scale Systems"


Metzner & Denn
Toor & Condiff



Fall 1970
"Interfacial Phenomena"
"Kinetics of Chemical Processes"
"Process Control"
"Design of Air Pollution Control Sys-
"Fluid Mechanics"
"Separation Processes"
"Heat and Mass Transfer"
"Biochemical Engineering"
Fall 1969
"Why Mathematics?"
"Theories, Correlations & Uncertainties
for Waves, Gradients & Fluxes"
"Fluid Dynamics"
"Stat. Theories of Particulate Systems"
"Diffusional Operations"
"Optimal Control of Reaction Systems"
"Molecular Thermodynamics"
"Reactor Design"

FALL 1979

. K

At Celanese,

we won't force you into a mold.

The challenge of being part of a large, growing
corporation could be offset by the fear of being swal-
lowed up, forced to conform to the company's way of
At Celanese, we didn't get to be successful by
sticking to the traditional way of doing things. Our un-
usually open working environment, our flexible handling
of responsibilities have won us a solid position in the
production of chemicals, fibers, plastics and polymer
When you come to work at Celanese, you'll be
assigned to a project right away. You can put your cre-
ativity and decision-making skills to good use. We won't
waste your time in lengthy training programs we won't
waste your mind by forcing you to fit into a corporate

mold. You'll have the freedom and the opportunity for
rapid growth and advancement at Celanese.
We're looking for people who are still growing, and
want to be part of an expanding industry. You just might
fit in-your way-at Celanese.
If you have a degree in engineering or chemistry,
and would like to learn more about us, write Tom Clark,
Celanese Building, 1211 Avenue of the Americas, New
York, N.Y. 10036.

An equal opportunity employer m/f





If [ class and home problems

The object of this column is to enhance our readers' collection of interesting and novel problems in
Chemical Engineering. Problems of the type that can be used to motivate the student by presenting a
particular principle in class or in a new light or that can be assigned as a novel home problem are re-
quested as well as those that are more traditional in nature that elucidate difficult concepts. Please sub-
mit them to Professor H. Scott Fogler, ChE Department, University of Michigan, Ann Arbor, MI 48109.
Our student readers are encouraged to submit their solution to the following problem to Prof. Robert
L. Kabel, ChE Dept., Pennsylvania State University, University Park, PA 16802, before December 15th,
1979. The student who submits the best solution before the deadline will be given a complimentary sub-
scription to CEE to begin either immediately or, if he prefers, after his graduation. (Penn State students
are not eligible.) We will publish Prof. Kabel's solution in a subsequent issue.


Pennsylvania State University
University Park, PA 16802

The Kabel bathroom cabinet has two sliding
panels very much like the windows in a classroom.
The panels have mirrored surfaces and when
closed are as shown in Figure 1.
As you can see, when the left panel is opened
it completely covers the right panel, leaving a
space between them 4 mm thick. One night at
10:00 P.M. my wife took a hot shower. The
panels were both closed and the mirrors became
completely clouded over with condensed water
vapor. After her shower she opened the left
panel fully to get some things from inside the
cabinet. Thus at 7:00 A.M. the next morning I
found the following arrangement shown in Figure
2 (where the items shown are merely bottles,
toothpaste, etc.). Before shaving I closed the left
panel and found most of the right panel still
clouded with moisture.
A. Create a microscopic model which could be used to
determine how long it would take for the covered
mirror to clear completely under the conditions that
prevailed during the night. No solution is required;
however, you may assume that a few days and a
computer are available to solve this problem if you
need them. Although it is clear that this is a simul-
taneous heat and mass transfer process, assume that

Closed Open

the heat transfer is inherently rapid enough that
only the mass transfer process need be considered.
B. Making any necessary assumptions, obtain a nu-
merical estimate of the time t, when the mirror is
completely clear if the thickness of the water film
R = 0.013 mm, the diffusivity of water vapor in air
DAB = 2.47 (10-5)m2es-1, the concentration of water in
saturated air is CAs = 17.3 g*m-3, distance between
panels is X = 4 mm, and the length of each panel
Y, = 0.3 m.
Continued on page 213.

Robert L. Kabel received his B.S. degree from The University of
Illinois in 1955 and his Ph.D. from The University of Washington in
1961. From 1961-1963 he served n the U.S. Air Force Space Systems
Division receiving the Commendation Medal for Meritorious Achieve-
ment. Since 1963 he has been at The Pennsylvania State University
where he is Professor of ChE. He was at The Technical University of
Norway (1971-72) and Pahlavi University in Iran (1978) as visiting pro-
fessor and lecturer, respectively. He has served recently as Chairman
of the AIChE's Chemical Engineering Education Projects Committee
(1976-77) and the Central Pennsylvania section of the American Chem-
ical Society (1970). His research centers around catalytic kinetics and
air pollution meteorology. He is active in industrial consulting, flying,
and squash.
Copyright ChE Division, ASEE, 1979

FALL 1979


1978 Awcid .Jec4ae


The 1978 ASEE ChE Division Lecturer was
Dr. Theodore Vermeulen of the University of Cali-
fornia, Berkeley. The 3M Company supports this
annual award.
Dr. Vermeulen, born in Los Angeles, completed
his B.S. and M.S. in ChE at CalTech, and his Ph.D.
in physical chemistry at UCLA. He did catalytic
research for Union Oil for two years and later
worked six years in process development and re-
search planning for Shell Development. He then
joined the University of California, Berkeley,
serving as founding chairman for ChE from 1947
to 1953, and being advanced to professor (his
present post) in 1951. He has been a Fulbright
Professor and a Guggenheim Fellow, and received
AIChE's William H. Walker Award in 1971.

University of California
Berkeley, CA 94720

SCIENTIFIC ANALYSIS OF explosions and flames
is not viewed today as an area of interest or
concern for us as chemical engineers. Neverthe-
less we often bear the responsibility for assuring
that no harm will come through explosion or flame
to a chemical plant or refinery we are operating or
planning, or to a laboratory experiment we are
conducting. Combustion takes on new importance
as we strive for higher energy efficiency, avoidance
of pollution, and use of alternate fuels. Intellectu-
ally, the "runaway" phenomena can enrich our
perceptions of thermodynamics, kinetics, and
thermal and mass transport. The award from
ASEE of this Lectureship, which has been es-
tablished through the generosity of the 3M
Company, has enabled me to focus my attention on

Nuclear explosions are the
most researched, most dramatic and most
unwanted ... The mushroom cloud is not
unique to nuclear explosions; it occurs also
even in middle-sized explosions on land or in
fairly small "shots" under water.

Copyright ChE Division, ASEE, 1979

"runaway" systems and to share my findings
with you about aspects of these areas which
appear accessible, interesting, and valuable.
The area of process dynamics comes close to
dealing with runaway problems, but even there
the emphasis is more on preventing the runaway
than on analyzing it.

N NUCLEAR EXPLOSIONS ARE the most researched,
most dramatic, and most unwanted. Scale-
down, rather than scale-up, will relate this proto-
type to conventional applications. The mushroom
cloud (Figure 1) is not unique to nuclear ex-
plosions; it occurs also even in middle-sized ex-
plosions on land or in fairly small "shots" under
water. Every explosion has both a build-up and a
let-down stage, and the mushroom cloud is part of
the let-down. Samuel Glasstone's book "The
Effects of Nuclear Weapons" is the source of
Figure 1 and of the following description of a
nuclear "blast":
The time scale for a nuclear explosion is so short
that we sense only the overall result. At the instant the
critical mass for nuclear fusion is brought together, only
a few neutrons are present. Fission begins promptly, with
a reaction time of about 10-8 seconds (10 nanoseconds).
Each fission step consumes one neutron and produces two
neutrons or a fraction more. A kiloton (as TNT) of
energy release requires production of 1023 neutrons, or
about 53 generations of reaction time-530 nanoseconds.
A megaton requires 1000 times more-another 7 genera-
tions, that is, another 70 nanoseconds. Thus the build-up
lasts less than one microsecond, and the bulk of the


"detonation" occurs in less than one-tenth of a micro-
The energy released raises the local temperature to
more than 10 million degrees Kelvin, and the local pres-
sure to more than 1 million atmospheres. X-rays rapidly
radiate into the surrounding atmosphere, heating the air
so high that it too becomes luminous. The mixture of air
and weapon residue forms a fireball which grows out-
ward and upward 500 feet in the first millisecond. This
volumetric rate of growth persists, so that the fireball
spreads to more than a mile across within 10 seconds. At
this time its center of mass is rising about 400 ft/sec. The
light intensity per unit exposed area of fire ball is greatest
at 1 millisecond, but the total light emitted from the fire-
ball peaks at 10 seconds. The expansion and upward motion
continue much longer. In about 1 minute, the fireball is 4
miles above the burst point; it no longer emits visible
light; and it has become a toroid, or "mushroom cloud."
An updraft of drawn-in air follows the cloud. A thermo-
nuclear bomb will give a larger cloud than one only
involving fission, but the pattern of behavior does not
The blast wave reaches its peak velocity (about 5
miles/sec) and peak pressure at the end of the build-up.
It pulls ahead of the spent charge, and travels outward at
sonic velocity-that is, at over 1000 ft/sec-with one to
two atmospheres of maximum overpressure, which persist
for one second or longer at each point. Its intensity is
heightened by reflection of the shock wave from the
ground, and by the kinetic energy of the 500 ft/sec wind
accompanying the wave. In another second or so, a suction
wave arrives with an underpressure of up to one-fourth
of an atmosphere, and this causes additional damage. The
blast or shock wave subsides with increasing distance
from the source, but an overpressure of one fifth of an
atmosphere may be felt 2 miles away from a small nuclear
explosion and 10 miles away for a large one.
To summarize the energy balance, one-third of the
energy leaves as radiation over all wavelengths; one-third
is dissipated as purely thermal molecular energy; and one-


FIGURE 1. Toroidal circulation inside the radioactive
cloud from a nuclear explosion (after Glasstone)

o Detonati

.3 2

D epfl ti
0 0.5 1.0 1.5 2.0
Relative volume
FIGURE 2. Hugoniot curves for shock waves under let-
down and build-up conditions

third is discharged by the blast wave as pressure energy,
attenuated by friction and turbulence. On a still larger
scale of nuclear explosions, novas are believed to be ex-
ploding planets; and supernovas, exploding stars.
As we adapt to these concepts, we become
interested first in how to identify potential runa-
way; then in how to monitor and control potential
runaway, to reduce its chance of happening; and
finally to strive for the supermonitoring and
supercontrol that might interrupt a runaway al-
ready started. For a nuclear bomb, we would have
to detect the neutron build-up within 30 nano-
seconds, and take evasive action within 300 nano-
seconds, in order to blunt the harmful effects of
the bomb. If this disruption were done by a laser
blast, the laser would have to be located within 50
meters' distance from the bomb.


P PRESSURE AND VOLUME ARE familiar coordinates
to us, along with their typical constant-
temperature and constant-entropy paths; but the
curves applicable to shock waves at sonic velocity,
shown in Figure 2, involve generally unfamiliar
The curved paths in the figure represent the
passage of a one-dimensional compression wave
through an ideal gas. The Bernoulli relation or
equation of motion relates the velocity change to
the pressure change, and the energy balance
records the temporary conversion of kinetic
energy to internal energy. With r- = p/po, P =
v/Vo, and 0 = T/To, the temperature and pressure
ratios follow the relation:

S 2y + 1, + r
2y + 1 + (1/ir)

FALL 1979


If frictional dissipation and spherical
geometry are neglected, for a shock wave
travelling through air after the build-up stage,
the Rankine-Hugoniot curve shows the
compressed condition of the gas corresponding
to the pressure rise in the shock.

with, for example, y = c,/c, = 1.4 for air. In the
event 7r is, very large, the least value of the
volume ratio 4) (=0/rT) is 1/(2y+l), or 0.26 for
air. Hence every different starting point will have
its particular Rankine-Hugoniot curve. Also, the
slope is steeper than for isentropic compression
at any given 0. It is worthwhile to note that the
Rankine-Hugoniot condition is not a differential
equation; rather, it is a finite difference relation,
implying a mathematical discontinuity between
start and finish.
If frictional dissipation and spherical ge-
ometry are both neglected, for a shock wave
travelling through air after the build-up stage, the
Rankine-Hugoniot curve shows the compressed
condition of the gas corresponding to the pressure
rise in the shock. Under ideal conditions, the gas
will revert to its initial condition when the shock
has passed, since the original balances again
apply, and a reciprocal rT gives reciprocal 0 and
reciprocal 4.
We consider next the behavior of the shock
during the build-up period. When combustion
occurs, the gas at a given point does not revert to
its starting condition, but instead its return to
initial pressure is characterized by higher volume
and temperature. This expansion reinforces the
shock, causing it to increase steadily in pressure.
The temperature reached by the combusted gas at
base pressure is represented by a Raleigh line,
and by the Hugoniot curve to which the Raleigh
line becomes tangent. At an early stage of build-
up, for example, ir reaches 2.7, and a Raleigh line
carries the mixture to Hugoniot curve 2; later
rT reaches 4.7, and another Raleigh line carries
the mixture to curve 3.
As combustion occurs in the high-pressure zone
of the shock, the thermal-energy release tends to
shift the gas from a lower to a higher isotherm.
Traveling at the relevant sonic velocity, the shock
traverses equal masses of gas in equal time (cor-
responding to a constant mass velocity of gas
through the shock). The resulting tendency
toward higher momentum must be offset by a drop
in pressure, which accounts for the linear be-

havior of the combustion path (the Rayleigh
line). Thus,
SUo 2
p + v = constant
where Uo is the sonic velocity at the point of maxi-
mum compression.
The reader will note that Figure 2 is drawn
on linear scales for the sake of simplicity. The
wide range of pressures and temperatures ordi-
narily encountered in an explosion would gener-
ally justify the use of logarithmic coordinates for
such plots.


A SMOOTHLY RUNNING nuclear reactor, or a
steady-state star like our sun, has crossed one
kind of threshold. It appears that there must be
one barrier--one criticality condition-for burn-
ing nuclear fuel; and another, higher, degree of
criticality for setting off a nuclear explosion.
Sometimes the burning condition is not a
stable state, but an antistable one, only kept in
balance by oscillatory controls-a push to in-
crease the rate, a pullback to reduce the rate. In
this case the measure of dynamic stability lies in
the adequacy of the combination of controls with
the reacting material, and not merely in the
properties of reacting material considered by it-
self. If fluctuations in the system cause an over-
riding of the controls, they may quench the burn-
ing on one hand, or they may launch an explosion
on the other.
An analogous situation exists with chemical
explosions and chemical flames. A flame is not
usually self-igniting. Within a certain range of
concentrations bounded by "critical" values, the
reaction mixture when ignited will produce a
flame that is self-sustaining. Inside a narrower
range of concentrations, bounded again by
"critical" values, the flames will reach sonic
velocity and thereby will attain the condition of
Neutron reactions are by nature "chain" re-
actions, and any branching chain which allows the
number of neutrons to increase without limit is by
nature "explosive". So too are there chemical re-
actions of branching-chain type, involving mo-
lecular fragments and single atoms, all collectively
termed free radicals. If the chain branching is
moderated, so that the concentration of radicals
tends toward a steady-state value, we might ex-
Continued on page 205.


Chemical Engineers play

key role at General Foods'

Research & Development

Chemical Engineers have a key role form, and get it to us with all its Unit Operations...
to play in research at General nutritive and taste values intact. For students who want to put their.
Foods Corporation, the nation's chemical engineering training to
leading package grocery products Demand Increases... work, General Foods Corporation
company. Food is no longer the An accelerated worldwide need to needs almost all elements of the
simple thing it was to our fore- supplement traditional agricultural unit operations background...
fathers. Most of us no longer pro- food sources with technology- dehydration, extrusion, heat and
duce our own food; but rely on based foods has created an un- mass transfer, extraction and
others to process and package it, precedented need for chemical separation.
preserve and improve it, change its engineering skills of a high order.
Team Contribution...
S.At General Foods, chemical
engineers work in small teams
where each team member can make
a large contribution.. and will
receive due recognition. The
atmosphere is informal, yet profes-
sional. And for the chemical engi-
neer who wants to obtain an
advanced degree while pursuing a
full-time career, General Foods
reimburses employees close to 100
& per cent of expenses for such after
hour studies.
Career Reference...
If you are interested in a career with
a leading processor of packaged
convenience foods who markets
over 400 familiar brand products
WHIP and many more...

Contact your placement office
or write to:
Technical Careers Dept. CEE-79
250 North Street
White Plains, New York 10625
An Equal Opportunity Employer, M/F/Hc.

FALL 1979




University of Wisconsin
Madison, Wisconsin 53706

T HE PROCESS CONTROL curriculum at Wisconsin
presently involves two faculty members and
consists of an undergraduate course (annual en-
rollment --80 students), a graduate course (en-
rollment -20 students), and an informal gradu-
ate research seminar. This paper will concentrate
on a description of the graduate course. An over-
view of the undergraduate course will follow in the
next issue of this journal. The objective of the
course is twofold: 1) to familiarize the students
with those classical and modern results of process
control theory which have been found useful in
practical applications and 2) to allow the student
to gain experience in the implementation of these
techniques via a real-time computer. Therefore
the course includes a laboratory. It is stressed
to the students that the computer is simply a
modern tool so that the discussion of hardware
aspects and specific programming techniques is
limited to only those subjects of importance to
the process control engineer. Software has been
developed so that almost all of the real-time pro-
gramming done by the students is in FORTRAN

Figure 1
B terminal port
16 A/D channels
Mtt. ZCilosurt

16 D/Ai chtnnelS DIS DRIVE o TPE STATION 196 X words
1.2 million Dords 9-TRACK 500 nte eRmorY

l.Floatlnq Poin t
16 Digital 1/0- 800 1 00 16

a Ana lo I/O A.Dl Pmgraiabl CPU
Line Pr er 16 Differential A/D Real Ti Clock 2.Mery Managemt
.16 chanlI 3.16t bipolE
16 Single-nde. D/A digital I/O 316 nIecD etI rO
lp sEc SEaory

DiaEl-up Line

4I80 cpS

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l o g C D RnSCED. 19 I
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iV'tD'* | Dp tt/U~tt., I D"l
Via'd ---- y
AnaloD Computir t A analog Coputer Analog Computer
I 2 II

Copyright ChE Division. ASEE. 1979


_44 Y3


FIGURE 2. Multi-sidestream Distillation Column with
Draw-off Rate used to Control Sidestream Composition.


control laboratory consist of both analog and
digital computers. There are three 100 volt
analog computers with a total capacity of 132
amplifiers used primarily for process simulation.
The digital computer available for the laboratory
is a PDP11/55 minicomputer operating under the
RSX11M operating system. The configuration,
shown in Figure 1, includes 128 K words of

Graduate Process Control Lecture Topics

1. Practical aspects of on-line data acquisition and
2. Control of systems described by ordinary differential
and difference equations
3. Control of systems described by partial differential
4. State estimation and stochastic control
5. Parameter estimation and adaptive control
6. Influence of process design structure on process dy-
namics and control
7. Control of interconnected systems of large dimension



memory, twin 1.2 magaword disks, a 9-track
magnetic tape unit, and graphics terminals. There
are digital and analog links to each of the labora-
tories as well as analog links to the analog com-
puter allowing hybrid computation. Analog to
digital and digital to analog conversion are done
at the computer with 16 channel, 12 bit con-


T HE GRADUATE PROCESS control course, offered
once each year, has attracted students from a
wide range of research areas and backgrounds.
The course consists of three hours of lecture each
week plus a project-oriented laboratory with in-
dividually arranged hours. The topics to be

3 ---

Manfred Morari was born in Graz, Austria on May 13, 1951. He
obtained his undergraduate education in chemical engineering at the
Swiss Federal Institute of Technology (ETH), Zurich. After his diploma
he started graduate school at the University of Minnesota in 1975.
Upon completion of his doctorate he joined the ChE faculty at the
University of Wisconsin in 1977 where he is currently assistant pro-
fessor. Last summer he worked for Exxon Research and Engineering
Company. His research interests include a variety of topics from the
areas of process synthesis and process control: synthesis of separa-
tion sequences, optimal measurement selection and inferential control,
optimizing control and the dynamics and control of large integrated
processing systems. (L)
W. Harmon Ray was born in Washington, D.C., on April 4, 1940.
He received the B.A. and B.S. Ch.E. degrees from Rice University,
Houston, Texas, in 1962 and 1963 respectively, and the Ph.D. degree
in ChE from the University of Minnesota in 1966. He has been on
the faculty of the University of Waterloo in Canada (1966-70), the
State University of New York at Buffalo (1970-76), and the Uni-
versity of Wisconsin, Madison, where he is presently Professor of
ChE. During the 1973-74 academic year, he was on sabbatical leave as
a Guggenheim Fellow in Belgium and Germany. His research in-
terests include chemical reactor engineering and process modelling,
optimization, and control. His publications include an edited volume
"Distributed Parameter Systems" (Dekker, 1977), and two monographs
"Process Optimization" (Wiley, 1973) and "Advanced Process Control"
to be published by McGraw-Hill in 1980. (R)

Some Recent Graduate Laboratory Projects
1. Multivariable computer control of a multi-side-stream
distillation column
2. State estimation and stochastic feedback control of a
nonisothermal continuous stirred tank reactor
3. On-line parameter identification for a reactor having
catalyst deactivation
4. State estimation and stochastic feedback control of
interacting gas storage tanks
5. On-line parameter identification for a steel ingot in a
three zone furnace
6. Implementation of the Self Tuning Regulator for level
control with widely varying process gains and time
7. Control of thermally coupled distillation columns
8. Control structures for heat exchanger networks

covered are selected from those shown in Table 1
and are designed to acquaint the student with the
wealth of powerful estimation and control tech-
niques resulting from modern control theory. The
emphasis is on algorithms likely to find wide ap-
plications in the process industries. Applications
and case studies are stressed more than mathe-
matically rigorous derivations. Many homework
problems involve computer simulation and the
development of control laws either through
numerical techniques or using interactive graphi-
cal design methods. Much of the lecture material
is available in a forthcoming textbook (W. H.
Ray, "Advanced Process Control," McGraw-Hill
(1980)). A large library of computer programs
for the design of control systems has been de-
veloped and is readily available to the student.
Those programs carry out the numerical calcula-
tions necessary to determine the controller or esti-
mator gains, compute the realization of a transfer
function or find the needed compensator for in-
teracting multivariable systems. Some well known
graphical methods for the design of multivariable
controllers (inverse Nyquist array, character-
istic loci, etc.) are also available.
The principal part of the laboratory activity
is devoted to a rather substantial term project
over which a formal oral and written report is
made. Most of these projects are carried out by
two students working together as a team. The
topics and the emphasis of the projects vary from
year to year. The titles of some projects recently
completed are listed in Table 2. Some of them
(1, 2, 3) involve hybrid computation where the
process is simulated on one of the analog com-
puters and the control algorithm is realized on the
digital computer. Others (4, 5, 6) deal with the

FALL 1979

testing of algorithms on actual physical processes
which are completely interfaced with the minicom-
puter for data acquisition and control. A third
category (7, 8) is mostly computational in nature
and has as its goal the investigation of the process
design-process control interactions.
As an illustration, one such recent project in-
volved the control of side stream compositions via
draw-off rate adjustment for a multi-side-stream
distillation column (Fig. 2). This is a multi-
variable control problem for a system having
strong interactions. The column was simulated on
the analog computer and a variety of feedback
control schemes ranging from classic single loop

FIGURE 5. Non-interacting Multivariable Feedback

Through projects such as this one,* the
students learn the specific advantages and pitfalls
of the various control algorithms and are able to
see clearly how actual implementation may be
carried out in practice.


A S WITH ANY CURRICULUM, the offerings in
process control at Wisconsin will change and
evolve with time. In addition to modifications in
the lecture material, we are constantly altering

FIGURE 3. Multiple Single-loop Control.

control to optimal control were implemented on
the digital computer and their performance evalu-
ated. Multiple PI single loop control, shown in
Figure 3, leads to strong oscillations and long
settling times (Figure 4) and was therefore not
acceptable. However, the implementation of a non-
interacting control scheme, for example, using a
dynamic compensator as shown in Figure 5 re-
sulted in much improved controller response
(Figure 6).

-9.14~ 8 .2440 88 0. E 2e 0.391E 03
0 1056 40

FIGURE 4. Product compositions for multiple-single loop
PI control.

,. :. -L LI

(a.v'.ti.. .
-9.373E-O8 o-

-0.528E-B1 -.o1
:I:520E E 0.244E O0 .. 97 0nute' 0.193Eo02
FIGURE 6. Product compositions under dynamic non-
interactive control.

the mix of laboratory projects in the graduate
course. Often experiments are developed in the
graduate course as special projects and subse-
quently included in the regular curriculum of
the undergraduate course. These revisions arise
partly in response to student comments and
suggestions, but mainly are the result of better
perceptions of the best integration of theory and
experiment in teaching process control. O

*This project was carried out by graduate students,
Lance Lauerhass and Paul Noble. Lance recently has
completed his thesis on process design strategies while
Paul is doing thesis research in bioengineering.


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FALL 1979



Pennsylvania State University
University Park, PA 16802

role in many of today's commercial processes,
particularly in the petroleum and chemical in-
dustries. The recent emphasis on energy conver-
sion and air and water pollution only serves to
provide two more areas in which catalysis can
have a significant impact. The field of hetero-
geneous catalysis draws heavily on the disciplines
of chemistry, engineering, physics, surface science
and materials science. It requires a major effort
for a researcher to bring together knowledge from
these diverse fields and to be cognizant of recent
developments in these areas. This requirement to
be knowledgeable about recent research presents
one of the two major challenges in teaching a
graduate course in catalysis; the other is the
realization that no single text is available in print
today which adequately covers all the aspects of
heterogeneous catalysis. Therefore, one must

M. Albert Vannice received his B.S. degree in Chemical Engi-
neering from Michigan State University and his M.S. and Ph.D. degrees
in Chemical Engineering from Stanford University. He spent a year at
Sun Oil Company as an industrial postdoctoral fellow before moving
to the Corporate Research Laboratories at Exxon Research and Engi-
neering Company in 1971. In 1976 he joined the Chemical Engi-
neering Department at The Pennsylvania State University as an As-
sociate Professor. His major research interests are heterogeneous
catalysis, adsorption, kinetics, and catalyst preparation and characteri-

gather material from a variety of sources such as:
texts, review articles, and original papers, both
past and current. However, this approach does
have the advantage of familiarizing the students
with the literature and emphasizing the role of
research in the development of this field.
In the reference section, a list of textbooks is
given which provides a nucleus of material for
studying the principles and theories of catalysis.
Unfortunately, some of these texts, designated by
an asterisk, are out of print. Chapters from these
texts which are particularly applicable to specific
topics are noted in the course outline. Original
papers from the literature which are especially
pertinent to certain subjects are also listed in the
reference section. This list is by no means com-
plete, but it does provide at least one reference
to introduce the student to each topic. Several re-
cently published books have been included which,
although not available for the original course,
should be useful for the development of certain
At Penn State, the class of 28 students con-
sisted of equal numbers from chemical engineer-
ing, chemistry, and materials science, plus a
physicist. This diversity is typical in catalysis
courses and forces one to maintain a balance be-
tween the breadth and depth of presentations of
chemistry, solid state physics, and mathematical
analysis. (I find that my own limitations tend to
provide this balance automatically!) In lieu of a
final exam, the students were asked to apply
principles, correlations, and theories discussed in
this course to a variety of topics which were ob-
tained from the recent literature. This forced the
student to study a particular area in depth, to
understand the principles involved, and to assess
their applicability to the problem. One such effort
was significant enough to result in a publication
in a refereed journal (reference 13).
A tremendous amount of time can be spent
looking for papers and data from which to de-
velop lectures and show examples of certain as-
pects of catalysis. It is hoped that the course de-
Copyright ChE Division, ASEE, 1979


scribed here, with the list of references, can save
time for others. The course outline is presented
in Table 1, and the appropriate references are
listed in parentheses. A 10-week term at Penn
State consists of ten 75-minute class periods per
credit. Since this was a 3-credit course, the 30
lectures represent material for a 3-credit semester
Because adsorption is the initial step in hetero-
geneous catalysis, this topic (Section II) was dis-
cussed first. The traditional approaches to rates
of adsorption and desorption were supplemented
by recent results in surface science. Also, a new
perspective on the Elovich equation was presented
and discussed.
The topic of kinetics (Section III) was intro-
duced by a discussion of the theories and approxi-

The recent emphasis an
energy conversion and air and water
pollution serves to provide two more areas in
which catalysis can have a significant impact.

nations which apply to homogeneous gas-phase
reactions. Reactions catalyzed on solid surfaces
were then discussed, and the consequence of as-
suming ideal surfaces was shown by the use of
Hougen-Watson type rate equations. The limita-
tions and simplifications involved in this ap-
proach were discussed in detail. With this back-
ground, various correlations in catalysis could
then be introduced.
The development of the science of catalysis
depends heavily on experimental research, and

Course Outline

A. Brief history of catalysis
B. Processes using heterogeneous catalysts (1)
C. Definitions
II. ADSORPTION (2-4) (4 Lectures)
A. Rates of adsorption and desorption (5-7)
B. Physical adsorption-BET eq.
C. Chemisorption
1. Ideal surfaces-Langmuir eq.
2. Nonideal surfaces-Temkin eq., Freundlich
3. Heats of adsorption
4. Activated adsorption-Elovich eq. (8)
A. Homogeneous Reactions
1. Collision theory
2. Absolute rate theory
3. Steady-state approximation
B Heterogeneous reactions on ideal surfaces
1. Derivation of rate equations-Langmuir
isotherm (9)
2. Simplifying assumptions-rate determin-
ing step, most abundant surface inter-
mediate (B, 10)
3. Estimation and evaluation of constants in
rate eg. (10-13)
C. Correlations in kinetics and catalysis (B -
Chap. 8, 14, 15-Chap. 7)
1. Polanyi relation
2. Briinsted relation
3. Hammett relation
4. Van Tiggelen formula
5. Compensation effect (16-17)
6. "Volcano" Plot-examples (18)
D. Catalysis on nonideal nonuniformm) surfaces
RATE EQUATIONS (20) (4 Lectures)
A. Interphase transport
B. Intraphase transport (pore diffusion)

C. Experimental tests for transport effects (21-
A. BET surface areas (D)
B. Pore size distribution (24)
1. Mercury porosimetry
2. Nitrogen desorption method (Kelvin eq.)
C. Metal crystallite size
1. Chemisorption (25, 26)
2. X-ray diffraction
3. Electron microscopy
4. Other physical techniques (Miissbauer
spectroscopy, magnetization, etc.)
A. Sabatier's Principle
B. Geometric factor (27, 28)
C. Ensemble theory-Kobosev
D. Electronic factor
1. Band theory (29)
2. Pauling's % d-character (30)
E. Alloys (31-34)
F. Structure sensitivity and insensitivity (35)
G. Activity, specificity, selectivity (36)
PROCESSES (3+ Lectures)
A. Catalytic cracking and hydrocracking-dual
functional catalysts (37)
1. Carbonium ion reactions
2. Acid sites on solid surfaces
3. Examples of activity and selectivity
B. Reforming-Hydrogenation, hydrogenolysis
(37, 38)
C. CO hydrogenation (39-40)
1. Methanation
2. Fischer-Tropsch synthesis
3. Alcohol formation
D. Ammonia synthesis (41)
E. Oxidation (ethylene oxide production) (42)
F. Others (CO oxidation, NO reduction)

FALL 1979

the importance of obtaining kinetic data free from
heat and mass transfer effects was stressed in
Section IV. A number of tests were described
which can be used to determine the absence of
transport limitations.
Section V introduced the class to characteriza-
tion techniques used for solid catalysts. Due to
their wide use, supported metal catalyst systems
were emphasized and chemisorption techniques to
measure metal surface area were stressed.
In Section VI, a historical approach was used
to introduce theoretical developments in hetero-
geneous catalysis. After this background, the
present status of heterogeneous catalysis was con-
sidered by discussing alloy systems and addressing
such topics as: differences between bulk and
surface compositions, ligand vs. ensemble effects,
and new models to describe the electronic be-
havior of metals and alloys. The work of Sinfelt
and of Sachtler and coworkers was especially
useful here to illustrate the potential benefits of
alloy and bimetallic cluster systems in catalysis.
Finally, a presentation of various catalytic
processes exposed the class to commercial reaction
systems, allowed a discussion of the basic chemis-
try involved, and provided an opportunity to delve
into fundamental studies which pertained to that
particular process. Ol


General Background Reading
*A. Bond, G. C., "Catalysis by Metals", Academic Press,
London (1962).
*B. Boudart, M., "Kinetics of Chemical Processes",
Prentice-Hall, Englewood Cliffs, N.J. (1968).
C. Clark, A., "The Theory of Adsorption and Catalysis",
Academic Press, N.Y. (1970).
*D. Emmett, P. H., ed., "Catalysis", Vol. I, Reinhold,
N.Y. (1954).
E. Laidler, K. J., "Chemical Kinetics", McGraw-Hill,
2nd ed., N.Y. (1965).
F. Thomas, J. M. and Thomas, W. J., "Introduction to
Principles of Heterogeneous Catalysis", Academic
Press, London (1967).
G. Thompson, S. J. and Webb, G., "Heterogeneous
Catalysis", J. Wiley, N.Y. (1968).

Particular Topics
1. Thomas, C. L., "Catalytic Processes and Proven
Catalysts", Academic Press, N.Y. (1970).
2. Hayward, D. 0., and Trapnell, B. M. W., "Chemi-
sorption", Butterworth, London (1964).
3. Wedler, G., "Chemisorption: An Experimental Ap-
proach", Butterworth, London (1976).
4. Hayward, D. O., in "Chemisorption and Reactions
on Metallic Films", ed. by J. R. Anderson, Academic

Press, N.Y. (1971).
5. Schmidt, L. D., Catal. Rev. 9, 115 (1974).
6. Madix, R. J. and Susu, A., J. Catal. 28, 316 (1973).
7. McCabe, R. W., and Schmidt, L. D., Surf. Sci. 65, 189
8. Ritchie, A. G., J. Chem. Soc. Faraday Tr. I 73, 1050
9. Hougen, O. A. and Watson, K. M., "Chemical Process
Principles-Kinetics and Catalysis", Wiley, N.Y.
10. Boudart, M., AIChE J. 18, 465 (1972).
11. Sinfelt, J. H., Hurwitz, H., and Shulman, R. A., J.
Phys. Chem. 64, 1559 (1960).
12. Boudart, M., Mears, D. E., and Vannice, M. A., Ind.
Chim. Beige. 32, Special Issue, 281 (1967).
13. Vannice, M. A., Hyun, S. H., Kalpakci, B., and
Liauh, W. C., J. Catal. 56, 358 (1979).
14. Butt, J. B., AIChE J. 22, 1 (1976).
15. Hill, C. G., "Introduction to Chemical Engineering
Kinetics and Reactor Design", Wiley, N.Y. (1977).
16. Galwey, A., Adv. Catal. 26, 247 (1977).
17. Exner, O., Coll. Czech. Chem. Comm. 38, 781 (1973).
18. Balandin, A. A., Adv. Catal. 10, 120 (1958).
19. Boudart, M., Chapt. 7 in "Physical Chemistry: An Ad-
vanced Treatise", ed. by H. Eyring, W. Jost, D.
Henderson, Academic Press, N.Y. (1975).
20. Carberry, J. J., "Chemical and Catalytic Engineer-
ing", Chapt. 5, McGraw-Hill, N.Y. (1976).
21. Weisz, P. B., Z. Physik. Chem. NF 11, 1 (1957).
22. Koros, R. M. and Nowak, E. J., Chem. Eng. Sci. 22,
470 (1967).
23. Madon, R., Ph.D. Thesis, Stanford University (1974).
24. Smith, J. M., "Chemical Engineering Kinetics", 2nd
ed., Chapt. 8, McGraw-Hill, N.Y. (1970).
25. Sinfelt, J. H. and Yates, D. J. C., J. Catal. 8, 82
26. Freel, J., J. Catal. 25, 149 (1972).
27. Baladin, A. A., Russ. Chem. Rev. 31, 589 (1962);
Ibid., 33, 258 (1964).
28. Trapnell, B. M. W., Adv. Catal. 3, 1 (1951).
29. Baker, M. McD., and Jenkins, G. I., Adv. Catal. 7, 1
30. Pauling, L., Proc. Roy. Soc. A196, 343 (1949).
31. Sinfelt, J. H., Science 195, 641 (1977).
32. Sinfelt, J. H., Acct. Chem. Res. 10, 15 (1977).
33. Sachtler, W. M. H., Catal. Rev.-Sci. Eng. 14, 193
34. Sachtler, W. M. H. and van Santen, R. A., Adv.
Catal. 26, 69 (1977).
35. Boudart, M., Adv. Catal. 20, 153 (1969).
36. Boudart, M., Proc. 6th Int. Cong. Catal. Vol. 1, 1, The
Chemical Soc., London (1977).
37. Gates, B. C., Katzer, J. R., and Schuit, G. C. A.,
"Chemistry of Catalytic Processes", McGraw-Hill,
N.Y. (1979).
38. Sinfelt, J. H., Adv. Chem. Eng. 5, 37 (1964).
39. Storch, H. H., Golumbic, N. and Anderson, R. B.,
"The Fischer-Tropsch and Related Synthesis", Wiley,
N.Y. (1951).
40. Vannice, M. A., Cat. Rev.-Sci. Eng. 14, 153 (1976).
41. Nielson, A., Cat. Rev. 4, 1 (1971).
42. Kilty, P. A. and Sachtler, W. M. H., Cat. Rev.-Sci.
Eng. 10, 1, (1974).



Departmental Sponsors: The following 138 departments contributed
to the support of CHEMICAL ENGINEERING EDUCATION in 1979.

University of Akron
University of Alabama
University of Alberta
Arizona State University
University of Arizona
University of Arkansas
Auburn University
Brigham Young University
University of British Columbia
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U. of Detroit
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University College Dublin
Ecole Polytechnique (Canada)
University of Florida
Georgia Tech
University of Houston
Howard University
University of Idaho
University of Illinois (Urbana)
Illinois Institute of Technology
Institute of Gas Technology
Institute of Paper Chemistry
University of Iowa
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TO OUR READERS: If your department is not a contributor, please ask your
department chairman to write CHEMICAL ENGINEERING EDUCATION, c/o
Chemical Engineering Department, University of Florida, Gainesville, Florida

FALL 1979



The University of Tennessee
Knoxville, TN 37916

IT HAS BEEN SAID THAT "The central activity
of engineering, as distinguished from science,
is the design of new devices, processes and
systems which create economic resources at
the expense of thermodynamic availability, time,
space and other natural resources" (Tribus,
1969). Chemical engineering curricula do not
always reflect the key roles of design and eco-
nomics in achieving the distinction between engi-
neering and science.
The Engineers Council for Professional De-
velopment has in recent years been exerting pres-
sure by means of accreditation procedures upon
engineering departments to offer a modicum of
design content in their curricula. This has re-
sulted in some increase of attention to design at
the undergraduate level, but design instruction
at the graduate level remains relatively un-
touched. The anomaly is much worse with respect
to economics. Many departments (including that
of the author) do not require a course in engi-
neering economics at the undergraduate level.
Some economics may be incidental to design
courses, and an elective may be available for a
course in the subject. But sadly, many B.S. ChE's
come out of school with little or no understand-
ing of this vital material. Again, as in the case
of design, the situation is much worse at the
graduate level. The author has no firm data, but
surmises that very few chemical engineering de-
partments require a course in chemical engineer-
ing economics in the core for graduate work. It
would be interesting to survey the departments
to see what the situation actually is.
Incidentally, the course in "Engineering
Economy" classically taught by industrial engi-
neers and frequently used by chemical engineer-
ing students falls short of what these students
really need.
Copyright ChE Division. ASEE, 1979

At The University of Tennessee, there are two
graduate-level courses in chemical engineering
economics, both of which are elective. One of
these, "Chemical Process Industry Economics,"
is intended for M.S. students, and the other,
"Venture Analysis in the Process Industries," is
intended primarily for Ph.D. students. The former
is prerequisite to the latter. Our University
operates a strong off-campus program for engi-
neers in industry by means of videotape. The fact
that some 80 percent of the students in these two
courses are off-campus engineers must be a
commentary on the status of education in eco-
nomics and on the importance that economics has
in the real world.
The M.S. level course is probably not much
different from such courses at other institutions.
The "Venture Analysis" course may, however, be
somewhat novel. It assumes that the student has a

Oran L. Culberson received his B.S. degree from Texas A & M.
After serving as an infantry officer in World War II, he obtained
M.S. and Ph.D. degrees at the University of Texas. He was with
Gulf Research and Development Company for 3 years in process
design and economics, and with Celanese Corporation for 12 years
in process design and economics, and in the management of com-
puter and operations research departments. Culberson joined the
University of Tennessee in 1965, and was selected as Alumni Asso-
ciation Outstanding Teacher in 1978. He is a fellow of AIChE, in
which he has served as chairman of two local sections and two
national committees.


working understanding of capital costs, manufac-
turing costs, measures of economic merit, distribu-
tion considerations, raw material and product
markets, marketing aspects, the time-value-of-
money and some notions about the need to opti-
mize among all these factors. The student is ex-
pected to apply this knowledge in a role-playing
development of an answer to a tough question.
The question posed at the last offering of the
course was (in condensed form) : "We are a
major producer of ethylene. We are thinking of
increasing our ethylene capacity by one billion
pounds per year. When should we have this ca-
pacity come on stream (if at all!), and what size
and feedstock should the plants) take?" Persons
familiar with the ethylene situation will recognize
that the question is fraught with difficulties about
uncertainties in the growth of demand, what the
other producers are going to do, about relative
merits and availabilities of alternate feedstocks,
about the trade-off between plant size and manu-
facturing cost, etc. An answer to the question is
developed by two-person teams, each of which
assumes the identity of a major corporate pro-
ducer. This relating of a team to a company, e.g.
Exxon, enables the team to develop a feel for the
team's position and attitude.
All of the work in the quarter is devoted to the
preparation of a report which contains the team's
analysis and recommendation. There are no
quizzes or homework. Suggested readings and
sources of information are provided to the
students, but the burden of the development and
analysis of information is on the team. Between
the first and last weeks, student-teacher contact
consists of weekly sessions with the individual
teams in which the instructor helps the students
in their worries about where they are and where
they need to go. At the beginning of the project
the teams are advised, but not required, to divide
the responsibility into a manufacturing/technical
role and a marketplace role.
Two very useful documents were provided to
the students. One of these was a paper which ad-
mirably summarizes ethylene manufacturing
technology in terms of processes, feedstocks,
products, and capital and manufacturing costs
(Baba and J. Kennedy, 1976). The teams were
not expected to get involved in details of design;
any scaling up or down of plant size and capital
cost was to be satisfactorily handled by an ex-
ponential relationship. The other vital document
was material from a major chemical company's

Many departments ... do not require
a course in engineering economics at the
undergraduate level... sadly, many B.S. ChE's
come out of school with little or no
understanding of this vital material.

procedures for evaluating projects proposed for
capital appropriation. Those procedures require
in part the development of ten-year forecasts of
sales volume, unit selling price, cash flow and re-
turn on investment, and of the compilation of in-
formation for checklists for each of marketing,
technical and manufacturing/engineering areas.
Typical of the numerous items from the check-
lists are-for marketing: "characteristics of
major end use markets (growing, static or declin-
ing; seasonal or cyclical nature; individual re-
quirements as to quality, package, technology,
service or price; vulnerability to substitution by
competitive products, etc.)"; for technical: "De-
gree of technical risk: highlight modifications
planned in construction and differences over
demonstrated technology, scale-up uncertainties,
raw material differences, etc."; and for manu-
facturing/engineering: "For the capital cost esti-
mate, give the source, degree of accuracy and
basis for the estimate, and the expenditure
The final class meeting consisted of all the
teams assembling on campus for an all-day oral
presentation of the information in the teams'
written reports. Each team used about one-half
hour to summarize its analysis and conclusions,
followed by a discussion of these. The critique of
a team's work focused on the substance of its in-
formation, analysis and reasoning. Obviously, it
would have been foolish for the instructor to tell
a team: "Your decision to go/not go with the ex-
pansion was wrong." The companies actually in
the business are at least (!) as capable as the
instructor, and they are by no means unanimous
in the decisions they are taking on this same
question. Only time will tell who is right and
We were extremely fortunate to have Mr.
Robert E. Kennedy of the Gulf Oil Chemicals
Company participate in the course. His position
as Marketing Manager for Olefin Derivatives
enabled him to provide data to the students on
suppliers and markets for ethylene. His presence
at the presentation did very much to hang flesh
on the bones of what was taking place. Perhaps

FALL 1979

the greatest value of his participation was
characterized in a comment of a student to me:
"I really busted a gut on the project so as not to
embarrass the Department and you in the eyes of
Mr. Kennedy."
Educators are always deeply appreciative of
a willingness by people from industry to get in-
volved in working with students. The author par-
ticularly valued this investment by Mr. Kennedy
and Gulf toward instruction in a subject so
foreign to universities. E

Baba, T. R. and Kennedy, J. R., "Ethylene and Its Co-
products: The New Economics," Cheon. Engr., V83,
No. 1, 116-128 (1976).
Tribus, M., "Rational Descriptions, Decisions and Designs,"
Pergammon Press, Elmsford, New York, 1969, p. xv.

W 5 book reviews

Part I. Chemical Processing and Engineering
Series, Volume 10
Clyde Orr, Ed.
Marcel Dekker, 1977. 544 pp. $45.00
Reviewed by Max S. Willis
University of Akron

Filtration is one of the most neglected areas
of chemical engineering. This is the consequence
of the fact that it is not based on a sound theo-
retical basis and is an art rather than a science.
Other areas, such as heat and mass transfer, re-
ceive much more attention because of their sound
theoretical basis.
Although this book attempts "to cover theory
as well as the practical considerations that enter
into actual applications," it does not achieve its
purpose. It also suffers a lack of careful organiza-
tion, common nomenclature and format.
In Chapter 1, Gas Filtration Theory is covered
extensively with numerous references (462 to be
exact!). Contrary to the other chapters of the
book, it does not have a notation section at the
end. It is possible to combine this Chapter with
Chapter 4, Industrial Gas Filtration.
Chapter 2, Liquid Filtration Theory and Fil-
tration Pretreatment, and Chapter 5, Filtration
in the Chemical Process Industry, basically cover

the same area and most of the equations are re-
peated twice. Notation is not consistent, for
example, mass fraction of solids in the slurry is
denoted by c and s in Chapters 2 and 5, respec-
tively. From the reader's point of view, some state-
ments are contradictory. For example, in Chapter
2, the value of B is claimed to vary between 0 to
0.25 (p. 189) but in Table 7 (p. 400) of Chapter
5, the general range of B is given to be 0.1 and
0.5. Also the flow direction in Figure 21 of
Chapter 5 is not correct.
In Chapter 2, which is attributed to Professor
Tiller, the basic flow equation for compressible
sludges (Eq. 41) is discussed and the Kozeny-
Carman equation is substituted for the permea-
bility term. This latter substitution is subject to
conjecture since in a recent article [Filt. & Sep.,
14, 122 (1977)] Professor Tiller claims that the
Kozeny-Carman Equation cannot be used to de-
scribe compressible cakes behavior.
In Chapters 2 and 5, the solids movement
within the filter cake is neglected in order to avoid
the use of a "sophisticated" form of Darcy's law
for the development of filtration theory. If the
solids velocity is zero, then, according to the equa-
tion of continuity, porosity at any point is in-
dependent of time and the superficial liquid
velocity is constant throughout the filter cake at
any instant. But, according to Equation (72) of
Chapter 5, which was derived on the basis of no
solids velocity in the filter cake, porosity at any
point is a function of time which is, of course, a
Recently, it has been observed that there are
a number of serious problems in the compression-
permeability test cell (CPTC) methodology which
leads one to question the ability of this device to
accurately and, more importantly, to uniquely
simulate a constant pressure filtration. In one of
his articles [AIChEJ 15, 405 (1969)], Professor
Shirato stated that ". most data found in the
literature have not taken wall friction into account
and consequently do not yield strictly accurate
values." Although almost all the figures in
Chapter 5 are from data based on CPTC observa-
tions from the papers of Professor Tiller and
Professor Shirato published over the past two
decades, the problem with compression-permea-
bility test cell data is never mentioned.
The rest of the book deals with the Filter
Media, Chapter 3, and Ultrifiltration, Chapter 6.
The price of the book is far too expensive! E


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have another and more significant mean-
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We offer bright and energetic people
with this drive the opportunity to help
solve some of the world's major problems
concerning food, energy, the environment
and others.
Challenging assignments exist for
engineers, scientists, accountants and

marketing majors at locations throughout
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We offer you opportunities, training
and career paths that are geared for
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*Rtet ^ "wl^^

/! Qoide in.



Purdue University
West Lafayette, IN 47907

T HERE HAVE BEEN A NUMBER of recent books by
mathematicians aimed at educating engineers
and applied scientists to varying degrees of depth
on the subject of functional analysis. For example,
we have "Linear Operator Theory in Engineer-
ing and Science," by A. W. Naylor and G. R. Sell
[1] and "Introductory Functional Analysis with
Applications," by E. Kresig [2], to name only a
couple. There are at least two main motivating
factors for this trend. The first is that mathema-
tical abstraction has accomplished a tremendous
unification of apparently diverse classes of
problems under a common framework. Conse-
quently, a given problem suitably cast in the fore-

Doraiswami Ramkrishna received his B(Chem)Eng. degree (1960)
from the Bombay University Department of Chemical Technology and
his Ph.D. (1965) from the University of Minnesota. After teaching for
two years at Minnesota, he returned to India in 1967 and taught at
the Indian Institute of Technology, Kanpur until 1974. He was a
Visiting Professor at Wisconsin (1974-75) and at Minnesota (1975-76)
and is now Professor of Chemical Engineering at Purdue University.
He is a consultant to General Mills, Inc., Minneapolis. His research
includes dispersed phase systems, stochastic modeling and applications,
bioengineering and problems of general applied math interests.
Normally quite gentle, he reacts rather violently to criticism of cricket.

... mathematical abstracting has
accomplished a tremendous unification
of apparently diverse classes of problems
under a common framework. Consequently,
a given problem suitably cast in
the foregoing framework derives
the benefits of its deductions.

going framework derives the benefits of its deduc-
tions. The second is that mathematical communi-
cations customarily use the language of functional
analysis and familiarity with it would greatly
facilitate commerce with mathematicians.
This article reports on a course at Purdue that
has evolved over several years since its inception
at the Indian Institute of Technology, Kanpur
where the author spent his initial years. To Neal
Amundson must go the credit for first suggesting
the study of modern analysis and for insisting that
mathematical abstraction should not be just an
instrument for elegant reformulation but must
rather be exploited for problem solving. In this re-
gard it is a pleasure to record here the author's
continuing collaborative effort with Amundson
that has led to numerous papers demonstrating
the usefulness of abstract mathematical concepts.

N THE DEVELOPMENT OF an engineering gradu-
ate course on the subject, one is first faced with
the task of laying out the somewhat heavy ma-
chinery of functional analysis in terms rudi-
mentary enough to be comprehensible but sub-
stantial enough to be useful. Secondly, the utility
of this machinery must be established by suitable
applications. Functional analysis is an investiga-
tion of function spaces in an abstract framework
which regards a function as a vector. The course,
under discussion, in its present stage of evolution,
restricts itself to linear problems, more specifically
analysis of linear operators on vector spaces. That
functional analysis has much to offer nonlinear


SCopyright CIhE Division, ASEE. 1979

problems in chemical engineering is well es-
tablished by Gavalas's masterly monograph [3].
The objective of the present course however is to
demonstrate that a much wider class (than
normally recognized) of linear boundary and
initial value problems of interest to chemical
engineers can be solved with the same conceptual
ease as is inherent in, say, a one dimensional un-
steady state heat conduction problem. The pre-
requisite is the proper formulation of the problem,
frequently in an abstract setting, so that the
theory of linear operators becomes applicable.
The class of what are called selfadjoint operators
is of focal interest to the course since they have
powerful properties that can be used to solve
equations involving them.
Just how one goes about laying out the back-
ground is the most difficult part of such a course.
The author's approach has varied from "theorem-
proof" style to qualitative arguments appealing to
geometric intuition. Indeed the entire elimination
of either feature would fail to inculcate apprecia-
tion for the benefits of abstract thinking, al-
though it must be admitted that the course has
gravitated towards more of the qualitative reason-
ing mainly because of the normal background
of engineering graduate students. Since the depths
to which background material has been treated
have varied considerably, the scope of this article
will be limited to a briefing of the preliminary
topics while focussing more on the useful applica-
tions of the theory of linear operators. It is this
latter issue that is particularly crucial and in
which many expositions have left something to be
desired. An interesting exception is Friedman's
"Principles and Techniques of Applied Mathe-
matics" [4].

semester's course:

Fields; real and complex numbers. Linear spaces.
Metric spaces. Normed linear and inner product spaces.
Spectral theory of linear selfadjoint operators in Hil-
bert Space. Sturm-Liouville theory. Partial differen-
tial operators. Applications to chemical engineering

Obviously, the foregoing list is too formidable
to permit a detailed treatment of each topic in
one semester. Thus, for example, the emphasis on
real numbers is limited to demonstrating the
structure of the real number system in an ele-
mentary way, which carries over to normed linear
spaces. As another example, the generalization of
a matrix operator in finite dimensional space to a
completely continuous operator in infinite dimen-
sional space is an important concept. This is in-
troduced sketchily by analyzing certain properties
of closed, bounded sets on the real line and in
finite dimensional space. The spectral theorem
for selfadjoint completely continuous operators is
a central feature of the course on which the ap-
plications are built. The background that is re-
quired of students includes familiarity with
matrices and differential equations at the level
of a first course on applied mathematics for
entering engineering graduate students.
We return to the main purpose of this article,
which is an exposition of key applications in the
course demonstrating the utility of abstract
formulations. Let us begin by recalling the
familiar concept of a physical vector as an entity
visualized by components w.r.t. a chosen frame
of reference but whose identity is preserved by
specified transformation rules for the components
when the coordinate frame of reference is
changed from one to another. This definition is
inspired by the necessity to protect the integrity
of a physical quantity regardless of the frame of
reference w.r.t. which it is viewed. Mathe-
matically, a vector is an abstract quantity from a
vast collection of similar objects characterized by
certain properties. These properties include the
concepts of multiplying a vector by a scalar to
obtain another vector and of summing any two
vectors to get a third vector such that certain
properties as commutativity, associativity and
distributivity are satisfied. Further, a zero vector
is defined with which summation of any vector
yields the same vector. One is then naturally led
to the idea of a linear combination of vectors
and the important concept of a basis set. Thus any
vector in the collection may be expressed as a
linear combination of vectors in a basis set, the
coefficients of expansion representing the com-

The objective of the present course however is to demonstrate
that a much wider class... of linear boundary and initial value problems
of interest to chemical engineers can be solved with the same conceptual ease as
is inherent in, say, a one dimensional unsteady state heat conduction problem.

FALL 1979

ponents of the expanded vector. The components
may then be used to identify a vector relative to
a basis in much the same manner as the physical
vector to which we referred earlier. A vector re-
garded in the foregoing terms is indeed an ab-
stract quantity. The collection of vectors is called
a linear space. The discussion so far has been on
algebraic concepts divorced from such notions as
magnitude (or norm) of a vector or angle be-
tween vectors. These additional notions are intro-

In other problems
featuring transient energy or
mass transfer, boundaries or interfaces
may be encountered with capacitance.

duced as abstract mappings of vectors into
numbers. Thus a norm must map a vector into a
real number consistent with the following stipula-


lxiI > 0, lxi = 0 if and only if x = 0
I|axl| = la lx|I
jjx + y|| < |lx|l + Ilyll

In the above x and p are vectors, a is a number
with Jaj as its absolute value and ]1 |I is the
symbol for the norm of the vector which it flanks.
Property (iii) is the triangular inequality.
The angle between two vectors arises from
their inner product (dot product), which is a
mapping of pairs of vectors into real (more
generally complex) numbers satisfying certain
properties. For real spaces the properties are
conveniently stated in symbols as follows.
(i) =
(ii) > 0, = 0 if and only if
x= 0
(iii) = +
(iv) = a
In (i) through (iv) <,> represents the inner
product of the enclosed vectors. Clearly the inner
product is a bilinear mapping from properties
(iii) and (iv). Another important point is that
properties (i)-(iv) help generate a norm from
the inner product. Thus we may write 1Ix|l
V. Orthogonality between two vectors is
described by the vanishing of their inner product.
The importance of the foregoing stipulations
(or axioms) for a linear space, norm and inner
product is that while one is quickly satisfied that
the familiar physical vectors are faithful to the
axioms, they are not the only conformists. There

are other collections of vectors that produce no
geometrical pictures in the mind but are at least
as useful. As an example, the collection of
functions f(x), a b

ff2 (x) dx < oo
represents a linear space of vectors f = [f(x):
a fined by

= f(x)g(x)dx
Other choices are available for defining the
inner product but the choice to be made depends
on the end to be met. It is this end that deserves
some discussion here.
Vital to engineering applications is the concept
of an operator which is a rule for transforming
one vector into another. This mapping is said to
be linear, when any linear combination of a pair
of vectors are transformed into the same linear
combination of the transformed vectors. In
symbols, denoting a linear operator by L we have
L(ax + py) = aLx + PLy
By continued application of the operator it is easy
to see how powers, polynomials, analytic func-
tions etc. of operators may be defined. Thus one
may talk about operators such as Ln or exp L and
so on. By the same token two operators may be
multiplied. Such operations are not necessarily
commutative. An operator of particular interest
is the projection operator P which, besides being
linear, has the property P2 = P.
Let us recall the operator of central im-
portance, the selfadjoint operator. It is defined
as the operator for which
= (1)
for any pair of vectors x and y. For a completely
continuous selfadjoint operator the spectral
theorem (see for example [1]) assures us the
existence of real eigenvalues [Xj] and associated
projection operators [Pj] with the property that
PjPk = 0 when j == k such that

L = Y XjP,
Continued on page 211.


-' -

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Engineers Constructors


*.... (il


Princeton University
Princeton, New Jersey 08544

T HE UNUSUAL AND USEFUL properties of colloidal
suspensions originate with the forces acting
upon and among the individual particles. Roughly
speaking, the colloidal domain encompasses all
particles large relative to the fluid molecules but
sufficiently small to be responsive to thermal
motion. At the lower end of this length scale
Brownian effects dominate and, as with low
molecular weight fluids, equilibrium among the
interparticle forces prevails. Nonidealities caused
by interparticle forces are generally thermody-
namic rather than mechanical. In the 0.1-10 pLm
range, however, diffusion becomes slow enough
for external influences to upset this equilibrium
with significant macroscopic consequences-
electrokinetic phenomena, electrically driven
separations, shear induced flocculation, and non-
Newtonian rheology.
Scientific study in this field began in the 19th
century with Robert Brown's observations of
thermal motion and Thomas Graham's studies of
diffusion, but practical applications appeared
many centuries earlier. For example, the ancient
Egyptians apparently produced inks by stabilizing
aqueous dispersions of carbon black with natural
substances such as gum arabic, egg albumin, and
Today both the science and the engineering
pertaining to colloids are well advanced. Mono-
disperse gold sols, polystyrene latices, silica, and
hydrous metal oxides can be purchased or readily
synthesized. These well-characterized model
systems have served to significantly improve our

... we developed a graduate
course in Colloidal Phenomena to address
the physical and dynamical side
of colloid science ...

0 Copyright ChE Division, ASEE, 1979

After obtaining his undergraduate degree at Cal Tech and gradu-
ate degrees at Northwestern (M.S.) and Stanford (Ph.D.) Dave Ollis
(on left) came to Princeton in 1969 where, in addition to research in
catalysis, his recent work has included studies of particulates in the
context of biochemical engineering problems. He is currently Pro-
fessor of Chemical Engineering.
Bill Russel's (2nd from left) interests in the behavior of poly-
electrolytes and other particulates in suspension began during a
stint as NATO Postdoctoral Fellow at Cambridge shortly after he
completed his PhD at Stanford in 1978. His B.S. and M.S. are from
Rice University. His research in the behavior of small particles in-
cludes the behavior of gas phase suspensions and he is currently
engaged in a study of coal hydropyrolysis with Dudley Saville. Russel
is currently Associate Professor of Chemical Engineering.
Since coming to Princeton in 1957, Bill Schowalter's (3rd from left)
research has centered on fluid mechanics, with an emphasis on the
behavior of polymer melts and solutions and particulate suspensions.
His undergraduate degree is from Wisconsin and his M.S. and Ph.D.
are from Illinois. He is Professor of Chemical Engineering and Chair-
man of the Department.
Dudley Saville (right) came to Princeton in 1968 after stints in in-
dustrial research at Chevron Research and the Shell Development
Company. His undergraduate degree is from the University of Ne-
braska and his PhD from Michigan. His current research includes
studies of electrokinetic phenomena in suspensions and electrically
stimulated aerosol filtration. He is Professor of Chemical Engineering.

quantitative understanding of phenomena and to
provide standards for testing processes. Many
other synthetic and natural colloids play central
roles in the chemical process industries. These
range from primary products such as pigments,
cements, and carbon blacks to necessary com-
ponents in the food processing, pharmaceutical,
photographic, and pulp and paper industries.
Most are associated with active research and de-
velopment efforts.
Prompted by a confluence of research interests


among a number of faculty within the chemical
engineering department we developed a graduate
course in Colloidal Phenomena to address the
physical and dynamical side of colloid science:
colloidal stability, electrokinetic phenomena, sepa-
rations techniques, and rheology. Excluded are
characterization techniques such as light scatter-
ing and osmotic equilibrium as well as purely
surface or interfacial phenomena. Nonetheless,
the course provides a broad introduction for
students entering a number of research areas.
Our efforts have been supported in part by grants

from the Camille and Henry Dreyfus Foundation
through their Innovation in Education in Chemis-
try Program and from the Xerox Corporation.

fundamental physical chemistry and mechanics
of colloidal suspensions beginning with the forces
and fields operative at the particle scale and pro-
gressing through to separations processes and
macroscopic properties (Table I). At each step
quantitative theories and corresponding experi-

Course Outline


(W. B. Russel)
Brownian motion
statistical description with probability densities
derivation of diffusivity from Langevin equation
role of hydrodynamic mobilities
formulation of conservation equations
Dispersion forces
intermolecular forces
Hamaker theory for particles
application of Lifshitz theory
experimental verification
Electrostatic forces
origin of surface charge
structure of equilibrium double layer
interparticle repulsion
experimental studies

Electrostatic stabilization
criterion for kinetic stability
kinetics of rapid flocculation
slow Brownian flocculation
shear-induced flocculation
Steric stabilization
origin of repulsive force
experimental studies
simple theory for absorbed layers

General description of phenomena
streaming current and potential
electro-osmosis and electrophoresis
electroviscous effects
Processes within capillaries
non-equilibrium double layers
limiting solutions
experimental results
Motion of suspended particles
perturbation expansions and solution techniques
effect of particle shape

electrophoresis of polyelectrolytes
primary electroviscous effect
forces responsible for collection
trajectory analyses
macroscopic balances and filter design
Field-Flow Fractionation
types of transverse fields
pulse velocity and dispersion
design considerations
isotherms and interfacial aspects
application of particle collection theories
experimental results
role of osmotic pressure
concentration polarization
Continuous flow electrophoresis
principles and general analysis
hydrodynamic instabilities
application to separation of cells
Examples of non-Newtonian behavior of disperse
General framework for analysis
description of microstructure
calculation of bulk stresses
dimensional analysis
Dilute suspensions
rigid spheres
drops and elastic spheres
rigid ellipsoids and rotary Brownian motion
Pair interactions: effect of colloidal forces
neutrally stable suspensions
effect of steric stabilization
electroviscous effects
flocculated suspensions
Highly concentrated suspensions
lubrication analyses of hydrodynamics
dilatancy in plastisols
mechanics of ordered latices

FALL 1979

Qualitative agreement with most data is unquestionable, but controversy
persists because of a few significant qualitative and quantitative inconsistencies. Experiments
with steric stabilization .... indicate polymer-solvent interactions to dominate, but several
schools of thought exist on the exact nature of the repulsive force.

ments on well-characterized model systems are
discussed, and areas in need of further theoretical
or experimental study are highlighted.
The lectures begin with the forces acting on
small particles suspended in liquids. For Brownian
motion the classical treatments of Smoluchowski,
Einstein, and Langevin suffice with a few exten-
sions. Study of the viscous forces on small par-
ticles, i.e. fluid mechanics at low Reynolds
numbers, began with Stokes and has experienced
a resurgence of late because of interest in colloidal
problems. The origins of those results relevant to
the course are described briefly. The Hamaker
treatment of the dispersion forces remains most
useful but eventually may be supplanted by a
simplified application of the rigorous Lifshitz
theory; so both deserve examination. For electro-
static forces we use numerous limiting forms de-
duced from the nonlinear Poisson-Boltzmann
equation. Despite their maturity each of these
remains an active area of research; so notable
recent developments, such as the direct measure-
ment of electrostatic and dispersion forces, are
reviewed as well.
Since the dispersion forces between suspended
particles become strongly attractive at short
range, flocculation can be avoided only by the
intervention of longer range repulsive forces. Our
treatment begins with the classical treatise of
Verwey and Overbeek which synthesized several
decades of work into a comprehensive theory for
electrostatic stabilization. Qualitative agreement
with most data is unquestionable, but controversy
persists because of a few significant qualitative
and quantitative inconsistencies. Experiments
with steric stabilization, i.e. repulsion between
layers of adsorbed polymer, indicate polymer-
solvent interactions to dominate, but several
schools of thought exist on the exact nature of
the repulsive force. Although time does not
permit a thorough exploration of such lingering
questions, the nature of the controversy is outlined
for the curious to pursue further.
When aqueous suspensions of charged
particles, proteins, or synthetic macromolecules
are subjected to an external electric field or are
forced to flow, interesting electrokinetic phe-

nomena appear. In some cases the motion en-
gendered by the field provides a means of charac-
terization, e.g. the determination of charge by
electrophoresis; in others the induced field retards
the flow, as with electroviscous effects and the
sedimentation potential. Analyses of these to-
gether with the analogous phenomena in charged
capillaries are developed in detail from Stokes'
and Maxwell's equations governing the mechanics
and electrostatics, respectively. The topic is a rich
one mathematically, because of innumerable per-
turbation expansions leading to analytical results,
and phenomenologically, because of the coupling
between the mechanical and electrical forces which
deform the equilibrium double layer.
Following these fundamentals our focus
shifts to larger scales, beginning with several
separations processes which capitalize on either
the colloidal forces or electrokinetic phenomena.
The first topic, filtration, is an interesting applica-
tion since small particles flowing near a large
collector can be captured by any one of several
forces. Analyses of the particle trajectories result-
ing from the balance among these forces yield col-
lection efficiencies, which are then integrated into
macroscopic balances to provide a systematic
means for designing packed beds and fiber filters.
Two relatively new approaches to preparative
separations employ an electric field transverse to
a laminar channel flow. In field flow fractiona-
tion, a long flow path with a narrow channel
permits selective redistribution of particles over
the cross-section; pulses of species with different
electrophoretic mobilities then travel with differ-
ent axial velocities. Continuous flow electropho-
resis, on the other hand, obtains spatial separa-
tion due to migration across a wider channel over
a shorter flow path. In both processes dispersion
and hydrodynamic instabilities can limit the sepa-
ration and scale up. Here the lectures examine
quantitative macroscopic analyses capable of
handling these complications and thereby predict-
ing process performance.
Many applications require both an under-
standing of and control over the mechanical
properties of colloidal suspensions. During pro-
cessing the viscosity and non-Newtonian charac-


Reading List
A. W. Adamson Physical Chemistry of Surfaces, 3rd. ed.,
Wiley, 1976.
J. T. Davies and E. K. Rideal Interfacial Phenomena,
Academic Press, 1961.
A. Einstein Theory of Brownian Motion, Dover, 1956.
P. C. Hiemenz Principles of Colloid and Surface Chemis-
try, Dekker, 1977.
H. R. Kruyt (ed.) Colloid Science (2 vols.), Elsevier, 1952.
V. G. Levich Physicochemical Hydrodynamics, Prentice
Hall, 1962.
J. Mahanty and B. W. Ninham Dispersion Forces, Aca-
demic Press, 1976.
E. Matijevic (ed.) Advances in Surface and Colloid
Science, Vol. 7, Wiley, 1974.
W. R. Schowalter Mechanics of non-Newtonian Fluids,
Pergamon, 1978.
D. J. Shaw Electrophoresis, Academic Press, 1969.
D. J. Shaw Introduction to Colloid and Surface Science,
2nd ed., Butterworths, 1970.
H. Sonntag and K. Strenge Coagulation and Stability of
Disperse Systems, Halsted, 1972.
M. J. Spaarnay The Electrical Double Layer, Pergamon,
E. J. W. Verwey and J. Th. G. Overbeek Theory of the
Stability of Lyophobic Colloids, Elsevier, 1948.

teristics may affect mixing, determine pumping
costs, or provide a simple means for monitoring
product quality. In addition, products such as
paints, cosmetics, and foodstuffs fail without the
desired theological characteristics. While compre-
hensive theories remain beyond our grasp, we
can systemically relate particular colloidal forces
to types of non-Newtonian behavior. For example,
rodlike particles generate viscosities which are
thinning in shear flows but thickening in exten-
sion even at infinite dilution because of competi-
tion between orientation by flow and disorientation
by rotary Brownian motion. Suspended spheres,
however, must interact to cause non-Newtonian
behavior. At moderate concentrations a range of
phenomena may result, depending on the domi-
nant interparticle force. In all situations the
orientations and spatial distributions of the parti-
cles, which represent a balance among hydrody-
namic and colloidal forces, determine the observed
macroscopic stress. Rigorous analyses of several
idealized systems are reviewed to provide some
insight into the complex behavior of practical

M MATERIAL PRESENTED BY THE individual faculty
as listed in the course outline corresponds
roughly to their research interests. Periodic aca-
FALL 1979

demic leaves and other teaching commitments
normally cause us to omit one of the last two
topics. The remainder fit gracefully into thirty-
six lectures over twelve weeks.
Students electing the course to date have been
chemical engineering PhD candidates. This means
that they have encountered a graduate applied
mathematics course, a few weeks of low Reynolds
number fluid mechanics, and some statistical me-
chanics and quantum mechanics. Some have re-
lated thesis topics, while others may be scouting
for areas of future research.
The lectures are supplemented with recom-
mended readings in several basic texts and a
number of monographs listed in Table II. Review
articles and original papers also are cited as ap-
propriate. In the future students will receive an
organized set of notes made possible by the
support from the Dreyfus Foundation. Finally,
at the end of the term a series of informal semi-
nars by industrial researchers, concerned with
paint pigments, pulp and paper operations, or
other colloidal problems, expose the class to the
practical side of the subject.
Scattered homework problems provide inti-
mate exposure to theoretical developments and
data analysis, but the major requirement is a
term paper. The topics offered attempt to identify
a problem to which a student can make an
original contribution, rather than serve solely as
the focus for a literature review. Of course, this
generates spectacular misses as well as some ele-
gant work suitable for publication. Either way
we stir some imaginations and enjoy the day of
oral reports on the topics. [
A Modified Carnot Cycle,
Y. K. Rao, University of Washington
Vol. 13, No. 3, Pages 147, 148
The Text should read as follows:
Pg. 147: Col. 1, line 4 from the bottom:
two reversible adiabatics (I and III') ...
Pg. 148: Col. 1, line 9:
dynamic states 3 and 3'. ASI,, = R In (v3'/v,)
Pg. 148: Col. 1, line 16:
Entropy change, ASI = R In vi/v4';
Pg. 148: Col. 1, line 19:
W = SWi= Q2 + Q1' = RT, in(vv,) + RT,1 n(v,/v,')
Pg. 148: Col. 1, line 21:
AScyle = R In (v3/v) + R In (v/v4') + R In (v3'/v3)
Pg. 148: Col. 1, line 34:
... The latter ...
Pg. 148: Col. 2, line 9 (Eq. 10):
.,- = -Q2/T = R In (v/v,)
Pg. 148: Col. 2, line 10 (Eq. 11):
... = -Q'/T = -R In (vi/v4')



University of Southern California
Los Angeles, CA 90007

0F ALL THE EFFECTS generated by the oil crises
of recent years, the most positive has been the
invigoration of research and development of al-
ternative energy sources. The U. S. Department
of Energy has been a prime mover in stimulating
university activity in this area by funding re-
search. However, the academic institutions them-
selves have, as yet, failed to reflect the concern
over and urgency of this activity in their cur-
ricula. It was this need for updating university
offerings that prompted T. D. Wheelock to publish
his outline of "A Course in Coal Science and
Technology" in a recent issue of Chemical Engi-
neering Education. In a similar vein, the ChE De-
partment of the University of Southern California
has produced a new course in Coal Liquefaction
Processes. It is hoped that this outline will serve
as a reference to other educators in establishing
similar courses.

Teh Fu Yen obtained his B.S. from Central China University, M.S.
from West Virginia University and Ph.D. from Virginia Polytechnic
Institute. His principle research intent in recent years is in fossil
fuels, their extractions, conversions, as well as their environmental
control technology. He has lectured extensively at major oil com-
panies worldwide and has authored over 160 technical papers and
edited nine books. He is the editor of Energy Sources as well as
the editor of Biomaterials, Medical Devices and Artificial Organs. He
has been associate professor of Chemical Engineering at the Uni-
versity of Southern California since 1971.

It is the purpose of this course
to provide a comprehensive background
to coal liquefaction in order to prepare the
student intent upon a career in a coal-related field.

From its first offering in the Fall of 1977, the
graduate course drew keen interest, with 20
students enrolling and a number of others audit-
ing. On the average, 75% of the enrollees have
been graduates in the ChE program, although
graduate students from Mechanical, Petroleum,
and other engineering and chemistry disciplines
have been attracted to the course. The enroll-
ment prerequisite is a B.S. in Physical Science or
Engineering. Some of the students participated
in the class via USC's Interactive Instructional
Television program, which allows students in
neighboring industries to have a two-way com-
munication with a live broadcast of the class.
A great deal of research is currently focused
on the production of synthetic fuel from coal.
The abundant reserves of coal in the United States
makes the enterprise attractive, and concrete
strides in Poland and Germany have created con-
fidence in the eventual realization of the process.
The state-of-the-art technology is the present
problem, though.
It is the purpose of this course to provide a
comprehensive background to coal liquefaction in
order to prepare the student intent upon a career
in a coal-related field. The author feels that the
way to serve the pursuit and the best interests
of the nation, is to insure that trained technical
manpower is available for research. Class cover-
age includes coal chemistry and physics, coal
petrography, coal types, carbonization, hydro-
genation, Fischer-Tropsch synthesis, solvent re-
fining, and other processes and aspects. The one-
term course is composed of 16 two-and-a-half
hour lectures (Table 1).
Since the technology is not established, there
is no textbook for the teaching of the course.

Copyright ChE Division, ASEE, 1979


This fact has been a major cause in keeping such
a course out of university curricula. However, to
remedy this situation, a massive literature search
was conducted during the spring and summer
prior to the first offering of the course. Besides
gathering material known to the author, over 240
specialists in industry, educational institutions,
and government agencies in this country and
abroad were solicited for useful papers, charts,
illustrations, and other literature relevant to the
subject. The response was voluminous. The result-
ing body of papers, publications, and suggestions
received from our correspondents created a pool
of information which gives full representation of
the current state of coal liquefaction. The vast
amount of material was collated, overlapping ma-
terial was eliminated, it's relative importance was
weighed, and, finally, sixty-four papers (roughly
separable into sixteen different topic headings)
were selected (Table 2). This textual material
was supplemented by a book list which effectively
covers the groundwork essential to understanding
the subject.


T HE WEEKLY LECTURES have been primarily de-
livered by the instructor. Because of the inter-
disciplinary nature of the course, careful control
has been exerted in order to keep the overall ob-
jective in clear view, and to keep the course from
being diverted into the other disciplines which are
touched upon tangentially (such as mining and
mechanical engineering, chemistry, and geology).
Occasionally, a guest lecturer is invited, but this
is not a general feature of the course's format.
The first five lectures lay the groundwork
necessary to an understanding of coal. They ex-
plore a number of topics, including the derivation
of coal and much coal science. Lectures 6 through
10 explore the major liquefaction processes in
detail. Included are thermal pyrolysis, carboniza-
tion, catalytic hydrogenation, and Fischer-Tropsch
synthesis, as well as others. The following group
of lectures concerns the product of liquefaction:
coal liquid. The final three lectures look toward
the future, discussing liquefaction processes still

Lecture Topics
1. Introduction-Coal Resources and Supplies; Coal
Mining Technology Development
2. Origin of Coal; Coal Types and Ranks; Petrography;
3. Coal Chemistry; Coal Reaction; Coal Structures
4. Physical Properties of Coal: Statistical Approaches
and Structural Parameters
5. Coal Preparation; Comminution; Coal Feed Engi-
neering Problems
6. Thermal Pyrolysis of Coal; Kinetics and Mechanism
of Thermal Decomposition
7. Carbonization; Mesophase; Cokes
8. Solubility Parameters; Solvent Refining; Nature of
Hydrogen Donors
9. Catalysis; Catalytic Hydrogenation
10. Fischer-Tropsch Synthesis-Generalized Gasification
11. Coal Liquids; Separation and Isolation of Asphal-
tenes; Characterizations
12. Refining, Upgrading, Desulfurization, Demetalliza-
tion, Denitrogenation
13. Coal-Derived Chemicals and Products; Other Syn-
14. Novel Approaches; In-Situ Production
15. Environmental, Safety, and Health Problems in Coal
16. Process and Reactor Design; Mathematical Models;
Reaction Control

in development and projecting future technology,
along with environmental and health impacts.
For class preparation the students read four
related papers which are held on reserve in the

C LASS WORK IS COMPRISED of three categories
which carry equal weight in the calculation
of grades: homework problems, term paper, and
Three times throughout the semester, sets of
homework problems are distributed to the
students. Usually, the sets contain five problems
whose solutions require quantitative and analytic
calculations. An example is: Calculate the thermal
efficiency (or the overall efficiency) for Fischer-
Tropsch Synthesis. The student would arrive at a
value by applying design criteria to chemical
principles and data conveyed in class. The home-

Besides gathering material known to the author,
over 240 specialists in industry, educational institutions, and
government agencies in this country and abroad were solicited for useful
papers, charts, illustrations and other literature relevant to
the subject. The response was voluminous.

FALL 1979

work serves a dual purpose: to illustrate chemical
engineering principles and to put into practice
formulas and data given in class.
In assigning topics for term papers, the
student "nominates" three possible subjects in the
order of his preference. The instructor makes the
final selection; in this way, control is exerted to
insure that papers do not duplicate topics. This is
desirable, because later in the semester students
present detailed outlines of their papers before
the class. In this way, students (as auditors) are
exposed to new material and are asked to question
the soundness of the various theses, and (as pre-
senters) are made to cogently deliver and defend
their works.
The term papers are not exhaustive literature
surveys, but rather, are the students assessments
of various aspects of coal liquefaction. Creativity
is stressed, and the student is encouraged to or-
ganize and substantiate his or her own ideas on
the subject, as well as to draw from interest or
background in other related disciplines in the for-
mulation of an original and personal position. Two
such student papers, resulting from the first offer-
ing of the course, were subsequently published
in technical journals, attesting to the relevance
of such work.
The midterm and final examinations are com-
posed of problems requiring quantitative and
analytic solutions, much like the homework
problem cited above.
As an adjunct to classwork, an open invitation
to participate in university research projects is
extended to the students. This is made possible by
a number of continuing coal research contracts
from DOE for which the author is the principal

liquefaction technology, university courses on
the subject must wage a battle on two fronts:
striving to keep abreast of the changing face of
the field, and seeking out the class format and
material which will best serve the subject. End-
of-semester student polling is a standard pro-
cedure at the University of Southern California

... the student responses
were heartening. The majority of the
class members remarked very favorably on the
worth and success of the course.

- -


n L U
U P. R

FIGURE 1. Graphic Representation of
to Course




Student Response

and the author has had a more than customary
interest in student reactions and suggestions,
with a view to shaping the best possible course
Taking one representative semester, the 18 en-
rolled classmembers were asked to complete a
course evaluation form anonymously, and 13 (or
72%) complied. The questionnaire and method
of interpretation applied to it were developed by
Dean Frederic Carlson, Jr., Director of USC's
Engineering Computer Laboratory. The graphic
representation of the student response to the
course is presented in Figure 1. In brief, the
questionnaire responses are interpreted for three
categories: effort vs. learning, amount learned in
the course, and overall rating. Each category of
responses is represented by a bar graph in which
black areas represent responses which are charac-
terized as "poor," crosshatched areas signify
"average," and white "excellent."
In the evaluation category of effort vs. learn-
ing for our course, six students responded that
the material was enjoyable and stimulating. Six
were satisfied with what they learned in view of
the effort exerted and only one found himself
struggling to get through the course rather than
attempting to learn.
Continued on page 215.




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In short, we think this is a very good time to work for Exxon. Candidates for engineering and other
degrees, see your placement officer or send your resume to Exxon, Professional Recruitment,
P.O. Box 2180, Houston, Texas 77001.

Exxon Corporation and its Domestic Affiliates,
Equal Opportunity Employers.
FALL 1979

4 QOm-ule iat



University of Notre Dame
Notre Dame, Indiana 46556

A TWO-SEMESTER, three lectures per week gradu-
ate course dealing with Mathematical
Methods in Chemical Engineering is offered every
year at Notre Dame. The course originated with
Merlin Howerton in Fall 1949 when he joined the
department. It was initially a one-semester
course, and was taken largely by graduate students
at the master's level (the doctoral program in
ChE at Notre Dame did not begin 'til the arrival
of Julius T. Banchero from Michigan as Chair-
man in 1959), although some seniors also took the
course as a technical elective. Two of our current
(and senior) faculty members, James J. Car-
berry and James P. Kohn, took the course to-

Arvind Varma is currently an Associate Professor of Chemical
Engineering at the University of Notre Dame. His degrees are all in
Chemical Engineering; B.S. from Panjab University, India, M.S. from
the University of New Brunswick, Canada, and Ph.D. from the Uni-
versity of Minnesota (1972). After staying on the faculty at Min-
nesota for a year, he was with Union Carbide for two years, and
joined Notre Dame in 1975. His research interests include chemical
and catalytic reaction engineering, modeling and simulation. His
friendship with the renowned Aris McPherson Rutherford began
while he was a graduate student, and was nurtured by their common
interests in Amundson's early work on distillation-the fruits of which
they both enjoy.
Copyright ChE Division, ASEE, 1979

gether in Fall 1950, the second time it was
offered; the former as a master's student, and
the latter as a senior. Howerton taught the course
'til 1954, using the early book of Marshall and
Pigford [8] on differential equations as text. He
left the department for the University of Denver
in June 1955; Howerton was particularly close
to John Treacy who had died that year in an ex-
plosion while conducting a kinetics experiment
with organo-nitrides used for propellants.
Fortunately, Jim Kohn joined the faculty in
Fall 1955 after completing graduate work at
Michigan and Kansas, and took over the course,
expanding it immediately to a two-semester se-
quence. His course was particularly oriented
towards modeling. Although he used the second
edition of Applied Mathematics in Chemical Engi-
neering [11] as text for one year, it did not prove
satisfactory and Kohn started developing his own
notes on the subject. Except for the years 1964-
67 when Francis Wehner taught it, using the first
edition of Jenson and Jeffrys [7], Kohn taught
the course for twenty years.
Because it was unique in the college of engi-
neering, Kohn's course consistently attracted
students as well as faculty from the other engi-
neering departments. In Fall 1963 enrollment in
the course was at its highest; 45, including 15
seniors. The course has been taught by the author
since Fall 1976. Enrollment in the course started
dropping during the middle sixties as other engi-
neering departments began their own courses, and
the department began a one-semester undergradu-
ate course in applied mathematics at the junior
level. This last course was dropped in 1967 in
favor of a similar college-wide core course.
Our present course is taken by all first-year
graduate students in the department, and the class
typically consists of twelve to fifteen students,
always including a few from other branches of
engineering, chemistry or physics. Although
technically it is open to seniors, only one has
elected to take it in the last three years.


Notre Dame has been at a disadvantage for
some time with respect to instruction in applied
mathematics within our mathematics department,
since it is more oriented towards "pure" mathe-
matics. That department is a distinguished one,
but most scholarly research is in areas such as
algebra, topology, logic and group theory. These
topics are not the most useful for our graduate
students, either in their research or in coping
with other graduate courses, so we must teach
them, within the department, what we would like
them to know in applied mathematics. Apart from
this need, I am certain we would teach our own
mathematical methods course even if there were
courses available within the mathematics depart-
ment. The reason is that the course not only
teaches techniques for solving mathematical
problems once they are formulated, but also
stresses model-building. In this sense, my ideas
of teaching applied mathematics to chemical engi-
neers closely match those of my mentor Neal
Amundson. Indeed, our current course bears a
striking similarity to his at Minnesota in the late
sixties [1].


T HE COURSE MEETS THREE times a week for
fifty minute lectures. Homework problems are
assigned almost every week, and are graded and
returned to the student. Somewhere between 25-
30 homework problems are assigned each se-
mester. I also give two mid-semester exams and
a final each semester, all closed-book. Lengthy
formulae are not required to be memorized, and
are provided for the examinations.
Approximately one-third of the homework
problems require use of the university computer
(IBM 370). No instruction in programming or
numerical techniques is given as part of this
course and almost all of our entering graduate
students take the separate Numerical Methods
course offered annually in the fall semester within
the department.
Topical Course Outline
1. Matrices and their Application.
2. First Order Nonlinear Ordinary Differential Equa-
tions and Stability Theory.
3. Linear Ordinary Differential Equations: Initial-value,
Boundary-value and Eigenvalue Problems.
4. Series Solutions and Special Functions.
5. Linear Partial Differential Equations.
6. Laplace Transforms.

An unusual characteristic
of the course is that the lectures are
given on transparencies shown by an overhead
projector. Students receive copies of the
transparencies in chapter form
well in advance.

An unusual characteristic of the course is
that the lectures are given on transparencies
shown by an overhead projector. Students receive
copies of the transparencies in chapter form, at
cost, well in advance. I prefer this method be-
cause teaching mathematics usually requires
lengthy manipulations which consume a good
amount of class time if performed on the black-
board. The additional, and main, advantage is that
students are not busy transcribing material from
the blackboard (an operation which can occur,
bypassing the mind) and thus can concentrate on
understanding the material. Students invariably
like this approach. Since classes are small, there
are frequent interruptions for questions, both by
students and the instructor.

A TOPICAL OUTLINE OF the course is shown in
Table 1. The following is a detailed descrip-
The first five to six weeks in the fall semester
are devoted to matrices and their application,
covering portions of Amundson's book [2]. This
includes material on determinants, solution of
linear simultaneous algebraic equations, matrix
eigenvalues and eigenvectors, expansion of an
arbitrary vector in terms of the eigenvectors,
solving a system of coupled first order linear
ordinary differential equations (ODEs) by the
method of eigenvalues and eigenvectors, similarity
transforms, quadratic forms, and functions de-
fined on matrices. Several non-trivial examples
from the book are covered in detail; they have
usually included transient analyses of staged sepa-
ration processes, and a sequence of isothermal
first order reactions occurring in a batch reactor
or in a series of continuous-flow stirred tank re-
The balance of the course deals with ordinary
and partial differential equations. The first aspect
in this area deals with first order nonlinear
ODEs and stability theory, and usually takes six
to seven weeks. Topics covered include the
existence and uniqueness result for initial-value
problems, continuous dependence of the solution

FALL 1979

Although second-order differential operators are
emphasized since they arise most frequently in applications such as
mass-diffusion and heat-conduction, higher order operators are also considered
because of their role in elasticity problems.

on a parameter or initial conditions, qualitative,
behavior of nonlinear ODEs, linearization, Liapu-
nov's theorem for the local stability of nonlinear
systems, classification of the phase plane for two-
dimensional systems, higher order systems, and
stability by Liapunov's Direct Method. This
portion is perhaps the most interesting part of
the course, for it brings out the essential
differences between linear and nonlinear dynamic
systems. Linear systems arising in nature in-
variably possess a unique steady state which is
asymptotically approached in time by all initial
conditions (global asymptotic stability). Non-
linear systems, of course, can have a multiplicity
of steady states (some stable, others unstable)
and frequently one encounters cases where either
a unique steady state or all the multiple steady
states are unstable-in which case the dynamic
behavior is a self-sustained oscillation. Examples
from reactor analysis and population balances are
covered to illustrate these features. In this
context, I hope to include in future offerings, re-
cently developed material on first-order nonlinear
difference equations which, although simple and
deterministic, can exhibit very surprising dynamic
behavior, from stable steady states to stable
periodic solutions, and eventually to apparently
random fluctuations implying "chaos." Such
equations have been used to great advantage in
analyzing biological populations [9, 10]. Also
recent experimental [14] and theoretical studies
[cf., 13] suggest that complex reactions in flow
reactors can also exhibit the same exotic features
even under isothermal conditions.
The theory of linear ODEs is treated next.
Topics in this category naturally subdivide into
three classes: initial-value, boundary-value, and
eigenvalue problems. Although second-order
differential operators are emphasized since they
arise most frequently in applications such as mass-
diffusion and heat-conduction, higher order
operators are also considered because of their
role in elasticity problems. In fact, general n-th
order linear differential operators are treated
throughout initial-value problems. The concept of
linear independence of solutions of homogeneous
equations is instilled early, and tests for it by

the Wronskian determinant are developed. This
leads to solution of non-homogeneous equations
by the method of variation of parameters, and the
resulting one-sided Green's function for initial-
value problems. Normally the fall semester ends
with a discussion of the adjoint operator and the
adjoint differential equation.
The spring semester begins with a treatment
of boundary-value problems, and in it, a discus-
sion of boundary conditions (BCs). Some time is
spent on how BCs actually arise in physical
problems, and what they mean. They are a mathe-
matical representation of interaction of the system
with the surroundings. As Amundson has often
said, "BCs arise from nature, and not mathe-
matics." To understand this further, it is profit-
able to take the approach of two observers near
the boundary, one just within the boundary and
the other just outside. The flux arriving at the
boundary from within the system is established
using the same principles employed in deriving
the model (i.e., the ODE) itself. However, the
observer just outside the boundary "sees" a flux
that depends on what is happening in the sur-
roundings. Thus in the context of a heat-conduc-
tion problem, external convection may be excel-
lent, poor, or only fair, leading to first (Dirichlet),
second (Neumann or 'insulation'), or third
(Robin or 'natural') kind BCs, respectively. All
these may be thought of arising as a consequence
of the magnitude of h/k, the ratio of external
heat transfer coefficient to the material thermal
conductivity. Depending on whether the ratio is
large, near zero, or finite, one gets the appropri-
ate BC, which physically imply that the surface
temperature equals that of the surroundings, the
surface is insulated, or Newtonian heat transfer
at the surface, respectively. These BCs are all
linear. Nonlinear ones can also arise in the same
manner if radiative exchange occurs at the sur-
face; in this case the surface flux from the view-
point of the internal observer remains unaltered,
but the external observer sees a radiative flux.
There is no counterpart of the nonlinear BC in a
mass-diffusion problem, except when a nonlinear
reaction occurs on the surface.
After a discussion of the BCs, the concept of


a self-adjoint differential operator and of self-
adjoint boundary-value problems (i.e., the opera-
tor plus the BCs) is developed. The Green's
function for solving non-homogeneous boundary-
value problems is derived from the one-sided
Green's function for initial-value problems, and a
physical interpretation is attached to it.
The origin of eigenvalue problems is discussed,
and following introductory examples, the general
Sturm-Liouville problem is treated for self-
adjoint operators with self-adjoint BCs. Several
examples are treated in this context, and the fact
that such problems possess an infinite number of
real eigenvalues, each with an eigenfunction be-
longing to it, is brought out. Completeness and
orthogonality of the eigenfunctions is responsible
for generalized eigenfunction expansions of
functions, and lead to finite Fourier transforms
and thus the solution of boundary-value problems
by this technique. The method of finite Fourier
transforms also plays a control role in solving
partial differential equations, and is thoroughly
The topic of power series solutions and special
functions is covered next, in about three weeks.
The distinction between ODEs with analytic co-
efficients and those with regular singular points
is made. Orthogonal polynomials associated with
Legendre and Hermite arise as solutions of
specific ODEs in the former class, and are de-
veloped. The extended power series method of
Frobenius is considered for the latter class, and
is applied in detail to develop the various Bessel
functions. Relationships among Bessel functions
and variety of ODEs having Bessel function solu-
tions are reported. The topic concludes with
several physical and chemical examples in cylin-
drical geometry which have solutions in terms of
Bessel functions, such as the temperature profile
with internal heat generation, heat transfer in a
fin, and diffusion-first order reaction in a catalyst
pellet. The remaining orthogonal polynomials,
those of Laguerre and Chebyshev, are normally
developed as homework problems, as special cases
of the confluent hypergeometric function-the
solution of the confluent hypergeometric equa-
tion. The various orthogonal polynomials play a
central role in numerical quadrature [4, 15].
The remaining weeks are devoted to second-
order partial differential equations (PDE's) and
Laplace transforms. Armed with the powerful
method of finite Fourier transforms, it becomes
a relatively straightforward matter to routinely

solve PDEs in many space variables and time. In
applying the method, a differential operator and
associated homogeneous BCs need to be identified
corresponding to each of the space variables. In
most physically motivated problems, these are
or can be made self-adjoint. The corresponding
eigenvalue problems are then solved, and succes-
sive transforms of the PDE are taken to eventu-
ally yield an ODE in the last independent vari-
able. This ODE can usually be directly solved,
and inverse transforms performed to yield the
solution in series form. A good rule to remember
is that the number of series summations is one
less than the number of independent variables;
the solution of a problem in three space variables
and time will thus be a triply infinite series. Non-
homogeneities in the BCs and the equation itself
are readily accommodated by the technique of im-
pulse response, for which a physically-based but
mathematically sound derivation is provided.
In Laplace transforms, other than basic re-
lationships, we usually cover Heaviside expansion
theorem for finding inverse transforms, and the
solution of ordinary and partial differential equa-
tions by the technique using examples.
a significant amount of applied mathematics in
our course. The mathematical content is quite
oldfashioned, but the aim is to insure that our
graduates have a thorough mastery of at least

The remaining weeks are
devoted to second-order partial
differential equations (PDE's) and
Laplace transformations

the old-fashioned mathematics. To make the
course more modern and to provide another set
of techniques, I plan to include some material on
perturbation methods [cf., 12] in future offerings.
These methods are powerful in giving solutions of
nonlinear problems in limiting cases, and have
been used in fluid mechanics as well as in reaction
engineering. They are currently introduced in one
of our advanced elective courses in reaction engi-
neering, but all students do not take that course.
There are no textbooks available for the
course, although Ince [6] covers the theory of
linear ODEs in depth, some aspects of stability
theory can be found in Davis [5] and in Boyce and
DiPrima [3], and Weinberger [16] gives a good

FALL 1979

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exposition of the method of finite Fourier trans-
forms. As mentioned before, we distribute a set
of notes to the students. These notes were de-
veloped in collaboration with Professor Amund-
son, and we plan to refine and publish them in
textbook form in the future. The use of overhead
transparencies is very helpful in covering the
relatively broad set of topics in the mathematical
detail necessary, and provides the student with a
feel for mathematics and its use. A great deal of
class time is spent on "talking about" problems,
and on the role and use of mathematics in chemi-
cal engineering in general.
A fundamental question arises as to whether
all this should be done in a chemical engineering
department. Some reasons for our doing so were
noted in the introductory section. In addition, it
is my observation that mathematics courses
offered in mathematics departments, even if they
are titled "applied", tend to be rather theoretical
in nature. Also, in general, mathematicians do
not care about solving problems, much less model-
building. The type of course we offer not only gives
the student a good mathematical background, but
also gives him confidence in formulating and solv-
ing problems. At the end of the course he is con-
versant with standard mathematical techniques,
knows their limitations, and can readily use them

to solve non-trivial problems in practice. Student
feedback has been uniformly positive. D

It is a pleasure to thank my colleagues, James J. Car-
berry and James P. Kohn for providing historical in-
formation regarding the course.

1. Amundson, N. R., Chem. Eng. Edn., 3, 174 (1969).
2. Amundson, N. R., "Mathematical Methods in Chemical
Engineering: Matrices and Their Application,"
Prentice-Hall, Englewood Cliffs, N. J. (1966).
3. Boyce, W. E. and R. C. DiPrima, "Elementary
Differential Equations and Boundary Value Problems,"
Third Edition, Wiley, New York (1977).
4. Carnahan, B., H. A. Luther and J. 0. Wilkes, "Applied
Numerical Methods," Wiley, New York (1969).
5. Davis, H. T., "Introduction to Nonlinear Differential
and Integral Equations," Dover, New York (1962).
6. Ince, E. L., "Ordinary Differential Equations,"
Dover, New York (1956).
7. Jenson, V. G. and G. V. Jeffrys, "Mathematical
Methods in Chemical Engineering," Second Edition,
Academic Press, New York (1977).
8. Marshall, W. R., Jr. and R. L. Pigford, "The Ap-
plication of Differential Equations to Chemical
Engineering Problems," Edwards Brothers, Ann
Arbor, Michigan (1948).
9. May, R. M., Science, 186, 645 (1974).
10. May, R. M., Nature, 261, 459 (1976).
11. Mickley, H. S., T. K. Sherwood and C. E. Reed,
"Applied Mathematics in Chemical Engineering,"
Second Edition, McGraw-Hill, New York (1957).
12. Nayfeh, A. H., "Perturbation Methods," Wiley, New
York (1973).
13. Rbssler, O. E., Z. Naturforsch., 1la, 259 (1976).
14. Schmitz, R. A., K. R. Graziani and J. L. Hudson, J.
Chem. Phys., 67, 3040 (1977).
15. Villadsen, J. and M. L. Michelsen, "Solution of
Differential Equation Models by Polynomial Approxi-
mation," Prentice-Hall, Englewood Cliffs, N. J.
16. Weinberger, H. F., "A First Course in Partial
Differential Equations," Blaisdell, Waltham, Massa-
chusetts (1965).

books received

Heat Pumps, R. D. Heap. Halsted Press, John Wiley &
Sons, New York, 1979, 155 pages, $9.95.
Advances in Photochemistry, Vol. 11, ed. by J. N. Pitts,
Jr., G. S. Hammond, Klaus Gollnick, and Daniel
Grosjean. John Wiley & Sons, New York, 1979, 538
pages, $35.95
Pulverized-Coal Combustion and Gasification, Theory and
applications for continuous flow processes, edited by
L. O. Smoot and D. T. Pratt. Plenum Press, New York,
1979, 333 pgs.


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development engineer, and as
S an on-campus recruiter for the
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stimulates growth.
Ron's story is typical of
and Electrical Engineers who
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If you're looking for
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A n Equal Opportunity
Employer, M/F



Stanford University
Stanford, CA 94305
N THE LAST THREE decades the growth of
polymers as engineering materials has been
phenomenal. As production levels have climbed,
so has employment of chemical engineers.
Currently, it is estimated that at least 30% of
all Ch.E. graduates will work in some polymer
related activity even though they often enter the
field with no prior coursework in polymers. Cer-
tainly it is a tribute to the broad educational back-
ground of most chemical engineers that this has
not impaired success. However, as demands on
material performance and processing require-
ments become more stringent, specific education
in polymer science is essential. Generally, course-
work in polymers is not to be found in the tra-
ditional chemistry departments, in spite of the
extensive employment of chemists in the polymer
industry. [1] This task has been taken over largely

Curtis W. Frank is an Associate Professor in the ChE Department
at Stanford University. He did his undergraduate work at the U. of
Minnesota, receiving his B.Ch.E. in 1967. His graduate training was
at the U. of Illinois from which he received his M.S. in 1969 and
Ph.D. in 1972. Before leaving Illinois he co-authored with Professor
H. G. Drickamer the monograph Electronic Transitions and the High
Pressure Chemistry and Physics of Solids (1972). He began his pro-
fessional career at Sandia Laboratories in Albuquerque, New Mexico
where he worked in the Polymer Science and Engineering Division
until joining the Stanford faculty in July 1976. His research interests
include the application of fluorescence methods to the study of
polymer blend compatibility, solid state relaxation phenomena, and
segmental diffusion in dilute solution at high pressure as well as
synthesis and characterization of polyvinylidene fluoride, a piezo-
electric polymer.

by materials science and chemical engineering de-
partments and by specialized polymer institutes or
interdisciplinary groups in "macromolecular
The polymer science research and teaching
program in the Department of Chemical Engi-
neering at Stanford consists of four faculty
members: C. W. Frank (fluorescence studies of
amorphous solid state blends and dilute polymer
solutions, piezoelectric behavior of polymers), G.
Fuller (dynamic light scattering of flowing poly-
mer solutions and colloidal suspensions), A. S.
Michaels (macromolecular transport through
ultrafiltration membranes, recombinant DNA bio-
engineering, gas permeation of semicrystalline
polymers) and C. R. Robertson (renal transport
phenomena, biomaterial compatibility, recombin-
ant DNA bioengineering). A series of four courses
in polymer science are offered or are currently in
preparation by three of these faculty members.
This series includes Ch.E. 170 (solid state
properties), Ch.E. 212 (thermodynamics and sta-
tistics), Ch.E. 217 (polymer synthesis) and Ch.E.
209 (hydrodynamics and scattering theory). The
first two have been taught by the author for the
past three years and will be considered in this
paper in some detail. The third course, given by
Professor Alan Michaels, has been presented be-
fore at the University of California-Berkeley and
will be offered for the first time at Stanford
during the 1979-80 academic year. The fourth
course will be taught by Dr. Gerry Fuller after he
joins the faculty in September 1980. The latter
two courses will be outlined briefly at the end of
the paper. This series should provide a sound
background in most of the important areas of
polymer science, with the exception of polymer
The selection of these courses is a result of
numerous compromises involving faculty interest
and the overall course structure. The philosophy
of the Stanford Ch.E. department is that a broad
background in chemical engineering fundamentals
is preferable to concentration in any given area.
An attempt has been made to balance this view
with the multifaceted nature of polymer science
by offering two of the graduate courses (Ch.E. 217
Copyright ChE Division, ASEE, 1979


and 209) as special topics on an alternate year
basis. In the future, Ch.E. 212 also may be given
in a similar manner. Thus, it will be possible to
put together a coherent polymer program while
at the same time leaving sufficient scheduling
flexibility for the remainder of the curriculum.
No separate polymer laboratory course is
offered at this time. However, several polymer
experiments (dilatometric measurement of the
glass transition, temperature, viscoelastic creep of
an amorphous polymer and measurement of
crystallization kinetics by differential scanning
calorimetry) are included in the two quarter
senior level chemical engineering laboratory.
Stanford is on ten week quarters with many
department courses, including Ch.E. 170 and
Ch.E. 212, being taught twice weekly for 75
minute periods. Since a single midterm is given
in each, the courses are divided into nineteen
lectures. Although a number of different texts
have been used in each course, the lectures are
organized closely around extensive class hand-
outs. Since the pace of both Ch.E. 170 and Ch.E.
212 is rather fast, there is always the danger that
the student could lose sight of the overall objec-
tives while immersed in the details of a particular
topic. Thus, much of the more tedious algebra or
matrix manipulation is written out in full and
supplied to the student before class. In addition,
copies of figures presented via viewgraphs are
provided as are detailed outlines of the lecture
topics. Students are encouraged to use space pro-
vided on the handouts for notes on additional
points of discussion or for analyses not written
out. Ideally, the handouts should allow more time
for thought on a particular topic without the
burden of note taking while at the same time re-
quiring enough effort to maintain attention. Al-
though the class notes are still evolving, student
response has been quite favorable.
Ch.E. 170, offered fall quarter, is a required
senior level undergraduate course which has been
taken also by most graduate students in the
terminal Master's program and a number of those
in the Ph.D. program who are working in one of
the polymer oriented research groups. The course
outline is given in Table 1 with the number of
lectures for a particular topic listed in parenthesis.
The first three lectures serve as an introduction
both to the structure of high polymers and to
selected topics of dilute solution behavior. The
remainder of the course emphasizes the solid state
with consideration of morphology, linear visco-

... it is estimated that... 30% of all ChE
graduates will work in some polymer related
activity even though they often enter the field
with no prior course work in polymers.

elasticity and rubber elasticity. Rheology is given
only brief mention since aspects of it are included
in the senior level fluid mechanics course. A much
deeper treatment of hydrodynamics will be in-
cluded in Ch.E. 209.
The required text for Ch.E. 170 is Mechanical
Properties of Solid Polymers, I.M. Ward, Wiley-
Interscience, 1971. Recommended texts in which
additional reading is assigned include:
* R. G. C. Arridge, Mechanics of Polymers, Clarendon
Press, 1975.
* J. J. Aklonis, W. J. Macknight and M. Shen, Introduc-
tion to Polymer Viscoelasticity, Wiley-Interscience,
* F. W. Billmeyer, Textbook of Polymer Science, Wiley-
Interscience, 1971.
* J. D. Ferry, Viscoelastic Properties of Polymers, Wiley,
* H. S. Kaufman and J. J. Falcetta, Introduction to
Polymer Science and Technology, Wiley-Interscience,
* F. Rodriguez, Principles of Polymer Systems, McGraw-
Hill, 1970.
* J. Schultz, Polymer Materials Science, Prentice-Hall,
* L. R. G. Treloar, The Physics of Rubber Elasticity,
Claredon Press, 1975.
Ch.E. 212, offered winter quarter, is the first
of two graduate courses which cover polymer be-
havior in solution. The course outline is given in
Table 2. It emphasizes the molecular and sta-
tistical approaches much more than the phenome-
nological and continuum treatments of Ch.E. 170.
Ideally, students should take Ch.E. 212 only after
an introductory polymer course, such as Ch.E.
170. However, this generally is not possible due to
competition from graduate level courses taken by
first year graduate students during fall quarter.
Thus, in order to ensure a basic familiarity with
polymers for all students, regardless of back-
ground, the first four lectures provided a rapid
overview of selected topics from Ch.E. 170. In
addition, all students are asked to read the paper-
back by S. L. Rosen, Fundamental Principles of
Polymeric Materials For Practicing Engineers,
Cahners Books, 1971, during the first two weeks of
class. This introductory text provides a broad
survey of polymer science and permits the course
to be placed in perspective.
The emphasis throughout the remainder of the

FALL 1979

course follows Professor P. J. Flory's application
of statistical mechanics to the thermodynamics
and configurational properties of high polymers.
Although most of our first year graduate students
have had undergraduate courses in statistical me-
chanics and linear algebra, brief reviews of im-
portant concepts and methods are given at ap-
propriate points. The course has been offered pre-
viously with the order of topics as in Table 2 and
with the configurational statistics preceding the
thermodynamics. The former approach works
much better, perhaps because student familiarity
with classical thermodynamics allows a more
gradual transition into thinking about macromole-
cules. Extensive reference to the original and
current literature is made throughout the course.
There is no required text for Ch.E. 212. How-
ever, the two books by P. J. Flory, Principles of
Polymer Chemistry, Cornell University Press,
1953 and Statistical Mechanics of Chain Mole-
Course Outline
I. Polymer constitution and solution properties
A. Introduction (1)
1. Commercial significance
2. Repeat unit and structural classification
B. Molecular weight (1)
1. Averaging procedures
2. Determination of Mn by osmotic pressure
3. Determination of Mw by light scattering
4. Determination of M, by viscosity
C. Polymer solution thermodynamics (1)
1. Solubility parameter
2. Prediction of polymer blend compatibility
II. Morphology
A. Semicrystalline polymers (2)
1. Molecular requirements for crystallization
2. Single crystal formation
3. Spherulite formation
4. Molecular models for chain folding
5. Macroscopic crystallization kinetics
B. Amorphous polymers (2)
1. Phenomenological observations of the glass
2. Theoretical approaches to the glass
3. Structure-property relationships for transi-
tion temperatures
III. Rheology (1)
1. Introduction to non-Newtonian and time
dependent flow
2. Power law constitutive relation
3. Effect of temperature on zero shear
4. Effect of molecular weight on zero shear
IV. Linear viscoelasticity
A. Phenomenological treatment using mechanical
models (2)

cules, Wiley, 1969 are highly recommended. Addi-
tional texts in which reading assignments are
made include:
* H.-G. Elias, Macromolecules, Vol. 1, Structure and
Properties, Plenum, 1977.
H. Morawetz, Macromolecules in Solution, Wiley-Inter-
science 1975.
C. Tanford, Physical Chemistry of Macromolecules,
Wiley, 1961.
H. Yamakawa, Modern Theory of Polymer Solutions,
Harper and Row, 1971.
Ch.E. 217 is a review of the principal methods
of polymer synthesis with emphasis on molecular
polymerization mechanisms and reaction kinetics
and their roles in influencing polymer composi-
tion, structure and ultimate properties. Topics
include: condensation, radical and ion initiated
chain polymerizations; heterogeneous and stereo-
regulated polymerizations; copolymerization;
bulk, solution emulsion and suspension polymeri-
zation; and application of the principles of syn-
--ChE 170
1. Stress relaxation and the Maxwell model
2. Creep and the Voigt Model
B. Dynamic response (2)
1. Frequency response of the standard linear
2. Complex variable notation for modulus and
3. Time-temperature equivalence
C. Extension to multiple relaxation and retarda-
tion times (1)
1. Maxwell-Reichert relaxation time model
2. Voigt-Kelvin retardation time model
D. Boltzmann superposition principle (1)
V. Rubber elasticity
A. Generalized definition of strain (2)
1. Displacement coordinate scheme
2. Principle axes and the strain ellipsoid
3. Components of infinitesimal and finite
4. Strain invariants
B. Stress-strain relationships (1)
1. Stress tensor
2. Material parameters-Young's modulus,
shear modulus, Poisson's ratio, Lame's
constant, bulk modulus
3. Strain energy functions
C. Statistics of molecular networks (1)
1. Model polymer chains
2. Gaussian distribution function
3. Entropy of deformation
D. Thermodynamic analysis of network
elasticity (1)
1. Force-extension relations for a Gaussian
2. Stress-temperature relations
3. Internal energy and volume changes


Course Outline-ChE 212

I. Introduction to polymeric materials
A. Molecular architecture (1)
1. Repeat unit and structural classification
2. Tacticity
3. Experimental determination of average
molecular weights
B. Morphology (1)
1. Single crystal formation
2. Spherulite formation
3. Structure property relationships for the
glass transition temperature
C. Mechanical properties (2)
1. Stress relaxation and the Maxwell model
2. Creep and the Voigt model
3. Dynamic mechanical testing
4. Time-temperature superposition
II. Thermodynamics of concentrated polymer solutions
A. Flory-Huggins lattice theory (1)
1. Introduction to statistical mechanics and
combinatorial probability
2. Configurational entropy
3. Enthalpy of mixing
4. Free energy of mixing
B. Phase equilibria (1)
1. Necessary and sufficient conditions for
phase stability
2. Binodal and spinodal curves
3. Critical conditions for phase separation
C. Applications of Flory-Huggins theory (1)
1. Regular solution theory and the solubility
2. Polymer/solvent compatibility
3. Polymer (1)/Polymer (2) compatibility
D. Corresponding states theory (1)
1. Configurational partition function
2. Equation of state
3. Derivation of equation of state parameters
E. Application of corresponding states theory to
mixtures (1)
1. Combining rules
2. Configurational partition function
3. Intermolecular energy
4. Chemical potential
III. Random coil statistics
A. The freely jointed model chain (1)
1. Bond vector representation for end-to-end
distance and radius of gyration
2. Gaussian distribution function
thetic polymer chemistry to the design of large
scale industrial polymer manufacturing processes.
Ch.E. 209 is a detailed treatment of macro-
molecular hydrodynamics in dilute and concen-
trated solutions along with analysis of various
scattering methods for monitoring flow proper-
ties. Topics include: statistical mechanics and
stochastic analysis (Gaussian statistics, excluded
volume) ; application of scaling laws to polymer
physics (excluded volume, concentrated polymer
systems, renormalization theory) ; radiation

FALL 1979

3. The equivalent chain
B. Excluded volume (1)
1. Mean field model
2. Probability of binary encounters
3. Probability of alteration of chain
C. Experimental characterization of random coil
dimensions in dilute solution (1)
1. Intrinsic viscosity
2. Light scattering
3. Determination of theta point from osmotic
pressure measurements
IV. Configurational statistics of real chains
A. Rotational isomerism in small molecules (1)
1. Independent rotational potentials
2. Interdependent rotational potentials
3. Rotational isomeric state approximation
B. Statistical weight matrix (1)
1. Conformational energy maps
2. First order interactions
3. Second order interactions
4. Statistical weight matrix for symmetric
C. Configurational partition function (1)
1. Fundamental concepts of statistical
2. Generation of configurational partition
functions by matrix multiplication
3. Evaluation of rotational state
D. Evaluation of configuration dependent
properties for a given chain configuration (1)
1. Bond vector coordinate system
2. Transformation matrix
3. Generator matrix for chain displacement
E. Evaluation of configuration dependent proper-
ties averaged overall chain configurations (1)
1. Statistical mechanical averaging of the
chain displacement vector
2. Generator matrix for the squared end-to-
end distance
V. Experimental methods of polymer physics (2)
A. Dynamic light scattering
B. Neutron scattering
C. Fourier transform infrared spectroscopy
D. 13C nuclear magnetic resonance
E. Fluorescence spectroscopy
scattering (light scattering, neutron scattering,
total intensity measurements, quasi-elastic scatter-
ing, flow birefringence, electric birefringence) ;
and transport properties (Yamakawa-Kirkwood
theories, nonlinear modeling of macromolecules
in flowing solution, viscoelasticity, introduction
to network models).


1. R. L. Rawls, Chemical and Engineering News, May
23, 1977, p. 19.



University of Delaware
Newark, DE 19711

of Delaware by J. Wei and an early descrip-
tion is available in Chemical Engineering Educa-
tion (Fall 1973). Jim was motivated to develop
the course by his experiences with Mobil which
he claims he wasn't able to put in the proper per-
spective until he attended the Advanced Manage-
ment Program at Harvard Business School and
accepted an assignment in Mobil's Corporate
Planning Department. In Jim's own words: "Had
I understood the "Big Picture" more thoroughly
in my early years, I would have done many
things differently; would have been much more
effective and would have been much more posi-
tive about the value of my work."
Jim Wei taught the course largely by the case
study method in 1972 and 1973. He asked me to
sit in and comment on the course in 1974 and I
was impressed enough with the approach to join
him teaching the material in 1975. This was the
year one of our better graduate students, Mike
Swartzlander decided to take the course and he
became interested enough to join us first as a
teaching and research associate in 1975 and as a
junior author in 1976. In August of 1977 we pre-
sented our material and methods of teaching at
the ASEE Summer School for Chemical Engi-
neering Faculty in Snowmass, Colorado. An en-
thusiastic group of some seventy faculty and in-
dustrial colleagues from some sixty different
schools and a dozen industrial firms attended our

*This paper is based on a presentation of a new course
made at the 1977 Summer School for Chemical Engineer-
ing Faculty by J. Wei, T. W. F. Russell and M. W. Swartz-
lander of the University of Delaware. H. J. Taufen a vice
president of Hercules and T. Baron, president of Shell
Development, helped the Delaware group describe the
course by presenting two very good case studies. This
article tells how the course was developed, what topics
are covered and how the course is taught.

T. W. F. Russell is a Professor of ChE and Director of the Institute
of Energy Conversion at the University of Delaware. He obtained his
bachelors and masters degree from the University of Alberta and after
working as a design engineer with Union Carbide, Canada for three
years, he obtained his Ph.D. from the University of Delaware. Professor
Russell is a coauthor of "Introduction to Chemical Engineering Analy-
sis" (J. Wiley 1972) and "Structure of the Chemical Process Industries-
Function and Economics." (1978)

Course Outline

Reader's Guide
Basic Economics
Basic Accounting
Input-Output Analysis
Products and Companies of the CPI
Specific Chemical Products
Specific Companies
General Characteristics of the CPI
International Aspects of the CPI
Future Prospects: Threats and Opportunities

sessions. I taught the course alone in 1978 and
1979 since Jim decided to become Head of Chemi-
cal Engineering at M.I.T. and Mike started to
work full time with Union Carbide in 1976. As a
result of the Summer School some twenty schools
in Canada and the United States used our text in
manuscript form in 1977 and 1978.
Our course development activities were put in
text form and the book is now available "The
Structure of the Chemical Processing Industries:
Function and Economics" McGraw-Hill, 1978. An
outline of the course based on the text is shown
in Table 1.
A key feature which makes the text unique
is the initial chapter entitled "Readers Guide".
This chapter serves three functions:
(i) It provides a way for the reader to en-
rich and update material by using the current
literature and supplementary sources of informa-
(ii) It outlines how to use the book, current
literature and supplementary information for
0 Copyright ChE Division, ASEE. 1979


self-directed study.
(iii) It provides an instructor's and student's
guide for those teaching from the text.
The course is designed to achieve the follow-
ing goals:
1. To expand the mental horizon of the chemical pro-
fessional beyond science and engineering and to show
the economic purposes of the chemical process in-
dustries (CPI) and how the CPI benefit society.
2. To help chemical professionals understand how their
work relates to the goals of their company and
3. To develop in the chemical professional an appreciation
for the potential impact of new developments in
technology, marketing, finance, politics, or inter-
national affairs as threats and opportunities.
4. To teach the chemical professional how to influence
an organization to move in new directions by making
fact-filled, comprehensive, and convincing economic
The preparation and planning of this course
differ from those of most engineering or science
courses. Much of the material discussed needs to
be current (no one today knows which problems
will be the crucial issues tomorrow). Our course
contains the relatively timeless fundamental eco-
nomic and accounting principles, examples of eco-
nomic analysis, and a detailed discussion of the
structure of the CPI in the United States. Ex-
perience has shown that one can develop a lively,
interesting, up-to-date, and effective course by ex-
panding upon and adding to the textual material
in a number of ways.
In almost every class, we discuss or at least
mention some item from one of the periodicals.
We have subscriptions to most and have developed
the habit of clipping articles for discussion. Some
are brought to the attention of the class im-
mediately, and some are filed until a particular
topic is covered.

Case studies are a particularly effective way
of meeting the objectives of the course and de-
veloping the student's skills. Case studies also
serve as examples, good and bad, of how a problem
should be handled. Critical analysis of case
studies helps develop the student's ability to detect
weaknesses, flaws in logic, and inappropriate in-
terpretation of facts and events.
A comprehensive listing of published case
studies is available in the "Intercollegiate Bibli-
ography [of] 1974, Selected Cases in Administra-
tion." We have used the following case studies
with some success.

Case studies are a particularly
effective way of meeting the objectives
of the course and developing the students skills.
Case studies also serve as examples, good and bad,
of how a problem should be handled.

* Industrial Chemicals, Inc. This Harvard Business School
case examines research and development in a company
by studying the personalities of the key people in-
volved, how they interact with each other, and their
career progression. This case study is well done and
relatively timeless.
* Mobil Chemical Company. This Harvard Business
School case is somewhat outdated, but it shows the
student what sort of information management and
technical personnel need in order to embark on a new
* Reichhold Chemicals, Inc. This University of Alabama
case study deals with waste-water treatment problems
of Reichhold's Tuscaloosa plant. Emphasis in the case
study is on methods of treating waste water with a
passing reference to some process improvements.
There is no central index of case studies pre-
pared by industrial concerns, many of which are
prepared for internal use and not made public.
Frequently, however, material can be presented in
lectures by guest speakers from industry, who can
discuss the case effectively.
Many topics suggest themselves as one teaches
a course and although it is not a trivial matter to
do so, an instructor can prepare short case studies
with the help of term papers and class assign-
ments. If a research effort accompanies the class-
work, one can prepare case studies of a sufficiently
high quality to meet the thesis requirements of
the master's degree.


T HIS ESSENTIAL AND rewarding part of the
course allows students to hear and question
people who are actually involved with the issues
dealt with in the text, the supplementary sources,
or the case studies. About 10 to 15 percent of the
lecture time should be devoted to outside speakers.
Industrial concerns and government agencies are
most cooperative, especially if you talk to people
at the highest level. The speaker and topic must
be chosen to fit into the course structure. The in-
structor should request background material
from the speaker in the form of handouts or
published articles and make sure that the
students are well read before the presentation.
Time for questions and answers should be pro-

FALL 1979

Typical product Assignments

Precipitated calcium
Titanium dioxide
Carbon black
Yellow iron oxide
Vitamin C

Caustic soda
Sulfuric acid
Polyester fiber

Carbon dioxide


AFTER 2 YEARS OF experimentation, we have
found that the following procedures greatly
enliven class discussion, allow the more reticent
student to participate more easily, and provide an
effective means of motivating the students to be-
come familiar with the basic references and to
gain practice in researching the economic litera-
ture of the chemical industry.

Product Specialist Assignment

T HE PLAN IS TO HAVE each student be the course
specialist on at least one chemical industry
product and to prepare a comprehensive term
paper. The products must be carefully selected by
the instructor, who should have a plan for class
discussion utilizing the detailed information
collected by the student.

Typical product assignments used at the Uni-
versity of Delaware are shown in Table 2.

Company Specialist Assignment

SHIS ASSIGNMENT REQUIRED each student to be-
come a class expert on a CPI company and to
prepare a comprehensive term paper. The student
was expected to provide both statistical and quali-
tative information on the company.

Development of Supplemental Materials

E ACH STUDENT IS GIVEN a package of material
at the start of the course which contains the
* Facts and Figures issue of Chemical and Engineering
* Two company reports and 10-K forms.
* Case studies. Plan on three.
* Reprints from current periodicals.
* Statistical Abstract of the United States
* Reprint of Barbara Lawrence. Preliminary Project
evaluation: Any Technologist Can Do It, CHEMTECH,
November 1975.

The preparation and planning
of this course differ from those of most
engineering or science courses. Much of the
material discussed needs to be current
(no one today knows which problems
will be the crucial issues tomorrow.)

Planning schedule


Collect articles which will expand upon
and complement text; decide on
reprints students should have
Order text


Begin to rough out in-class course

Not knowing class registration can
be troublesome; class enroll-
ment should have an upper limit
to ensure adequate class dis-
cussions and interaction

Order reprints, Facts and Figures issue of
Chemical and Engineering News, case
studies, company reports, etc.
Decide upon companies and products to
assign to student specialists; make a
list in order of importance
Invite outside speakers

Prepare package of supplemental material

In-class schedule should now be
fairly well decided

The last bit of information needed
to firm up the class schedule



TO PREPARE FOR A course we try to follow the
planning schedule presented in Table 3. In
the three-credit (42-h) course all 10 chapters
can be adequately covered with time for guest
speakers, case studies, and discussion of current
problems of interest to the CPI. A flexible inclass
schedule is shown in Table 4.
Class schedule

1 1-2 5 1-2 9 2-4
2 5-7 6 11-2 10 2-4
3 1-3 7 1-2 Guest speakers 3-5
4 2-4 8 4-6 Case studies 3-5

The course has been well received by our
students at the graduate and senior level. For the
last four years we have limited enrollment to
thirty students and the class is always oversub-
scribed, in excess of forty-five students have tried
to register each year. A short form of the course
has also been given as part of the AIChE today
series and to date has been taught in Houston
twice, once in New York and once in Philadelphia.

books received

"An Introduction to Industrial Organic Chemistry," 2nd
edition, Peter Wiseman, Applied Science Publishers Ltd.,
London, 1979, 366 pages (paperback) $16.80.
The organic chemical industry is subject to a high
rate of technological change. This second edition text
attempts to update the presentation on how organic
chemistry is applied in society.
"How to Succeed in Organic Chemistry," J. E. Gordon.
John Wiley & Sons, New York, 1979, 594 pages (paper-
back) $8.95.
This is a Wiley Self-Teaching Guide designed as a
supplement to an organic chemistry text or as a guide
for self-instructional study or review. This practical
book in 21 units presents a streamlined step-by-step
method for learning organic chemistry.
"What Every Engineer Should Know About Product
Liability," J. F. Thorpe and W. H. Middendorf. Marcel
Dekker, Inc., New York, 1979, 104 pages, $9.75.
The growth of technology has led to an increasing
interaction between engineering and society's expecta-
tion of the new products. This book shows how the
process of designing safer products is a natural ex-
tension of traditional engineering aptitudes and pro-
"Industrial Hazard and Safety Handbook," R. W. King
and John Magid. Newnes-Butterworth, 10 Tower Office
Park, Woburn, MA 01801, 1979. 793 pages, $67.50.

Use CEES reasonable rates to advertise. Minimum rate
% page $50; each additional column inch $20.


Assistant or Associate Professor Position
This is a tenure-track position and will be approxi-
mately half-time teaching and half-time research. We
will help the successful candidate establish research by
providing initiation funds, co-investigation opportunities
with senior faculty, and proposal preparation-processing
assistance from our Office of Engineering Research.
Candidates must possess an earned Ph.D. degree from an
accredited Department or School of Chemical Engineer-
ing. We welcome applications from candidates with com-
petencies and interests in any field of chemical engineer-
ing, but especially seek those with strengths in material
sciences. The position is available as early as January,
1980. Salary and rank are commensurate with qualifica-
tions and experience. If you are interested in joining an
established School of Chemical Engineering (in the
pleasant Southwest) that offers exciting professional
growth opportunities, please send your resume and list
of three references to: Professor Billy L. Crynes, Head,
School of Chemical Engineering, 423 Engineering North,
Oklahoma State University, Stillwater, Oklahoma 74074.
405-624-5280. (Calls for additional information invited).
OSU is an equal opportunity/affirmative action employer.

This book is an attempt to identify and warn of the
main hazards found in industry and to provide ap-
propriate references for further study. It was written
for safety specialists, representatives and students, for
managers and engineers in industry as well as insurers
and lawyers whose work is concerned with industrial
accidents and their consequences.
"Introduction to Macromolecular Chemistry," 2nd ed.,
Hans Batzer and Friedrich Lohse. John Wiley & Sons,
New York, 1979, 297 pages, $34.50.
The chemistry of macromolecular compounds is pre-
sented under the topics of synthesis and isolation;
characterization and identification; and physical
properties and technical processing of macromolecular
substances. It will be a valuable aid to students who
wish to become acquainted with the problems in
this field.
"Structure of Crystalline Polymers," Hiroyuk Tadokoro.
John Wiley & Sons, New York, 1979. 465 pages, $35.00.
Understanding the properties that distinguish one
polymer from another requires knowledge of structure
at the molecular level. X-ray crystallography and vi-
brational spectroscopy are the richest sources of struc-
tural data on macromolecular substances. This book
gives a basis for understanding the current literature
on polymer structure as it is revealed by x-ray analysis,
infrared and Raman spectroscopy, and energy calcula-
tion. It is recommended both for students and research
workers in this area.

FALL 1979



University of Minnesota
Minneapolis, Minnesota 55455

W HAT IS DESCRIBED IN this paper is the first
quarter of a three quarter graduate course
on the molecular theory of thermodynamics and
transport phenomena. The course material of the
first quarter is designed for the general chemical
engineering student. In the subsequent two
quarters there is increasing specialization, suited
primarily for students with at least some research
interest in molecular theoretical subjects. A book
on the equilibrium part of the course sequence is
in preparation and will perhaps be published
next year.
In the course we try to focus on those subjects
of traditional importance to chemical engineers,
such as bulk fluid phase behavior and transport
properties, as well as those subjects rapidly being
incorporated into the mainstream of chemical
engineering, such as colloid and interfacial pheno-
mena, fluid microstructures (e.g., thin films, liquid
crystals, and micellar solutions), and the auto-
correlation function theory of transport and re-
laxation processes.
The structure of the theory is developed at
two levels: first concepts are introduced heuristic-
ally and their utility established by examples,
and then the rigorous basis of the theory is laid.
For example, the barometric formula, well-known
to chemical engineering students, is used to invent

Our course differs from
those usually given to first year graduate
students in that the modern theory of
inhomogeneous fluids and interfacial
phenomena occurs naturally along
side the theory of equilibrium phases.

( Copyright ChE Division, ASEE, 1979

H. Ted Davis received his B.S. from Furman Univ. (1959) and his
Ph.D. from the Univ. of Chicago (1962). He joined the ChE depart-
ment at the University of Minnesota in 1963 and is the author of
over 100 publications in scientific and engineering journals and edited
books. His research interests include statistical mechanics of equi-
librium and transport processes, experimental and theoretical investi-
gation of the physico-chemical processes in flow in porous media as
related to petroleum recovery, interfacial and colloid science, mathe-
matical modelling of transport, reaction and mechanical properties of
disordered media, liquid electronics, and heat and water movement
in food systems.

the partition function which is then used to intro-
duce the molecular origins of fluid behavior long
before the full trappings of ensemble theory are
unveiled in the course.
Our course differs from those usually given to
first year graduate students in that the modern
theory of inhomogeneous fluids and interfacial
phenomena occurs naturally along side the theory
of equilibrium phases.
The following sections, which appeal more to
the heuristic than to the rigorous elements of the
course, are chosen to try to exemplify the spirit
and substance of the course.

T HE KINETIC BEHAVIOR OF a dilute gas derives
directly from the fact that molecules have non-
zero velocities. Effusion or leakage through a small
hole in a containing vessel and pressure exerted
on a confining wall of a vessel are probably the
most familiar manifestations of the existence of


molecular velocity. In 1845, Waterston [1] had
correctly recognized the connection between
molecular velocity and, Dalton's law of partial
pressures, Avogadro's law of equal molecular
density of gases at equal pressure and tempera-
ture, and Graham's law of effusion. However, con-
servatism of the Royal Society prevented publica-
tion of Waterston's work, so that it remained for
Maxwell [2] (1860) to rediscover these things
along with his Gaussian distribution of velocities,
according to which

4(v) = ( nT3/2 exp[- 2] ,


where (v)d"v represents the probability that a
gas molecule has a velocity between v and v +
dv. The absolute temperature T of the gas and
the mass m of a molecule of the gas characterize
the dispersion of molecular velocities about a
mean value of zero. k is Boltzmann's constant
and equals the gas constant divided by Avogadro's
number. Maxwell's velocity distribution has been
verified experimentally and is predicted from en-
semble theory as well as the kinetic theory of
The pressure P exerted by a dilute gas cal-
culated from the momentum exchange between a
wall and particles rebounding from the wall is

2 1
3 n V
P = ]r < omv ,


where <- -mv2> is the average kinetic energy

and n the number density of gas molecules. The
empirical ideal gas law is
P = nkT (2.3)
The combination of Eq. (2.2), with the average
< 1 mv2> predicted from a Gaussian distribu-
tion, and Eq. (2.3) enabled Maxwell to identify
the mean square velocity dispersion as kT/2m, the
value used in Eq. (2.1).
The Maxwell velocity distribution predicts an.
average molecular speed of = V8kT/irm,
a result demonstrating the connection between
the speed of sound, c = V(dP/mdn), = VkT/m,
and the movement of molecules in a dilute gas.
The average flux of dilute gas molecules.
against a wall is
1 1 /8kT
= n 4 .n m (2.4)
4 4 m ,

This result is the origin of Graham's law, accord-
ing to which the rates of escape through a pin-
hole of different gases at the same temperature
and pressure vary inversely as the square roots
of the molecular weights or mass densities
( mn). The ratio of times for equal volumes to
escape through the same size pinhole of two
different gases at the same temperature and pres-
sure equals the ratio of the molecular weights or
of the mass densities of the molecules-of the two
gases. This is the basis of the effusiometer de-
vised by Bunsen [3] for measuring relative densi-
ties or molecular weights of dilute gases.
If two components are in a dilute gas at densi-
ties n, and n%, occupy the same container, and
escape from the same pinhole, then the gas densi-
ties n,' and n2' of the escaping stream obeys the

V m2


Thus, the molecular component of lower molecu-
lar weight is enriched upon effusion. This effect
is important for isotope separation processes, the
most important example of which was the sepa-
ration of U235 from U238 during World War II by

The structure of the theory is developed
at two levels: first, concepts are introduced
heuristically and their utility established by
examples, and then the rigorous basis
of the theory is laid.

staged gaseous effusion of the hexafluorides of
Molecules of a dilute gas collide with one an-
other, even when obeying ideal gas equations of
state. Collision rates determine the rates of chemi-
cal reactions in dilute gases. If the diameter of a
molecules is d, then the frequency v of inter-
molecular collisions and the mean free path X
(average distance travelled between collisions)
are given by

v = V2rd2 n and
X = /v = V2d2n

The probability that a particle will travel a
distance x (or time t) without collision is
q = e-x/ (or e -.t) (2.7)
The average particle separation I n-1/3, mean
free path, collision frequency, and width X of a
vessel for which the probability is 0.95 that a

FALL 1979


nl,' nl,
n2 n2

Dilute nitrogen at 300K. The molecular diameter d
is assumed to be 2 x 10-8 cm.


3.46 x 10-6
3.46 x 10-7

2.34 x 10-2
2.34 x 10-6

2.03 x 106
2.03 x 109

1.20 x 10-3
1.20 x 10-6

tide. Thus, the probability that particle 1 of the
gas is in d r with velocity in the range v, to vi +
dv,, particle 2 is in dar, with velocity in the range
v2 to v2 + dv,, etc., is

PN (r, .. ,VN) d3Vid rl ... d vNd3rl

=---d3vd3r, ... d3vNd3r ,


particle can cross without collision are illustrated
in Table 1 for dilute nitrogen.
Although the mean free path is large com-
pared to the average separation of particles in a
dilute gas, the molecules of the gas collide fre-
quently with one another by the time they traverse
a system of macroscopic size. Thus, the concept
of particle equilibrium (and therefore tempera-
ture) makes sense even though the ideal gas law
holds for pressure and average energy.


If an isotropic fluid is subject to a conservative
external force, whose potential energy is u(r),
then the equation of hydrostatics is

VP = -nVu.
In an isothermal ideal gas, P= nkT, so tha
(3.1) can be integrated to yield the baron
formula P(r) = P(ro) exp (-[u(r)-u(r,)]
Or, eliminating pressure in favor of densit

n(r) = n(ro)e

t Eq.
y, we


The density n(r) can be interpreted statistically:
n(r)dar is the probable number of particles in
the volume d3r, so that if p(r) dr is the proba-
bility that a particle is located in the volume d3r
fixed on r, then p(r) = n(r)/N, N being the total
number of particles in the system. According to
Eq. (3.2), p(r) is proportional to the "Boltzmann
factor", exp -u (r) /kT.
Combining the results of the preceding para-
graph with Maxwell's law of velocity distribution,
we conclude that the probability that a particle
is in a volume element centered on r and having
velocity between v and v + dv is proportional to

e-'/kT d3v d3r (3.3)

where = -- mv2 + u (r) is the energy of the par-

where E =



[-- mvi2 + u(r,)] is the

total energy of the particles of the medium and
Q is the normalization constant for PN, i.e.,

;Q = \ ... e-E/kT d3v ...... dvNdrl... d3rN

m N
= ( rkT)N/2 e-u /kT d r, d3rN
"21rkT ...


-( )3N/2Z.

Q is called the partition function and Z is called
the configuration partition function. In Eq. (3.5),
uNE s u(ri).

The formula for PN given above is rigorously
established by the equation of hydrostatics for
ideal gases. The heuristic step allowing us to
treat real fluids is to assume that PN is of the
same form for interacting particles, i.e., that the
external force on a particle is that exerted on it
by the other molecules in the fluid. Thus, for pair,

N 1 N
centralforces u" = i u(ri) = u(rij).
i= 2 i,j

With this generalization, the thermodynamic
energy of the system is

d 3.V.. d3rN
U= = e-E/kT E dv dr

and the pressure is
and the pressure is

P = /A,



where Fw is the force between a flat wall of area
A and the particles of the fluid.
Comparing the statistical mechanical expres-
sions for U and P with the thermodynamic expres-



sion dU = TdS-PdV, we can show S = -k
+ C(N), where C(N) is a function whose N de-
pendence can be determined from the extensivity
of entropy. This formula for entropy brings out
the relationship between entropy and disorder of
a system-the more localized a system is in ve-
locity and coordinate space the smaller is
-k. By combining the entropy and
energy relation, we obtain the basic starting
point of statistical thermodynamics, namely,
F = -kT In Q, (3.8)
where F is the Helmoholtz free energy and
Q = Q/N!h3N for a pure system or

Q = Q/ r (N,!h3N,) for a system of v com-
ponents. From Eq. (3.8), all the thermodynamic
functions of interest can be generated as ap-
propriate derivatives of the partition function
(S = -DF/DT, P = -aF/aV, etc.). The quantity
h, Planck's constant, enters the classical theory
only as an undetermined constant but is identi-
fied in later lectures on quantum ensemble theory.
With the connection provided by Eq. (3.8),
prediction of the thermodynamic properties of
classical fluids involves evaluation of the integrals
of the configuration partition function Z. If the
molecules have internal energies (rotational, vi-
brational, electronic) that contribute, this will
only affect the temperature dependent multiplier
of Z in Eq. (3.5) but not Z to a good approxima-
tion. In a later section of the course quantum
mechanical ensemble theory allows incorporation
of the internal energies. The partition function in
the quantum mechanical limit is similar to the
classical formula of Eq. (3.5) except that the
integration over velocity and configuration
states are replaced by summation over energy
levels. In the usual approximation for classical
fluids, the partition function is expressed in the
form Q = [q (T)]N Z/N!, where qi (T) arises from
kinetic, rotational, vibrational, and electronic
energies of a single molecule and contributes only
to the ideal gas part of the thermodynamic func-
tions. The nonideal part is determined by Z.

ALMOST A CENTURY AGO Van der Waals [5] de-
rived an equation of state that has provided
ever since our simplest model for understanding
the relation of phase behavior and molecular
forces. Moreover, empirical extensions of Van der

Waals' equation, known variously as the Redlich-
Kwong [6], Soave [7], Peng-Robinson [8], etc.
equations, have provided in many cases quantita-
tive descriptions of phase behavior.
In Van der Waals' model, one divides the
pair potential into the sum of two parts, a short
ranged repulsive part uR(rij) and a long ranged
attractive part uA(rij). Then, supposing that the
repulsive forces restrict the configurations allowed
to the particle centers, one assumes that the total
attractive energy, u N = ur),isnever

far from its average value in the integrand of Z.
Thus, the approximation

Z -- e

-uN /kT
e dar,... darN (4.1)

is introduced. Since pair potentials are assumed,

= N(N-1) ,
N(N-1) /2 being the number of interacting pairs
and uA(r12) the potential of a typical pair.
Let p(r,,r) d3rrd3r2 denote the probability of
a pair of molecules being in a configuration such
that one is in d3r, and the other is in d3r2. If F
and r2 are far apart, then p (r,r2) =p(r,) p (r), i.e.,
the particles are statistically independent. Since
the molecules cannot overlap, p(r,,r2) must go to
zero as I r7-r2 | becomes small. Thus, p(r,,r2) =
g(r,,r,) p(r,) p(r2), where g(r1,rB) is the pair
correlation function which represents the devia-
tion of local molecular structure from random
packing, g has a first peak representing the
nearest neighbor shell, a second peak represent-
ing next nearest neighbors, etc. In an isotropic
fluid p(r) = 1/V and g(rj,r,) = g(|r,-r2 ) so that
= N(N-1) S p(r,r2) uA(Ir-r1) dsardar2
1 N(N-1)
1 N2 (N1) S g(|r,-rj) uA(jrl-r21) d3rxd3r2 (4.2)
2 V2
Introducing the coordinate transformation rm,r2 -
r, r = r,-r2, we can integrate over one of the
volumes in Eq. (4.2) to obtain
N2 1
= V a;a-- a g (r) uA (r) dr .
Van der Waals assumed that the constant a is
independent of density and temperature. Since
g(r) depends on these quantities, this assump-
tion is an approximation, but not a bad one as has
been shown in model calculations.

FALL 1979

. we try to focus on those subjects of traditional importance
to chemical engineers as well as those subjects rapidly being incorporated
into the mainstream of chemical engineering, such as colloid and interfacial phenomena,
fluid microstructures and the autocorrelation function theory of transport and relaxation processes.

The integrals over positions in the repulsive
part of Eq. (4.1) can be approximated by assum-
ing that the repulsive forces are rigid sphere
forces so that their only role is to exclude from
the integration over V a volume Nb occupied by
the molecular centers of the particles. Thus, the
N-particle integral can be approximated as
(V-Nb)N, yielding with Eq. (4.3), the configura-
tion partition function
Z = exp (- ) (V-Nb)N, (4.4)

and therefore the free energy expression
F = NW(T) -NkTln(V-Nb) + N- (4.5)

where k+ (T) can be interpreted as the chemical
potential of the fluid in an ideal gas reference
state. The negative volume derivative of F yields
the famous equation of Van der Waals (VDW)
NkT N2a
P V-Nb V2 (4.6)
In terms of the molecular diameter, d, the ex-
cluded volume is b = d3, so that mean free
path, solid density, and the VDW parameter b can
be cross checked with one another. Rigorous de-
rivations of Van der Waals theory have appeared
in recent years. [9, 10]
From the conditions of the critical point,
(aP/aV) = Z2P/aV2, the relations a = 27k2T,2/
64P, and b = kT/8P, can be obtained. Thus, the
parameters of the VDW equation can be deter-
mined from the critical pressure and tempera-
ture. It also follows that the reduced pressure,
Pr = P/Pc obeys the equation
8Tr 3
3Vr-1 V,' 47)
where the reduced temperature and volume are
Tr = T/Tc and V, = V/V,. Equation (4.7) implies
that the reduced pressure of all fluids will be the
same if they are compared at the same reduced
temperature and equation of state. This law of
corresponding state, being the basis of the so-
called generalized charts, has been extremely
useful for engineering estimation of thermody-
namic properties.

The PVT diagram predicted by the VDW
equation is shown in Fig. 1. Level pressure lines
(Maxwell tie-lines) connecting coexisting liquid
and vapor volumes are given in the figure. The
liquid-vapor coexistence states are determined by
requiring that the pressure and the chemical po-
tential, (aF/aN)T,v, of the liquid and vapor
phases be equal. This is equivalent to finding the
pressure such that SVdP = 0, i.e., that the area
the pressure isotherm makes with the Maxwell
tie-line from below equals the area it makes from
The PVT state lying underneath the dashed
dome in Fig. 1 are in what is called the spinodal
region, where bulk fluid is unstable. These are
sometimes called unphysical. This is not strictly
true. Such states can be stabilized with density
gradients and in fact play an important role in
fluid microstructures such as interfaces, drops,
bubbles, etc. [11]
The VDW model generalizes easily to multi-
component fluids. The first term in the Helmholtz
free energy function, Eq. (4.5), is replaced by

Y Nazea (T) and the parameters b and a be-

come composition dependent, b = 2 xab.

and a = xaxpaap.
a,/ =1
x, and ba denote the mole fraction and excluded
volume of species a. ap is defined as in Eq.
(4.3) for the potential of interaction between
particles of species a and ft. The equation of state,
Eq. (4.6), unchanged in form. A useful em-
piricism, aap = Vaaa pp, allows one to predict
mixture properties using only the critical point
parameters of pure fluids.
Liquid-vapor, liquid-liquid, and liquid-liquid-
liquid phase equilibria are easily investigated with
the VDW equation. The qualitative features of the
phase behavior are determined primarily by the
relative magnitudes of the excluded volume and
energy parameters b, and aa,. Liquid-vapor phe-
nomena result largely from a balance between







FIGURE 1. Pressure-volume isotherms of a Van der
Waals fluid. P* Pb2/a, V* V/Nb, and T*
bkT/a. At the critical point T* = 0.296.

the effects of molecular repulsion (through b) and
the effects of molecular attraction (through a).
Liquid-liquid phenomena are also sensitive to the
relative magnitudes of the attractive energy pa-
rameters (aa/app).
In liquid-liquid equilibria one can often
simplify the thermodynamic theory by assuming
that the molecules are restricted to lattice sites.
Such a restriction removes pressure from the
problem, equates the Gibbs and Helmholtz free
energies, and yields such well-known models as
the regular solution model for low molecular
weight molecules and the Flory-Huggins model
for mixtures of low and high molecular weight
molecules. [12] Most of the patterns of phase be-
havior observed in nature can be explained with
the VDW theory and/or the lattice models. How-
ever, even with adjustable parameters in the
models hydrogen-bonded fluids, unlike the others,
are particularly resistant to quantitative predic-


AS ILLUSTRATED BY THE material outlined above,
one of the key concepts of the course structure
is the development of a molecular theoretical basis
that not only leads to an understanding of the
molecular origins of thermodynamic behavior but
also to semiempirical formulas which can be ex-
ploited quantitatively to predict thermodynamic
properties of real systems. In addition to the
topics outlined in this article, we also discuss the
molecular theory of fluid microstructures,* the
theory of intermolecular forces, quantum princi-

5 10 15 20 25 30 35

- T= 0.20
- -

FALL 1979

T*= 0.3.


0-1 M 's

' / 1 \ I


ples, and statistical mechanical ensemble theory.
Fluid structure is treated in an elementary fashion
in the first quarter course, the advanced theory
being reserved to the next quarter. We strive to
balance the modern and the traditional elements
of the subject, the rigorous and the useful re-
sults, and the mathematical and the physical
understanding of the phenomena of the field. O

*This will be the subject of a subsequent paper by Pro-
fessor Davis in CEE. Editor

1. Waterston's work was eventually published by Lord
Rayleigh, Phil. Trans. 183A, 1 (1892).
2. J. C. Maxwell, "Collected Works", p. 377.
3. See J. R. Partington, "An Advanced Treatise on
Physical Chemistry", p. 754, Longmans, London
4. H. De W. Smyth, "Atomic Energy for Military
Purposes", Princeton University Press (1948).
5. J. D. Van der Waals and Ph. Kohnstamm, "Lehr-
buch der Thermodynamik", Vol. 1, Mass and van
Suchtelen, Leipzig (1908).
6. 0. Redlich and J. N. S. Kwong, Chem. Rev. 44, 233
7. G. Soave, Chem. Eng. Sci. 27, 1197 (1972).
8. D. Y. Peng and D. B. Robinson, Ind. Eng. Chem. Fund.
15, 59 (1976).
9. M. Kac, G. E. Uhlenbeck, and P. C. Hemmer, J. Math.
Phys. 4, 229 (1963); 5, 60 (1964).
10. J. L. Lebowitz and 0. Penrose, J. Math. Phys. 7, 98
11. V. Bongiorno, L. E. Scriven, and H. T. Davis, J. Coll.
Int. Set 57, 462 (1976).
12. J. M. Prausnitz, "Molecular Thermodynamics of
Fluid-Phase Equilibria", Prentice-Hall, Englewood
Cliffs (1973).
13. V. Bongiorno and H. T. Davis, Phys. Rev. A12, 2213
14. B. S. Carey, L. E. Scriven, and H. T. Davis, AIChEJ.
24, 1076 (1978).
15. B. S. Carey, L. E. Scriven, and H. T. Davis, J. Chem.
Phys. 69, 5040 (1978).


Dr. Imre Zwiebel has been appointed Chair-
man of the Department of Chemical and Bio
Engineering at Arizona State University, effec-
tive July 1, 1979.

Dr. Richard G. Rice has been appointed Pro-
fessor and Head of the Chemical Engineering De-
partment at Montana State University, effective
August 1, 1979.

9lo Me4Wemiao

Mitchel Shen passed away on August 7, 1979
after an illness of several months. The students
and faculty at Berkeley will miss an inspirational
teacher and dedicated colleague, and the field of
polymer science has lost an outstanding young
researcher. Our sympathies are extended to his
wife Vivian and their family.
Mitchel Shen was born in Tienjin, China on
September 1, 1938 and came to the United States
for his college education and professional career.
He took a B.S. in Chemistry at St. Francis College
in 1959, an M.A. in Physical Chemistry at Prince-
ton University in 1962, and a Ph.D. at Princeton
(where he studied under A. V. Tobolsky) in 1963.
Following graduation, he joined the Chemical
Physics staff at the North American Rockwell
Science Center in Thousand Oaks, CA. He was
invited to join the Chemical Engineering Depart-
ment of the University of California, Berkeley in
1969, arriving as Associate Professor and advanc-
ing to Professor in 1973. While at Berkeley, he
held one of the prestigious Dreyfus Scholar
awards (1970) and was elected a Fellow of the
American Physical Society (1972).
Mitch taught undergraduate and graduate
courses on polymers, undergraduate courses on
thermodynamics, and graduate seminars on
various research topics. The research he con-
ducted was focused on rubber elasticity, rheology
of entangled liquids, membrane properties,
polymer alloys, and plasma-generated polymers.
Since 1976 he served as Vice Chairman of the
Chemical Engineering Department, and he had
been Acting Chairman for half of 1978. In his
capacity as the campus Assistant Dean of Foreign
Students in 1972-73, he fulfilled an advisory func-
tion officially which he exercised unofficially
through his academic career.
He was an assistant editor of Trans. Soc. Rheol.
(1970-75), co-editor of Rev. Macromol. Chem.
(1969- ), and editor-at-large for J. Macromol.
Sci., Part A (1971- ).
The volume of high-quality work he was able
to publish in such a short career was astonishing.
In addition to the book "Introduction to Polymer
Viscoelasticity" (Interscience, 1972), which he
coauthored with J. J. Aklonis and W. J. Mac-
Knight, he edited five other volumes and
published 107 research papers (with 24 more in

various stages at this time).
A perpetual fund, in his name, has been es-
tablished in the College of Chemistry at U. C.
Berkeley to assist foreign students with financial
difficulties, a project Mitch would have endorsed
strongly. Donations can be made to the Mitchel
Shen Memorial Fund and sent to the Chemical
Engineering Department, University of Cali-
fornia, Berkeley, CA 94720.

Robert E. Treybal was a great chemical engi-
neer dedicated to the chemical engineering pro-
fession. He devoted his life to chemical engineer-
ing education, chemical engineering research, and
the advancement of his profession. He was re-
spected and admired by his students and col-
Born in New York City on March 31, 1915,
he received his Bachelor's degree in ChE from
New York University, his Master's degree in ChE
from New York University and his doctorate
from Columbia University. His doctoral subject
was "Countercurrent Liquid-Liquid Extraction in
a Wetted-Wall Tower."
His distinguished teaching career began at
New York University. He rose through the ranks
and from time to time served as Chairman of the
ChE Department. After the College of Engineer-
ing was dissolved at NYU he became Chairman of
the ChE Department at the University of Rhode
He has worked for Atlantic Refining Co., the
Fire-Control Research Division of Frankford Ar-
senal in Princeton, and the M. W. Kellogg Co. and
has consulted with more than twenty five of the
leading Chemical and Process Industry Companies.
Dr. Treybal was keenly interested in mass
transfer and mass transfer operations. His book,
"Liquid Extraction" was the first comprehensive
book on that subject. Two editions were published
by McGraw-Hill Book Company, the first in 1951
and the second in 1963. It also was published in
Spanish, 1968, and Russian, 1966. In 1955 the first
edition of his text "Mass Transfer Operations"
was published by McGraw-Hill Book Company.
The second edition was published in 1968 and the
third edition was in the process of being prepared
for publication. "Mass Transfer Operations" has
Continued on page 217.



Continued from page 158
pect to avoid explosion. However, often another
consideration arises.
Temperature rise has an accelerative effect on
chemical reaction rate, which is without direct
parallel in nuclear reactions. In addition to chain
runaway, we may encounter thermal runaway of
any strongly exothermic reaction, limited only by
its respective adiabatic-maximum temperature
rise. Again the velocity at which the reaction
spreads determines whether smooth burning
("deflagration") or explosion ("detonation") re-
It is a question of whether the rate increases
because the temperature rises, or whether the
temperature rises because the rate increases. The
thermal system is controlled by removing heat,
while the chain reaction is controlled by removing
neutrons or (in the chemical case) free radicals.
In one case, we select a container lining for its
thermal conductivity; in the other, for its capacity
to absorb or adsorb the chain carriers.

Combustion, thermal pyrolysis, and organic
photochemistry all occur by multi-step reactions
involving the production and consumption of free
radicals. Most studied of the combustion reactions
as a prototype, and still imperfectly understood, is
the hydrogen-oxygen reaction-cited in almost
all physical chemistry texts, and explained ade-
quately and correctly in almost none.





FIGURE 3. Ignition limits for stoichiometric hydrogen-
oxygen mixture in a 15-cm spherical vessel (after Lewis
and Von Elbe)

Figure 3 is a classic diagram of the ignition
limits for H, with 02, developed largely through
the pioneering work of Bernard Lewis and
Guenther Von Elbe in the U.S. Bureau of Mines
during the 1940's. This diagram applies to stoi-
chiometric properties of hydrogen and oxygen,
which give a flame speed that usually exceeds
sonic velocity; thus the ignition limits are also
explosion limits. If we start at very low pressure,
at a given constant temperature (say, 450C),
and move upward in pressure, we
start in a zone of slow, measurable reaction
advance through the "first explosion limit" into a
region of high temperature and fast reaction.
If we start at a still higher pressure (say 1 atm.),
and then lower the pressure, we
start in a zone of slow, measurable reaction
drop through the "second explosion limit" into the
same high-temperature fast-reaction region we had
previously encountered.
Starting again at 1 atm. and increasing the pres-

It is a question of
whether the rate increases because
the temperature rises, or whether the temperature
rises because the rate increases.

sure, we
advance through the "third explosion limit" into a
new overlying region of high temperature and fast
First Explosion Limit. If we describe ac-
curately the chemical behavior which occurs in
the measurable region, we find that the kinetics
will predict the existence and nature of the ex-
plosion limits. For steady-state concentration of
radicals, the rates of all the propagation steps
must be equal, and also, below the first explosion
limit, collision of radicals with the vessel walls
must occur at an equivalent rate:


H, + 02 (at wall) -> 20H (1)

(Propagation) OH + H, -> HO + H (2)
H + 02-> OH + 0 (3)
0 + H2 OH + H (4)
(Net reaction) 3H2 + O = 2H20 + 2H
(2, 3, 4, 2)
(Termination) H (at wall) -> 1/2H2 (5)
At steady state, then, the net production of
radicals is
k, (H) (02) + k. (H) (0,)-
2[K/(P r2)] (H) = 0.
where the parenthesis denote gas-phase concen-

FALL 1979


trations for partial pressures, (if the coefficients
are adjusted appropriately), and K,/P is an effec-
tive diffusivity for H atoms based on an assumed
uniform concentration through the entire sphere
of radius r, at total pressure P. If we solve for
(H) from this relation, then take the total rate
equal to that of step 3 and substitute (H) into
that rate under constant-volume conditions, the
total steady-state reaction rate is given by:
d(O,) kka (H,) (O,)'P
dt 2[K,/r2] k (02) P
Because (02) is proportional to P, an increase in
P will bring on explosion by causing the denomi-
nator to approach zero, and the quotient to ap-
proach infinity.
Second Explosion Limit. In the explosive
region between the first and second limits, re-
action steps 2, 3, and 4 continue to predominate.
As the total pressure increases, a three-body re-
action competing with step 3 (with T the "third
body") grows in and forms the radical HOa and
its daughter product hydrogen peroxide. Above
the second limit the initiation and termination
steps have shifted from the vessel surface to the
near-homogeneous phase within. After a short in-
duction period, the reaction path in the steady-
state region above the second limit can be repre-
sented as follows:
(Initiation, augmented by Step 2 above)
H,02 + T --20H + T (11)
(Propagation: H202 as product)
H + 02 + T- HO, + T (12)
HO, + H,-H ,20, + H (13)
(Propagation: HO as product, by addition of
Step 2 above)
H + H,,0 HHO + OH (14)
H + HO, + T-* HO, + T (15)
We now identify a steady-state reaction con-
dition involving three independent relations.
First, the rate of oxygen consumption (ex-
cluding step 3) is
kl,2(H) (O,)P = ka,(HO,) (H,)
Second, the rate of HO production is
k,(OH) (H,) = k14(H) (H202)
Third, the net production of radicals is
k, (HO,) P + k. (H) (0,) k, (H) (HO) P = 0
Excluding step 3, we have
kH, k lk2P (H,0,) (02) 1
(HO,) =- [ (H,)
s K (H202) P%
This relation indicates that the H,20 concen-
tration is controlled by the termination reaction.

It will grow rapidly, ahead of the steps producing
H,02, until a limiting ratio to the reactants is
reached (which increases with total pressure),
and will then subside slowly as the reactants are
consumed. At high H20, a different termination
step may predominate (2HO0 -> H,O, + 0,), but
this will produce very little change in the kinetic
Finally, the total rate (including step 3) is
d( O) (k,,P + kj)k, (H20,) (02)P
dt kisK (H120) VP" k, (02)
-~ ikl2k1 12
Sk15 (H202) (02)P-

As P falls, the denominator tends toward zero,
giving a runaway rate. The second explosion limit
(unlike the first and the third) is seen to be rela-
tively independent of the vessel radius.
Third Explosion Limit. Considerable ingenuity
has been expended by researchers in the field in
formulating chain-branching reactions that would
explain the uppermost explosion limit. However,
the rates measured in this region do not give any
indication of impending chemical runaway, such
as is seen near limits 1 and 2. If we use the exist-
ing rate data or rate equations to predict where
normal runaway should occur in a spherical
vessel of 3-inch radius, by a calculation method
to be described below, the prediction places it
almost exactly at the experimental locus of the
third explosion limit. If instead we assume that
some type of chain branching occurred in this
region which accelerated the kinetics, we then
predict that a thermal runaway would occur at
a lower temperature or pressure than the experi-
mental value.
The mechanism given above has been simpli-
fied, and other radicals are also present; but it
appears that the proponents of a chemical runa-
way are neglecting the temperature difference
that develops between the reaction vessel contents
and the isothermal outside wall of the vessel. The
problem has not been laid to rest, but the case for
a thermal runaway here is very strong.

T HE PRESUMED THERMAL ignition limit for a
hydrogen-oxygen mixture is one of a myriad
of cases of "spontaneous" ignition. Runaway
occurs if the body of combustible mixture that is
heated is large enough so that the heat released



cannot all be lost by conduction and convection,
allowing the temperature (and reaction rate) to
rise to a point where the mixture can react to
completion. If this reacted portion is part of a
larger body of combustible mixture, the heat
liberated in this way is usually sufficient for com-
bustion to spread through the entire mixture.
Every time you strike a match, or a spark plug
fires in your automobile engine, the same principle
is involved.
We will now examine the criticality condition
for a spherical vessel which is kept isothermal at
the vessel surface. For a given mixture composi-
tion, the criticality can be expressed in terms of a
mass or volume for a given temperature, or a
surface temperature for a given mass or a given
dimension (thus the concept of ignition tempera-
ture, which may not be truly constant), or even as
a value for the rate coefficient at the vessel surface.
Let R be any radius, R. the entire radius of
the vessel, and r the relative radius R/R,. Let k,
be the "rate of conversion" (fractional conversion
per unit time), or first-order rate constant, for
unreacted mixture at the surface temperature.
The effect of temperature on rate is approximated
by a linear exponential term: k = k, exp (w0).
Here 0 is the fractional temperature rise, with
0 = 1 at the adiabatic maximum temperature
and 0 = 0 at the vessel surface; 0 increases from 0
at the surface to 0e at the center of the sphere.
The coefficient is related to effective activation
energy E by the relation w = EJ/RTB2, where J
is the adiabatic maximum temperature rise. Also,
kH is the effective thermal conductivity of the re-
action mixture, and A is the heat release per unit
volume of reaction mixture for complete conver-
Following Frank-Kamenetskii and Damkdhler,
we may now equate the integral for heat release
over the entire vessel to the heat-transfer rate

from the mixture to the vessel wall:

4 1 riw do
A* RR k e r2dr= 47r RkHJ -
3 0 dr
With the aid of the spherical heat-conduction
equation (much as in the derivation for effective-
ness factor of spherical catalyst particles) we can
establish the entire profile of 0 vs. r, and substi-
tute the result into our present equation.
The temperature gradient do/dr at the surface
increases steadily with 0e. We find that no steady
state exists if *0, is greater than 1.6, or exp
(0oe) greater than 5. The corresponding value of
the dimensionless group formed from the
variables in the equation is
1ks A R2/kH J O] = 2.1
An alternative group can be formed by introduc-
ing *0,:
[k, A R2 /kH J) = 3.3
All these values are upper limits for avoiding ig-
nition, and lower limits for achieving ignition.
It should be noted that the subgroup kH J/A is
the same as thermal diffusivity. Hence either of
the above groups can be viewed as the thermal
counterpart of the Thiele modulus for spherical
catalyst particles, which is used to calculate the
effect of mass diffusivity on the effectiveness
For a well-stirred spherical tank reactor, with
the entire contents at a single concentration and
a single temperature, similar criteria again apply;
the batch and continuous-flow cases are not very
different. For this reactor, K2/ku is replaced by
R to the first power divided by U, the overall heat-
transfer coefficient. Again the mathematical
analytic solution ceases to exist when the critical
value is reached, the latter group above now being
e or 2.718 instead of 3.3.

Flammability Limits In Air


Hydrogen .040 .258 .745 1500
Methane .050 .095 .150 1535
Ethane .033 .056 .063 .125 4040 1340
Acetone .030 .050 .058 .116 3820 1500
n-Butane .017 .031 .035 .103 4060 1270
n-Heptane .010 .019 .023 .084 3980 940
iso-Octane .008 .017 .019 .059 4020 1300

FALL 1979

It is quite revealing to develop the temperature
profile in the spherical reactor as an evolutionary
problem on a programmable hand calculator. A
value for the critical factor just 0.01% low results
in a temperature 1.5% below the critical value.
A value 0.01% too high leads to a very leisurely
runaway. This close to the critical, an enormous
time is required to creep past the critical region.
This brings to mind the ignition and eventual
devastating detonation of kilotons of ammonium
nitrate in Texas City, Texas, on April 16, 1947.
With a plug-flow reactor cooled from outside,
the sharp distinction between stability and in-
stability disappears, and is replaced by the con-
cept of parametric stability. A relatively steep
transition occurs from a low conversion to a very
high one within a narrow range of values of a
dimensionless factor equivalent to the two groups
given above. If any particular criterion of
temperature or conversion is applied, say a
temperature rise not more than x degrees, then a
specific value of the factor can be applied as the
The rate of fractional conversion, referred to
above, is a strong function of temperature and
comparatively a weaker function of mixture com-
position. For any given type of fuel, the tempera-
tures corresponding to the k, values which fit the
criticality criteria will always lie in a narrow
range which can be defined loosely as "ignition
temperature." Table 1 gives flammability limits
for several combustible compounds, along with ig-
nition temperatures measured for the stoichio-
metric mixtures. In every case, the lower and
upper flammability limits are the mixtures having
adiabatic maximum reaction temperatures which
just reach the reference ignition temperature. This
means that the flammability limits can be esti-
mated quite accurately from a single value of ig-
nition temperature. Also, one flammability limit
can be calculated if the other has been measured.
The lower flammability limit always shows an
excess of air over combustible which is greater
than the excess of combustible over air for the
upper flammability limit. The reason for the
asymmetry is that CO2, the main product from
lean-mixture combustion, has a high exothermic
heat of formation; and that formation of CO, the
main product from a rich mixture, is considerably
less exothermic.
Ignition temperatures have the philosophic
drawback that they seriously oversimplify the
kinetics, and thus tend to obscure the detailed be-

havior of combustion systems. Essentially the rate
of burning is considered zero below the ignition
temperature, and infinity above. Our concluding
section provides another instance of the advant-
ages of detailed modeling.

W E HAVE ALREADY SEEN that combustion
generally proceeds by a sequence of free-
radical reactions. For a premixed gas, the flame
sustains itself by projecting free radicals and
heat backward into the oncoming cold feed. A
very simple physical model of a flame results if we
assume that the Lewis number is unity; that is,
that the thermal diffusivity and mass diffusivity
are the same. With this assumption the fractional
extent of stoichiometric reaction matches the
fraction of adiabatic temperature rise; conversion
and temperature collapse into a single variable.
This method enables two partial differential
equations to coalesce into a single 2nd-order
ordinary differential equation, which involves (1)
dimensionless length (a form of Peclet number),
(2) dimensionless temperature 0 or conversion f,
(3) the activation energy factor g, and (4) a
dimensionless maximum-temperature rate pa-
rameter involving the first-order constant koo. The
dimensionless length and dimensionless rate
constant each contain both the effective diffusivity
D and the flame velocity Uo. Any one kinetics,
starting temperature, and diffusivity will con-
verge for only one particular value of the rate
constant; that is, the numerical integration does
not converge on 100% conversion unless the right

(3103 ,Second-order


O -First-order

I" 10
0 20 40 60
Rote-range porometer 4, or In(ka /ko)
FIGURE 4. Effect of rate-range parameter on flame-
velocity group



S20 40 60
Rote-ronge parameter *,or In(k0o/O)
FIGURE 5. Effect of rate-range parameter on flame-
thickness group

dimensionless rate constant is used which corre-
sponds to the right Uo.
We let X represent both the fraction con-
verted f and the dimensionless temperature rise
0; Y = 1-X; D, both the mass diffusivity and the
thermal diffusivity; z, distance within the flame,
measured from a reference plane (e.g., where X=
0.05) ; Az, the specific distance between X = 0.05
and X = 0.95; a, the order of reaction, assuming
stoichiometric proportions of the reactants; Z =
zUo/D; and C = Dkoo/Uo2.
The ordinary differential equation is
dX d2X
Uo d + D = koo e(1-x) (1-X)"

In dimensionless form,
dY d2Y
= C e-"TY"Y
dZ dZ2
The results of numerical integration of this
equation, for a = 1 and 2, and for different 9, are
given in two new plots. Figure 4 gives C as a
function of *, and can be used to determine the
flame velocity Uo from the rate coefficient koo, or
vice versa; Figure 5 gives AZ, also as a function
of w, and can be used with Uo to define the true
flame thickness. If one has an experimental flame
thickness and does not know D, the figures are used
in reverse order.
The AZ group has been called the Karlovitz
number, after a longtime staff member of the U.S.
Bureau of Mines. This group was observed em-
pirically to be always in the vicinity of 1, lending
credence to the approximations in our calculation.
The low-w, low-ko end of these curves once


FALL 1979


= .,

more represents the point where the solution
vanishes-i.e., the flammability limit, which may
involve a flame speed of only a few feet per second.
It is a matter of convenience to use koo, rather
than the starting value ko, as the rate constant;
Figure 4 would show many more orders of magni-
tude if C contained ko. The flame velocity in-
creases rapidly with increasing *, and sonic
velocity is likely to occur in the rate of 25 to 40
for *.
These few concepts with their accompanying
mathematical models go a long way toward elimi-
nating the mystery that seems to surround flames
and explosions. Let's work together to examine
how and where they might be given increased
attention in the undergraduate curriculum. O

David A. Frank-Kamenetskii, "Diffusion and Heat
Transfer in Chemical Kinetics," Plenum Press, New
York (1969).
Samuel Glasstone, editor, "The Effect of Nuclear
Weapons," U. S. Atomic Energy Commission (1962).
Bernard Lewis and Guenther Von Elbe, 'Combustion,
Flames, and Explosions of Gasses," 2nd ed., Academic
Press, New York (1961).
Antoni K. Oppenheim, "Gasdynamic Analysis of Gaseous
Detonation," Fourth Symposium on Combustion, 471-
480, Williams and Wilkins, Baltimore (1953).
Daniel R. Stull, "Fundamentals of Fire and Explosions,"
AIChE Monograph Series 73, no. 10 (1977).
A. Van Tiggelen, "Oxydations et Combustions," Editions
Technip, Paris (1968).
Lev A. Vulis, "Thermal Regimes of Combustion," McGraw-
Hill, New York (1961).
Y. B. Zeldovich and A. S. Kompaneets, "Theory of Detona-
tion," Academic Press, New York (1961).

stirred pots

And in the beginning there was "Control." And Control
created r. And Control saw that this was good, but that
7 was lonely, so Control created r a mate and Control saw
that this also was good. T's mate was called rs+l. But
before long rs+1 led r down the path of sustained oscilla-
tion. Control saw this and He was troubled. He granted
r and Ts+1 a transfer function to the land of instability
where through the wonders of "Control" Ts+1 begat Gain.
And before long Ts+1 also begat Routh. One day while
tending the process, Gain became quite angry with Routh
and rattled his array but good. And then Gain fled to
the caves of Frequency Response, emerging only at odd
multiples of T to wash his B.V.D.'s and read the weekly
edition of the "Control Gazette."
ChE Class, Auburn University

Individuals are alike.

Arent they?

Obviously they're not. Everyone knows that each
individual is different. But, it's not always as obvious as
it sounds. Corporations seem to be trending towards
putting people into methodical boxes everyone in
box A is supposed to be like everyone else.
At Rohm and Haas we don't think people work creatively
when they're put in boxes.
We believe that everyone is more creative in an informal
organization of people working with people on the basis
of their own unique talents.
That's why we look for Chemical Engineering grad-
uates who are, first of all, individuals. Engineers whose
attitudes and motivation are leading them to excel in
both life and a career. Their sex or color doesn't make
any difference. They can be black or white; male or
female; but, one thing stands out, they all seem to know
where they're going in life.

When we find people like that we try to move them along
as rapidly as possible. We can do this because we're a
growing organization that sets high standards for our
We are a major U.S. chemical company with over 2500
products that are used in industry, agriculture and health
services. Therefore, we do require that you have a solid
academic grounding in Chemical Engineering that will
contribute to our mutual success. Openings are in
Manufacturing, Research and Technical Sales.
If this sounds like your type of future, write to: Rohm and
Haas Company, Recruiting and Placement #32/ ,
Independence Mall West, Philadelphia, Pa. 19105.
An Equal Opportunity Employer.

Continued from page 174
Where Pj is defined by its action on any vector x,
Pjx = zj (3)
where Zj is the normalized eigenvector of L cor-
responding to the eigenvalue Xj; i.e.
Lzj = XjZj, I|lzj = 1
The equality (2) along with the property PjPk= 0
implies that
00 00
L" = Xji"Pj, expL = Y e'j Pj,
j=1 j=1
L-1 = Xj-1 Pj (4)
whenever it is meaningful to talk about the left-
handsides of the above qualities. The foregoing
expansions make it possible to solve steady state
equations of the form
Lx = y (5)
where ly is a known vector. The solution x using
the last equality in (4) is given by
x = xj-1 Py (6)
where Pjy is given by (3). Unsteady state initial
value problems of the form
dx Lx, x(0) = x (7)
are solved using the second equality in (4) to
0o Xjt
x = S e Pjxi (8)

differential operators are involved. By a differ-
ential operator is meant a differential expression,
for example of the Sturm-Liouville type such as
1 d d
1() d [p(x) d ] + q(x)
r (x) dx dx
along with homogeneous boundary conditions
representing the domain of the differential ex-
pression. The domain of definition (or equivalently
along with homogeneous boundary conditions
representing the domain of the differential ex-

pression. The domain of definition (or equivalent-
the homogeneous boundary conditions) is crucial
to whether or not the differential operator is self-
adjoint. Although a selfadjoint Sturm-Liouville
differential operator does not directly satisfy the
conditions for the spectral resolution (2), the
existence of a Green's function, i.e., a completely
continuous inverse operator, makes it possible to
apply formula (2).
To summarize, many linear problems in engi-
neering may be cast in the form of an operator
equation* (5) or (6) in which the operator has
the selfadjointness property (1) and consequently
the solution is obtained from either (7) or (8).
The essential point is that the scope for abstrac-
tion at each of the various stages of the above
development offers manipulative flexibility to fit
the given problem to the mold of selfadjoint
operators. Indeed it is not implied that all
problems would yield to such manipulation by be-
coming selfadjoint problems. Rather the implica-
tion is that there is a class of selfadjoint problems
not easily recognized without such abstract
formulations. We consider some examples below.
Let A and B be symmetric matrices (or com-
pletely continuous operators selfadjoint under the
same inner product). The operator L = AB is not
necessarily selfadjoint. If however A is positive-
definite, then a new inner product may be defined
on the space of vectors by

= (A-ix,y) (9)
where the inner product (,) is that w.r.t. which
A and B are selfadjoint. The definition (9) earns
its legitimacy by satisfying all the properties of
an inner product. Now it is readily shown that L
is selfadjoint w.r.t. the inner product (9).

= (Bx,y) (x,By) = 0
Thus L has real eigenvalues and its eigenvectors
from an orthonormal basis w.r.t. the inner
product (9). This concept has been applied to
problems in heat transfer [5], first order kinetics
and multicomponent rectification [6].
With differential operators the domain of de-
finition (homogeneous boundary conditions) is
important. Transport of energy or mass in com-
posite (or multiphase) media lead to selfadjoint

*Frequently, inhomogeneous differential equations
and inhomogeneous boundary conditions are involved but
they pose no special problems.

FALL 1979

problems in which the domains of the differential
operators include the boundary conditions and
interface conditions. Different inner products
must be used depending on the interface condi-
tions [7].
In other problems featuring transient energy
or mass transfer, boundaries or interfaces may be
encountered with capacitance. The selfadjoint
nature of these problems can be realized by de-
fining linear spaces in which the vectors would
consist of not only the dependent variable (such as
temperature or concentration) in the interior but
also the values at boundaries and interfaces which
have capacitance, "appended" as separate com-
ponents. The details are available in [8, 9]. These
methods are also useful, for example, in dealing
with heat (or mass) transfer in composite media
in which one or more of the media may possess
transport properties considerably higher than
those of other media so that gradients of tempera-
ture (or concentration) may be neglected therein.
There are also problems in steady state energy
or mass transfer in stationary media (solids) in
which energy or mass generated in the medium is
removed by a peripherally flowing fluid, whose
temperature or concentration changes in the di-
rection of flow. The boundary conditions here de-
part from the normal Dirichlet, Neumann or
Robin boundary conditions. Although the original
problem is nonself-adjoint, it is shown [10] that
by decomposing the second order Poisson equation
into a pair of first order equations a selfadjoint
problem is obtained.
As another illustration of the above idea con-
sider the classical Graetz problem at low Peclet
number which necessitates the axial conduction
term in the energy equation. The differential
equation is
k a aT 2T aT
S (r T )-k +pCpv,(r) 0,
r ar ar az2 az
0 Although in what follows the nature of the
boundary condition is immaterial we will assume
for the sake of specificity the following boundary
r aT
r = 0, T 0,-o ar

IT = To z < 0, T < 0o as z4 oo
Ti z>0
This problem treated in the usual way (as in the
literature) is a nonselfadjoint problem. However

by defining what one might refer to as the axial
energy flow function,
S(r,z) = j -k + pCpv,(r)T]27rrdr (11)
Eq. (10) is readily found to be equivalent to a
pair of partial differential equations written in
terms of a matrix differential expression

pCpv, (r)


r1 ar T(r,z)

0 (r,r
0 S (r,z)

= (
z S (z,r)


If we denote the matric differential expression in
(12) by L then its domain is contained in a vector
space in which each vector is an ordered pair of
functions of r satisfying some conditions to be dis-
covered presently. Denote a typical vector in this

space by f = (r). From the boundary con-
f, (r)
editions it can be shown that we must have f2(r)
- 0 faster than r and fl(R) = 0, which then is
the domain of L. Thus we have a differential
operator L which is defined by L and its domain.
If we define the inner produce to two vectors f
and g by

E [f,(r) g(r)2r +f(r)g2(r)1 ]dr
it implies that our linear space must consist of
vectors f such that f (r) must be square-inte-
grable in [O,R] with weight 2r and f2 (r) must be
square-integrable with weight 1/2r. Moreover, it
is readily seen that

= [f,(r)g2) -f(r)g(r)] R = 0


Thus L is found to be selfadjoint and the problem
has fitted the mold we were talking about. Hence


analytical solutions can be obtained for this and
other problems via the spectral representation of
L. This work is as yet unpublished and is
presently the subject of a doctoral dissertation by
Papoutsakis [11].
There are thus a substantial class of problems
of interest to engineers that can be solved using
the elegant theory of selfadjoint operators. The
need for familiarity with abstract formulations
should now be evident. This entire subject has
been for some years under preparation into a
book by the author in collaboration with Amund-
son, which it is hoped will some day see the light
of print. O

1. Naylor, A. W. and Sell, G. R., "Linear Operator
Theory in Engineering and Science," Holt, Rinehart
& Winston, Inc., New York, 1971.
2. Kreysig, E., "Introductory Functional Analysis with
Applications," Wiley, New York, 1978.
3. Gavalas, G. R., "Nonlinear Differential Equations of
Chemically Reaching Systems," Springer-Verlag,
New York, Inc., 1968.
4. Friedman, B., "Principles and Techniques of Applied
Mathematics," Wiley, New York, 1956.
5. Feijoo, L., Davis, H. T. and Ramkrishna, D., J. Heat
Transfer (101), 137-143, 1979.
6. Ramkrishna, D. and Amundson, N. R., Chem. Eng.
Sci. (28), 601-605, 1973.
7. Ramkrishna, D. and Amundson, N. R., Chem. Eng.
Sci. (29), 1457-1464, 1974.
8. Ramkrishna, D. and Amundson, N. R., Chelr. Eng.
Sci. (29), 1353-1361, 1974.
9. Ramkrishna, D. and Amundson, N. R., J. Appl. Mach.
(41), 1106-1112, 1974.
10. Ramkrishna, D. and Amundson, N. R., Chem. Eng.
Sci. (34), 309-318, 1979.
11. Papoutsakis, E. Ph.D. Thesis, Purdue University,

Continued from page 155

We first remember the steps in model building:
define specific objectives, establish physical and
chemical principles, make assumptions, derive
equations, specify initial and boundary conditions.
tf when the mirror is completely clear. Part A: since this
will be a moving boundary problem, t, will be the time
when the fog line reaches the closed end of the vapor
space. Part B: we can calculate the amount of condensate
on the mirror, so the time would be the time required to
evaporate that much material.

are no chemical principles involved. Since heat transfer
is taken to be rapid, the system may be taken as iso-
thermal and the problem is simply one of evaporation and

Y= 0


- Y -** -;

I. .



FIGURE 3. All surfaces impermeable except front

diffusion. Given the two closely spaced large parallel plates
it may be expected that there will be little concentration
difference across (x-direction) the space between the plates.
Also because of the fact that there is no flux at any
boundary except at the open end (-y direction) and the
system is symmetric in z direction, the problem is one di-
mensional (i.e., at any value of x and y, nothing will vary
with z). Mass will be transferred out because of a con-
centration gradient established between the fogged region
(where C = Csaturated) and the opening y = 0 (where
C = Croom). Following the shower, it is assumed that the
room returns to house ambient conditions (this is easily
achieved overnight with the door open, i.e., rapidly, com-
pared to the defogging process since the outside mirror
clears in < 0.5 hr.). However note that the point in the
slit where C = C, retreats farther into the slit as time
goes on. Thus the diffusional path increases and we have a
moving boundary problem.

ASSUMPTIONS: Several assumptions have been indi-
cated already.
* CA f f(x,z).
* The system is isothermal.
* All boundaries except the open end are impervious to
mass transfer (doubtful in the actual experiment).
* The room air returns quickly to constant composition.
* The initial amount of condensate is known.
* Bulk flow in the system is negligible (air flows in to
balance H20 flow out). The error due to this assump-
tion was shown to be about 5.5%.
* The volume of condensate film is negligible.
You are now ready for Part A and B. O

FALL 1979

The people behind these products

still remember looking for

their first job.

They were people who wanted a
good job with a good company. A
chance to show what they could
do. And to be recognized for
doing it.
They were people like you.
The products they researched,
produced and marketed have
already touched every part of your
life. Food wrapping, herbicides,
antifreeze, medicine, packing mate-
rial, home insulation, paper, photo-
graphic chemicals, fertilizers, and
carpet backing, just to name a few.

The careers they took with Dow
gave them a chance to do some-
thing. To take responsibility. To
set their own goals and plan their
own schedules. And evaluate the
It's an environment for people
to develop themselves. And to
develop the 2,200 products and
services we offer.
We need more people like that.
Help us get in touch with them.
Because if you know one of the
people we're looking for, we've

probably got the job he-or she-
is looking for.
If you Know of qualified graduates
in engineering or the sciences,
or with an interest in marketing,
finance or computer science, we
hope you will encourage them to
write us:
Recruiting and College Relations,
P.O. Box 1713-CE, Midland, Mich-
igan 48640. Dow is an equal oppor-
tunity employer-male/female.
TIde rk The Do Chemical Company-*

Continued from page 182
In the category of amount learned in the
course, 8 students felt that they had learned a
great deal, 2 had learned an adequate amount,
and 3 felt they had learned very little. The over-
all rating was very similar, with 8 giving a rating
of excellence, three average, and two poor.
Moreover, the student responses were hearten-
ing. The majority of the class members remarked
very favorably on the worth and success of the
course. The lack of a textbook drew several re-
sponses, most feeling that when a textbook does
become available the course will be better served.
The large body of reading prompted comments
ranging from "challenging" to "hard and
laborious." It is unfortunate that no such text
exists, and this is something which should be recti-
fied as soon as possible. Until then, a collection
of papers seems to be the only adequate substi-
tute, as undistilled and inconcise as it is. O

Course Reading List
(Arranged Under Lecture Headings)

1. J. A. Barlow, "Coal Mining" in Coal and Coal Mining
in West Virginia, Coal Geology Bull. No. 2, 1974.
2. M. King Hubbert, "Survey of World Energy Re-
sources" in Energy and the Environment, Cost-Bene-
fit Analysis, (R. A. Karam and K. Z. Morgan, ed.)
Pergamon, 1976 pp. 3-36.
3. B. L. Sagmiller and J. E. Wilson, "Mining of Fossil
Hydrocarbons", Chem. Eng. Prog. (Symposium series
No. 85) 64, 51-56 (1968).
4. G. T. Fettwers, "Contribution to the Assessment of
World Coal Resources or Coal is Not So Abundant,"
in Energy Resources (M. Gonon, ed.) pp. 467-530

1. A. Davis, W. Spackman and P. H. Given, "The In-
fluence of the Properties of Coals on Their Conversion
into Clean Fuels", Energy Sources 3(1) 55-81 (1976).
2. B. C. Parks, "Origin, Petrography and Classification
of Coal", in Chemistry of Coal Utilization, Supple-
mentary Volume (H. H. Lowry, ed.) pp. 1-34, 1965.
3. W. Francis, "The Origin of Coal", in Coal-It's For-
mation and Composition, Chapter 1, 1961.
4. W. Spackman, "The Maceral Concept and the Study of
Modern Environments as a Means of Understanding
the Nature of Coal", Trans. New York Acad. Sci., 20
411-423 (1958).

1. S. K. Chakrabarty, "Organic Chemistry of Coal and
Chemical Oxidation", The Fundamental Organic
Chemistry of Coal, Proceedings, pp. 89-104 (1975).
2. F. R. Majo, J. Huntington, and N. Kirshen, "Oxida-
tion of Coal, Coal Fractions, and Coal Models", Pre-
print, 1976 Coal Chemistry Workshop, pp. 189-201
3. H. J. Gluskoter, "Mineral Matter and Trace Elements
in Coal", Trace Elements in Fuel (S. P. Babu, ed.),
pp. 1-22 (1975).
4. T. F. Yen, "Chemical Aspects of Interfuel Conversion",
Energy Sources, 1, 117-136 (1973).

1. H. Tschamler and E. de Ruiter, "Physical Properties
of Coals", Chapt. 2 in Lowry's Chemistry of Coal,
Utilization (supplementary), Wiley, 1963, p. 35.
2. H. L. Retcofsky, "Spetrometric Investigations of
Coal", in The Fundamental Organic Chemistry of Coal,
1975, pp. 59-79.
3. M. Oka, H. C. Chang and G. R. Gavalas, "Computer-
assisted Molecular Structure Construction for Coal-
derived Compounds", Fuel, 56, 3 (1977).
4. T. F. Yen, "Resonance Topology of Polynuclear Aro-
matic Hydrocarbons", Thoret. Chim. Acta, 20, 399

1. R. C. Neavel, "Coal Plasticity Mechanism: Inferences
from Liquefaction Studies," Proc. Coal Agglomeration
and Conversion Symposium, WRU, pp. 119-133, 1976.
2. Duane Skidmore, "Agglomeration as a Factor in the
Non-Catalytic Liquefaction of Coal," Proc. Coal Ag-
glomeration and Conversion Symposium, WRU, pp.
135-145, 1976.
3. W. Francis, "Coal Preparations-Grading and Crush-
ing" and "Coal Cleaning Representations of Washer
Performance", Fuels and Fuel Technology, Vol. 1, pp.
55-87, 1965.
4. P. Howard, A. Hanchett and R. G. Aldrich, "Chemical
Communication for Cleaning Bituminous Coal", Clean-
ing Fuels from Coal Symposium II Papers, Institute
of Gas Technology, pp. 733-750, June 1975.

1. H. C. Howard, "Pyrolytic Reactions of Coal," in
Lowry's Chemistry of Coal Utilization (Supplementary
Volume) Wilby 1965, pp. 340-384.
2. H. W. Sternberg, R. Raymond and F. K. Schweighardt,
"The Nature of Coal Liquefaction Products," Pre-
print, ACS Chicago Meeting, Aug. 1975, pp. 198-209.
3. R. T. Eddinger, "Pyrolysis to Coal Conversion", Paper
at World Coal Conference, London, England, Sept.
4. C. S. Wen and T. F. Yen, "Optimization of Oil Shale
Pyrolysis", Chem. Eng. Sci., 32, 346-349 (1977).

FALL 1979

1. N. Y. Kirov, J. M. O'Shea and G. D. Sergeant, "The
Determination of Solubility Parameters for Coal",
Fuel (London), 46, 415-424 (1967).
2. D. W. van Krevelan, "Chemical Structure and Proper-
ties of Coal, XXVIII-Coal Constitution and Solvent
Extraction", Fuel (London), 44, 229-242 (1965).
3. Battelle Energy Program Report "Solvent Refining
Processes in Liquefaction and Chemical Refining of
Coal, 1974, pp. 14-28.
4. J. M. Angelovich and H. F. Silver, "A Study of
Solvents" for the Liquid Phase Conversion of Coal",
Reprint 10B, AIChE, 61 Annual Meeting, 1968.

1. J. L. White, "Mesophase Mechanisms in the Forma-
tion of the Microstructure of Petroleum Coke," ACS
Symposium Series, No. 21 (1975).
2. J. E. Zimmer and J. L. White, "Disclinations in the
Carbonaceous Mesophase," Mol. Cryst. Liq. Cryst., 38,
177-193 (1977).
3. R. W. Shoenberger, "Formcoke Preparation in Clean-
Coke Process", ACS Preprint, Div. Fuel Chem. 20(4),
46-69 (1975).
4. A. Sass, "The Production of Liquid Fuels from Coal",
Minerals Sci. Eng. 4(4),pp. 18-27, (1972).

1. VanKrevlen "Chemistry of Coal Hydrogenation", in
Coal, Elsevier, 1961 p. 201-218.
2. J. L. Cox "Catalysts for Coal Conversion", Clean Fuels
from Coal, 1973 Symposium, IGT, pp. 271-297.
3. G. C. A. Shuit and B. C. Gates, "Chemistry and Engi-
neering Catalytic Hydrodesulfurization", AIChE
Journal, 19(3), 417 (1973).
4. W. H. Wiser, "Some Chemical Aspects of Coal Lique-
faction", Coal Workshop, Penn State, 1975.


1. H. Pichler and A. Hector, "Carbon Monoxide-Hydro-
gen Reactions" in Encyclopedia of Chemical Tech-
nology, Kirk-Othmer, 2nd ed., Vol. 4, 446-489 (1964).
2. G. A. Mills and F. W. Steffgen, "Catalytic Methana-
tion", Catalysis Rev. 8, 159 (1973).
3. J. B. O'Hara, N. E. Jantz and R. V. Teeple "Con-
version of Coal to Liquids by Fischer-Tropsch and
Oil/Gas Technologies", ACS Div. Fuel Chem., Pre-
print, 22(7), 20 (1977).
4. K. H. Hedden, "Coal Gasification," in Alternative
Energy Sources (J. P. Hartnett, Ed.), Academic Press,
1976. pp. 111-148.

1. H. N. Sternberg, R. Raymond and F. K. Schweighardt,
"Acid-Base Structure of Coal-Derived Asphaltenes",
Science, 188, 49 (1975).
2. I. Schwager and T. F. Yen, "Separation of Coal Liquids
from Major Liquefaction Processes in Meaningful

Fraction," in Liquid Fuel from Coal, (R. T. Elling-
ton, ed.), Academic Press, 1977, pp. 233-248.
3. M. Farcasiu, T. O. Mitchell, and D. D. Whitehurst, "On
the Chemical Nature of the Benzene Insoluble Com-
ponents of Solvent Refined Coals," A.C.S. Div. Fuel
Chem., Preprint, 217, 11 (1976).
4. T. F. Yen, "Chemistry of Asphaltene in Coal Liquids,"
in Preprint, Workshop on Coal Chemistry, Stanford
Research Institute, 1976, pp. 144-164.

1. R. A. Meyers, "Chemistry of Desulfurization Re-
actions" in Coal Desulfurization, Marcel Dekker, Inc.,
Chapter 3, 1977.
2. W. K. T. Gleim, "Role of Asphaltenes in Refining", in
Bitumens, Asphalts and Tar Sands, Development in
Petroleum Science, Vol. 7 (G. V. Chilingar and T. F.
Yen, ed.) Elsevier, Chapter 10, 1978.
3. E. Gorin and H. E. Lebowitz, "Recovery Sulfur and
Mineral Matters from Coal," Chem. Eng. Prog. 64-68
4. G. A. Mills and H. Perry, "Fossil Fuel -> Power +
Pollution", Chem. Tech., Jan. 1973, pp. 53-63.


1. A. M. Squires, "Chemicals from Coal", Sci. 191, 689-
700 (1976).
2. G. A. Mills and B. M. Harney, "Methanol-The "New
Fuel" from Coal", Chem. Tech., 4(1), 26-31 (1974).
3. J. B. O'Hara, E. D. Becker, N. E. Jentz and T. Hard-
ing, "Potential for Petrochemical Feedstocks and
Chemicals from Coal," AIChE Meeting 82nd National
Meeting, 1976. Symposium on Chemicals from Coal-
New Frontiers.
4. H. G. Davis, "Coal as a Raw Material for the Chemi-
cal Industry," Fourth Annual Illinois Energy Con-
ference, Chicago, IL, 1976.

1. D. V. Keller, Jr. and C. D. Smith, "Spontaneous Frac-
ture of Coal", Fuel (1977).
2. W. K. Sawyer, "Reviewing Current UCG Model
Capabilities", Proceedings of 2nd Annual UCG Sym-
posium, MERC, 1976, pp. 477-488.
3. D. R. Skidmore and C. J. Konya, "Liquefaction Study
of Several Coals and a Concept for Underground
Liquefaction", Proc. Coal Agglomeration and Conver-
sion Symposium, WVU, 1976.
4. G. A. Mills, "Catalytic Chemistry of New Syn Fuels
Processes", I.E.A. Coal Science Conference, Coal Re-
search Establishment, England, 1977.

1. Harry Perry, "Environmental Aspects of Coal Mining",
in Power Genrations and Environmental Change (D. A.
Berkeowitz and A. M. Squires, ed.) MIT Press, 1971,
pp. 317-339.


2. G. N. Reddy, "Environmental Aspects of Coal Conver-
sion Plant Siting and Cost of Pollution Control", Third
Annual International Conference on Coal Gasification
and Liquefaction, Pittsburgh, Pa., August, 1976.
3. R. G. Lett, C. E. Schmidt, R. R. De Santis and A. G.
Sharkey, Jr., "Screening for Hazardous Elements and
Compounds in Process Streams of the 1/2 Ton Per
Day Synthoil Process Development Unit", PERC RI
77/12, 1977.
4. B. I. Loran and J. B. O'Hara, "Specific Environ-
mental Aspects of Fischer-Tropsch Coal Conversion
Technology", Third Symposium on Environmental
Aspects of Fuel Conversion Technology, Hollywood,
Florida, Sept. 1977.
1. C. Y. Wen, "Optimization Studies of Various Coal-
Conversion Systems", ERDA Reports FE-2274-2, 1976.
2. Y. P. Hsia and T. F. Yen, "Evaluation of Coal Lique-
faction Efficiency Based on Various Ranks", Energy
Sources, 3(1)39 (1976).
3. C. Y. Wen and K. W. Han, "Kinetics of Coal Liquefac-
tion", ACS, Div. Fuel Chem., 20(11), 216 (1975).
4. P. Wellman and S. Katell, "The Economics of Coal
Conversion Systems", SPE Paper 5097 (1974).

Supplementary Course Reading List
ACS, "Coal Science," Advances in Chemistry Series 55,
Washington, D C., 1966.
AIChE, "Coal Processing Technology," Chemical Engi-
neering Progress,
AIChE, "Coal Processing Technology, Volume 2," Chemical
Engineering Progress,
Ellington, R. T., (ed.), "Liquid Fuels from Coal," Academic
Press, San Francisco, 1977.
Elliott, M. A., (ed.), "Chemistry of Coal Utilization,
Second Supplementary Volume," Wiley, New York, 1963.
Francis, W., "Coal, Its Formation and Composition," Ed-
ward Arnold, London, 1961.
Howard-Smith, I. and G. J. Werner, "Coal Conversion
Technology," Noyes Data Corp., Park Ridge, New Jersey,
IGT, "Clean Energy Fuels from Coal, Symposium II
Papers," 1975.
Katzer, J. K. and B. C. Gates, "Catalytic Processing in
Fossil Fuel Conversion," AIChE Today Series,
Lowery, H. H., (ed.), "Chemistry of Coal Utilization,
Vol. I and II, Wiley, New York, 1945.
Lowery, H. H., (ed.), "Chemistry of Coal Utilization,
Supplementary Volume," Wiley, New York, 1963.
Tetra Tech, Inc., "Energy from Coal, a State-of-the-Art
Review," U.S. Printing Office, Washington, D.C., 1976.
Van Krevelen, D. W., "Coal, Typology-Chemistry-
Physics-Constitution," Elsevier, New York, 1961.
William, D. A. and G. Jones, "Liquid Fuels," Pergamon,
Elmsford, N. Y., 1963.

Continued from page 204
had a strong influence on chemical engineering in
the United States where a majority of depart-
ments of chemical engineering use it as a text.
It has also been published in Hungarian, 1961, as
an International Students Edition in Tokyo in
1962 and 1968, and in Spanish in 1973. He also
contributed to Perry's Chemical Engineering
Handbook and the Encyclopedia of Engineering
and Sciences.
During his career he published more than
seventy technical papers primarily dealing with
mass transfer and mass transfer operations. His
research interests included liquid-liquid extrac-
tion, distillation, absorption and mixing in multi-
phase systems. His most recent research centered
on mass transfer in baffled and unbaffled agitated
vessels and three phase mixing in agitated full
baffled columns and vessels. He was honored for
his teaching with the George Westinghouse award
for Distinguished Engineering Teaching by the
ASEE in 1957. In 1963 he was the recipient of the
William H. Walker Award for outstanding contri-
butions to the chemical engineering literature,
awarded by AIChE. In 1968 and again in 1970
he received additional teaching awards, first from
the NYU Alumni and then from the Manufactur-
ing Chemists Association.
Dr. Treybal was a fellow of the American In-
stitute of Chemical Engineers, the New York Aca-
demy of Science and the American Institute of
Chemists. He was a long time member of the
American Chemical Society and the American
Society for Engineering Education. He was a
member of Sigma Xi and Tau Beta Pi Honor
Societies. He was also a registered professional
engineer in both New York and Rhode Island.
His former dean at NYU, John Ragazzini, re-
membered him as "a superb technical person with
enviable human qualities." Part of his human
qualities showed through his interest in art and
music. He had an intense interest in opera and
was a fine artist.
The students and faculty have started a me-
morial fund in his name at the University of
Rhode Island. They hope to honor his name and
tradition with an endowed chair at the University
of Rhode Island,

FALL 1979


Graduate Programs in Chemical Engineering

Financial Aid
Ph.D. Candidates; up to $8,000/year.
M.Sc. Candidates; up to $7,500/year.
Commonwealth and Industrial Scholarships are
Tuition: $690 for M.Sc. (plus $330 for Visa students)
Married students housing rent: $204/month.
Room and board, University Housing: $250/month.
Department Size
13 Professors, 20 Research Associates
30 Graduate Students.
For additional information write to:
Department of Chemical Engineering
University of Alberta
Edmonton, Alberta, Canada T6G 2G6

Faculty and Research Interests
I. G. Dalla Lana, Ph.D. (Minnesota): Kinetics, Hetero-
geneous Catalysis.
D. G. Fisher, Ph.D. (Michigan): Process Dynamics and
Control, Real-Time Computer Applications, Process De-
C. Kiparissides, Ph.D. (McMaster): Polymer Reactor Engi-
neering, Optimization, Modelling, Stochastic Control,
Transport Phenomena.
J. H. Masliyah, Ph.D. (Brit. Columbia): Transport Pheno-
mena, Numerical Analysis, In situ Recovery of Oil
A. E. Mather, Ph.D. (Michigan): Phase Equilibria,
Fluid Properties at High Pressures, Thermodynamics.
W. Nader, Dr. Phil. (Vienna): Heat Transfer, Air Pol-
lution, Transport Phenomena in Porous Media, Ap-
plied Mathematics.
F. D. Otto, (Chairman), Ph.D. (Michigan): Mass Transfer,
Computer Design of Separation Processes, Environ-
mental Engineering.
D. Quon, Sc.D. (M.I.T.): Applied Mathematics, Optima-
zation, Resource Allocation Model 5.
D. B. Robinson, Ph.D. (Michigan): Thermal and Volu-
metric Properties of Fluids, Phase Equilibria, Thermo-
J T. Ryan, Ph.D. (Missouri): Process Economics, Energy
Economics and Supply.

S. Shah, Ph.D. (Alberta): Linear Systems Theory, Adap-
tive Control, System Identification.
S. E. Wanke, Ph.D. (California-Davis): Catalysis, Kine-
R. K. Wood, Ph.D. (Northwestern): Process Dynamics
and Identification, Control of Distillation Columns,
Modelling of Crushing and Grinding Circuitts.

The University of Alberta
One of Canada's largest universities and engineering
Enrollment of 20,000 students.
Co-educational, government-supported,
Five minutes from city centre, overlooking scenic river

Fast growing, modern city; population of 500,000.
Resident professional theatre, symphony orchestra,
professional sports.
Major chemical and petroleum processing centre.
Within easy driving distance of the Rocky Mountains
and Jasper and Banff National Parks.


PkroR E O 44325






G. A. ATWOOD ---________-. Digital Control, Polymeric Diffusivities, Multicomponent Adsorption.
J. M. BERTY ______ Reactor Design.
L. G. FOCHT -___ __ Fixed Bed Adsorption, Design and Process Analysis.
T. H. FORSYTH ____ Coal Liquifaction, Polymer Processing, Emulsion Polymerization.
H. L. GREENE Biorheology, Kinetic Modeling, Contaminant Removal from Coal Gasification.
J. P. LENCZYK High Pressure Kinetics, Activity and Diffusion Coefficients via Ultracentrifuge.
R. W. ROBERTS Atomization Processes, Fusion and Adhesion Characteristics of Polymer Powders.
R. F. SAVINELL Electrochemical Phenomena.
M. S. WILLIS _Multiphase Theory, Filtration and Diffusion in Foamed Plastics.

Graduate assistant stipends for teaching and research start at $3,600. Industrially
sponsored fellowships available up to $10,000. These awards include waiver of
tuition and fees. Cooperative Graduate Education Program is also available. The
deadline for assistship application is March 1.

Dr. Howard L. Greene, Head
Department of Chemical Engineering
University of Akron
Akron, Ohio 44325

FALL 1979



The Chemical Engineering Department at the University of Arizona is young and dynamic with a fully accredited
undergraduate degree program and M.S. and Ph.D. graduate programs. Financial support is available through gov-
ernment grants and contracts, teaching, research assistantships, traineeships and industrial grants. The faculty
assures full opportunity to study in all major areas of chemical engineering.

WILLIAM P. COSART, Assoc. Professor
Ph.D. Oregon State University, 1973
Transpiration Cooling, Heat Transfer in Biological Sys-
tems, Blood Processing

JOSEPH F. GROSS, Professor and Head
Ph.D., Purdue University, 1956
Boundary Layer Theory, Pharmacokinetics, Fluid Me-
chanics and Mass Transfer in The Microcirculation,

JOST O.L. WENDT, Professor
Ph.D., Johns Hopkins University, 1968
Combustion Generated Air Pollution, Nitrogen and Sul-
fur Oxide Abatement, Chemical Kinetics, Thermody-
namics Interfacial Phenomena

THOMAS W. PETERSON, Asst. Professor
Ph.D., California Institute of Technology, 1977
Atmospheric Modeling of Aerosol Pollutants,
Long-Range Pollutant Transport, Particulate
Growth Kinetics.

DON H. WHITE, Professor
Ph.D., Iowa State University, 1949
Polymers Fundamentals and Processes, Solar Energy,
Microbial and Enzymatic Processes

Ph.D., Iowa State University, 1962
Simulation and Design of Crystallization Processes,
Nucleation Phenomena, Particulate Processes, Explo-
sives Initiation Mechanisms

THOMAS R. REHM, Professor
Ph.D., University of Washington, 1960
Mass Transfer, Process Instrumentation,
Distillation, Applied Design

Packed Column

JAMES WM. WHITE, Assoc. Professor
Ph.D., University of Wisconsin, 1968
Real-Time Computing, Process Instrumentation and Con-
trol, Model Building and Simulation

FARHANG SHADMAN, Asst. Professor
Ph.D., University of California-Berkeley, 1972
Reaction Engineering, Kinetics, Catalysis

Tucson has an excellent climate and
many recreational opportunities. It
is a growing, modern city of
400,000 that retains much of the
old Southwestern atmosphere.

For further information,
write to:
Dr. A. D. Randolph
Graduate Study Committee
Department of
Chemical Engineering
University of Arizona
Tucson, Arizona 857T1

The University of Ar;zona is an
equal opportunity educational
insl;tulion/equal opportunity employer



Graduate Degrees

The Department of Chemical Engineering
at Auburn University offers graduate work
leading to the M.S. and Ph.D. degrees in
chemical engineering. The research empha-
sizes experimental and theoretical work in
areas of current national interest. Modern
research equipment is available for ana-
lytical, process and computational studies.

Area Description

Auburn University, which has 18,000
students, is located in Alabama between
Atlanta and Montgomery, Ala., with Co-
lumbus, the second largest city in Georgia,
only 35 miles away. The local population
is about 75,000. University-sponsored activi-
ties include a lecture series with nationally
known speakers, a series of plays and
artistic and cultural presentations of all
kinds. Recreational opportunities include
equipment at the University for participation
in almost every sport.

Research Areas

COAL: Coal liquefaction, magnetic de-
sulfurization and beneficiation, solvent re-

BIOMASS: Chemical and enzymatic con-
version of forest and agricultural waste to
fuels, petrochemicals and animal feed.

FUNDAMENTALS: Kinetics, catalysis, en-
zymatic and fermentation reactors, high
gradient magnetic separation, process
synthesis and control, transport phenomena,
solid-liquid separation, biomedical engi-

ENVIRONMENTAL: Air and water pollu-
tion control processes.
NEW TECHNOLOGY: Advanced coal con-
version, novel enzymatic reactors, applica-
tions of high gradient magnetic separation,
photography by immobilized enzymes,
novel thickener design, polymeric replace-
ment of textile size, enzymatic artificial

For financial aid and ad-
mission application forms

Dr. R. P. Chambers, Head
Chemical Engineering
Auburn University
Auburn, AL 36830

FALL 1979

The University of Calgary

Program of Study

The Department of Chemical Engineering provides unusual opportunities for research and study leading to the M.Eng., M.Sc. or Ph.D. degrees.
This dynamic department offers a wide variety of course work and research in the following areas: Petroleum Reservoir Engineering, Environ-
mental Engineering, Fluid Mechanics, Heat Transfer, Mass Transfer, Process Engineering, Rheology and Thermodynamics. The University operates
on an eight-month academic year, thus allowing four full months per year for research.
The requirements for the M.Eng. and M.Sc. degrees are 4 to 8 courses with a B standing or better and the submission of a thesis on a
research project.
The requirements for the Ph.D. degree are 6 to 10 courses and the submission of a thesis on an original research topic for those with a B.Sc.
The M.Eng. program is a part-time program designed for those who are working in industry and would like to enhance their technical educa-
tion. The M.Eng. thesis is usually of the design type and related to the industrial activity in which the student is engaged. Further details of this
program are available from the Department Head, or the Chairman of the Graduate Studies Committee.
Research Facilities

The Department of Chemical Engineering occupies one wing of the Engineering Complex. The building was designed to accommodate the
installation and operation of research equipment with a minimum of inconvenience to the researchers. The Department has at its disposal an
EAl 690 hybrid computer and a TR48 analog computer an Interdata 7132 mini computer for data acquisition and control and numerous direct
access terminals to the University's Honeywell level 68 DPS computing system. In addition, a well equipped Machine Shop and Chemical
Analysis Laboratory are operated by the Department. Other major research facilities include a highly instrumented and versatile multiphase pipeline
flow loop, an automated pilot plant unit based on the Girbotol Process for natural gas processing, an X-ray scanning unit for studying flow in
porous media, a fully instrumented adiabatic combustion tube for research on the in-situ recovery of hydrocarbons from oil sands, a laser ane-
mometer unit, and environmental research laboratories for air pollution, water pollution and oil spill studies.
Financial Aid

Fellowships and assistantships are available with remuneration of up to $11,000 per annum, with possible remission of fees. In addition, new
students may be eligible for a travel allowance of up to a maximum of $300. If required, loans are available from the Federal and Provincial
Governments to Canadian citizens and Landed Immigrants. There are also a number of bursaries, fellowships, and scholarships available on a
competition basis to full-time graduate students. Faculty members may also provide financial support from their research grants to students
electing to do research with them.
Cost of Study

The tuition fees for a full-time graduate student are $687 per year plus small incidental fees. Most full-time graduate students to date have
had their tuition fees remitted.
Cost of Living

Housing for single students in University dormitories range from $235/mo. for a double room, to $293/mo. for a single room, including board.
There are a number of new townhouses for married students available, ranging from $200/mo. for a 1-bedroom, to $219/mo. for a 2-bedroom
and to $238/mo. for a 3-bedroom unit, including utilities, major appliances and parking. Numerous apartments and private housing are within
easy access of the University. Food and clothing costs are comparable with those found in other major North American urban centres.
Student Body

The University is a cosmopolitan community attracting students from all parts of the globe. The current enrollment is about 10,500 with ap-
proximately 1,280 graduate students. Most full-time graduate students are currently receiving financial assistance either from internal or external
The Community

The University is located in Calgary, Alberta, home of the world famous Calgary Stampede. This city of half a million combines the traditions of
the Old West with the sophistication of a modern, dynamic urban centre. Beautiful Banff National Park is 60 miles from the city and
the ski resorts of the Banff and Lake Louise areas are readily accessible. Jasper National Park is only five hours away by car via one of
the most scenic highways in the Canadian Rockies. A wide variety of cultural and recreational facilities are available both on campus and in
the community at large. Calgary is the business centre of the petroleum industry in Canada and as such has one of the highest concentrations
of engineering activity in the country.
The University

The University operated from 1945 until 1966 as an integral part of the University of Alberta. The present campus situated in the rolling hills
of northwest Calgary, was established in 1960, and in 1966 The University of Calgary was chartered as an autonomous institution by the
Province of Alberta. At present the University consists of 14 faculties. Off-campus institutions associated with The University of Calgary include
the Banff School of Fine Arts and Centre of Continuing Education located in Banff, Alberta, and the Kananaskis Environmental Research Station
located in the beautiful Bow Forest Reserve.

The Chairman, Graduate Studies Committee
Department of Chemical Engineering
The University of Calgary
Calgary, Alberta T2N 1N4















Alexis T. Bell
Harvey W. Blanch
Elton J. Cairns
Alan S. Foss
Simon L. Goren
Edward A. Grens
Donald N. Hanson
Dennis W. Hess
C. Judson King (Chairman)
Scott Lynn
David N. Lyon
John S. Newman
Eugene E. Petersen
John M. Prausnitz
Clayton J. Radke
Edward K. Reiff, Jr.
Mitchel Shen
Charles W. Tobias
Theodore Vermuelen
Charles R. Wilke
Michael C. Williams

Department of Chemical Engineering
Berkeley, California 94720



Degrees Offered
Master of Science
Doctor of Philosophy

Course Areas
Applied Kinetics and Reactor Design
Applied Mathematics
Biomedical, Biochemical Engineering
Process Dynamics
Separation Processes
Transport Phenomena
Transport Processes in Porous Media

R. L. BELL, University of Washington
Mass Transfer, Biomedical Applications
RUBEN CARBONELL, Princeton University
Enzyme Kinetics, Applied Kinetics, Quantum
Statistical Mechanics, Transport Processes in
Porous Media
ALAN JACKMAN, University of Minnesota
Environmental Engineering, Transport Phenomena
B. J. McCOY, University of Minnesota
Chromatographic Proceses, Food Engineering,
Statistical Mechanics
J. M. SMITH, Massachusetts Institute of Technology
Applied Kinetics and Reactor Design
STEPHEN WHITAKER, University of Delaware
Fluid Mechanics, Interfacial Phenomena, Transport
Processes in Porous Media

Davis is one of the major campuses of the Uni-
versity of California system and has developed great
strength in many areas of the biological and physical
sciences. The Department of Chemical Engineering
emphasizes research and a program of fundamental
graduate courses in a wide variety of fields of interest
to chemical engineers. In addition, the department
can draw upon the expertise of faculty in other areas
in order to design individual programs to meet the
specific interests and needs of a student, even at the
M.S. level. This is done routinely in the areas of en-
vironmental engineering, food engineering, biochemi-
cal engineering and biomedical engineering.
Excellent laboratories, computation center and
electronic and mechanical shop facilities are available.
Fellowships, Teaching Assistantships and Research
Assistantships (all providing additional summer support
if desired) are available to qualified applicants. The
Department supports students applying for National
Science Foundation Fellowships.

Davis and Vicinity
The campus is a 20-minute drive from Sacramento
and just over an hour away from the San Francisco
Bay area. Outdoor sports enthusiasts can enjoy water
sports at nearby Lake Berryessa, skiing and other alpine
activities in the Sierra (1 1/2 to 2 hours from Davis).
These recreational opportunities combine with the
friendly informal spirit of the Davis campus to make
it a pleasant place in which to live and study.
Married student housing, at reasonable cost, is
located on campus. Both furnished and unfurnished
one- and two-bedroom apartments are available. The
town of Davis is adjacent to the campus, and within
easy walking or cycling distance.

For further details on graduate study at Davis, please
write to:
Chemical Engineering Department
University of California
Davis, California 95616
or call (916) 752-0400






Ph.D. (Princeton)
Chemical Reactor Modeling,
Applied Mathematics

Ph.D. (M.I.T.)
Nuclear Systems Design and Safety,
Nuclear Fuel Cycles, Two-Phase Flow,
Heat Transfer.

Ph.D. (Michigan)
Statistical Mechanics, Polymers,
Radiation Damage to Materials,
Nuclear Reactor Theory.
Ph.D. (Purdue)
Theoretical Methods, Chemical
Reactor Analysis, Transport

Ph.D. (M.I.T.)
Radiation Damage, Mechanics of

Ph.D. (Purdue)
Computer Control, Process
Dynamics, Real-Time Computing.

Ph.D. (Michigan)
(Dean of Engineering)
Boiling Heat Transfer.

Ph.D. (M.I.T.)
(Vice Chairman, Nuclear Engineering)
Radiation Effects in Solids, Energy
Related Materials Development.

Ph.D. (M.I.T.)
Bionuclear Engineering, Fusion
Reactors, Radiation Transport

Ph.D. (Caltech)
Chemical Reactor Design, Catalysis,
Energy Conversion, Air Pollution.

Ph.D. (Berkeley)
Transport Phenomena, Separation

Ph.D. (Princeton)
Process Control, Computer Control,
Process Identification.

The Department offers M.S. and Ph.D. de-
gree programs. Financial aid, including
fellowships, teaching assistantships, and re-
search assistantships, is available. Some
awards provide limited moving expenses.

One of the world's few seashore campuses,
UCSB is located on the Pacific Coast 100
miles northwest of Los Angeles and 330
miles south of San Francisco. The student
enrollment is over 14,000. The metropoli-
tan Santa Barbara area has over 150,000
residents and is famous for its mild, even

For additional information and applications,
write to:

Professor Dale E. Seborg, Chairman
Department of Chemical & Nuclear
University of California,
Santa Barbara, CA 93106

FALL 1979

PROGRAM OF STUDY Distinctive features of study in
chemical engineering at the California Institute of Tech-
nology are the creative research atmosphere in which the
student finds himself and the strong emphasis on basic
chemical, physical, and mathematical disciplines in his
program of study. In this way a student can properly pre-
pare himself for a productive career of research, develop-
ment, or teaching in a rapidly changing and expanding
technological society.
A course of study is selected in consultation with one
or more of the faculty listed below. Required courses are
minimal. The Master of Science degree is normally com-
pleted in one academic year and a thesis is not required.
A special terminal M.S. option, involving either research
or an integrated design project, is a newly added feature
to the overall program of graduate study. The Ph.D. de-
gree requires a minimum of three years subsequent to
the B.S. degree, consisting of thesis research and further

advanced study.
FINANCIAL ASSISTANCE Graduate students are sup-
ported by fellowship, research assistantship, or teaching
assistantship appointments during both the academic
year and the summer months. A student may carry a
full load of graduate study and research in addition to
any assigned assistantship duties. The Institute gives
consideration for admission and financial assistance to
all qualified applicants regardless of race, religion, or sex.
APPLICATIONS Further information and an application
form may be obtained by writing
Professor L. G. Leal
Chemical Engineering
California Institute of Technology
Pasadena, California 91125
It is advisable to submit applications before February
15, 1980.


WILLIAM H. CORCORAN, Institute Professor
Ph.D. (1948), California Institute of Technology
Kinetics and catalysis; biomedical engineering;
air and water quality.
Ph.D. (1964), University of Minnesota
Applied kinetics and catalysis; process control
and optimization; coal gasification.
ERIC HERBOLZHEIMER, Assistant Professor
Ph.D. (1979), Stanford University
Fluid mechanics and transport phenomena
L. GARY LEAL, Professor
Ph.D. (1969), Stanford University
Theoretical and experimental fluid mechanics;
heat and mass transfer; suspension rheology;
mechanics of non-Newtonian fluids.
Vice-Provost, and Dean of Graduate Studies
Ph.D. (1955), California Institute of Technology
Liquid state physics and chemistry; statistical

JOHN H. SEINFELD, Professor,
Executive Officer
Ph.D. (1967), Princeton University
Control and estimation theory; air pollution.
FRED H. SHAIR, Professor
Ph.D. (1963), University of California, Berkeley
Plasma chemistry and physics; tracer studies
of various environmental problems.
fessor Ph.D. (1978), University of Minnesota
Biochemical engineering; chemical reaction
Ph.D. (1958), University of New South Wales
Mechanical properties of polymeric materials;
theory of viscoelastic behavior; structure-
property relations in polymers.
Ph.D. (1970), University of California, Berkeley
Surface chemistry and catalysis.

Ever think of Grad School as an Adventure?


Graduate Chemical Engineering
Carnegie Mellon University
Pittsburgh. Pennsylvania 15213

4 ....


Want to find out? Heaven can't wait!
Write to:
Graduate Coordinator
Chemical Engineering Department
Case Western Reserve University
Cleveland, Ohio 44106

Graduate Study
in Chemical Engineering


* M.S. and Ph.D. Programs
* Friendly Atmosphere
* Freedom from Big City Problems
* Personal Touch
* Vigorous Research Programs Supported by
Government and Industry
Faculty with International Reputation
Skiing, Canoeing, Mountain Climbing and
Other Recreation in the Adirondacks
Variety of Cultural Activities with Two
Liberal Arts Colleges nearby

W. L. Baldewicz Richard J. Nunge
Der-Tau Chin D. H. Rasmussen
Robert Cole Herman L. Shulman
David O. Cooney R. Shankar Subramanian
Joseph Estrin Peter C. Sukanek
Sandra Harris Thomas J. Ward
Richard J. McCluskey William R. Wilcox
John B. McLaughlin Gordon R. Youngquist

Research Projects are available in:
Materials Processing in Space
Multiphase Transport Processes
Health & Safety Applications
Electrochemical Engineering and Corrosion
Polymer Processing
Particle Separations
Phase Transformations and Equilibria
Reaction Engineering
Optimization and Control
And More....

Financial aid in the form of fellowships,
research assistantships, and teaching
assistantships is available. For more details,
please write to:


Chemical Engineering at



A place to grow...

with active research in:
biochemical and biomedical engineering
computer simulation
environmental engineering
heterogeneous catalysis
surface science
reactor design
fluid flow and coalescence
physics of liquids
with a diverse intellectual climate-graduate students
arrange individual programs with a core of chemical
engineering courses supplemented by work in
outstanding Cornell departments in
applied mathematics
applied physics
food science
materials science
mechanical engineering
and others

with outstanding recreational and cultural
opportunities in one of the most scenic regions of the
United States.
Graduate programs lead to the degrees of Doctor of
Philosophy, Master of Science, and Master of
Engineering. (The M.Eng. is a professional,
design-oriented program.) Financial aid,.including
several attractive fellowships, is available.

The faculty members are:
Joseph F. Cocchetto, George G. Cocks, Claude Cohen,
Robert K. Finn, Keith E. Gubbins, Peter Harriott,
Robert P. Merrill, William L. Olbricht, Ferdinand
Rodriguez, George F. Scheele, Michael L. Shuler,
Julian C. Smith, William B. Street,
Raymond G. Thorpe, Robert L. Von Berg, Herbert F.

Professor Michael L. Shuler
Cornell University
Olin Hall of Chemical Engineering
Ithaca, New York 14853.


Newark, Delaware 19711

The University of Delaware awards three graduate degrees for studies and
practice in the art and science of chemical engineering:
An M.Ch.E. degree based upon course work and a thesis problem.
An M.Ch.E. degree based upon course work and a period of in-
dustrial internship with an experienced senior engineer in the
Delaware Valley chemical process industries.
A Ph.D. degree for original work presented in a dissertation.
The regular faculty are:
Gianni Astarita (/2 time) S. I. Sander
C. E. Birchenall G. L. Schrader
K. B. Bischoff (Chairman) G. C. A. Schuit (/2 time)
M. M. Denn J. M. Schultz
C. D. Denson L. A. Spielman
B. C. Gates A. B. Stiles (1/2 time)
J. R. Katzer
R. L. McCullough Visiting Faculty
A. B. Metzner F. Gioia
H. Olson A. L. Gordon
M. E. Paulaits M. C. Marti de Gordon
R. L. Pigford M. A. Streicher
T. W. F. Russell
The adjunct and research faculty who provide extensive association with in-
dustrial practice are:
R. B. Akell ---_ Mass transfer, thermodynamics, extraction
L. A. DeFrate -- Momentum transfer, single- and two-phase
A. W. Etchells -_--Fluid mixing operations
R. J. Fisher _--------Catalysis, chemical reaction engineering
G. F. Froment -- -Reaction engineering, reactor modeling
P. M. Gullino -------Pathophysiology, cancer physiology,
A. W. Hancock ------ Reaction kinetics, reactor design
H. F. Haug ___ Reaction engineering, mass transfer, design
M. J. Kelley _-------Materials science, electron spectroscopy
H. S. Kemp ..__ Distillation, separation processes
T. A. Koch -__....- -- --_Catalysis
W. H. Manogue __--------Heterogeneous catalysis, reactor analysis
D. Milstein H_____---- -- Homogeneous catalysis, organometallic
C. W. Mortenson _-------Attorney-patents and inventions
F. E. Rush --_ ---Process conception and design, mass transfer
A. W. Sleight -- Catalysis, inorganic chemistry
E. A. Swabb ------Cancer chemotherapy, hematology
E. A. Uebler __ __----Attorney-patents and inventions
V. W. Weekman _------Chemical reaction engineering
J. Wei __ --_ Cancer chemotherapy, reaction engineering
K. F. Wissbrun __--- Polymer physics
For information and admissions materials contact:
S. I. Sandler, Graduate Advisor

FALL 1979

Only the


of Florida's


of Chemical

gives you both
and all the
advantages of
the Florida climate.
An equal opportunity/affirmative action employer

The academic opportunities offer you
a four-quarter (12 month) Master's degree
program with research;
an unusually broad program in enhanced
oil recovery by surfactant-polymer flooding,
solution interfacial and phase behavior
and rock-fluid interactions;
special expertise in applied molecular
theory, catalysis, semiconductors, interfaces,
reactors and biomedical engineering;
excellent facilities in a large, modern, fully-
equipped chemical engineering building.
The Gainesville, Florida location offers you
natural, blue water springs only 30 minutes away;
fishing and water sports most of the year;
Daytona Beach, Disney World, St. Augustine,
other resorts;
concerts, plays, dance, theater and lectures
possible only at a major university.

For more information, contact
John C. Biery, Chairman
Chemical Engineering Department
University of Florida
Gainesville, FL 32611 -



Graduate Studies in Chemical Engineering ...


Chemical Engineering

Center for Disease Control
Commercial Center of the South
High Museum of Art
All Professional Sports
Major Rock Concerts and
Recording Studios
Sailing on Lake Lanier
Snow Skiing within two hours
Stone Mountain State Park
Atlanta Symphony
Ten Professional Theaters
Rambling Raft Race
White Water Canoeing within
one hour

Air Quality Technology
Biochemical Engineering
Catalysis and Surfaces
Energy Research and Conservation
Fine Particle Technology
Interfacial Phenomena
Mathematical Modeling
Mining and Mineral Engineering
Polymer Science and Engineering
Pulp and Paper Technology
Reactor Design
Stagewise Processes
Transport Phenomena

For more information write:
Dr. Gary W. Poehlein
School of Chemical Engineering
Georgia Institute of Technology
Atlanta, Georgia 30332


Graduate Programs in Chemical Engineering at the...

University of Houston

The Department of Chemical Engineer-
ing at the University of Houston Central
Campus has developed five areas of
special research strength:
> chemical and biochemical reaction
> applied fluid mechanics and transfer
> energy engineering
> environmental engineering
> process simulation and computer-
aided design
The department occupies more than
52,000 square feet and is equipped with
more than $1.5 million worth of experi-
mental apparatus.

The faculty:
N. R. Amundson
A. Attar
J. E. Bailey
E. L. Claridge
J. R. Crump
A. E. Dukler
R. W. Flumerfelt
E. J. Henley
W. I. Honeywell
C. J. Huang
D. Luss
A. C. Payatakes
R. Pollard
H. W. Prengle, Jr.
J. T. Richardson
F M. Tiller
J. Villadsen
F L. Worley, Jr.

'-- "

mum I;' 2 ie r

Financial support is available to full-time
graduate students with stipends ranging
from $6,000 to $7,800 for twelve months.
For more information or application
forms write:
Director, Graduate Admissions
Department of Chemical Engineering
University of Houston Central
Houston, Texas 77004
(Phone 713/749-4407)


The Departmenl of Energy Engineering


Graduate Programs in

The Department of Energy Engineering

leading to the degrees of



Faculty and Research Activities in
Paul M. Chung
Ph.D., University of Minnesota, 1957
Professor and Dean of the College of Engineering
David S. Hacker
Ph.D., Northwestern University, 1954
Associate Professor
John H. Kiefer
Ph.D., Cornell University, 1961
G. Ali Mansoori
Ph.D., University of Oklahoma, 1969
Irving F. Miller
Ph.D., University of Michigan, 1960
Professor, Dean of the Graduate College and
Associate Vice-Chancellor for Research
Sohail Murad
Ph.D., Cornell University, 1979
Visiting Assistant Professor
Satish C. Saxena
Ph.D., Calcutta University, 1956
Harold A. Simon
Ph.D., University of Minnesota, 1961
Professor and Acting Head of the Department
Stephen Szepe
Ph.D., Illinois Institute of Technology, 1966
Associate Professor
The MS program, with its optional
thesis, can be completed in one year.
Evening M.S. can be completed
in three years.
The department invites applications for
admission and support from all qualified
candidates. Special fellowships are
available for minority students. To obtain
application forms or to request further
information write:

Fluid mechanics, combustion, turbulence,
chemically reacting flows

Chemical kinetics, mass transport phenomena, chemical
process design, particulate transport phenomena

Kinetics of gas reactions, energy transfer processes,
molecular lasers
Thermodynamics and statistical mechanics of fluids,
solids, and solutions, kinetics of liquid reactions,
solar energy

Thermodynamics, biotransport, artificial organs,

Thermodynamics and transport properties of
fluids, computer simulation and
statistical mechanics of liquids and
liquid mixtures
Transport properties of fluids and solids, heat and
mass transfer, isotope separation, fixed and fluidized
bed combustion
Heat transfer, fluid mechanics

Catalysis, chemical reaction engineering, energy
transmission, modeling and optimization

Professor J. C. F. Chow, Chairman
The Graduate Committee
Department of Energy Engineering
University of Illinois at Chicago Circle
Box 4348, Chicago, Illinois 60680



The Department is deeply committed to teaching and research. Everyone
is expected to maintain an active, first-class research program. Administrators
or "older members" are not exceptions. The standards are high. A third of
the faculty are members of the National Academy of Engineers or the
National Academy of Sciences. The Department prides itself on the large
number of major national or international awards its members have won,
an average of 3.6 awards per tenured faculty member.
Even so, the faculty is accessible. The Department views research as the
highest form of teaching, where students and faculty work together on a
joint project. It is not unusual to find faculty members in the lab, and
doors are always open for questions, comments or help.

The Department, as a part of the School of Chemical Sciences maintains
some of the most up-to-date facilities in the country, including for example
a multichannel analyser capable of counting the nanosecond range, and
pressure and vacuum equipment giving a useful operating range of 10 to
10-13 atm. The School has extensive service facilities including a glass shop,
electronic shop, machine shop, electronic design facility, analytical and laser
labs. The shops are some of the best in the country, and the analytical and
laser labs are truly exceptional. The campus library is one of the largest in
a major university with over 5,000,000 items in its collection including
more complete run journals in the chemical sciences than can be found
in any other education institution. The School is committed to keeping its
equipment up to the state of the art, and so for example, we have just
purchased a VAX 11/780 to replace our IBM 1800, and have requested
money to add NMR capabilities beyond our 200 MHZ machine.


Applied Mathematics
Biological Application of
Chemical Engineering
Chemical Reactor Dynamics
Colloidal Phenomena
Computer-Aided Process
Simulation and Design
Electronic Structure of Matter
Electrochemical Engineering
Energy Sources and Conservation
Environmental Engineering
Fluid Dynamics

Heat Transfer
High Pressure
Interfacial Phenomena
Mass Transfer
Materials Science and Engineering
Molecular Thermodynamics
Phase Transformations
Polymer Crystallization
Process Control
Reaction Engineering
Resource Management
Statistical Mechanics
Surface Science
Two-Phase Flow


Department of Chemical
113 Adams Laboratory
University of Illinois
Urbana, Illinois 61801





Institute of Technology

M.S. and Ph.D. programs in Chemical Engineering and Inter-
disciplinary Areas of Polymer Processes, Chemical Plant Opera-
tions and Management, Energy Conversion and Resources.


Heat Transfer and Energy Conversion
Electrochemical Engineering
Process Dynamics and Controls
Reactor Design and Dispersed Phase Systems
Polymer Science and Transport Phenomena
Mass Transfer and Surface and Colloid Phenamena
Chemical Reaction Engineering Analysis

D. T. Wasan, Chairman
Chemical Engineering Dept.
Illinois Institute of Technology
10 West 33rd St.
Chicago, IL 60616

FALL 1979




THE INSTITUTE is an independent, privately-
supported graduate school offering interdisci-
plinary degree programs designed for the B.S.
Chemical Engineering Graduate.

RESEARCH ACTIVITY spans the breadth of the
papermaking process. Current research programs
I r are underway in:
process engineering
simulation and control
surface and colloid chemistry
laser, Raman and x-ray diffraction studies
S .environmental engineering
/ cell fusion
fluid mechanics
heat and mass transfer
polymer science

WE HA VE a teaching faculty of 45, a student body
of 100 and maintain close ties with the U.S. Pulp
and Paper Industry.

supplier of technical manpower to the pulp and
paper industry.

FULL FINANCIAL SUPPORT and tuition scholar-
ships are granted to all U.S. and Canadian citizens
without obligation. Current fellowship stipends
amount to $7,000 per calendar year. On the job
industrial experience is arranged for each student
through summer employment in the paper indus-
For further information contact:
Director of Admissions
The Institute of Paper Chemistry
P. O. Box 1039
Appleton, WI 54912



Energy Conversion
(Coal Tech, Hydrogen Production,
Atomic Energy)
Renato G. Bautista
Lawrence E. Burkhart
George Burnet
Allen H. Pulsifer
Dean L. Ulrichson
Thomas D. Wheelock

Biomedical Engineering
(System Modeling,
Transport. process)
Richard C. Seagrave
Charles E. Glatz

Biochemical Engineering
(Enzyme Technology)
Charles E. Glatz
Peter J. Reilly

Polymerization Processes
William H. Abraham
John D. Stevens

as well as
Air Pollution Control
Solvent Extraction
High Pressure Technology
Mineral Processing




Chemical Engineering

Transport Processes
(Heat, mass & momentum transfer)
William H. Abraham
Renato G. Bautista
Charles E. Glatz
James C. Hill
Frank O. Shuck
Richard C. Seagrave

Process Chemistry and
Fertilizer Technology
David R. Boylan
George Burnet
Maurice A. Larson

Crystallization Kinetics
Maurice A. Larson
John D. Stevens
Process Instrumentation
and System Optimization
and Control
Lawrence E. Burkhart
Kenneth R. Jolls

write to:
Department of Chemical Engineering
Iowa State University
Ames, Iowa 50011

Graduate Study in Chemical Engineering


DURLAND HALL-New Home of Chemical Engineering

M.S. and Ph.D. programs in Chemical
Engineering and Interdisciplinary
Areas of Systems Engineering, Food

Science, and Environmental

Financial Aid Available
Up to $7,000 Per Year
Professor B. G. Kyle
Durland Hall
Kansas State University
Manhattan, Kansas 66502









Energy Conversion Processes Polymer Chemistry and Engineering

Environmental Quality Process Dynamics and Process Control
Biochemical and Biomedical Engineering Computer Aided Design
Transport Phenomena Surface and Colloid Chemistry

Chemical Reactor Engineering Applied Chemistry
Chemical Kinetics and Catalysis Combustion

EIm 0 E

R. C. ARMSTRONG, Ph.D. (1973); Associate Professor, M. MODELL, Sc.D. (1964); Associate Professor,
R. F. BADDOUR, Sc.D. (1951); Professor, C. M. MOHR, Sc.D. (1961); Senior Lecturer,
J. M. BEER, D.Sc. (1968); Professor, F. A. PUTNAM, Ph.D. (1976); Assistant Professor,
R. A. BROWN, Ph.D. (1978); Assistant Professor, R. C. REID, Sc.D. (1954); Professor,
R.E. COHEN, Ph.D. (1972); Associate Professor, A. F. SAROFIM, Sc.D. (1962); Professor,
C. K. COLTON, Ph.D. (1969); Professor, COMBUSTION
L. B. EVANS Ph.D. (1962); Professor, S. M. SENKIN, Sc.D. (1977); Assistant Professor,
C. GEORGAKIS, Ph.D. (1975); Associate Professor, K. A. SMITH, Sc.D. (1962); Professor,
H. C. HOTTEL, S.M. (1924); Professor Emeritus, C. G. VAYENAS, Ph.D. (1977); Assistant Professor,
J. B. HOWARD, Ph.D. (1965); Professor and Executive Officer P.S. VIRK, Sc.D. (1967); Associate Professor,
J. P. LONGWELL, Sc.D. (1943); Professor,E. VAN, Sc.D. (1945); Professor
COMBUSTION, FUE PRO NG J. E. VIVIAN, Ec.L. (194S); Professor
M. P. MANNING, Sc.D. (1976); Assistant Professor, PROCESS
J. WEI, Sc.D. (1955); Professor and Department Head,
E W MERRIL, Sc G. C. WILLIAMS, Sc.D. (1942); Professor and Graduate Officer,

FALL 1979 241






At The


Of Michigan



Dale Briggs
Louisville, Michigan
Brice Carnahan
Case-Western, Michigan
Rane Curl
Francis Donahue
LaSalle, UCLA
H. Scott Fogler
Illinois, Colorado
Erdogan Gulari
Roberts, Cal Tech
James Hand
NJIT, Berkeley
Robert Kadlec
Wisconsin, Michigan
Donald Katz
Lloyd Kempe
Joseph Martin
Iowa, Rochester, Carnegie
John Powers
Michigan, Berkeley
Jerome Schultz, Chairman
Columbia, Wisconsin
Maurice Sinnott
Henry Wang
Iowa State, MIT
James Wilkes
Cambridge, Michigan
Brymer Williams
Gregory Yeh
Holy Cross, Cornell, Case
Edwin Young
Detroit, Michigan

Laser Light Scattering
Reservoir Engineering
Applied Numerical Methods
Dynamic Process Simulation
Ecological Simulation
Electroless Plating
Electrochemical Reactors
Polymer Physics
Polymer Processing
Composite Materials
Coal Liquefaction
Coal Gasification
Biochemical Engineering
Periodic Processes
Tertiary Oil Recovery
Transport In Membranes
Flow Calorimetry
Ultrasonic Emulsification
Heat Exchangers
Renewable Resources






Department Of Chemical Engineering

For Information Call 313/763-1148 Collect

FALL 1979



chemical reactor modeling catalysis enhanced oil recovery polymer rheology biomedical engi-
neering process synthesis film coating mixed cultures kinetic theory statistical mechanics trans-
port in blood polymerization nuclear engineering physical metallurgy population dynamics
surface science artificial organs photochemistry air pollution solid spectroscopy electromigra-
tion food science superconductivity particle technology


Responses of some of our current
graduate students to the question

"I chose Minnesota simply because of
the quality of the school-it is a large,
diverse, excellent graduate school-and because
the size of the department allows a choice
between several possible areas of research."

"I really like the community. I think
Minneapolis is one of the nicest of all
Northern cities."

"I chose Minnesota because of the faculty
here and the courses that are offered."

"I like Minneapolis. I knew the faculty at
Minnesota was very good. Then my visit
here gave me a very favorable impression of
the school and community."

R. Aris R. Carr J. Dahler
H. T. Davis A. Fredrickson W. Gerberich
H. Isbin C. Jensen K. Keller
C. Macosko M. Nicholson W. Ranz
L. Schmidt L. E. Scriven
J. Sivertsen G. Stephanopoulos
M. Tirrell L. Toth H. Tsuchiya
J. Wallace S. Wellinghoff


Young specimens of Minnesota's state tree, the red
pine, growing on the Saganaga Granite in the
Boundary Waters Canoe Area, Cook County.
(Photo courtesy A. Fredrickson)


Name __--.-------------------______.

-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -
Univ. of Minnesota, Chemical Engr. &
Matls. Sci. Dept., 421 Washington Ave. S. E.
Minneapolis MN 55455


Department of Chemical Engineering



Contact Dr. J. W. Johnson, Chairman

Day Programs

Established fields of specialization in which re-
search programs are in progress are:

(1) Fluid Turbulence Mixing and Drag Reduction
Studies-Dr. G. K. Patterson and Dr. X. B.

(2) Electrochemistry and Reactions at Electrode
Surfaces-Dr. J. W. Johnson

(3) Bioconversion of Agricultural Wastes to
Methane-Dr. J. L. Gaddy and Dr. N. L. Book

(4) Polymers and Polymeric Materials-Dr. H. K.

M.S. and Ph.D. Degrees

In addition, research projects are being carried
out in the following areas:
(a) Optimization of Chemical Systems-Dr. J. L.
(b) Design Techniques and Fermentation Studies
-Dr. M. E. Findley
(c) Multi-component Distillation Efficiencies and
Separation Processes-Dr. R. C. Waggoner
(d) Separations by Electrodialysis Techniques-
Dr. H. H. Grice
(e) Process Dynamics and Control; Computer
Applications to Process Control-Drs. M. E.
Findley, R. C. Waggoner, and R. A. Mollen-

(f) Transport Properties, Kinetics, enzymes and
catalysis-Dr. O. K. Crosser and Dr. B. E.
(g) Thermodynamics, Vapor-Liquid Equilibrium
-Dr. D. B. Manley

Financial aid is obtainable in the form of Graduate and
Research Assistantships, and Industrial Fellowships. Aid
is also obtainable through the Materials Research Center.

FALL 1979



Dr. James K. Ferrell, Head
Department of Chemical Engineering
North Carolina State University
Raleigh, North Carolina 27650


Full Text


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create. construct and control vour career with MIWKEN We provide an expanding range of opportunities to accelera te yoor managerial and professional career development M, l liken's commitment 10 techno~k;al leader s hip in providing new produc t s. processes and oouipment is exempli f ied by the Milli t ron ma c hine a computer coot r ol led, ietinjectiOn dyeing SYS1em crea ted and developed by Milliken engi neer, and scientists for the product,on ol mulh colored carpel, rugs a nd upholsleiy products. The men and women we need have open minds. opeo enough to lef us expose yc,u to the details al the Milliken challeooe When we select eacn other horizons broaden for both o1 us. c.o~A1),, =-~ ,j;" MILLIKEN ~l'f.~


HETEROGENEOUS CATALYSIS M. A.IIANNICE p ,.,...i,....;,.si.t u.;,.,,;11 u.;,.,..;c,P,~.P..i 16802 H ~:."':!1 ~~:~:1 ='. :=:;;;,i~'..;;s::~=~ pomidd~N<&bout...,.,.t......,.riohodeq"l

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    PAGE 21

    ACKNOWLEDGMENTS Deportmental Sponsors: T M followlr.g 138 deportment< contributed t ol he suppo,tof CHEMICAL ENGINEERING EDUCATION in 1979 u.i ..... ,o1A 1, ... LA" J o >""" A'-""'""' ....a,ca1 ..... ,.,.., _,A,.__ ,.. .., c, ... .... ,._"_ .,_,.,.....,..,..... c-,.,...,. -.,_ .. ._, ..... ., .... .,..._ ..... __ c_ __ .,....._ -.. --_,,..,_, -,-~<-) C ..... ol< ,_,C........,(11,nMJ ,.,,._ ..... .,_, ., ... ,.,,;..w ""'o, '4 kW ,. ,T,. Jol,onM1 u .. .. ... .. ,,__,. ... ,,..,._, Clo'-Collo10ol T ...... u ... ,.,.,., .. .......... Clo-U 11 O(C _,_.., c,,..,, .. ..... .,, ....... ,, ....... .. -1 (-) ~~~' .......... .. -. .,. ~ ..... ;_...., .,., ...., ., c .. .... .... o,_,..,' ... ,_, ~ ~.. -, .. ..., u ., ,....., ., ,,_,,, .... _,_ ......... .. ... ""' ., .. _,,, __ c_,.,__,,.,..._... ... ._-.... -. T TN IUol,o ... 1 -r,,.,.......,. 4 hlJol,. ... 1 .,_, .. __ ;.,.,...,, ,, _, _, ,._,...,,.,. .... Uol A, .t "' 1 10 0\III IU.DI U. ",._-, ..,,_,,..__.,_ ~....;...:......,..:_ ............. -. 0 ..... ....

    PAGE 22

    PAGE 23

    .. .. ., ... 111 .... ___ ,_ ::..~-.:' .. -::!i-:!:i= -... .. u.. "--_ .... ___ .... _1ooptl.. 1 .. -..11~,-,,,. .. ..... Pl'<\O
    PAGE 24

    IM~-ofhi1,-,tld ........ w -1-of----, "1....,.-..lplUoo-_lotodonlo. Thtoolhor po,-. tlc1tocttha\!tiol>Olbuodon a-odth.. rotlclrthonacland Otho----i-, ..... _, .... ..... ==llffllicwlbeco,...oltbolr,\llhoqlltlmbook-IIU"lo-11-,.. ..... ----.. i.,laleocl ... ,,.,._,.1, ___ i,, ....--naloolfen,-ofeo..tlll_..... u..-.. l aCkal'lerl.O...FlltnlNol,-.Ylo..-td .. ,.......,_,.m, ........... m.-t"210bo ""8<11).C.OtrorJIOlheother....,ptc,rwotll>cl -.11-ootiu. .... ...,.,1oa...uo.,a11 -,d. lt ll~l,loto romb! M thloCb-oiMrMth ci,.,p1tt,, JJ>d ootm!O... l"l ltnlloa Cliot. Lic[uicl Flttrollol> Md f'll1ro11o1> l'm--t. &DC1 a..J,1t r l, Fll\ntlM 111-u..~-1-.,. .....u,-

    PAGE 25

    This sign marks the road that le;ids marketingmajorsatlocationsthroughout into our l ntcmatiooa! Headqu:lfters in the U.S. St.Louis. WeoffCTyouopportunities,training 1nese words. ""Monsanto Drive and ratter paths that are geared for have another and more significant mean upward mobility. If >'OU are a person inga1Monsa11to. l fsawayofei,;pressing wh:, has set high goals and has an thespecialqualitiesofMonsantopeople. achie\ementreoord,andwhowantsto who ha\'C' the will to meet challenges advance and succeed. be sure to lalk head-on-to accomplish and soccttd. with the Mon saoto represemative when W eofferbrightandel!Cfgeticpeople he visit~ your C.lmpu!! or write t o: Ray with this drive the opportunity to help Nobel, Monsanto Company, Professional solve some of the ,,,orld"smajorproblems Employment Dept .. Bldg.A3S B 800 theenviroflm em North Lindbergh, St. Louis. Mo. 63166. andothers engi~~~t!1l~~'.gi=1~L:nx~'lt a 1 ::i Monsanto

    PAGE 26

    II e;,. FUNCTIONAL ANA L YSIS FOR CHEMICAL ENG IN EER S I), l.,OIK K l.$HNA ,..,_u .. ..,..., WMll,,o/t,JoYU)i .. ~ofcloptk llloMll>}oolf\l,..._~yor.,._,pk .. 1u1 .. u-,0po,aio,ThoorJla f.,..I,,_. l"""lklotlff,"byA,W.NaylorudG.R.Sell [11 nd "lol;od0<1<1ry F ul><'llona l Anol,.;. with Appll<0tloolluoll11<1oduc,. tio,u.Tht-di 1 U1 tmotO1l<11,.,.....i,,.., ......... rurn .. u.., --~ .... ... ,...,...,..;_1u1no.p1i. at lM lndlu lutltu""' Toct,noloa. Kupur .,1,o,. ... ,.U-,_tt11miw_,._ T oN.I A.... rou..,nm, f<>,ftnt-nwt1.. ,...,....,o1........,__.,.....i,..,.1.....u .. --.u...ioliot--OOlboj-H ..... ..._, ,.,. olocaat ..,....., .. ,1,on but .. ..t =J!r-E:::.~ ':~t~~= lh t h u le,:! 10 """"'"""' Pl' ... .. -.1 ... u, .,..1.1,,_otobo!1116r ...-__,...,..i-., ......,.o,(ij_, _____ ..._ ................... lboffer--r

    PAGE 27

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    PAGE 28

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    PAGE 29

    Career Oppor1unltles In Engineering, Oeslgn. Research. and Construction f o,--1&,-,.cfs,...., 1 Coho0 __ ,n ___ "'ll_,,_inoc.wo .... _,,.... ____ .. ,_,......_ ________ ,__, ___ ........,. __ ...... _,_.,. __ ,, ___ "''"""'"''"'"--""--ca, ___ ~-----.... prot __ .. __ _,a, ........ ___ .,,...,,..c, ... .. ..._,ng -. ..... -.,...,~..._,..,,,,,.,....,.., c.,,,..._,,,.,.,...,..,._"_"" .... ..... .. ... ., H No .. .... N, .. ..... ....... '' ..... '"""'"'"'Cf B ,, .... eo.0o1> n K .AO,oo,""' Col ~ o,nlot 1 1102 o, M .,.,., .... ,.. ,. .,.....,g111 10 CF BRAUN & Co Engln eers-Cons1ructcn

    PAGE 30

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    PAGE 31

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    PAGE 32

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    PAGE 33

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    PAGE 37

    WHAT? WORK FOR EXXON? Wllholll'llto/k<:t>o,.d~er.erf/f~ar>d,uch,.""''"' ollenoslcedflhisls o!on. Oll'"""""' b alway,lhesom,, : "YM,W .. Yes.Wy01Jcrn/,elpkx;ld8ooc""v<:rillcd"'""<'.!klrollcica"lll!ledmillerol> becousealE>xon~,..~ Yes. W)Q.(re oltloc!edto"-"'11oon-ene.vy'"'""Wormolionsy,tems.~molerlatondoct,or,u,d~sy>tems becousea!E>::&-rdh:1 )'9&cl'dllnge>~""':-==~ n """'1,...,.,lhili
    PAGE 38

    1/{Jowi,ui,i MATHEMATICAL METHOD S IN CHEMICAL ENGINEERING A R VINUVAR MA ~:::-:~17:!:!i.~ A T.-;.<>-U.:.'!.na.!~:c'~~p,,rM:=~:i MrihodolnGl,...,I .. IE,..l-rln,laolrr,,::1""''7 ,-,.1Not,.Damo.Tho<0un,e.,..;,ri,,.Uo ....,.,._Lltulnitiallyo__, i~;~~g~-;~ :-!!-:'~~-=-";'!:t:.: (&DdNOlo,lfoaoJIJ,_ l J .C.;. borry&nc1J.r K<>11-.-u..-. .... -.. __ _____ ,._ __ ..__,. __ ... __ ... .... ____ ..._ .... __ ,. __ < ____ ... _,._, _______ _._,_ .. _8__.,. __ ___ .. ,..._ ... ___ _______ .., ---------...... _,., _____ ., __ ----------lrOd U..l&l!e.llo"(I l~ J lotd [SJ ~iWor,,odio lli'lio f,...,otoOUIOil .roolltp..;.i.a,n..,...,._ .... ~::~:-~::.ift=-= m,;,-.111 _.loot 1.....i .. "" ~n..., hodont ,1.,._,.h,dudloiaf,..,f.---I .,.,.;-.iJ,
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    PAGE 40

    ==~=-1~~EiFi. .,.....,., ........ t.,..olthoph.. .... frdt,--....t ll&bilil)' by IJ&pu- Dind Wetlood. Thia portifflioptfllap tti.fflOOtinlareolinrp rtof :::. :,,,:'.:,, ::-.:::~ uotemo u_, ,,,..,.. orlsin in ~I ,. in lbb'-unlq .. ot,adyt>dlllons ( .-ioi, .I uyml)t,>li< tobmt,) Non llnHroyot lo ) o ndr.....,..,,u,oMdovflopodmoloriol""A"'t-<>....,_non l inttr ,;,.,..,,. .. u,tlono -hitk.canxhlbl\v,ry urpri,,inslor,from.,_blo,i-fyotalMnu..,ltor-"11, onUg,>ln anall""nr l,lok>p:al PQP,,lotlona ~ IQ ]. Alto ..,,.n\uperl....,ta1(14]andtheo.iooT)'ol 11-, OOEa iot,.te,1 next. ~= .::.::.~ ~:1:..:'".:!.i.-:..~.:: = -..-. ... -..., ud tod;-..ionol1Modjoln1..,.,...,....ii111o adjointdHfe...,tia!bl....,ot1dln l t odioinor'rtAturo l ')kiodBC...-.. .... tl,elJ,.AII t1-<>durtivit> 0.pelldi,..-oowbttherthoratiolo io,p ... ,-..,.1.o, ... --thoPJ>N>l>rl. "" BC. hl
    PAGE 41

    .,1f..adjoi n\dii!e=tl l o1><" """"dof.,lf dioin\boonda17-va l .. pn>l>ltm> (i.o ., the.....i, an dfo l lowinrintroducto17e.amploo.thee!lr>I sw ..... u...,;u. problem 1 ,,...teo:1 to, .. 1r adjoint oper a1ora..-ith ..lf-adioi nt nc s.,,..,.1 xarop!M ,. ,,...,..i in thi 1 '""""'" a nd the f oct thst o ..,hprol,lomonioftnitenumhnof rt&J el-valu.., h with an oipnfm>etioo I,.,. lonrin~ to i t, lo b""""ht out. Complotoneu and orthopoolityofth lpofl.nction1i 1 ,...JK>Oihl< ::;et::~::_....i 1 ... t~n~~:i~oo~:",: : :,:.:: ond\husU..oolotlonofboo n do17-, lu,p...,t,lem, ~:,!~,:h:::O"~ :':~tf.!i~ :"!; :;;'.::!.;: i l!e,.nli a l eouotiono ndl o tllo,ooghly .. :E~;};x~~:tE n> of aoo,,;Hlc0014inth ar< reported. Tho \ol>lc 0011< l """ with ... .,.. 1 ph)"lkalandd1emif',)_, ...,,1 .. ... -the old-foohi.....:l m&lh
    PAGE 42

    [ ................... ___ ....., .. ... __ ,.u.s.,._,_.,.,_,. =-~:: .. -=-:::.::::; ::-...--111.--.. -_.,_,, __ JP .. ;.=~=~= _.,..i----A:=:.::.:::..-::.~~ --io-,.Mlptllll -mclM l"IIMl.-.t,... oftopi,ol IM-"'-"tico.l -11-'7,udproridoo\ho.,IOdfflt..;th f Hlfo, .. n..,,._,;,.andlta"'"'"'dMlof ~~~~~~;::::_!~=.::~~ Ar.-,-tal...,.tioo,a..i..utot,,oU,o, allU.lo-bo-ina.--.1.. =~~~::.=:i:ii~-: .,,-.-u.., __ __ .. -1,,--..,.._..,_ 1,u..,, ... .......... ..... ..-.-1 ...i. ... Aloe. ia -ni. _,_,_ do "' .... .... ; .. w11 .............. .... llooluLllt- f--k MO lfon,oly pooi1;..,_ C ..... ___ _,_,_, c,,,. ...,. ... ,_r_,. __ ..,_ -... .. L A-,11,L"IO,_..,,._._.__ ____ .. __ ..,_..._....__..,..,,"- u"' L-W 11. ... &.C.lh"-",_.,_.., ___ ,_..._ .. E::~~~1~~ri II~ fiffl]I books received _,._.,11, _____ -N-Yon..1-.1A,....__ A..,,_,....,_,-~,,, ....... ""' ,,.,o,._,,,~-,o..,Goll..,.,..,.,,...,, c_,..._, .... ...,._,,., .. v ..... ,m,IM ...,.-..,c_...,..,. ... r_.,..., _, ... __ .. ____ ..... .., L.0.--0., ....... -.._,._, ..... ,m.

    PAGE 43

    'Tm designing process instrumentation for a $9 million plant expansion at Du Pont." Ronald Hayn es BS. Chemical Engineering lnvoiwdindttig,ingp,o,:,,ss inJirumMtationfromduign ~:~-:;.job AtDuPont ... lhe~sa worldoflhiRgsVOOcan dosomethingabool.

    PAGE 44

    POLYMER SCIENCE CURTIS W, ntA!db)l o Pot.obom-tobo-tt,l,vi.-,, ..W.U......ttll-..t-n
    PAGE 45

    and 209) .. peoinl lopica oo an lternote ,,.., bwo.lnthtfutu..,,Cl,, ;.212 al oomoybeV,,.n ln aoi mila,mannor.Thua,itwillbNibloto r~~:.:~;:1::~~i~~l:;~ No..,,.ntepolyme,laboraloryrounoia ~;..~...:!uttu;d;~~~;:::;;..=::!,~~: ~a:=i:;::,tu~~:~-::;,,:r:Pj ::.:::~;-~~"!:; ~~rr-=1\:, "':~":: Mlliorlov,l-iealon~-ri~lboral<>r7, SWll o rdisonteot coo,-. i nlhootud'i>ri= ~:~:!1:.'=n~:::.=: !:! ;:-:::: Ch.J,:.212, oll'" wint,rquarter. i 1 thtftro\ or1,...,rra<1uate>0 ....... hi,hco,-.,pobmo,be"""'""tit;onlrom,rn,lu ate -couroeoto~enl,y flm.-..,..,,.duate,tudentodurlnrfallqoorto, Thu,,inoroo,1<>,nou"'abuiofamWari\7,ri U, ~~;{t~~~~~Jl:} Nr,
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    L ___ ,_ ............ ..... ._ ______ __ .. .......... .. .. ................... ................. c:.-----.. -(1) .... -. .... .. .. r, ... .... ...,._. __ .. u .-- ......... ... ...... .. .. (t) ... ... ....... ... ..,. .. .... -, ..... .. ..... .,. ............... ... .._....-........ ... ---.. -.. _,...._,.. .. ..,.,_..,..,_ ULJU) .. .... ____ ........... ........... .... .. ...... .............. ..... LU .... ... ,ri1 ............ v ... ............ ...... .... .......... .... ..... .. -.Wiit)-, INton .. lrt,b"-.Addi (;l, l t217lo-ofU..pri"'
    PAGE 47

    , ............. ...,_............ .. ........ .. ....... .. A. >1 -, 1, ,.,.. 1\ .. ,.\l) ........ .. .. ............ .......... ... ,.....,.,., ,. r ,....,,.., 01o",_..,. &.,. .... ,. ..., ... ... .. .. ., :,. r .... ,. ............ .. ...... """'"'" ........ .. .. B..11 0l Ko ...... .., .............. ....... ... ....... .., .... .... ... ......... ()) ._ s..., .. n,, .... ,. .. + ........ _,, ................ .. .. u ,., ...... .... ..... ... .................... .. ........ ......... ...... .... ,_ ., .... .. C. ... .. ........ ,.,..,.,., ......... .. ........... ,, ...... .. .... v ..... ... 1 .er..., .. ... ...,_ A .......... ...... .......... ...... loo (l) .. """ ............ ,, .. v '. ... ,.... ..... ., .. ....... .. ....... .. ....... .. ...... ,.. .... ................ ... ... .... no ......... ., ... _,,.,..,..,_.....,., ._ ~ .... ..,., .,.,.,.... ., A B. St,y to tho d,,o; cp ~ o, ~ ,. -=~ ~ ~-c. ,CS(liP I """\teriD.,lf. n .. tron ac> t t,ring, :.;:r:::~~}S~~::fE 1: ;::~~~=~:;::~1~;;; \ roted ... uli{ln a a loo i wi th onaly,,i of ,oriOUI! lheoriea. nO?>lin eu modeli n r of macromolocu l ~.:."~:.., ~!~/"'ot-t":t:~!..,n;:;.;~"'':,,~ !':t:,~k =~ filtopOl yme, ph)'lli ,,. (nolud@d ,olumt, ron-"

    PAGE 48

    THE STRUCTURE OF THE CHEMICAL PROCESSING INDUSTRIES T W F RUSS~:LL uo1......-i,,ofr>, ......,,. N ...., l,Di"t9711 T :r'"r::." .. "".;"t~::i :. '::.,~=~ :!: 7.-:~~ :~/Jf~ :-' .;.-=-.: !:: ~.:i:ht'::'t"":1eri:":t :~:lip:~;~,:: O Po
  • -l in J97~ Thia,. .. u,. ,...,.,...ofoorboc.moin,.,..LodtlKKWllojoln .. ftrrt .. a IH1Uoi<><1C o .-bidoin1916.M o H ltoflhtrormin\911 a ndl978. Oo,.,.., ......... i.,,m..O""McGn. w ill.1'78.An outlineor,,...,,. .,,. "'-looth<,..t4....,.. A k., f,.ue w ~i,h m,k,o U.. ""' on!<,"" ia,r,ntltlt,d"'ll,,ptor.,,,...,fo"'tion>' (I) ltp,.,,, ld.I by""'"" the<11n-,n\ m .. a,,,. a nd oopplern
    PAGE 50

    , _......,_ ~..--..... _.a111oe u _.,.~De1o ........ -..1o~1. ..__.,,._,._.,_ ---,.., ... ~,., ... .,. ~..... --_, ,_ .. ,.. ~ li~~~!l~~--;n== Jt ..... l lo portkl .. lo..,,.;i,-,&ndpro,,ld.o ao =i~,,,~~:rihi::~ ~= 13 ::'.t p inp .-..tloel n -,dll,..U.. -lil,ra to ,.o fll1
    PAGE 51

    . ..... 1 ~ I U O 1-1 I 0 .. 0 M 1 0 2t I >J 7 I > 1 ._ .. .. ... ,...__, ,.. h .. ,-. ,... 11 ....,. ;,rty.6 ,.. .. u,i,,n 1S h o.-. lri
    PAGE 52

    II e.,. 11.e INTRODUCTION TO THE MOLECULAR THEORY OF THERMODYNAMICS 11 TF.DDAVLS ~==tJl':.=-w :::,:. ':':::.'~";, "'::.! .. Ibo..!:: :;.:-,_-:=,:_~~:! fttOt-!1oril
    PAGE 53

    --1Jf. l o 1$16.W -l l ]had _,, __ "'"_""'_ -la ---Loofpartial --A>'Lodpublh t iono!Wlets\Otl'~Otl,oolll>LIL ,_ lnodlor M ull!2]0860)to,tdi......,,_u,1op alonl thh l&C.- ndi tiibo\lorloltlo M-l'Sff") ..,. n,r .;;:;1. (it.II ()~=::.: ,nd,quala t heuromi. ntdivldt ,.-.if,..., c.-... ....... !'4 (U) -)iuwd lol -+ <>-+J'.(:t. t) -a::-:: c .., r Tllu.,\htmolfj" < >! The pr<>bobll ll y th at p&rtl
    PAGE 54

    --.... .. ,u 1 11Ma1 N,a.J ~t-/ -) St-} ---It U h lt U0 ,1 0 ._.. ,.. U h lt I I.M o l ... UO IO ._.. ,. UhlO ..,un.-----lllT.w. 1t .. .. ._ AllliaslborolportltlNlo =IJ"~.:;:.:i:\!:':;)1!"u!==:-.; =~:-=~~~):..!,_-,:.:~ Kol, (U), ,c ) lo,,_.i,.11,o -f~~':. of tllt __,. _.._ ............. ~--:.. 00:::.. ..... :.=.t='-~.:.= ~Mt-~""' ~ ... -~ .. ~ ..... ............ -1:1 J 1 t+ .,..,+( r ,IJlotM total_,.,,,.oftl1-,i.1Noltllo--""' -lo..,..1:,_ -~.,.,. (UJ P< P> A. (UI -F.lttlltf-""-- .. wallol A ... lllo...,udooollllo c....-io.r111o-_,_Uaod P wlllltllt.--Y ........

    PAGE 55

    -ofU T .SS-PdV,_...,.._8-lc<""'"> +C(/f),-C(l<)loo l,_. :=,~~~.::-..:;=-: !":,:'"..::=:olJ>..::.":'oi:!i"':'.;:t ... ~::. Jochr oM ooor. B r >mbl nin J tho ontropy o nd ... ..,. ,olallo n,,.. obtai n tl>e bul< ,to r tlnr 1><1lntolotollotlul~"'"'"""""""" ..-." ., ;k't,: ~ ;.._. ,,.. _I: ottnocti ... -.:+~fro).l,oQQN1ti toroP<1n-or ~":. 1 !".,;...i~""""U.,lai.ovu,lotZ.. o-ii 1 _; 1 11<.,. ... ,1.., .,..._.,,_ ::_ ':"'1.~u!~ allbe prnprlotodori .. 11-oftl>tpordtlool fu nctioll ($ -31'/a T. I' -~ r 1a v, ot< .) Tho qua nll\Jf h,l'lon ::: .~ ':~ ::;'1,.:~~,:; mo<-lepo.rtltioofunhonlt.ol Limit I, oln,llar to tho clooolto lf Offlllaof &<:,.( 3.l)nptlhottho int.wn~ o-er velo,;\Jf Olld -'cu n U... .UINanffplotal-._ ril,n,\-._ Olld _,,_ _.....,.,1q1e-...,oac1 ..... 1r11,,, .. ...,. totholclnlpopo.rtolthethertt>od;y .. ,.lof tloM.Tl>o...,l.TAOO V ondo, W oo .. [llf otota thot !loo pl"OV!dod ... ,o1.. ,,1.,p1oot.-forondo.....,,ndi,... U.reloU.ofpllMObtllaiorud-.i.., f-111-,-pirieal-ofVM.i.. -<:~:,; ... \, ... d'r, d'r,(U) ioio~!IIANpo.ltpoteotioloon_,,,,.i, N(N l) f2bolortheo m ber<>f lnlar>orlolad'r~lf ~ Olld r 0Nlor-.1~p(r .r p{ r )p(r ,),l.o., U.,po,tlt---~p{ r ,,r,)-..,to -l r -, ,-..,..11.n..... p{rJ,) r{ r ,.r ,) p( 1 ,)p 0 ,).-1{ r ,r ,Jiotho pot, :E~!::;:~;.i.:~,"~:~~ .. ouo1 .. !J, M> o r o h tl l, o-nd i-k relfhboro,ete l n o o loo t n,pk ftldp( r / Vud 1 ( r ,,r,)r( .r ...,. ,l ) OC>tl,o t -+N .. 1-1! jJ .. ..-,J ,-,,D ... .. -+~tjo<,, l,o.r,.,,~ ... ... lo ........,_,,tho_--...... r r r ,~,...,ulotesn,leonff-olU.0 ...i.,,...1nr,i.1U)toobtoio <-:> -~ o:-+ \r( r)u ,(r)~:.S; V o
    PAGE 56

    Tholnl,vda-y,ooillotulnll,eropul,,I .. portol F,<1.fU) <.t- be -lmalt ,tpui,;., ,.,... ,,.. rl1!J o ph ,n 1..oo ti..1 tt.t;, ..,1, rol, lo ltl\ocnti0110Vfl"Vo~""'Nb-Jliodllf U,omolocul&i-oolo N ,JIO'll-l>tln,:Hqld ond po,olumooo,..riv,nl nt htftaur,o.Tho l iqiclPDl"- .. t-ott .. oredttormlMt eboMlcol S'"llol, 1a r 1~ s1 ... o1 u .. '"'""' u.i pi,...1,eoq..a.n.i. .... -...,~u.. .,_,.oud,lrlot!','dP-0,11,U..tlllo.,... th,-,.iooti..n. ........ wlllltl,elb.>-. :!.~lrombtlo-.. uolotht-11_.. .. ,,_ Tho PVT ,ta1 t,-1.,. nde.,,..lh lhoduhed -lnl'1J. 1 .,..loloalialll l heopl....._l ~.,.. llenbo l kftkll, labl<.n-,,.. """"'tlm,o,alloJunphyoiI _,.and,...,.,.. 1 .... 1 1&1oo1--u..-.,,_ .. Pr -P/P,...., M-P ,-:b-+.-, .. 1-o.1r1o...i..... po,-a .... ..., ....... ..., T T /T, ondV V V ~Equo l lon( t .fllo,plioo lhtl Ml'OdUNdprooa u uofollftukto.-lllbttho Mmollt h oyoN ccmpond o tth oM.,. ndUNd ..,.,,..,.tnol>doquo tlono(o ute. Th .. lo"ot -dl"ll 01&1<, btln~ ti .... ol tho 00= ::-.:-.1!:...,""':;,= IWl -,.i,~,,_tho_tn'oo oad H dyitW.Ilhept,t14 ,,.0f~h-b. hlo< -...ttll nnaturo,an boe pl,,loedwl th tbeVDWt """'7aOO/orU,elaUllopo r amtttnl nt oe modclohYdedftuH!o.unl ;k ,11,eothfn, :::-!"licu~lr-5.LOI toq .. ntl tatlo prod!.,. A :.:.~f,:-=;:,::.":i':!.='!":1.: isU.. __ ,.,,.-..111,11 ... ,_ .. tll.o.t-J<......... 1aa<1i..-ollllo ......,,.la ..-1,rluot..............,boloav\oo-Ml -lo-plrieoJ f -IM~kliuabo.,._ ............. tltatlwlyto,,...ict~ ,._..__, .... __ l-Uoaltnldun,i1t...,teryf lolhoftrotuoou....,lheadv>n.v .... .-... .._-...,_ ... _..., ... ___ --"l.0.._. ... ,.11.1.K-.a..u. ,.a ....... -..... n.llfl(lrrl) I. l>.T_,._ ... l>..__, .._ __ ,_,._ 0.11.EM.o.: "'-c.-., ... .... ....,_,_.( ,..1 1,u.,) .. ... ~-0 ....._,, .............. U-J u v __ ,.._.., ..., ... H .T.,,....,,.c.n. .. .. ,.,,. ........... -. .. ___... .. """-. ~= ,.. ....... COJM")11. v.-,_ ,,. K T.O."",....._ ... Au, .. IO 1' .B.LC.NJ',I.L-K T .O.""-A I CHCI. I.B ,t.C.,.,,1.1.--.. ... n .T D, .... J """'......... -(tm) _, n..;,/7i:: =....i.:: ::~U
    PAGE 58

    ----J,,. M~ ---

    PAGE 59

    AWAJIO LECTURE C-.0-, __ .. :::.::: :-:::.-11 --. ":=-.:~i:::i.= ,onllollo-l oddlU.ledwa ..,.. .,,,.._,_nt::..:.~ = ~~loo~J.,.nplooi,o,lt..__~,,.. 1, 1o.-.o1-t1io .. 1e=::.:::::=~-~.;:: __ .. __ ..,._,..Mot. h1lo11M,Mlo,_,_loo.,_!~"'1b)'.....,,.;nJ ~=:.:. (! : ~~.::t ,;~.'"1.~"1! ~h,.::;=~ ~:h,:';!~t.th1d-nn--11oc1Joalnq1 oll ph11k a l ,Mmi,tl')' tnu, aod uplalnod &de ~tol,on,I <111 in a1moo, ,_, .._.,..i..,'-~ottlooipllloo, tioaluror 11 w1u,o,.......,..1o,pt,,-111-. .. .:;: ,~ ..... 17 x, :: doriUIIMllf10'0.Tlilodlarramapplioa1<1.iu...oir1<--ot"1<1-&.ncl-..-. dld,rl"-opooclU..1-it, -i. ftlorilJ'; lllu tho lpotl,_ limita ON .... ""plooioolif0i1t,,lf.,..a1&nol.....,.lowp,-u,., al a rl_, eon&\,..l 1.em.,..,..1 .,, (..,., UO C), ~ ;.:;:~;; lf nooana
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    (110,) :J1{~~J 1'1,i,.,,.._lloabw l lnln>1rnd!nthlo ,...,..,whkho
    PAGE 61

    -llllolootbyONduoNn1o,r-.-,r....,_.i...,,..raioio .,.,.o1, ,i...1. .... ............ rr ... 1-pen,1, ... :-::.:."''==~:~"~ :':":::. '= =.._~ ~~2t:=T.f~::.~::-s;d ..,.,_,.gh7Mrelotion' .J / RT .. J i< tho odlobolk muhn,,m t,,mll",..l,. ri.oo. A loo ~::~:!::~~~ =.. '":. ":11:":.ot lho~::..i ~::-;~:: I ::-,.,_ .. ,..,(-:-). Wlllolliooldoltlloopl,tricol-~l_., .. ... olorl_f... __ .,,""""-.iy.po.rt;c1oo1-... .. .............. -. ......... 1t1,1-o .. ,...-1-,;.,,. Tll4t0fflp,on.turosndicntan6 Tho<0r,..oo,,dinrv&lueof th o dl ..... ,wotliffa TOUP forme,11,ha"d..,.ll.. 11o..-,._,,.,notn dl"""'' 1' ... thi<-.K ll.lo~by ::=:.=.'.'1-:...1,y~U..--=--. ooolJ'll<""""--lo--tlloeriti
    PAGE 62

    111&qui10-iinc1<1......,IIM_,.,.....,. ,.-1.u.o~.................. ,y ...W------" lIIM.,.;a;,,,11-jwtUl ':I, .... _,.. i.o_..c.tol.l'JI -IIM<,.. P pMl\hoIII .i.. .. 10Udttmoento_M .,. Lhoplu ........... .... -u..,u..,,MriouolJ-.,....i.,,plltytM llaotb,ud\l,ateaCIOP\AMtl i w ;..:;:.i = ~= !".!.::',~~ ,-1;,,,u.-1ono.r..o pnmi.od-,U..,..._ ..-1,.. !lNlfW pro)tlnr 1ndlt.o.lo oad i-t -nl lokl tho -inr
    PAGE 63

    d i ""'nsi"""""'"'"""' '" "t b,-d whiion """ tn"'"-f~. -*-17.--c~ "' .., u !;;'on'.7o': 1 ~ ~', ::.i"'"t:~d :. ~ :~~::n1'!.. 1 !: f.,';;;.;: .:i~:.::.; ~;._t~:ire,: ::~~c .. n...,., l<>n of.and ca nho"""'1 w ihU to de1\nolhe\mt ~!~n":k:'/i.=:.!.."::~~":: Th o AZ sruu p "->booneall1.-Gn v B ................ ".. -..-.-. .. -.
    PAGE 64

    Individuals are alike. Aren't they? =-~~./;::-:.=.=: --Co,J,cw--lOl>O~::-:.i:.:::-=-..:::. ;_---., "'-----1---~ :-'...:::..:=..._.__ .. ..,....,,_ ===:.::-~ ... -"" .. ll_,.,....,.,.._lt.,,..11__,,IO.,_ ... _,_,..,._ ...... ~==-~==!: ==--~!..i~~== -~ ..... _...,.,.,. __ =~En=::."! Mon.ll~--1.,.._ .... \'0lo"ll'P"ol"-...... ., __ ::::...=. .. "=~~.:'~

    PAGE 65

    ~)-,, m l>tr.tholMOr,,.....l'<\{.Jlathatw. r .t .h kk AandUo ,o .. lfodjolll\.Tlitdt -h .. ;:t.ir1> fx-1q() ~i,1!.~o1~d:r~.=~ P'-""'.Tiot-loof <: o.A1 >-( ll> JIJ' )-O ,,,_LUO-it1_.-...i11,..__ r ....... on--..-w ... .Ltl,ol ....,.ion(t) .ftlo-llao- pplllt,o i>m>'"-lolooot1ruofor(l1ff...,......,.ti_ on
    PAGE 66

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    The people behind these products still remember looking for their first job.

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    UNIVERSITY OF ALBERTA lOMONTON .uaEIIT.t., CANADA Gr......, i. Prottms in O.-. ic.ol f"9 ~ ""-0.c.ndklo""'""'"OOO/ .... -~ .... ...00, .... f-16'10lo,M.k.(pblCllo,VIM_.,. ---..-,, ___ _...,......,u,o -,,-..:io __ 11(10,--h,,~ -lnfo,... ... .. ... o..r,.,.. ~al0.-.,1~ ---~IIIG206 :~.:.:-:o. -=-----~"t:i.~.e:::-~o: S::-~~':"C:.~'c..';: .l.L.l'h.D.~-~ ----Kgl,-.r-..,-. :=-":!:r...=:--~--=: ~~;~.= D L-, "'-D.--.,..~Tho,,nolon,I ....... =-.,..,_...,a1,i..;.,-(q,,,IM:,,lo,n..,:.,:;::::-.,~--'-91' G~ .. ~t~~:::=:: LILW,""-D---~ ---c-.--~ ..-.. .. C""""'9_~~ ... _...__...,,_..... .. .soo.-. ~----l""P""'I'.. ...,__,...,...,._~::-~-...,"O=:.:'..:'--

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    PAGE 74

    THE UN IVER S ITY OF ARIZONA =~E:=~'.':'.=t.:~;;:,:,.~:!.7.:!.1,~-:::::~ 1 .:!" l~ od;! .,.,.._,.., o1, ondoon 1' arn .-og,,...Hd,,,.~,..,w,;,..." ;,_....,,_..,.,,. ,,; ,1"'"'" '"''""'1.., .,,u,..ful loppo,t,.,o llyto $!0II WIU.IAM ~0$A.IT ,.,>0<. P ,.,!tiw, Ph.O.~S1,,.Un1 .. ,.0y,1973 ~::.=~ _, 1,..,.i., In liologi<.ol S,... K>l ll'HF .GOOSS ,l'rom""and>lood ,t,.O ,,,,,..i,,.-.0y,1956 ~t.y.:..~, f :-~~';1 .. :; /OIT 0 .~ WENDT ,""" '' l'h.O.,JoM,Hopk..,IJnJ-, l ty, \ %8 CorrobONH.WHll(, P,,of.,,o, Ph.0 k>w SI ... UnJ-, lt)',\9 Po11---- ond "'"""' So1 ... -.,,. Miaro,l nd&uy"'"'le'""",..' ALA ANDOtPH, ...,,-o,.,. Ph.0 1ow,s,.,,_,...,, ,u> SiMu l olionond~ott,yo1, IIFHt'"~ ~~;:, .. ~.::.,, ia,1 -Pr,;,ooum. bp<>TitOMA,LHHM, ,,_ ~:,~:f: i::..:~= t ~9!. P011 Rffl.nmoCompu,,..,,.._,.,.,,,.,....,, ,1on ,nd Con1~.-av;ld""'onds.n.,ra11on 11 lH .. ..OSH,..,,..,H, .-...1 P2 -..,,;onEog<,_."'11, Kl notl<,..C.
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    AUBURN UNIVERSITY CAL ENGINEERING GRADUATE STUDIES G,adut 0-.g, Ns A,HD <>iption oo~~ c...iliquo!..,...,,_...,... .,,11 .. ;,.,..,..,. -'" ........ -.. ..... _,..., ~_,....,._ __ ::-..:=.-:z:::i: 00 "' NO..-iHta lS ,~~ ----- ,.. _.,_ .. ...__ .,.-~ .... ..... ...... ..................... 0 1 ...,.; _., ,...,> tO MM!tTo -...i_,. _____ ....,...._ .. .. ____ -... ---. ::;,,":.:."::'.'-:::=:=

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    The Univeriity of Colgory :..==---=z~-=-===~,:,-..::= ... .......... -------.. -......,... ________ ..... _________ ... _,_ .. _., .. --:.__ ___________ .,.____ -------------.. ----. ---' ___ ._ ................. ., ___ g;-..::"S:.

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    PAGE 79

    UNIVERSITY OF CALIFORNIA SANTA BARBA R A H OO lAM S AN O.,NANCI .... SUP1'0l T 11 ,. o.p.,mvo toll .,.M..;r,~43~~=~:: .. -.. ... ""'' :r:_ ...... ~1-,,,., ............

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    PAGE 81

    Ever think of Grad School as an Adventure? -writc GraduateChemical Engineering Carnegie Mellon University Pittsburgh.Pennsylvania 15213 $

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    ' IS THERE LIFE AFTER GRADUATE STUDY? Wa nt to find out? H eaven can t wait -""""'Case'o\t!slerl'I~~ CIMl!and Ohio441()6

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    Graduate Study cI~;f;~n M S... 0-... C,0,. ,,_ ____ .. ----? Fae"""'""', ____ ,_,_ S>""11 ,C0,-'"11 MO<"'"C'"''""ll"" "'_,...,..,_ .. .,,. __ .,...,,.,c.,,,...,..., ... ,..,...,_ .__ .. ,.,.,~..

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    C h em i ca l Engin ee rin g a t CORNELL UNIVERSITY A pl ace to grow ... ---....-... ---....-... ~..,~ ~~------11'... -----oor. ol cllomo
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    U#IVFIISITY OF DELAWARE Newrit.o.low ... 19711 "'"_.,.,, ___ .,_..,_.., __ .. -If, ........ _.,,_.,.._... ,.,...._"'..,_ _____ ,_....,__ ""~-~~~:..:=~: ....... o. ................. ... __ ... ......,, ...... -""'b !'lll.._.._~
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    Onlylhe Unlversl~ of norlda's Department of Chemical Engineering gives you both outstanding academic challenge and all the advantages of the Florida c:Umate. TI,o---- --412_! __ .,..,. ---: .. _ly __ .,_ oil--,by--~ 1-... :.i"'=.=== = ==-----......-.: __ 111,,...,.,-.,..., ......,._....._.,...,._,. ""' __ f ___ _____ ...,._,lO __ ; tw.i.. _____ ... ; .,.,__,IHIM\<_ld,St.~. =...~---~_, ... ...,.......,;,,,.

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    GEORGIA TECH Cooado,o; ..... eco""' eom,,..,.,,.ic.,,,.,o0oo lS oos Mojo:Co ou, .. Ol'>d RoltR0< w:;::::; ~ C. n ,...,g w"h ;,, 41 <0,, tli1YToeh"""'9v 8>.,.,k ol E"lli<> -inoj ea .. .,.i,aMS,,rl..,... EnotgyAOSff,chtg o ndM ; ,..,.1E~"'lj Potvm,,S< -ongy A...:to,"' ; g n Stag~ .. P,oc o .... T,.,,_,.-.,.,,. ... ..,,. ..... ,., ...... .. .... O, G,..,W .-oln S
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    111111111 SIIIII III IISWCII DIIMIIII-~ IIIIIIIITI I ILLI E II C ICIIO CI IL E GrMu>IO,....,._loo ~o.,..i ... eotEneoa,~ -i. o,....,_of MASTEROl'SCIENCE....i ,-_...,,_._.,.,.,,ki..lo C,...ic,.~1t,~CIHa l1'" -... ... ~~.i::~a .... .._,.._. .. ~.l'"-E&E .... .._.,_, ... .... 1).,~ ........... ::,.~~= ~,.,T:J'~'Et'JL-t-.E, h:;:; ...... ..,_-"""" 1'1,.11.Coko!<>"' ""~S.:: ....,_'!:r;_" :;'ii"..:;" K ..W~. ,...,,_,_,_k ... :"::5.!= ~'!:.~";~-~ _,_,., ..... .. ~E",;:.:.-::; i: .:i ... .., ____ .... .. -, ........... l'Nof 1 .C.l'.Chw.<-,.,_...., n..r. ... ,~c--~, .. ~:7:~~3;..

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    UNIVERSITY OF ILLINOIS UUANA, CHAMPAIGN ACTlVE, l tIBPECTED. A CCl-.SS IULJ, ~ PA C U LTY """~ .. ...,.,............. --,_.,._ ... ....., .. .. ...... ------.. --..................... ,1oo .. --l,Ogl, lhotowloy ... -.o1 ....... ,.... _,,.o1~ .. ""' ......... ...,_,.o1-.n.o~p,1-...... r::::~?~~~-~~ k ~;:.; =-~..:.:.. .. .:.::--':!"'..!::.."::"'"'"lobEX CE PT I ON AL PACIU'flt .S Tho~ .... ,...,., ... .. ___ .,. ... _.,.,_., ___ ~........ -.....,_~..,_... .... _,_, ..... _._.....,....,.i.,..-..... -"''O'"' llt'"--... --l........... 09'-_...., ____ ._I.....,,~-.......... ,,_ __ ol...,._ ., ... ___ ... ...,tyt;a,lond ---~ .............. Tho_i;i....,,._o1 .... .. --.... _......,.,..,i<-noh.,,... _____ -----n.-.. ..-. ............ -........ .... ...... -..... =.::~~~ 1 7 .... ~---~':i".!.."":-_,,...,, .. ..,. ,oc1o1_ ---~ ::::-:-~ ==~-s::

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    ILLI N OIS In s titut e of T ec hnolo gy M S .... dPh D.progrffllinC ...... i
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    I I THE INSTITUTE OF PAPER CHEMISTRY rHE INSTITvrE .. ., __...,, ""' ....,. -'""--offcrio:IIJi,lffotlo<~ ............. ,...._......,, ....... .s. 0-01< .. ~"'l&..i... ... lfUA/fCHACTIVf1Y_ .... _,>d.,of .... .,_ ....... ,. .. _ew,,,,,,....,,,,,...,_ .. .,. .. ,. .................... --'"""ol ............ -~ ............... ,t crilh,.i., .................. -.. ,.. ...,.,_,._ WfHAVf11u,hln1l..:ul1yo/4S, 1 ,1U nl<.i...,po-o"""""'""' _......., f/JU 1/NANCIALSU'fORT"' ............. u.S....d C:........< _,..i;,.,-.c.-,-... ....... -n.000,-.,-y, ... O...,.loll -I.IIIOA,.,ltflcOli ........ fetud,-1 ~-_,..,._ ., .. __

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    IOWA STATE UNIVERSITY SCIENCl ANO TKHNOI.OOY =~i:.ll-r1 ... ..,_.. .,1oo1 i;:boGu..DUATESTUDYand GU.DUATIWEAltCH n_.-,,..,,,., rro...C ... lotq ... d t en1111tt T ttbol ff

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    Graduate Study in Chemical Engineering KANSAS STATE UNIVERSITY M.5.ondPh..o .,,....omo l nO...,,icol fngi.-ring oncl ln!WtlCiplillCl,Y At.o1of$ys-f119 ...... in9,food s.;.,,ce,onclEtwil'OMMntolEngi f inoncNI I A.f A~ilo l, l,o Up 10 S7,000 P., ____ _,..TO _._C..l .... ----COAL,.__,CON'il""""' --.......-s ...... -~-NQCUSOY~ANOIN'Ttol -~IUCTIQH-tlNG u.,..,,. ~ --, Qr'INlU.--l'tOCUSlmtllO .... -~

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    CHEMICAL ENGINEERING ATM.I.T. GE NERAL ARE AS OF FUN DAME N TAL A ND A PPL IE D RE SE AR CH Eatrl'/CNwffliN ,,_._ """-~-~ &tt--..D-,. l'rlc 1 ao,..ic11Ml'rlcHS&tn!rlll .... ... .... .. bfiottriol C. ..,itrl.i6N Oe llp T,. Uptrt PIM,,.m na s.wt 1e1 1ndc-i!I Chl lllistrf Chemic al ftuc tw Ellglne"""I themlslry Cht mic al Klnttict 1 IIIICmly1il C.m ntlt n ----'"'" "" .. ..... -~; ~ i:::::. ... w,,,o _.,., =.";..-.,,:."=,, .... .. -. : =:: ... :::::== .. _____ u::::::-,--:.:--..::..0::::.=--.-::::.~ -------.. ... -~:.t,.~.,J, -; =::.=..--=--... ~"' tt;:=,:=:.::-.:;~~ ~~"";:-==-. ._ .. __ ____ .. ,_ .. .. ... __ ,,..;....,.,..---.. .. .. e.,.._,w -, ,,.,..,_, ,_. __ ~ "'' :::: m:=~-.. .. ~:". "!:' .:o: ,:,: l'.'1' =:. .:....:.: ... ..... ~:=-:: .... ,._,_......,.. :.:.=.. -:==:=-=-=--k"---:-.:..,7-"' --~-::.t= ~ ';'o,., '" t. s :~-::.;-;::; :.:..~ ~"-:;:; ... "::::::;-, ...... .. .... ... """' .... ......

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    PAGE 97

    THEFACUllY -. ............. -c, ... w _,-.., .... ... "-~-t ,s.llo,UCIA H ,._,.. ... 11-.~ .. ( ...... 0. 1 ..i 1 ....... ,C. I T 0< h J-o, H, ool ,.,. ,,_...., ""--Mkhig n ....... = "',:::;.i~ : ~~:1 c, .. Chemical Engineering At The University Of Mi,higan THE lllSEAR ot l'II OG IAM THEPU.(E D e pcirt .. e nl Of C h111l< al E119i11 H rh19 THE UNIVERSITY OF MICHIGAN ANN ARBOR MICH I G A N 43 109 For l nf0
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    btpon ... of som e of our,.,,,..,, a,.du.tet1 \HMt'l111oth.q .... 1 ion "WHT MINNESOTA ?" ~ 1<"'-M....,,oplybcao-ol ,1w, 1 .ui,.,o1wochool-i1;..i...,., d11coool rontu..,th >1 arc<>liortd WHY MINNESOTA? v .. 1rU:ASI/SE.\"D/l>'f'ORJIAT,O.VO.\' 1t'OVRCRADUA Tl1 P/IQCRAJI TO : :Mo,..,

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    UNIVERSITY OF MISSOURI ROLLA ROUA,MISSOURl6S401 Con t ~ 0. J. W. Johnson, Chairman Oay P rogr"'"" ~'=-~~.::.... 1rE:..:..~ ".";=~~ mf:'~~_..:::-.,o,-"'~"w-,. -.J..LGoddy-,dDo N.Lf.i=--l'oly,-'<-......0. H,1<. M.S.andPh.o.o.g,!. ~""'~.::" ... """'_,,... (ol=otk>ool~Sy,--0..J.L (b)~M.':.=_,_,.....,_ lllol ... ftf_...., s..,--.0..l.C.Wlo)-~-""""'~ .......,.._ .. -.~M.L ~,l.C.W-,ondl."-_,_ (f)~F~=:;;v;;;' .. (gl~;.~'!:.;./_.._ "Pl""""" :,:. Finncllid il obt1 i n 1blaln th 1 fonnofGr1du 1hl 1nd l ,d, A1 1i1 1 1 ntsh ip1, ind l nduml1I h ltowohip& Aid itoloo obtoin1b la throughth 1 1 r i1hR rd, Cenfe,,

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    Gr.duateStudyinChnnieal~at NORTHEASTERN UNIVERSITY ""'-"' _.I)_,,.. _____ _,, ., ...---U..tog,..-,0-.~IMl-n.t.OU._....,.,. .. ...-.., .... C-. ..... ol ,,....,,,_ ..... .....,_~-----_. __ "r-nk> __ llgl'O __ ____ _..,_,_.......,.. __ ...... ,-. For (urthninformation plea&e rontart --"'~ ---0:1111

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    pennsylvanla chemical and biochemical engineering i' \ .. __ ~I _; / Jo .. :J .. :: w"",;1~ ....... .3.:;,..._.., ... -f" .. .... :....::.... ,_ .. _.. ____ .., ___ .. --

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    LOOKING PENN STATE .. --............ __ ....,_,.., ... asutoo _..,.,_..._Cono,d ... _,,.... .. _...., IIACI O ll>IIIO N A ,.OC A T AlVll1 r~EZ -......--,.._....._._,,_ ~---,. -----c........---P'tOfUTU =~ rl OCIII OYl<~U.NO CO NTI Ol ::=-'.:'.!-:!\:.~ A"'1.11 0 CHUll'I TIYANDIO"" OC:I -'-'~c,,,,,,,loo-S.,._.....,!..,ii_ ~"""''"" '"'_ .. INIIU J,.ClAl "'lNOMINA =:::;..,:.,_:~a I N IIGYllUUJICH lonlo
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    @ @ @ UNIVERSITY OF QUEENSLAND POSTGRADUATE STUDY ~IN -!fl.:!i CHEMICAL ENGINEERING .. ,__ ~ ~-, .. _______ ~=-~ Q FURTHER ~~-...:..__.,_ Q V IMFORMATION ~.. --""' V

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    Advanced Study and Research Areas Thermoctynamic s D Hee! T rans e,, Kinel ics-Calalysis 0 Fluozalion 0 Fluid-PamcleSysterm 0 ln1ertacil"f'h&nornena 0 ProcessDelign&Con!r OI 0 Polyme,Mat ll'iell 0 PolymerPl" ()CflSl ng SiochemicalSystems D Airl'Ollu t ionCootrOI Al mosphericOlemistry v.AllerAesourees ErMronmentalSrudies Or OMdHansen.Cllainnan RENSSELAER POLYTECHNIC INSTITUTE M S. and Ph.D Program s in Chemical Engineering The Faculty MiehilelM.Abbotr PhORens:se,l;w ElmarR.Altwicker Ph.O.O'woSlatfl YamanArl(IIJlm PhO WillianWShusler DCIIE.Rensselaer SamordS.S1ernstein f'hD.Rertss#Jlllef" HendrickC VanNess DEng, Y ale PeterC W9:yner Jr PhD .. Notfh'NfJSlem SrllllhenWYe
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    Graduate Study in Chemical Engineering at Rice University """'""'""''"'"""'"'II-Ing """""",,....., --,T""",77001

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    I I I I University of south Carolina Th o COU"11 0 lifl'tMt ,.i .. ~ lt l,on> T .. ,..,, ,.., ,.,.,01Sou,r,Co,oi;n o, w;m on.,,.> ll m o nto!2J,IIOO on 1 n, Colum~ lo em/><' O. ofl oro ,orloty ot ""'"" "" ""'""Hoo" ..,~.m .. Co..,m0 1.o. 1, P 01,,,.. ot me,,.,.., g rowi "ll'"o ln1n o eount,y 0.L.. ,~-~ ......... 0 ., -5' ... ............... ... ( __ ... ., _M.__,I .... ,,_ .... .. __ .... .,.,...........,..,c-,,,,;..,._,, .. !>< -~--..,-,.,. .. ...... .. _.__ .,, __ .... _,.,.,,...._,_, ... ( ~ ... .... ,..__ ,,, ___ _____ .. ,c,._, .... _,,.,, ,c., ...... ... ... .,"-' "' '"'"""'"'" .. .. "" .. -----... D.,....._ .. __ ,., ( ~, .. w...,.., ,.._,,, ., _

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    Chemical Engineering at Stevens Institute of Technology Master 's Chemical Engineer-Doctoral Degrees Programsin Chemical Engineering Science Proce ss and Polymer Engineering Research in T...._,,._ f loidl))'..,it,. ~ ;< Tt>nlf., s.p.ra,;.,,,"""",.. -~-"''"''l''ion..boxtlooo -E,,pnm;,.: C.IMyli<. ob'Mffl
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    THE UNIVERSITY OF TENNESSEE, KNOXVILLE Graduate Studies in Chemi cal. Metallurgical and Polymer Engineering

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    M S a nd Ph.D Pr og r a m s in C h em i ca l E n g in ee ring Faculty ,_,.r,:h int~, .. ,. includeAerotol T echnology, Bioen1ineerins,Combustion, Computer-Aid! Design, Enersy,Enviromental. Kineti< 1endCeta lysi1, M ate rial,.Optimlution, Polymer En,inttring. Pn,c,eq Con uol, P l'Offlt ~;n,inttring, P'""'Simuletion, Surface P h eno men a, TnnsportProceseo fa,..dd11101/t1/mfarma ti
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    :cl y z y A Chemical Engineering a l Virginia Polyte c h nic I nstit u t e a nd Stat e Un i ve r s it y .. ;,pplyir,g chenll$ 1ry IQ !he needs ol mllfl K .. ,. .1,1, R .. ...,,;~, :E?.::.t~ .. -~..::r:,,~ Co.olSl,,-S d "" """ E,_,;..,. ..... =-~~-:::,,,_i..:,...,_.., ...... fog; =~~..,;:=; ;.;-.,,.,_,.,.._, !l.;,ch,n>ko l t..,ln,.,;.., =.,:.=:.~===~ W ri l ot,o:Or. ll ,A, .11 <(' .... J, .,Uopa~\ ll ..,d, =;ft~=Pr1~F~~~.;.tov~I< CHU ICACN~INEEIUHGl:OI/CA.TIOH

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    E i,ergy Engi n eeri n g Env i ronmental Engineering ----~st V1rg1rna University Other Topic s Op,1,,,1, ..... -$wl--c.aM__ "' __ .. ,_... M.S and Ph D Programs :=:;.i:--...:.--w .., v;.,,.,.. 2H06 w

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    CHEMICAL ENGINEERING DEGRE1$ M.S ., l'tt D. e HIATAHD"""'551RAN!.f9 KA<;ll()Pj l'JNfllOANDCA I All'SIS l'l()Cf$$ DVNAMICSANCCONll!Ol l'l()CfSe M0D(UNG IN COAl OA$ 1f 1CATl0H. C HfM -.....,. ..... :u. ..... ASU __ ,,., ,, G,oduo M otud,.. in CHEMICAL ANO BIO ENGINEERING l u dingtow rd 1 MS nd Ph.D .dg M I -t-a..... .. -..... ::.::::.~

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    THE CLEVELAND STATE UNIV E RSITY DOCTOR OF ENGINEERING MASTER OF SCIENCE PROGRA M IN CHEMICAL ENGINEERING AREAS OF SPECIALIZATION Tr""'f""" "-Bioengiing Simul.tion,._ po,.,.,.Ml,d ;. .. KlionEt.gin-ing z...litft ::..."":.,.::/ .. ::::\ .... :"' .. .., __ ... .... ....... ...... FOR FUR T HER INFORMAT I ON PLEASE CONT,tiCT: Oopa r1r ,,...,<>1Chemle.iE<>ginee
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    CHEMICAi. ( t,I N( EJ: I NG M S nd Ph.D PROGRAMS University ot ldaho Unn.ersity of Kentucky ----------------... .._ .... __ --.. __ .,. __ Departn, e nt ofC hem1calEngmee r 1ng

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    UNIVERSITY Of MAINE "' GRA D UAT t ; S TUDY I N C HE: \ II C,\ L ENG I NEER I NG M.S. a nd Ph.D. Prognm e ..... ,_.___. --CHEMICAL ENGINEERING DEPARTMENT -----C.... --~'":::.': 4. L '"'1o ,C~, ..... Dopt,,,.,,tolC-k,1u....nit,W.. o. -.w.-u UNIVERSITY o, MARYi.AND ~--b.oodp,og,o! ,i,od_,....__,.ri>oMSI,.;,,,' ___ .,._..,.___ .. ____ Enfl~-..ioo..-. ........... --._,c-,......_.._ .... ........ 191'9-tQ--;. ... ---......--,,,,.,.. ___ ,,,_ c., ..,,_ .... ._klo<, 1--fno,,W---D.C ...ditw.,-~~~~"1:~~~-=-:t?i"~=

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    UNIVERSITY OF MISSOURI COLUMBIA Studi esleadi ngToM.S ndPhO Deg r ees AA~'~t~~~~::,:=- ~~:=:::o1-Tbomo<1l;q.,;d> ,._. ... '"""'.1s,-,,..,,,. .,..lff, t ~'::;:" t;.. ~~:::. ::o~;:-o1 c,_i<,l .. ,.._."1, 1030f ""' UNIVERSITY OF NEBRASKA ci r pollo r ;on mi<,oproc0>>0
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    THE UIIIVE1tSIT'I OF IIEW MEXICO M.S, nd Ph.D. G,a.du.i Studiu in Chemica l ( ngin .. ring """"'--~ .. ly,,_ ...._....._ i::? ~lf_:_ f.J-o.. ;.. o..m .. Oopl, of C'-i
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      M S a nd Ph.D. Degrees i n Chemi cal Engineering []] Oklahoma State University ORE G ON STATE UNIVERSITY a..,,,1c lfn 9i-in9 M S nd Ph D Progr1 m1 """".,.,..,.., '" ~ _:,: :, :: .-, .. ... .. -...., ------~~ .... ~~-=:..::.."'=1..t.~;:"".i:..-:...,..-:.:::,c::.~7,'1 -ol---~-..---c.,..,...,.....,_ol ~..., ,,,....,_ lo .,..,.1-.lo,.,_._,.ol...,Will_,,.V.....,_..,_,_....,"'lll!N ~eo...-10 ...... -.,..,.i ........... -~ ........... c-..s... ,.. -. o.-...1 .,.,__, .,._ ., _~ c.. ....,.,._.,. n1

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      Princeton Universi ty M.5.E AND l'l, O l'IOGlAMS IN CHEMICAL ENGINEERING ~tl<. Holl, E mo, t f.-,Jel!,oy-.,.;,,,,,.,,,.,,.O Ko
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      U N I V E RS I TY O F R OC HE S TE R UNIVERSITY OP SOUTIIERN CALIFORN I A Ull!Angelee Gnaduate S t udy in Chemica l E n gineering F ACULTY ------=-=--~-===

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      Chemical Engineering at Stanford S ,orllOr d oflor p rogram J ol aod -"'"'" __ ,... .. ... o .. ~ i;;;;.:~ Choo.~olState Unil"ersity of New York al Buffalo, ..,.,.,_ ., .... ........ :: .~"':,A ....... NY~:"'L ......... ., ,.

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      CHfM>CAl "''"""" GRADUATE SruDY IN SYRACUSE UNIVE R S I TY ~-:-.~~==7 __ -.. =-...... ~-:.===-=-= =-"::...-=-=-=---=--::.==---~... nLlOWSHl~:~~E ,_~=~ ~~~:!::a AVA I LA&I.E ,....,__ C-K,5=:~~~ E~~:;;~~ ~=~.lc1mo The University of Toledo -S...,T- M S and Ph D De grees

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      TUFTS Ult/VFRSITY .... .... _,.._ .............. ... .. ... .. .... CHEMICAL AND MANAGEMENT ENGINEERING TULANE UNIVERSITY ~_, <;._ ... ___ ..... _____ LU..... -~~- ";.:::-.:t... ~__E:' ~=---= -----"'-"'~-

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      GRADUATI: PROGRAMS IN CHEMICAi. ENGINEERING T he Uni versity of Tulsa Nllntll-TION H ,.,.,-.ldll h __ lo_..........,.~f_ond__,,,,_.., .... ~,_,Aa-.kol&.i,;,-"'9(1,of. """'-~ ....... ~--ond---bo _.,.,.0.0,,<11 ... c;,-n.,_...,. ... ,.. n..-.....-, ........ -1,........ ~ -OK oo ..._,.__i.,_ i,1111-11 _,_..,__ VANDERBILT UNIVERSITY GRADUATE STUDIES IN CHEMICAL ENGINEERING M.S. AND Ph.D. DEGREE ,ROGRAMS ~ I ond Adv.....,! w ,,.. w .,.. ,._.._. ,_ ,_ llqIH ltlKMtlAA T ION W. o..,,,;, T"-
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      DUCKME:LL 8UCKNELLlJNIVERSITV Oop;,ttm o noof Chomlc a lEngln .,. ,1"11 MSPROGRAM :., p~ ;:.;,! ~:=_a:.g Canada' l a ,9 91 1 Ch e mic.ol Engln M ring 0.. pertment off ert a gularand co-operaliY a :;A.Sc., Ph.D. a nd pott.doeloralpr09ram 1 ._.,.,_, ....,.....,_.... a.....: 1-,ct1,fyM,_,~l ond ,oll"' '" ~ ......... ...... ,,_,,...., :==.:.:;..":-:;:::::"ano1c-.. :~:;,~'::::M H:~

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      """' ......... ,,.,., ...... u,.;.,~ "' '"'' lowoClly,...,,1>2 1 THIUNOVUIITYO,MOTIIHCOUI G~DU ATIITUO JlSIHC>IEMICALINGONUllNG : ... ::.. ""';L=.---=:;,.,:~=..w---... MONASH UNIVERSITY Dopo""''"'"'"-'k" l "I;-.. ... ..... .... _.. ........ g:i=.c :::2":::.".!'-:::;:...= ,.. ,..._,1,1,..,,_,...,u.;..,,;,., W olli nglon Cl, .... ,3161 v-. ....... ..

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      MON T ANA STATE 0... 0l>lill ~/ romCool ~:='C:::.... b1todMoC,,,..~,-;o..olO>ol=-;:;:.::..,._..._.)~:.::":' ... ~NEWARK COLLEGE OF ENGINEERING --. .... -----_ __ ... -. ,_ ... __ ,_Nhlh .. .,,....nol f '"onRTM DAKOTA ........ _,. .. _..~

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      UniwnityofthodeblMcl -stvctr ChemialEngin-ingMS PhO ,.__ .......... oor..a.. ----.. """"""""' ___ .... _.._ ,.. __ ----"------._,_ -Al'ft,OC.TIOlao-an,..,_ot ~:..:=.::~!' .. 'i.J:.:! IIOIM$$\/1'-lV.TION l'IOCl!SS(HGINU I NG 1'01.YMl'.SCllNQITfOINOlOGY fNIIIIIONM(NIAlCQNTlt()l -~ COMl'I.VCKUICIKCIW5 =-=~.:::;'::: -. .. .. ::...-:::---..i---UNIVERSITY OF VIRG INI A CHIMICMINGINlUING GU.Ol,IATI ITUOIH M.S.,ond .... 0."', .. ,,,. .. """""'~ .... a-...,~,.,, .. ,-., ,-..-i. .. -. l8U.IOll'ITU!H11, __ ,,_, =-~ =.. -...=: ------~~-:;=-=

      PAGE 147

      Che m ~I En g ineerin g a t YA I .Jo: y J W G i bbs l' h l>-En gr g 1 863 Yo u PhD -E n gTg. 1 983 Spec ifi c f a c t u a l k n ow l e d g e s t a rt s t od a y ... fo r so lu ti o n s to t o m or r ow 's e n g in ee rin g problems l' ,<>m<>11r, l,r,,l ,d """'""""''l'r<'""h,ndth< motth'ffl thro<0~hou,. 1oeo.l(l,.lpp. ot.S'4.9J r.~;..... ... ,., ,.,, 11.._..., _u.,.. 1-1+o,~li;;..N.1t:'d

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      PROCTER & GAMBLE is looking for in R&D/Product Development <~~~..!'!: elQY-.. soMng,.,tv>lc .. p,<>l>l,,m!.. -ll'lisorgani:!atiol1~""'VI 1ang, o/ soontdic(1..-.gineering ~ltogirlttmg,M;n.ilact'-"'9...,., M arlSherto.,.,.,,.. R &D/Proo,ct~dM,""""""P &c; ,..,;nt,.;wid~ t hnitedlnthl, ., H,plear>end T1>el'to<1 e ,&Gaml>!tlo,,Ofllc e l"'yd aleT e d>nlc a lCenter ~~~~.::~~~;';A""nues PROCTER & GAMBLE