Citation
Chemical engineering education

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Title:
Chemical engineering education
Alternate Title:
CEE
Abbreviated Title:
Chem. eng. educ.
Creator:
American Society for Engineering Education -- Chemical Engineering Division
Place of Publication:
Storrs, Conn
Publisher:
Chemical Engineering Division, American Society for Engineering Education
Publication Date:
Frequency:
Quarterly[1962-]
Annual[ FORMER 1960-1961]
quarterly
regular
Language:
English
Physical Description:
v. : ill. ; 22-28 cm.

Subjects

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

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Citation/Reference:
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-

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

UFDC Membership

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Chemical Engineering Documents

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3M COMPANY








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CHEMICAL ENGINEERING EDUCATION
wdihA a dowitioa oa ja#nd.






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EDITORIAL AND BUSINESS ADDRESS
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:
Chairman:
Klaus D. Timmerhaus
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Vice Chairman:
Lee C. Eagleton
Pennsylvania State University
SOUTH:
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University of Virginia
CENTRAL: Leslie E. Lahti
University of Toledo
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University of Wisconsin
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Illinois Institute of Technology
WEST: R. W. Tock
Texas Tech University
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University of Colorado
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NORTH: J. J. Martin
University of Michigan
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NORTHEAST: Angelo J. Perna
New Jersey Institute of Technology
NORTHWEST: Charles Sleicher
University of Washington
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LIBRARY REPRESENTATIVE
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PUBLISHERS REPRESENTATIVE
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Drexel University
UNIVERSITY REPRESENTATIVE
Stuart W. Churchill
University of Pennsylvania
James H. Hand
N.S.F., Washington, D.C.
FALL 1979


Chemical Engineering Education
VOLUME XIII NUMBER 4 FALL 1979

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

GRADUATE COURSE ARTICLES
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.










YOU SEE CARBON.k I ,


UNION CARBIDE SEES MORE.


WITHOUT CARBON, LIFE VANISHES.
Carbon is part of every living
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MORE STEEL FROM LESS ENERGY.
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THE SECRET OF MIXING CAKES,
OR MOVING TRAINS,
WITH ELECTRIC POWER.
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WORKING WITH NATURE TODAY,
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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
CEE.


AUTHOR

Aris

Butt & Peterson
Kabel

Middleman

Perlmutter

Rajagopalan

Wheelock
Carbonell &
Whitaker


Dumesic

Jorne
Retzloff

Blanch, Russell
Chartoff

Alkire
Bailey & Ollis
DeKee
Deshpande
Johnson
Klinzing
Lemlich
Koutsky
Reynolds
Rosner


Astarita
Delgass
Gruver
Liu
Manning
McCoy
Walter

Corripio


Ray Fahien, Editor CEE
TITLE
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-
cessing"
"Reactor Design From a Stability
Viewpoint"
"The Dynamics of Hydrocolloidal
Systems"
"Coal Science and Technology"
"Transport Phenomena in Multicom-
ponent, Multiphase, Reacting
Systems"
Fall 1977
"Fundamental Concepts in Surface In-
teractions"
"Electrochemical Engineering"
"Chemical Reaction Engineering Sci-
ence"
"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-
port"
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"


Donaghey
Edgar
Gates, et al.
Luks
Melnyk & Prober
Tavlarides
Theis
Hamrin, et. al

Merrill
Locke & Daniels
Moore
Wei

Hopfenberg

Fricke
Tierney

Bell
Chao &
Greenkorn
Cooney

Curl & Kadlee
Gainer
Slattery

Kelleher & Kafes
Douglas &
Kittrell


"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-
tries"
"Polymers, Surfactants and Colloidal
Materials"
"Polymer Processing"
"Staged Separations"
Fall 1972
"Process Heat Transfer"
"Equilibrium Theory of Fluids"

"Biological Transport Pnenomena and
Biomedical Engineering"
"Modeling"
"Applied Surface Chemistry"
"Momentum, Energy and Mass Trans-
fer"
"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
Systems"
Beamer "Statistical Analysis and Simulation"
Himmelblau "Optimization of Large Scale Systems"


Berg
Boudart
Koppel
Leonard
Licht

Metzner & Denn
Powers
Toor & Condiff
Tsao

Amundson
Churchill

Hanratty
Hubert
Lightfoot
Lapidus
Prausnitz
Dougharty


Fall 1970
"Interfacial Phenomena"
"Kinetics of Chemical Processes"
"Process Control"
"Bioengineering"
"Design of Air Pollution Control Sys-
tems"
"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
thinking.
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
specialties.
When you come to work at Celanese, you'll be
assigned to a project right away. You can put your cre-
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waste your time in lengthy training programs we won't
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mold. You'll have the freedom and the opportunity for
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We're looking for people who are still growing, and
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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.


e E LANESEm
An equal opportunity employer m/f


V


~


~r~F
s
a


a6









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.


THE MIRROR FOG PROBLEM


R. L. KABEL
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
FIGURE 1 FIGURE 2


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


I









1978 Awcid .Jec4ae


THE DYNAMICS OF RUNAWAY SYSTEMS


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.

THEODORE VERMEULEN
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.

THE ANATOMY OF AN EXPLOSION
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


CHEMICAL ENGINEERING EDUCATION











"detonation" occurs in less than one-tenth of a micro-
second.
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
change.
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-

UPDRAFT THROUGH
CENTER OF TOROfD


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


o Detonati

.3 2
03




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.

THE RANKINE-HUGONIOT DIAGRAM

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
balances.
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


,157











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.

CRITICALITY

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
detonation.
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 ENGINEERING EDUCATION








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FALL 1979

















THE INTEGRATION OF REAL-TIME COMPUTING INTO


PROCESS CONTROL TEACHING

PART I: THE GRADUATE COURSE


M. MORARI and W. H. RAY
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
IV.


Figure 1
-atch Panel MINICOPUTER SYSM
B terminal port
16 A/D channels
Mtt. ZCilosurt

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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
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Tennal
C~K 00 CCI SORE_
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I 2 II

Copyright ChE Division. ASEE. 1979


FEED


OVERHEAD
REFLUX YI
u2
j. SIDESTREAM
U3
SIDESTREAM
_44 Y3


BOTTOMS

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


THE COMPUTING FACILITIES

T HE COMPUTING FACILITIES for the process
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

TABLE 1
Graduate Process Control Lecture Topics

1. Practical aspects of on-line data acquisition and
control
2. Control of systems described by ordinary differential
and difference equations
3. Control of systems described by partial differential
equations
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


CHEMICAL ENGINEERING EDUCATION


l










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-
verters.

COURSE DESCRIPTION

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









t
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)


TABLE 2
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
constants
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
Control.

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.

CONCLUDING REMARKS

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


PRODUCT
STREAM
COMPOSITIONS y .---
(a.v'.ti.. vs...i.bl .
-9.373E-O8 o-
-0.373E-08
-0.37,E-08




-0.528E-B1 -.o1
:I:520E E 0.244E O0 .. 97 0nute' 0.193Eo02
10
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.


CHEMICAL ENGINEERING EDUCATION























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FALL 1979











HETEROGENEOUS CATALYSIS


HETEROGENEOUS CATALYSIS


M. A. VANNICE
Pennsylvania State University
University Park, PA 16802

H ETEROGENEOUS CATALYSIS plays a dominant
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-
zation.


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
subjects.
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


CHEMICAL ENGINEERING EDUCATION










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
course.
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


TABLE 1
Course Outline


I. INTRODUCTION (1 Lecture)
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
eq.
3. Heats of adsorption
4. Activated adsorption-Elovich eq. (8)
III. CHEMICAL KINETICS (E) (11 Lectures)
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
(19)
IV. HEAT AND MASS TRANSFER EFFECTS ON
RATE EQUATIONS (20) (4 Lectures)
A. Interphase transport
B. Intraphase transport (pore diffusion)


C. Experimental tests for transport effects (21-
23)
V. CATALYST CHARACTERIZATION (2 Lectures)
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.)
VI. THEORETICAL CONCEPTS IN CATALYSIS (4
Lectures)
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)
VII. CHEMISTRY AND KINETICS OF CATALYTIC
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

REFERENCES

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
(1977).
8. Ritchie, A. G., J. Chem. Soc. Faraday Tr. I 73, 1050
(1977).
9. Hougen, O. A. and Watson, K. M., "Chemical Process
Principles-Kinetics and Catalysis", Wiley, N.Y.
(1947).
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
(1967).
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
(1955).
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
(1976).
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).


CHEMICAL ENGINEERING EDUCATION

















ACKNOWLEDGMENTS


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


University of Akron
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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
32611.


FALL 1979














DOCTORAL LEVEL

CHEMICAL ENGINEERING ECONOMICS


ORAN L. CULBERSON
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.


CHEMICAL ENGINEERING EDUCATION









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
schedule."
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
wrong.
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

REFERENCES
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

FILTRATION: PRINCIPLES AND PRACTICES
(TWO PARTS),
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
contradiction.
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


CHEMICAL ENGINEERING EDUCATION






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Challenging assignments exist for
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FUNCTIONAL ANALYSIS

FOR CHEMICAL ENGINEERS


D. RAMKRISHNA
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.

COURSE OBJECTIVES AND CHALLENGES
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


CHEMICAL ENGINEERING EDUCATION


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].

SCOPE OF COURSE
T HE FOLLOWING TOPICS ARE dealt with in a
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
problems.


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-
tions.


(i)
(ii)
(iii)


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
a
represents a linear space of vectors f = [f(x):
a fined by
b

= f(x)g(x)dx
a
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


c00
L = Y XjP,
j=1
Continued on page 211.


CHEMICAL ENGINEERING EDUCATION






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COLLOIDAL PHENOMENA


WILLIAM B. RUSSEL, DUDLEY A. SAVILLE,
DAVID F. OLLIS and
WILLIAM R. SCHOWALTER
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
casein.
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


CHEMICAL ENGINEERING EDUCATION











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.

TECHNICAL CONTENT
THE LECTURES AND READINGS emphasize the
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-


TABLE 1
Course Outline


INTRODUCTION

FORCES ACTIVE AT THE COLLOIDAL SCALE
(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

COLLOIDAL STABILITY (W. B. Russel)
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

ELECTROKINETIC PHENOMENA (D. A. Saville)
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
SEPARATIONS PROCESSES (D. F. Ollis)
Filtration
forces responsible for collection
trajectory analyses
macroscopic balances and filter design
Field-Flow Fractionation
types of transverse fields
pulse velocity and dispersion
design considerations
Flotation
isotherms and interfacial aspects
application of particle collection theories
experimental results
Ultrafiltration
role of osmotic pressure
concentration polarization
Continuous flow electrophoresis
principles and general analysis
hydrodynamic instabilities
application to separation of cells
SUSPENSION RHEOLOGY (W. R. Schowalter)
Examples of non-Newtonian behavior of disperse
systems
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-


CHEMICAL ENGINEERING EDUCATION









TABLE II
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,
1972.
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
suspensions.

TEACHING THE COURSE
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. [
ERRATA
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')










ACOAL Le PRO


COAL LIQUEFACTION PROCESSES


T. F. YEN
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

CHEMICAL ENGINEERING EDUCATION









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.

LECTURES

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


TABLE 1
Lecture Topics
1. Introduction-Coal Resources and Supplies; Coal
Mining Technology Development
2. Origin of Coal; Coal Types and Ranks; Petrography;
Metamorphism
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-
fuels
14. Novel Approaches; In-Situ Production
15. Environmental, Safety, and Health Problems in Coal
Conversion
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
library.

CLASS WORK
C LASS WORK IS COMPRISED of three categories
which carry equal weight in the calculation
of grades: homework problems, term paper, and
tests.
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
investigator.

STUDENT POLL
DUE TO THE STILL-EVOLVING nature of coal
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.
tI


- -


K


n L U
IM E U
OA E
U P. R
SNM A
TE L
D L


FIGURE 1. Graphic Representation of
to Course


S
A
S
P
L
E
S
I
Z
E

S



1
3


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
offering.
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.


CHEMICAL ENGINEERING EDUCATION







AT?


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











4 QOm-ule iat


MATHEMATICAL METHODS

IN CHEMICAL ENGINEERING


ARVIND VARMA
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.


CHEMICAL ENGINEERING EDUCATION









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].

COURSE FORMAT

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.
TABLE 1
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.

COURSE DESCRIPTION
A TOPICAL OUTLINE OF the course is shown in
Table 1. The following is a detailed descrip-
tion.
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-
actors.
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


CHEMICAL ENGINEERING EDUCATION








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
discussed.
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.
CONCLUDING REMARKS
A S THE PREVIOUS DESCRIPTION indicates, we do
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

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

REFERENCES
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.
(1978).
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.


CHEMICAL ENGINEERING EDUCATION






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Ron's story is typical of
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POLYMER SCIENCE

POLYMER SCIENCE


CURTIS W. FRANK
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
science."
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
processing.
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


CHEMICAL ENGINEERING EDUCATION









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,
1972.
* F. W. Billmeyer, Textbook of Polymer Science, Wiley-
Interscience, 1971.
* J. D. Ferry, Viscoelastic Properties of Polymers, Wiley,
1970.
* H. S. Kaufman and J. J. Falcetta, Introduction to
Polymer Science and Technology, Wiley-Interscience,
1977.
* F. Rodriguez, Principles of Polymer Systems, McGraw-
Hill, 1970.
* J. Schultz, Polymer Materials Science, Prentice-Hall,
1974.
* 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-
TABLE
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
transition
2. Theoretical approaches to the glass
transition
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
viscosity
4. Effect of molecular weight on zero shear
viscosity
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-
1
--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
solid
2. Complex variable notation for modulus and
compliance
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
strain
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
network
2. Stress-temperature relations
3. Internal energy and volume changes


CHEMICAL ENGINEERING EDUCATION









TABLE 2
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
parameter
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
configuration
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
chains
C. Configurational partition function (1)
1. Fundamental concepts of statistical
mechanics
2. Generation of configurational partition
functions by matrix multiplication
3. Evaluation of rotational state
probabilities
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
vector
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).

REFERENCES

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














THE STRUCTURE


OF THE CHEMICAL PROCESSING INDUSTRIES*


T. W. F. RUSSELL
University of Delaware
Newark, DE 19711

T HIS COURSE WAS INITIATED at the University
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)

TABLE 1
Course Outline


Reader's Guide
Introduction
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-
tion.
(ii) It outlines how to use the book, current
literature and supplementary information for
0 Copyright ChE Division, ASEE. 1979


CHEMICAL ENGINEERING EDUCATION








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
society.
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
studies.
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.

USE OF CASE STUDIES
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
business.
* 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.

SPEAKERS FROM OUTSIDE THE UNIVERSITY

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-
vided.


FALL 1979










TABLE 2
Typical product Assignments


Precipitated calcium
carbonate
Titanium dioxide
Carbon black
Yellow iron oxide
Penicillin
Aspirin
Vitamin C


Caustic soda
Ammonia
Sulfuric acid
Nylon
Polyester fiber
Rayon


Carbon dioxide
Nitrogen
Oxygen
DDT
Pesticides
Herbicides


ASSIGNMENT OF STUDENT SPECIALISTS

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
following:
* Facts and Figures issue of Chemical and Engineering
News.
* 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.)


TABLE 3
Planning schedule


MONTHS BEFORE
COURSE BEGINS
12-10


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


COMMENT


Begin to rough out in-class course
schedule

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



CHEMICAL ENGINEERING EDUCATION










PLANNING

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.
TABLE 4
Class schedule

CHAP. HOURS CHAP. HOURS CHAP. HOURS
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

CONCLUSIONS
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-
cedures.
"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.


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

OKLAHOMA STATE UNIVERSITY

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














INTRODUCTION TO

THE MOLECULAR THEORY OF THERMODYNAMICS





H. TED DAVIS
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.

DILUTE GAS KINETICS
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


CHEMICAL ENGINEERING EDUCATION









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] ,


(2.1)


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
gases.
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 ,


2.2)


1
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
< 1 mv2> predicted from a Gaussian distribu-
2
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
relation


V m2


(2.5)


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
uranium.
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
1
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


(2.6)


nl,' nl,
n2 n2









TABLE 1
Dilute nitrogen at 300K. The molecular diameter d
is assumed to be 2 x 10-8 cm.


P(atm)
10-s
1


1(cm)
3.46 x 10-6
3.46 x 10-7


X(cm)
2.34 x 10-2
2.34 x 10-6


p(sec-1)
2.03 x 106
2.03 x 109


X(cm)
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


e-E/kT
=---d3vd3r, ... d3vNd3r ,
Q


(3.4)


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.

THERMODYNAMIC FUNCTIONS AND THE
PARTITION FUNCTION

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
obtain


-[u(r)-u(ro)]/kT
n(r) = n(ro)e


(3.1)
t Eq.
metric
/kT).
y, we



(3.2)


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)

1
where = -- mv2 + u (r) is the energy of the par-
2


where E =


N

i=1


1
[-- mvi2 + u(r,)] is the
2


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 ...


(3.5)


-( )3N/2Z.
2rkT


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

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,


(3.6)


(3.7)


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-


CHEMICAL ENGINEERING EDUCATION


200









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-
U=1l
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.

PHASE EQUILIBRIA OF FLUIDS
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


-/kT
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
1
= 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 .
(4.3)
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
Nza
Z = exp (- ) (V-Nb)N, (4.4)

and therefore the free energy expression
N2a
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-
27r
cluded volume is b = d3, so that mean free
3
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
above.
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-
a=l

come composition dependent, b = 2 xab.
a=l

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


CHEMICAL ENGINEERING EDUCATION










Po*
0.06

0.04

0.02

0
-0.01
-0.02
-0.03


-0.06


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-
tions.

CONCLUDING REMARKS

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


I I I I I I
T*= 0.3.

0.296
-0.275

0-1 M 's


' / 1 \ I


I I 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

REFERENCES CITED
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
(1962).
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
(1949).
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
(1966).
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
(1976).
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).


Sanews

ZWIEBEL APPOINTED CHAIRMAN
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.

RICE APPOINTED HEAD
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
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
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-
leagues.
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
Island.
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.


CHEMICAL ENGINEERING EDUCATION


I









AWARD LECTURE
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-
sults.
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.

CHEMICAL REACTION LIMITS
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.


10,000


1000

E
00

01


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
reaction.
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:


(Initiation,
weakly)


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


205









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)
(Termination)
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
relations.
Finally, the total rate (including step 3) is
approximately
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.

THE THERMAL RUNAWAY LIMIT
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


CHEMICAL ENGINEERING EDUCATION


206









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-
sion.
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
factor.
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.


TABLE 1
Flammability Limits In Air

MOLE-FRACTIOtN OF COMPOUND TEMPERATURE, OR.
COMPOUND LOWER STOIC MAX. VEL. UPPER MAX. VEL. IGNITION

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
control.
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.

ONE-DIMENSION MODELING OF PREMIXED FLAMES
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
104

g
o
10
(3103 ,Second-order




2
IM

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


CHEMICAL ENGINEERING EDUCATION



















0.5F-


0
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


Second-order


FALL 1979


First-order


= .,


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

REFERENCES
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

THE CREATION
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
employees.
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.
ROHMi
IHRRSr
An Equal Opportunity Employer.









FUNCTIONAL ANALYSIS
Continued from page 174
Where Pj is defined by its action on any vector x,
viz.,
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
o00
L-1 = Xj-1 Pj (4)
j=1
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
oo
x = xj-1 Py (6)
3=1
where Pjy is given by (3). Unsteady state initial
value problems of the form
dx Lx, x(0) = x (7)
dt
are solved using the second equality in (4) to
obtain
0o Xjt
x = S e Pjxi (8)
j=1

BOUNDARY VALUE PROBLEMS
TN DEALING WITH BOUNDARY value problems
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
conditions.
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,
r
C DaT
S(r,z) = j -k + pCpv,(r)T]27rrdr (11)
0
o
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)
k

2r
ar


r1 ar T(r,z)

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


T(z,r)
= (
z S (z,r)


(12)


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
R

E [f,(r) g(r)2r +f(r)g2(r)1 ]dr
0
(13)
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
0


(14)


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


CHEMICAL ENGINEERING EDUCATION









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

REFERENCES
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,
1979.



MIRROR FOG PROBLEM
Continued from page 155

PRELIMINARY DISCUSSION
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.
OBJECTIVES AND CRITERIA: To find the time
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.


PHYSICAL AND CHEMICAL PRINCIPLES: There
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




fogged
fogged


- Y -** -;

I. .

partially
clear


clear


FIGURE 3. All surfaces impermeable except front
opening.


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
results.
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.
DOW CHEMICAL U.S.A.
TIde rk The Do Chemical Company-*










COAL LIQUEFACTION
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

TABLE II
Course Reading List
(Arranged Under Lecture Headings)

INTRODUCTION-COAL RESOURCES AND
SUPPLIES, COAL MINING TECHNOLOGY DEVELOP-
MENT
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
(1976).

ORIGIN OF COAL; COAL TYPES AND RANKS;
PETROGRAPHY; METAMORPHISM
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).


COAL CHEMISTRY, COAL REACTION, COAL
STRUCTURES
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
(1976).
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).

PHYSICAL PROPERTIES OF COAL, STATISTICAL
APPROACHES AND STRUCTURAL PARAMETERS
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
(1971).

COAL PREPARATION, COMMINUTION, COAL FEED
ENGINEERING PROBLEMS
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.

THERMAL PYROLYSIS OF COAL, KINETICS AND
MECHANISM OF THERMAL DECOMPOSITION
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.
1975.
4. C. S. Wen and T. F. Yen, "Optimization of Oil Shale
Pyrolysis", Chem. Eng. Sci., 32, 346-349 (1977).


FALL 1979









CARBONIZATION, MESOPHASE, COKES
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.

SOLUBILITY PARAMETERS, SOLVENT REFINING,
NATURE OF HYDROGEN DONORS
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).

CATALYSIS, CATALYTIC HYDROGENATION
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.

FISHER-TROPSCH SYNTHESIS-GENERALIZED
GASIFICATION

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.

COAL LIQUIDS, SEPARATION AND ISOLATION OF
ASPHALTENES, CHARACTERIZATIONS
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.

REFINING, UPGRADING, DESULFURIZATION,
DEMETALLIZATION, DENITROGENERATION
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
(1974).
4. G. A. Mills and H. Perry, "Fossil Fuel -> Power +
Pollution", Chem. Tech., Jan. 1973, pp. 53-63.

COAL-DERIVED CHEMICALS AND PRODUCTS,
OTHER SYNFUELS

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.

NOVEL APPROACHES, IN SITU PRODUCTION
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.

ENVIRONMENTAL PROBLEMS IN COAL CONVER-
SION, ASPECTS OF SAFETY AND HEALTH
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.


CHEMICAL ENGINEERING EDUCATION









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.
PROCESS AND REACTOR DESIGN, MODELS,
REACTION CONTROL
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).


TABLE III
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,
1976.
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.


IN MEMORIUM
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











UNIVERSITY OF ALBERTA


EDMONTON, ALBERTA, CANADA
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
available.
Costs.
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.
Applications
For additional information write to:
Chairman
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-
sign.
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
Sands.
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-
dynamics.
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-
tics.
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
schools.
Enrollment of 20,000 students.
Co-educational, government-supported,
non-denominational.
Five minutes from city centre, overlooking scenic river
valley.

Edmonton
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.


CHEMICAL ENGINEERING EDUCATION










ITHLE UNIVERSITY OF flKRON
PkroR E O 44325


DEPARTMENT OF

CHEMICAL ENGINEERING




GRADUATE PROGRAM


FACULTY


RESEARCH INTERESTS


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.





ADDITIONAL INFORMATION WRITE:
Dr. Howard L. Greene, Head
Department of Chemical Engineering
University of Akron
Akron, Ohio 44325


FALL 1979








THE UNIVERSITY OF ARIZONA

STUCSON, AZ



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.
THE FACULTY AND THEIR RESEARCH INTERESTS ARE:


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,
Biorheology

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

ALAN D. RANDOLPH, Professor
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









AUBURN UNIVERSITY


CHEMICAL ENGINEERING GRADUATE STUDIES


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-
fining.

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-
neering.

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
liver.







For financial aid and ad-
mission application forms
write:

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.
degree.
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
sources.
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.
Applying

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


CHEMICAL ENGINEERING EDUCATION









UNIVERSITY OF CALIFORNIA

BERKELEY, CALIFORNIA


RESEARCH

ENERGY UTILIZATION

ENVIRONMENTAL

KINETICS AND CATALYSIS

THERMODYNAMICS

ELECTROCHEMICAL ENGINEERING

PROCESS DESIGN
AND DEVELOPMENT

BIOCHEMICAL ENGINEERING

MATERIAL ENGINEERING

FLUID MECHANICS
AND RHEOLOGY


FOR APPLICATIONS AND FURTHER INFORMATION, WRITE.


FACULTY
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
UNIVERSITY OF CALIFORNIA
Berkeley, California 94720











UNIVERSITY OF CALIFORNIA, DAVIS

UC DAVIS OFFERS A COMPLETE PROGRAM OF GRADUATE
STUDY AND RESEARCH IN CHEMICAL ENGINEERING


Degrees Offered
Master of Science
Doctor of Philosophy

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

Faculty
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


Program
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.




Information
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


CHEMICAL ENGINEERING EDUCATION


224












UNIVERSITY OF CALIFORNIA


SANTA BARBARA


FACULTY AND RESEARCH INTERESTS PROGRAMS AND FINANCIAL SUPPORT


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

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

HUSAM GUROL
Ph.D. (Michigan)
Statistical Mechanics, Polymers,
Radiation Damage to Materials,
Nuclear Reactor Theory.
OWEN T. HANNA
Ph.D. (Purdue)
Theoretical Methods, Chemical
Reactor Analysis, Transport
Phenomena.

GLENN E. LUCAS
Ph.D. (M.I.T.)
Radiation Damage, Mechanics of
Materials.

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


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

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

A. EDWARD PROFIO
Ph.D. (M.I.T.)
Bionuclear Engineering, Fusion
Reactors, Radiation Transport
Analyses.

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

ORVILLE C. SANDALL
Ph.D. (Berkeley)
Transport Phenomena, Separation
Processes.

DALE E. SEBORG
Ph.D. (Princeton)
(Chairman)
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.


THE UNIVERSITY
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
climate.


For additional information and applications,
write to:

Professor Dale E. Seborg, Chairman
Department of Chemical & Nuclear
Engineering
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.


FACULTY IN CHEMICAL ENGINEERING


WILLIAM H. CORCORAN, Institute Professor
Ph.D. (1948), California Institute of Technology
Kinetics and catalysis; biomedical engineering;
air and water quality.
GEORGE R. GAVALAS, Professor
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.
CORNELIUS J. PINGS, Professor,
Vice-Provost, and Dean of Graduate Studies
Ph.D. (1955), California Institute of Technology
Liquid state physics and chemistry; statistical
mechanics.


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.
GREGORY N. STEPHANOPOULOS, Assistant Pro-
fessor Ph.D. (1978), University of Minnesota
Biochemical engineering; chemical reaction
engineering.
NICHOLAS W. TSCHOEGL, Professor
Ph.D. (1958), University of New South Wales
Mechanical properties of polymeric materials;
theory of viscoelastic behavior; structure-
property relations in polymers.
W. HENRY WEINBERG, Professor
Ph.D. (1970), University of California, Berkeley
Surface chemistry and catalysis.




Ever think of Grad School as an Adventure?


-write-


Graduate Chemical Engineering
Carnegie Mellon University
Pittsburgh. Pennsylvania 15213






























4 ....


IS THERE LIFE

AFTER GRADUATE STUDY?
Want to find out? Heaven can't wait!
Write to:
Graduate Coordinator
Chemical Engineering Department
Case Western Reserve University
Cleveland, Ohio 44106
228 CHEMICAL ENGINEERING EDUCATION















Graduate Study
in Chemical Engineering
at


Clarkson

* 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

Faculty
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:
Energy
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
Crystallization
And More....

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

DEAN OF THE GRADUATE SCHOOL
CLARKSON COLLEGE OF TECHNOLOGY
POTSDAM, NEW YORK 13676







Chemical Engineering at


CORNELL

UNIVERSITY


A place to grow...


with active research in:
biochemical and biomedical engineering
computer simulation
environmental engineering
heterogeneous catalysis
surface science
polymers
microscopy
reactor design
fluid flow and coalescence
physics of liquids
thermodynamics
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
chemistry
biochemistry
microbiology
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.
Wiegandt.

FOR FURTHER INFORMATION: Write to
Professor Michael L. Shuler
Cornell University
Olin Hall of Chemical Engineering
Ithaca, New York 14853.











UNIVERSITY OF DELAWARE

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
systems
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,
chemotherapy
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
chemistry
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

University

of Florida's

Department

of Chemical

Engineering
gives you both
outstanding
academic
challenge
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 -
904/392-0881


Y

























SEC -


Graduate Studies in Chemical Engineering ...


GEORGIA TECH


Chemical Engineering


Ballet
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
Kinetics
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


Atlanta







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
engineering
> applied fluid mechanics and transfer
processes
> 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.
.0


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
R.Jackson
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
Campus
Houston, Texas 77004
(Phone 713/749-4407)







GRADUATE STUDY AND RESEARCH


The Departmenl of Energy Engineering



UNIVERSITY OF ILLINOIS AT CHICAGO CIRCLE




Graduate Programs in

The Department of Energy Engineering

leading to the degrees of

MASTER OF SCIENCE and

DOCTOR OF PHILOSOPHY


Faculty and Research Activities in
CHEMICAL ENGINEERING
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
Professor
G. Ali Mansoori
Ph.D., University of Oklahoma, 1969
Professor
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
Professor
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,
biophysics

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









UNIVERSITY OF ILLINOIS

URBANA, CHAMPAIGN

ACTIVE, RESPECTED, ACCESSIBLE FACULTY
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.

EXCEPTIONAL FACILITIES
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.

A DIVERSITY OF RESEARCH INTERESTS


Applied Mathematics
Biological Application of
Chemical Engineering
Catalysis
Chemical Reactor Dynamics
Colloidal Phenomena
Computer-Aided Process
Simulation and Design
Corrosion
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


FOR INFORMATION AND APPLICATIONS: Professor J. W. Westwater


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


Engineering


CHEMICAL ENGINEERING EDUCATION


236
















ILLIOIS


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.


Faculty
D. GIDASPOW
J. R. SELMAN
B. S. SWANSON
L. L. TAVLARIDES
J. S. VRENTAS
D. T. WASAN
C. V. WITTMANN


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


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


FALL 1979


237










THE INSTITUTE OF


PAPER CHEMISTRY

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.

OUR GRADUATE PROGRAM is the Number 1
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-
try.
For further information contact:
Director of Admissions
The Institute of Paper Chemistry
P. O. Box 1039
Appleton, WI 54912











IOWA STATE UNIVERSITY

OF
SCIENCE AND TECHNOLOGY


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


GRADUATE STUDY and

GRADUATE RESEARCH

in

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:
Chairman
Department of Chemical Engineering
Iowa State University
Ames, Iowa 50011








Graduate Study in Chemical Engineering


KANSAS STATE UNIVERSITY


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
neering.

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


Engi-


AREAS OF STUDY AND RESEARCH
TRANSPORT PHENOMENA
ENERGY ENGINEERING
COAL AND BIOMASS CONVERSION
THERMODYNAMICS AND PHASE EQUILIBRIUM
BIOCHEMICAL ENGINEERING
PROCESS DYNAMICS AND CONTROL
CHEMICAL REACTION ENGINEERING
MATERIALS SCIENCE
SOLID MIXING
CATALYSIS AND FUEL SYNTHESIS
OPTIMIZATION AND PROCESS SYSTEM
ENGINEERING
FLUIDIZATION
ENVIRONMENTAL POLLUTION CONTROL
CHEMICAL ENGINEERING EDUCATION





















Elill
_ NEESE Ia


-


CHEMICAL


ENGINEERING

AT MIT


GENERAL AREAS OF FUNDAMENTAL AND APPLIED RESEARCH

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


THE FACULTY OF THE DEPARTMENT
R. C. ARMSTRONG, Ph.D. (1973); Associate Professor, M. MODELL, Sc.D. (1964); Associate Professor,
POLYMER FLUID MECHANICS, TRANSPORT PHENOMENA, THERMODYNAMICS, WASTE TREATMENT, CHEMICAL KINETICS
APPLIED MATHEMATICS AND CATALYSIS
R. F. BADDOUR, Sc.D. (1951); Professor, C. M. MOHR, Sc.D. (1961); Senior Lecturer,
CATALYSIS, PLASMA CHEMISTRY, ENZYME TECHNOLOGY PROCESS DESIGN AND SYNTHESIS, INDUSTRIAL CHEMISTRY
J. M. BEER, D.Sc. (1968); Professor, F. A. PUTNAM, Ph.D. (1976); Assistant Professor,
COMBUSTION, FLUIDIZED COMBUSTION OF COAL SURFACE PHENOMENA, THERMODYNAMICS, CATALYSIS
R. A. BROWN, Ph.D. (1978); Assistant Professor, R. C. REID, Sc.D. (1954); Professor,
MATHEMATICAL MODELLING, FLUID MECHANICS, THERMODYNAMICS, PROPERTIES OF MATERIALS, LIQUEFIED
TRANSPORT AND INTERFACE PHENOMENA NATURAL GAS
R.E. COHEN, Ph.D. (1972); Associate Professor, A. F. SAROFIM, Sc.D. (1962); Professor,
PHYSICS AND CHEMISTRY OF POLYMERS, VISCOELASTIC THEORY APPLIED CHEMICAL KINETICS, HEAT AND MASS TRANSFER,
C. K. COLTON, Ph.D. (1969); Professor, COMBUSTION
BIOMEDICAL AND BIOCHEMICAL ENGINEERING, MASS TRANSFER C. N. SATTERFIELD, Sc.D. (1946); Professor,
W. M. DEEN, Ph.D. (1973); Assistant Professor CHEMICAL REACTION ENGINEERING, MASS TRANSFER AND
BIOENGINEERING, FLUID MECHANICS, MASS TRANSFER HETEROGENEOUS CATALYSIS
L. B. EVANS Ph.D. (1962); Professor, S. M. SENKIN, Sc.D. (1977); Assistant Professor,
PROCESS CONTROL, OPTIMIZATION, COMPUTER-AIDED DESIGN CHEMICAL REACTOR DESIGN, MATHEMATICAL MODELLING
C. GEORGAKIS, Ph.D. (1975); Associate Professor, K. A. SMITH, Sc.D. (1962); Professor,
CHEMICAL REACTOR DESIGN, PROCESS DYNAMICS AND FLUID MECHANICS, HEAT AND MASS TRANSFER, BIOMEDICAL
CONTROL, APPLIED MATHEMATICS ENGINEERING
H. C. HOTTEL, S.M. (1924); Professor Emeritus, C. G. VAYENAS, Ph.D. (1977); Assistant Professor,
RADIATIVE HEAT TRANSFER, COMBUSTION. SOLAR ENERGY HETEROGENEOUS CATALYSIS, FUEL CELLS
J. B. HOWARD, Ph.D. (1965); Professor and Executive Officer P.S. VIRK, Sc.D. (1967); Associate Professor,
COMBUSTION:,COAL CONVERSION, ENERGY TECHNOLOGY DRAG REDUCTION, PYROLYSIS PATHWAYS, COAL LIQUIDS
J. P. LONGWELL, Sc.D. (1943); Professor,E. VAN, Sc.D. (1945); Professor
COMBUSTION, FUE PRO NG J. E. VIVIAN, Ec.L. (194S); Professor
COMBUSTION, FUELS PROCESSING MASS TRANSFER AND CHEMICAL KINETICS, SEPARATION
M. P. MANNING, Sc.D. (1976); Assistant Professor, PROCESS
KINETICS AND CATALYSIS, SOLAR ENERGY, PROCESS DESIGN
J. WEI, Sc.D. (1955); Professor and Department Head,
H. P. MEISSNER, D.Sc. (1938); Professor Emeritus, CATALYSIS AND KINETICS, CHEMICAL REACTORS, TRANSPORT
ELECTROCHEMISTRY, THERMODYNAMICS, PROCESS PHENOMENA, BIOCHEMICAL ENGINEERING
METALLURGY
E W MERRIL, Sc G. C. WILLIAMS, Sc.D. (1942); Professor and Graduate Officer,
E. W. MERRILL, Sc.D. (1947); Professor, COMBUSTION, CHEMICAL KINETICS, AIR POLLUTION
POLYMER CHEMISTRY, BIOMEDICAL ENGINEERING, MEMBRANE
TECHNOLOGY


FALL 1979 241






* McMASTER UNIVERSITY


M.ENG.
AND
PH.D.
PROGRAMS
PROCESS AND ENERGY
ENGINEERING
CHEMICAL REACTION
ENGINEERING AND CATALYSIS
COMPUTER CONTROL,
SSIMULATION AND
OPTIMIZATION
POLYMER ENGINEERING
[= BIOMEDICAL ENGINEERING
WATER AND WASTEWATER
TREATMENT
FOR FURTHER INFORMATION,
PLEASE CONTACT:
CHAIRMAN
DEPT. OF CHEMICAL ENGINEERING
McMASTER UNIVERSITY
HAMILTON, ONTARIO, CANADA L8S 4L7


CHEMICAL ENGINEERING EDUCATION











Chemical

Engineering

At The

University

Of Michigan


THE FACULTY


THE RESEARCH PROGRAM


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


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


For

Tomorrows

Engineers

Today.


THE PLACE

Department Of Chemical Engineering
THE UNIVERSITY OF MICHIGAN
ANN ARBOR, MICHIGAN 48109

For Information Call 313/763-1148 Collect


FALL 1979


i


I









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


WHY


Responses of some of our current
graduate students to the question
"WHY MINNESOTA?":




"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


MINNESOTA?


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)

I Yes! PLEASE SEND INFORMATION ON
YOUR GRADUATE PROGRAM TO:

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

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


CHEMICAL ENGINEERING EDUCATION










Department of Chemical Engineering


UNIVERSITY OF MISSOURI ROLLA

ROLLA, MISSOURI 65401



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.
Reed

(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.
Yasuda


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.
Gaddy
(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-
kamp


(f) Transport Properties, Kinetics, enzymes and
catalysis-Dr. O. K. Crosser and Dr. B. E.
Poling
(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


245








CHEMICAL ENGINEERING
AT NORTH CAROLINA STATE UNIVERSITY
RALEIGH, N.C. J-


FOR ADDITIONAL INFORMATION, A CATALOG, AND APPLICATION MATERIALS, WRITE
Dr. James K. Ferrell, Head
Department of Chemical Engineering
North Carolina State University
Raleigh, North Carolina 27650


CHEMICAL ENGINEERING EDUCATION




Full Text

PAGE 1

z 0 u ::, C w C) z a: w w z C) z w a: 0 u. w l u. 0 z 0 V) > C C) z 11:11: w w z .C) z w ....I u w u VOLUME XIII NUMBER 4 FALL 1979 GRADUATION EDUCATION ISSUE DOCTORAL LEVEL ChE ECONOMICS CULBERSON MOLECULAR THEORY OF THERMODYNAMICS . DAVIS COURSES IN POLYMER SCIENCE . FRANK INTEGRATION OF REAL-TIME COMPUTING INTO PROCESS CONTROL TEACHING MORARI, RAY FUNCTIONAL ANALYSIS FOR Ch E'S RAMKRISHNA COLLOIDAL PHENOMENA . RUSSEL, SAVILLE, OLLIS, SCHOWALTER STRUCTURE OF THE CPI HETEROGENEOUS CATALYSIS MATHEMATICAL METHODS RUSSELL .. VANNICE VARMA COAL LIQUEFACTION PROCESSES . YEN THE MIRROR FOG PROBLEM ALSO 1978 .,(J~ .eecJwie DYNAMICS OF RUNAWAY SYSTEMS KABEL .VERMEULEN

PAGE 2

3M COMPANY CHEMICAL ENGINEERING EDUCATION wdlt, a tkatm o/ /unril.

PAGE 3

CHEMICAL ENGINEERS A high technology development ancl process manufacturing company 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 FindOut 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 TumPage

PAGE 4

Mail This Confidential Rapid Resume Tell us a little about yourselfand 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 I nitial ahd Middle Initial Address Home Phone No Business Phone No ___ _,POSITION DESIRED .... _________ Type of Position Date Available Salary Desired ____ .._ErJUCATIONAL BACKGROUN-D _____ College Location Degree/Major ------EMPLOYMENT HISTOR-------Present Employer Position Dates of Employment Duties Previous Employer Position Dates of Employment Duties

PAGE 5

EDITORIAL AND BUSINESS ADDRESS 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: Chairman: Klaus D. Timmerhaus University of Colorado Vice Chairman: Lee C. Eagleton Pennsylvania State University SOUTH: 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: i Charles Bleicher University of Washington Charles E. Wicks Oregon State University LIBRARY REPRESENTATIVE Thomas W. Weber State University of New York PUBLISHERS REPRESENTATIVE D. R. Coughanowr Drexel University UNIVERSITY REPRESENTATIVE Stuart W. Churchill University of Pennsylvania James H. Hand N.S.F., Washington, D.C. FALL 1979 Chemical Engineering Education VOLUME XIII NUMBER 4 FALL 1979 FEATURES 15 6 1978 -AUJO/ld. ./!eclw,,e The Dynamics of Runaway Systems, Theodore Vermeulen 155 Class and Home Problems The Mirror Fog Problem, R. L. Kabel GRADUATE COURSE ARTICLES 160 The Integration of Real-Time Computing into Process Control Teaching, M. Morari and W. H. Ray 164 168 172 176 ISO 184 190 Heterogeneous Catalysis, M. A. Vannice Doctoral Level Chemical Engineering Eco nomics, Oran L. Culberson Functional Analysis for Chemical Engineers, D. Ramkrishna Colloidal Phenomena, William B. Russel, Dudley A. Saville, David F. Ollis, and William R. Schowalter Coal Liquefaction Processes, T. F. Yen Mathematical Methods in Chemical Engi neering, A rvind Varma 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 Engineerinir Division, American Society for Engineering Education. The publication la edited at the Chemical Eni,;ineering Department, University of Florida. Second-clua postage la paid at Gainesville, Florida, and at DeLeon Springs, Florida. Correspondence regarding editorial matter, circulation and changes of address should be addreued to the Editor at Gainesville, Florida 32611. Advertising rates and information are available from the advertising representatives. Plates and other advertisini,; material may be sent directly to the printer: E. 0. Painter Prlntlni,; Co,, P. 0. Box 877, DeLeon Springs, Florida 32028. Subscription rate U.S., Canada, and Mexico is $15 per year, $10 per year mailed to members of AICbE and of the ChE Division of ASEE. Bulk subscription rates to CbE 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 CbE Division of the ASEE which body assumes no responsibility for them. Defective copies replaced if notified within 120 days. The International Organization for Standardization bas assii,;ned the code US ISSN 0009-2479 for the identification of this periodical. 161

PAGE 6

WITHOUT CARBON, LIFE VANISHES. Carbon is part of every living thing, and of everything that ever lived. Union Carbid e makes this basic material into products es sential to th e way we live: every thing.from space-age fibers to giant steel-making e l ec trod es. MORE STEEL FROM LESS ENERGY. The steel indus try's ~ electric arc furr,..;. :c::::,::,,, n~ces feed elecI tnc power through graphite ., electrodes eight feet \ tall that r' handle 80,000 amperes, of curL rent. These furnaces make new steel from scrap, so they help clean up the countryside and cut pollution while they save energy. THE SECRET OF MIXING CAKES, OR MOVING TRAINS, WITH ELECTRIC POWER. Many electric motors share a basic problem: how to conduct electric current between moving and stationary parts. The solu tion for motors as diverse as your e le ctric mixer and this giant diesel electric engine, is a piece of manufactured carbon called a brush. No substitute can do the job as well. THORNEL A UNION CARBIDE FIBER THAT'S HELPING MAKE SPACE FLIGHT AN EVERYDAY AFFAIR. 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 Thorne! carbon fiberamazing l y light, yet so strong it will stand up to re peated launches and reentries. For a more down-to-earth appli cation, cars with Thorne! carbon fiber parts will weigh less and use l ess gas than today s models. / WORKING WITH NATURE TODAY, FOR THE RESOURCES WE'LL NEED TOMORROW. Union C arbide Co rporat io n 270 Park Avenue New York N Y 1001 7

PAGE 7

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 CEE. AUTHOR Aris Butt & Peterson Kabel Middleman Perlmutter Rajagopalan Wheelock Carbonell & Whitaker Dumesic Jorne Retzloff Blanch, Russell Chartoff Alkire Bailey & Ollis DeKee Deshpande Johnson Klinzing Lemlich Koutsky Reynolds Rosner Astarita Delgass Gruver Liu Manning McCoy Walter Corripio FALL 1979 Ray Fahien, Editor CEE TITLE 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 cessing" "Reactor Design From a Stability Viewpoint" "The Dynamics of Hydrocolloidal Systems" "Coal Science and Technology" "Transport Phenomena in Multicom ponent, Multiphase, Reacting Systems" Fall 1977 "Fundamental Concepts in Surface In teractions" "Electrochemical Engineering" "Chemical Reaction Engineering Sci ence" "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 Transport" 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" Donaghey Edgar Gates, et al. Luks Melnyk & Prober Tavlarides Theis Hamrin, et. al. Merrill Locke & Daniels Moore Wei Hopfenberg Fricke Tierney Bell Chao& Greenkorn Cooney Curl & Kadlee Gainer Slattery "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 Industries" "Polymers, Surfactants and Colloidal Materials" "Polymer Processing" "Staged Separations" Fall 1972 "Process Heat Transfer" "Equilibrium Theory of Fluids" "Biological Transport Pnenomena and Biomedical Engineering" "Modeling" "Applied Surface Chemistry" "Momentum, Energy and Mass Transfer" Kelleher & Kafes "Process and Plant Design Project" Douglas & "Engineering Entrepeneurship" Kittrell Reid & Modell Theofanous Weller Westerberg Kabel Wen Beamer Himmelblau Berg Boudart Koppel Leonard Licht Metzner & Denn Powers Toor & Condiff Tsao Amundson Churchill Hanratty Hubert Lightfoot Lapidus Prausnitz Dougharty Fall 1971 "Thermo: Theory & Applications" "Transport Phenomena" "Heterogeneous Catalysis" "Computer Aided Process Design" "Mathematical Modeling "Noncatalytic Heterogeneous Reaction Systems" "Statistical Analysis and Simulation" "Optimization of Large Scale Systems" Fall 1970 "lnterfacial Phenomena" "Kinetics of Chemical Processes" "Process Control" "Bioengineering" "Design of Air Pollution Control Systems" "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" 153

PAGE 8

At Celanese, we won't force you 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 thinking. 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 specialties. 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 programswe won t waste your mind by forcing you to fit into a corporate into a mold. 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 wayat 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 Cl.eLANESE. An equal opportunity employer m/f

PAGE 9

I (eJ n. 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, Uni ver sity 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. THE MIRROR FOG PROBLEM R.L.KABEL 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 FIGURE 1 FALL 1979 Open FIGURE 2 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 tr 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 (105 )m 2 s1 the concentration of water in saturated air is CAs = 17.3 gm 8 distance between panels is X = 4 mm, and the length of each panel YM = 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 Dit>isi01', ABEE, 1979 155

PAGE 10

1978'4~.e~ THE DYNAMICS OF RUNAWAY SYSTEMS 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. andM.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. THEODORE VERMEULEN University of California Berkeley, CA 94720 s CIENTIFIC ANALYSIS OF explosions and flames is not viewed today as an area of interest or concern for us as chemical engineers N everthe 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 Di 11ision, ASEE, 1979 156 "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. THE ANATOMY OF AN EXPLOSION 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 108 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 10 23 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 CHEMICAL ENGINEERING EDUCATION

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"detonation" occurs in less than one-tenth of a micro second. 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 rndiate 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 change. 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 oneUPDRAFT THROUGH CENTER OF TOROID FIGURE 1. Toroidal circulation inside the radioactive cloud from a nuclear explosion (after Glasstone) FALL 1979 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. THE RANKINE-HUGONIOT DIAGRAM P RESSURE 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 balances. 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 7T = P/Po, cp = v/v 0 and 0 = T/To, the temperature and pressure ratios follow the relation: 2y + 1, + 7T 8 2y + 1 + (l/1r) 157

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If frictiona.l dissipation and spherical geometry are neglected, for a shock wave travelling through air after the build-up stage, the Rankirie-Hugoniot curve shows the compressed condition of the gas corresponding to the pressure rise in the shock. with, for example, 'Y = Cp/C v = 1.4 for air. In the event '11" iS; very large, the least value of the volume ratio cf, ( = 8 /Tr) is 1/ (2-y+ 1), 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 cf,. 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 Tr gives reciprocal 8 and reciprocal cf,. 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, Tr reaches 2. 7, and a Raleigh line carries the mixture to Hugoniot curve 2; later Tr 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 off set by a drop in pressure, which accounts for the linear be158 havior of the combustion path (the Rayleigh line) Thus, p + ( ~: f 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. CRITICALITY 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 detonation. 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 radica_Is .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 ENGINEERING EDUCATION

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Chemical Engineers play key role at General Foods' Research & Development Centers. Chemical Engineers have a key role to play in research at General Foods Corporation, the nation's leading package grocery products company. Food is no longer the simple thing it was to our fore fathers. Most of us no longer pro duce our own food; but rely on others to process and package it, preserve and improve it, change it s FALL 1979 form, and get it to u s with all it s nutritive and ta s te value s intact. Demand Increases ... An accelerated worldwide need to supplement traditional agricultural food sources with technology based foods has created an un precedented need for chemical engineering skills of a high order. Unit Operations ... For students who want to put their chemical engineering training to work, General Foods Corporation needs almost all elements of the unit operations background ... dehydration, extrusion, heat and mass trans fer, extraction and separation. Team Contribution ... 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 s ional. 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 s tudies. Career Reference ... If you are interested in a career with a leading proce s sor of packaged convenience foods who markets over 400 familiar brand products s uch a s : MAXWELL HOUSE, JELL-O, POST GAINES, BIRDS EYE, KOOL-AID, SANKA, TANG, SHAKE 'N BAKE, COOL WHIP and many more Contact your placement office or write to: Technical Careers Dept. CEE79 GENERAL FOODS CORPORATION 250 North Street White Plain s New York 10625 A n Eq u a l O pp o rtun i t y E mpl o yer M / F / H c. 159

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THE INTEGRATION OF REALTIME COMPUTING INTO PROCESS CONTROL TEACHING PART I: THE GRADUATE COURSE M. MORAR! and W. H. RAY University of Wisconsin Madison, Wisconsin 53706 THE 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 IV. Patch Panel 8te r11.lnalport 16 11 /D cha nneh f'igurel C HEMICAL NClNER tNG MINICOMPUTER SYSTEM 16 D/A channels = o, = sc = oRNE = to~T ~==~i",,",,=!;""~~;='"'~' -=-,cc=,---; 1. 2 111Ul1on vorda 9 TRACK 16 Digita l I/0 1--== --leoo + 1600 DISC ORIVI! ll BPI PDP 11/55 1.2 million words CPU '"""""'=-~ /-:: ~:-::---k ~~~ Jl .Fl oat ln9P0int 1 180 c,ps Analog I /0 A Dud Proguaab l e CPU 160 Line Printer 116 Differen t h l 11/D B.~~h'!!:l C lock ~:~~~r;~~~9e111t 16 Single Ended D/A digital 1/0 300 nsee 11e110ry Analog Compute r 4,161: COH Analog Computer 11 Copyright ChE D i 11isi01l, ABEE, 1979 FEED 1-----f:::ICl---'SIDESTREAM Y2 1--'-D,q---SIDESTREAM Y3 BOTTOMS FIGURE 2. Multi-sidestream Distillation Column with Draw-off Rate used to Control Sidestream Composition. THE COMPUTING FACILITIES THE COMPUTING FACILITIES for the process 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 PDPll/55 minicomputer operating under the RSXllM operating system. The configuration, shown in Figure 1, includes 128 K words of TABLE 1 Graduate Process Control Lecture Topics 1. Practical aspects of on-line data acquisition and control 2. Control of systems described by ordinary differential and difference equations 3. Control of systems described by partial differential equations 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 CHEMICAL ENGINEERING EDUCATION

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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 verters. COURSE DESCRIPTION THE 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 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) FALL 1979 TABLE 2 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 s tochastic 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 constants 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 multi variable 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 161

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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 PROCESS G ~ p 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). Product St re am Composition -0.3M E01 0.31Je E-01 -0.30\iE-O I 0 39!E 02 FIGURE 4. Product compositions for multiple-single loop Pl control. 162 FIGURE 5 Non-interacting Multivariable Feedback Control. 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. CONCLUDING REMARKS As 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 PRODUCT STREAM COMPOSITIONS lil e wiat.ioA Y ai-iable1) -0. 373E-08 -o 373 E03 -0 37J E-0 8 8 979E 01 TIM E minutes 10 0 t !i3 E 82 ,0 FIGURE 6 Product compositions under dynamic noninteractive 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. D 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. CHEMICAL ENGINEERING EDUCATION

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create. construct and control your career with MILLIKEN FALL 1979 We provide an expanding range of opportunities to accelerate your managerial and professional career development Milliken s commitment to technological leader ship in providing new products processes and equipment is exemplified by the Millitron ma chine a computer controlled jet-injection dyeing system created and developed by Milliken engi neers and scientists for the production of multi colored carpet rugs and upholstery products. The men and women we need have open minds open enough to let us expose you to the details of the Milliken challenge When we select each other horizons broaden for both of us. Ca ll or write : Milliken Co l lege Rel a ti o n s D ept. P os t O ffice Box 1926 MILLI KEN Spar t a n b u rg, SC 29304 P hone (803) 573-2508 An equal opportunity employer. 163

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HETEROGENEOUS CATALYSIS M. A. VANNICE Pennsylvania State University University Pa r k, PA 16802 HETEROGENEOUS CATALYSIS plays a dominant 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. Thei 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 S S. degree in Chemical Engi neering from Michigan State University and his M.S and Ph.D. d\!grees 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 zation 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 subjects. 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 deCo pyright ChE D ivisio-n, ABEE, 19 79 CHEMICAL ENGINEERING EDUCATION

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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 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. lectures represent material for a 3-credit semester mations which apply to homogeneous gas-phase course. reactions. Reactions catalyzed on solid surfaces Because adsorption is the initial step in heterowere then discussed, and the consequence of asgeneous catalysis, this topic (Section II) was dissuming ideal surfaces was shown by the use of cussed first. The traditional approaches to rates Hougen-Watson type rate equations. The limitaof adsorption and desorption were supplemented tions and simplifications involved in this apby recent results in surface science. Also, a new proach were discussed in detail. With this backperspective on the Elovich equation was presented ground, various correlations in catalysis could and discussed. then be introduced. The topic of kinetics (Section III) was introThe development of the science of catalysis duced by a discussion of the theories and approxidepends heavily on experimental research, and TABLE 1 Course Outline I. INTRODUCTION (1 Lecture) A. Brief history of catalysis B. Processes using heterogeneous catalysts (1) C. Definitions IJ. 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 eq. 3 Heats of adsorption 4. Activated adsorption-Elovich eq. (8) III. CHEMICAL KINETICS (E) (11 Lectures) 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. Bronsted relation 3. Hammett relation 4. Van Tiggelen formula 5. Compensation effect (16-17) 6. "Volcano" Plot-examples (18) D. Catalysis on nonideal (nonuniform) surfaces (19) IV. HEAT AND MASS TRANSFER EFFECTS ON RATE EQUATIONS (20) (4 Lectures) A. Interphase transport B. Intraphase transport (pore diffusion) FALL 1979 C. Experimental tests for transport effects (2123) V. CATALYST CHAltACTERIZATION (2 Lectures) 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 (Mossbauer spectroscopy, magnetization etc.) VI. THEORETICAL CONCEPTS IN CATALYSIS (4 Lectures) 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) VII. CHEMISTRY AND KINETICS OF CATALYTIC 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-H y drogenation, 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) 165

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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 v s. 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. REFERENCES General Background Reading A. Bond, G. G., "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. 0., in "Chemisorption and Reactions on Metallic Films", ed. by J. R. Anderson, Academic 166 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 (1977). 8. Ritchie, A. G., J. Chem. Soc. Faraday Tr. I 73, 1050 (1977). 9. Hougen, 0. A. and Watson, K. M., "Chemical Process Principles-Kinetics and Catalysis", Wiley, N.Y. (1947). 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, 0., Coll. Czech. Chem. Comm. 38, 781 (1973). 18. Balandin, A. A., Adv. Catal. 10, 120 (1958). 19. Boudart, M., Cha pt. 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., "C hemical Engineering Kinetics", 2nd ed., Chapt. 8, McGraw-Hill, N.Y. (1970). 25. Sinfelt, J. H. and Yates, D. J. C., J. Catal. 8, 82 (1967). 26. Freel, J., J. Catal. 2 5, 149 (1972). 27 Baladin, A. A., Rus s 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 (1955). 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 (1976). 34. Sachtler, W. M. H. and van Santen, R. A., Adv. Catal. 26 69 (1977). 35. Boudart, M., Adv. Catal. 2 0, 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). CHEMICAL ENGINEERING EDUCATION

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ACl{NOWLEDGMENTS Departmental Sponsors: The following 138 departments contributed to the support of CHEMICAL ENGINEE : RING 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 Bucknell University University of Calgary California State Polytechnic California Institute of Technology University of California (Berkeley) University of California (Davis) University of California (Santa Barbara) Carnegie-Mellon University Case-Wes tern Reserve University University of Cincinnati Clarkson College of Technology Clemson University Cleveland State University University of Colorado Colorado School of Mines Columbia University University of Connecticut Cornell University University of Dayton University of Delaware U. of Detroit Drexel University 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 Iowa State University Kansas State University University of Kentucky Lafayette College Lamar University Laval University Lehigh University Loughborough University Loui s iana State University Louisiana Tech. University University of Louisville University of Maine Manhattan College University of Maryland University of Massachusetts Massachusetts Institute of Technology M cMaster University McNeese State University University of Michigan Michigan State University Michigan Tech. University University of Minnesota University of Mississippi University of Missouri (Columbia) University of Missouri (Rolla) Montana State University University of Nebraska University of New Brunswick New Jersey In s t. of Tech. University of New Hampshire New Mexico State University University of New Mexico City Univer s ity of New York Polytechnic Institute of New York State University of N.Y. at Buffalo North Carolina State University University of North Dakota Northwestern University University of Notre Dame Nova Scotia Tech. College Ohio State University Ohio University University of Oklahoma Oklahoma State University Oregon State University University of Ottawa University of Pennsylvania Penn sy l va nia State University University of Pittsburgh Princeton University University of Puerto Rico Purdue University Queen's University Rensselaer Polytechnic Institute University of Rhode Island Rice University University of ~ochester Rutgers U. University of South Carolina University of Saskatchewan South Dakota School of Mines University of South Florida University of Southern California Stanford University Stevens Institute of Technology Syracuse University Tennessee Technological University University of Tennessee Texas A&M University Texas A&I University University of Texas at Austin Texas Technological University University of Toledo University of Toronto Tri-State University Tufts University Tulane University University of Tulsa University of Utah Vanderbilt University Villanova University Virginia Polytechnic Institute University of Virginia Washington State University University of Washington Washmgton University University of Waterloo Wayne State University West Virginia University University of Western Ontario University of Wisconsin (Madison) Worcester Polytechnic Institute University of Wyoming Yale University Youngstown State University 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 32611. FALL 1979 167

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DOCTORAL LEVEL CHEMICAL ENGINEERING ECONOMICS ORAN L. CULBERSON 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. Co p y rig ht ChE Di visi on A SEE 19 7 9 168 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 put e r 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 CHEMICAL ENGINEERING EDUCATION

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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 plant(s) 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 FALL 1979 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 schedule." 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 wrong. 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 169

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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. REFERENCES Baba, T. R. and Kennedy, J. R., "Ethylene and Its Co products: The New Economics," Chetm. Engr., V83, No. 1, 116-128 (1976). Tribus, M., "Rational Descriptions, Decisions and Designs," Pergammon Press, Elmsford, New York, 1969, p. xv. [i) ;j Ii book reviews FILTRATION: PRINCIPLES AND PRACTICES (TWO PARTS), 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 170 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 O 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 contradiction. 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 Shira to published over the past two decades, the problem with compression-permea bility test cell data is never mentioned. The rest of the book deal& :with the Filter Media, Chapter 3, and Ultrifiltration, Chapter 6. The price of the book is far too expensive! CHEMICAL ENGINEERING EDUCATION

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Monsanto Drive. It takes you a very long way. This sign marks the road that lead s into our International Headquarters in St. Louis These words, "Monsanto Drive" have another and more significant mean ing at Monsanto. It's a way of expressing the special qualities of Monsanto people who have the will to meet challenges head-on-to accomplish and succeed. 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 the U.S. We offer you opportunities, training and career paths that are geared for upward mobility. If you are a person who has set high goals and has an achievement record, and who wants to advance and succeed, be sure to talk with the Monsanto representative when he visits your campus or write to: Ray Nobel, Monsanto Company, Professional Employment Dept., Bldg. A3SB, 800 North Lindbergh, St. Louis, Mo. 63166. Monsanto A n e qu a l o p p o rtu nit y e mp l oye r

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FUNCTIONAL ANALYSIS FOR CHEMICAL ENGINEERS D. RAMKRISHNA Purdue Uni versity West Lafayette, IN 47907 THERE HAVE BEEN A NUMBER of recent books by mathematicfans 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 fi r st is that mathema tical abstraction has a ccomplished a tremendous unification of apparently diverse classes of problems under a common framework. Conse quently a given problem suitably cast in the foreDoraiswami Ramkrishna received his B(Chem)Eng degree (1960) from the Bombay Univers it y Department of Chemical Technology and his Ph D (1965) from the Univ e rsity of Minnesota. After teaching for two years at Minnesota he re turned 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 M i lls Inc ., Minneapolis. H i s research includes d is persed phas e systems, stochastic modeling and applications, bioengineering and problems of general appl ie d math interests Normally quite gentle he reac ts rather violently to cr i ticism of cricket Copyright ChE Division, ASEE 1979 172 ... mathematical abstracting has accomplished a tremendous unification of apparently diverse classes of problems under a common framework. Ccmsequently, 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. COURSE OBJECTIVES AND CHALLENGES }N THE DEVELOPMENT OF an engineering graduate 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 CHEMICAL ENGINEERING EDUCATION

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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]. SCOPE OF COURSE T HE FOLLOWING TOPICS ARE dealt with in a 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 problems. 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 173

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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 ref erred 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 introIn 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 tions. (i) l l x ll 0, l l x ll. = 0 if and only if x = 0 (ii) l l axll = lal 1 1x1 1 (iii) llx + Y II S ll x ll + II YI I In the above x and /Y are vectors, a is a number with l al as its absolute value and 11 1 1 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=O (iii) = + < Y,z> (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 ll xl l = y. 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 174 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), asxsb such that b f f 2 (x)dx < co a represents a linear space of vectors f == [f (x) : a s x s b]. The inner product in this space is de fined by b = f f(x)g(x)dx a 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 + {3y) = aLx + {3Ly 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 P 2 = 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 [Ai] and associated projection operators [jPi] with the property that PiP k = 0 when j =I= k such that (2) Continued on page 211. CHEMICAL ENGINEERING EDUCATION

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COLLOIDAL PHENOMENA WILLIAM B. RUSSEL, DUDLEY A. SA VILLE, DAVID F. OLLIS and WILLIAM R. SCHOW ALTER Princeton University Princeton, New Jersey 08544 THE 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 endJ 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 ,m 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 casein. Today both the science and the engineering pertaining to colfoids 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 ... Co p y rig h t ChE Di visi o n, AS EE 1 9 79 176 After obtaining hi s 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 i n the context of biochem i cal engineering problems He is currently Pro fessor of Chemical Engineering. Bill Russel's (2nd from left) interests in the behav i or of poly electrolytes and other particulates in suspension began during a stint as NATO Postdoctoral Fellow at Cambridge shortly after he completed h i s PhD at Stanford in 1978 His B.S and M.S. are from Rice University His research in the behav i or 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 Pr i nceton 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 i s from Wisconsin and h i s M S and Ph.D are from Illinois He is Professor of Chemical Engineering and Chair man of the Department Dudley Saville (right ) cam e to Princeton in 1968 after stints in in dustrial research at Chevron Research and the Shell Development Company. His undergraduate degree i s from the University of Ne braska and his PhD from Michigan. His current research includes studies of electrokinetic phenomena in su s pens i ons 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 r esearch and de velopment efforts. Prompted by a confluence of research interests CHEMICAL ENGINEERING EDUCATION

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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. TECHNICAL CONTENT THE LECTURES AND READINGS emphasize the 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 experiTABLE 1 Course Outline INTRODUCTION FORCES ACTIVE AT THE COLLOIDAL SCALE (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 COLLOIDAL STABILITY (W. B. Russel) 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 ELECTROKINETIC PHENOMENA (D. A. Saville) 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 FALL 1979 electrophoresis of polyelectrolytes primary electroviscous effect SEPARATIONS PROCESSES (D. F. Ollis) Filtration forces responsible for collection trajectory analyses macroscopic balances and filter design Field-Flow Fractionation types of transverse fields pulse velocity and dispersion design considerations Flotation isotherms and interfacial aspects application of particle collection theories experimental results Ultrafiltration role of osmotic pressure concentration polarization Continuous flow electrophoresis principles and general analysis hydrodynamic instabilities application to separation of cells SUSPENSION RHEOLOGY (W.R. Schowalter) Examples of non-Newtonian behavior of disperse systems 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 177

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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 vvi.th 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\78 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 equilib r ium 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 characCHEMICAL ENGINEERING EDUCATION

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TABLE II 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 Su rface 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, 1972. E. J. W. Verwey and J. Th. G. Overbeek Theory of th e 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 rheological 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 suspensions. TEACHING THE COURSE M ATERIAL PRESENTED BY THE individual faculty as listed in the' course outline corresponds roughly to their research interests. Periodic acaFALL 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 r esearch. 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 thElj 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. ERRATA 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'. ~Sll' = R ln (v s' /v 3 ) Pg. 148: Col. 1, line 16: Entropy change, ~S IV = R ln v 1 / v 4 '; Pg 148: Col. 1, line, 19: W = lW ; = Q 2 + Qi'= RT 2 ln(v 3 / v 2 ) + RT 1 ln(v 1 /v/) Pg. 148: Col. 1 line 21: ~S cyc i e = R ln (v 3 / v 2 ) + R ln (v 1 /v 4 ') + R ln (v//v 3 ) Pg. 148: Col. 1, line 34: ... The latter ... Pg. 148: Col. 2, line 9 (Eq. 10): = -Q 2 / T 2 = R ln (v 3 / v 2 ) Pg. 148: Col. 2, line 10 (Eq. 11): ... = -Q // T 1 = R ln (v 1 /v 4 ') 179

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COAL LIQUEFACTION PROCESSES T. F. YEN University of Southern California Los Angeles, CA 90007 O F 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. 180 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 Div isi on, ASEE, 1979 CHEMICAL ENGINEERING EDUCATION

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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 institut'ions, 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. LECTURES THE WEEKLY LECTURES have been primarily delivered 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). Occassionally, 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 majoi 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 TABLE 1 Lecture Topics 1. Introduction-Coal Resources and Supplies; Coal Mining Technology Development 2. Origin of Coal; Coal Types and Ranks; Petrography; Metamorphism 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 fuels 14. Novel Approaches; In-Situ Production 15. Environmental, Safety, and Health Problems in Coal Conversion 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 library. CLASSWORK C LASS WORK IS COMPRISED of three categories which carry equal weight in the calculation of grades: homework problems, term paper, and tests. 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 homeBesides 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 181

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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 investigator. STUDENT POLL D UE TO THE STILL-EVOLVING nature of coal 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. l 182 L -I L F E M E F A 0 A 0 R u R R H H H T I T E H 0 V G s s A M p L E s I z E I s 1 3 FIGURE 1. Graphic Repr esentation of Student Response to Course and the author has had a more than customary interest in student reactions and suggestions, with a view to shaping the best possible course offering. 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 on~ found himself struggling to get through the course rather than attempting to learn. Continued on page 215. CHEMICAL ENGINEERING EDUCATION

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? i With all the talk about dwindling energy supplies and such, we're often asked if this Is any time to work for a company like Exxon. Our answer is always the same: "Yes, if.,." Yes, if you can help tackle society's critical need for oil and gas and coal for nuclear and solar energy ... for petrochemicals and minerals because at Exxon we're involved in all those fields. Yes, if you're attracted to such non-energy areas as information systems, space-age ma~ terials and advanced business systems because at Exxon we're involved in these and other new ventures Yes, if your down-the-road hopes might include overseas service, because Exxon's world~ wide affiliates often look to our U.S. operations for specialized skills. Yes, if you want to be part of a growth company. because at Exxon our U S. work force will increase by 30 percent in the next three years. Yes, if you war1tlchallenge because at Exxon the challenges are r'ndny and diverse and show no signs of abating. 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. FALL 1979 E>f{ON Exxon Corporation and its Domestic Affiliates, Equal Opportunity Employers. 183

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MATHEMATICAL METHODS IN CHEMICAL ENGINEERING ARVIND VARMA Un iv ersit y of Not r e D a me Notre D a me, Ind i ana 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 toArvind Varma is currently an Associate Professor of Chemical Engineer i ng 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 wa s with Union Carbide for two years and joined Notre Dam e in 1975 His research interests include chem i cal 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 Amundsen's early work on distillation-the fruits of which they both enjoy Co p y rig ht ChE D i11iBi on A SEE, 19 7 9 184 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 196467 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. CHEMICAL ENGINEERING EDUCATION

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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]. COURSE FORMAT THE 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 2530 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. TABLE 1 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. FALL 1979 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. COURSE DESCRIPTION A TOPICAL OUTLINE OF the course is shown in Table 1. The following is a detailed descrip tion. 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 actors. 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 185

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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 CHEMICAL ENGINEERING EDUCATION

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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 centrol role in solving partial differential equations, and is thoroughly discussed. 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 .QDEs 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 FALL 1979 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 per :rp rmed 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. CONCLUDING REMARKS As THE PREVIOUS DESCRIPTION indicates, we do 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 mathematic s 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 187

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NEED QUICK~ ACCESS TO~ PATENTS Ever been in the midst of research and realized that easy access to U.S. Patents would be the answer to your problems? U S Patents on microfilm from Research Publications, Inc. offers to attorneys researchers, inventors and librarians the largest single body of scientific and technical information in existence RPI offers a complete retrospective file of U.S Patents and current subscriptions, as well as the Official Gazette and the CDR File Access is immediate, and information retrieval is quick and easy. Delivery of current subscriptions is weekly, within four weeks of date of issue. Find the answers to your questions with U S Patents on microfilm from: m research publications, in~.t-' 12 Lunar Drive, Woodbridge, Ct 06525 (203) 397-2600 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 188 to i,olve non-trivial problems in practice. Student feedback has been uniformly positive. ACKNOWLEDGMENT It is a pleasure to thank my colleagues, James J. Car berry and James P. Kohn for providing historical in formation regarding the course REFERENCES 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 Differ ential Equations a nd 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 Int egr al Equation s," Dover, New York (1962). 6. Ince, E. L ., "Ordinary Differ ential Equations, Dover New York (1956). 7. Jenson, V. G. and G. V Jeffrys, "Mat hematical 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, 2 61, 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. Rossler, 0. E., Z. Naturforsch., 31a, 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. (1978). 16. Weinberger, H. F "A First Course in Partial Differential Equations," Blaisdell, Waltham, Massa chusetts (1965). [iiNI books received ] Heat Pumps, R. D. Heap. Halsted Press, John Wiley & Sons, N ew York, 1979, 155 page s, $9.95. Advances in Photochemistry, Vol. 11, ed. by J N. Pitts Jr. G. S. Hammond, Klaus Gollnick, and Daniel Grosjean. John Wiley & Son s, New York, 1979 538 pages, $35.95 Pulverized-Coal Combustion and Gasification, Theory and applications for continuous flow processes, edited by L. 0 Smoot and D. T. P ra tt. Plenum Press, New York, 1979, 333 pgs. CHEMICAL ENGINEERING EDUCATION

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11 l'm designing process instrumentation for a $9 million plant expansion at Du Pont." Tm an instrument engineer with the Design Division of the Engineering Department at Du Pont Ronald Haynes BS, Chemical Engineering involved in designing process instrumentation from design to specification writing to working with vendors. This job offers me plenty of technical challenge. That's what I wanted when I came to Du Pont. I was recruited from Howard University in 1972. As soon as I saw how many con tributions by Du Pont people were listed in Perry s Chemical Engineering Handbook ,' I was sold on the technical compe tence of the Company. Since he joined Du Porit Ron has also worked as a project engineer a process development engineer and as an on-campus recruiter for the Company. He s experienced the kind of job variety that stimulates growth. Ron s story is typical of many Chemical Mechanical and Electrical Engineers who have chosen careers at Du Pont. We place no limits on the progress our engineers can make. Or the contributions they can make-to themselves the Company or to society If you re looking for technical challenge and a chance to grow do what Ron Haynes did Talk to the Du Pont representative who visits your campus Or write: Du Pont Company Room 36816 Wilmington DE 19898. At Du Pont ... there's a world of things YOO can do something about. QEC, US PAt 8 T M 0fF An Equa l Opport u n i ty Emp l oyer M / F

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POLYMER SCIENCE CURTIS W. FRANK Stanford Uni v ersity Stan/ ord, CA 94305 I 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 h i s 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 Illino i s he co authored with Professor H. G. Drickamer the monograph Electronic Transitions a!ld 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 compat i bility, 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 190 by materials science and chemical engineering de partments and by specialized polymer institutes or interdisciplinary groups in "macromolecular science." 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 fl.owing 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 processing. 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 Co p y right C h E Di 11 i sicm AS E E 1979 CHEMICAL ENGINEERING EDUCATION

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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 viscoFALL 1979 ... 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, 1972. F. W. Billmeyer, Textbook of Polymer Science, Wiley lnterscience, 1971. J. D. Ferry, Viscoelastic Properties of Polymers, Wiley, 1970. H. S. Kaufman and J. J. Falcetta, Introduction to Polymer Science and Technology, Wiley-Interscience, 1977 F. Rodriguez, Principles of Polymer Systems, McGraw Hill, 1970. J. Schultz, Polymer Materials Science, Prentice-Hall, 1974. 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 191

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course follows Professor P. J. Flory's application cules, Wiley, 1969 are highly recommended. Addiof statistical mechanics to the thermodynamics tional texts in which reading assignments are and configurational properties of high polymers. made include: Although most of our first year graduate students H.-G. Elia s Macromolecules, Vol. 1, Structure and have had undergraduate courses in statistical meProperties, Plenum, 1977. chanics and linear algebra, brief reviews of imH. Morawetz, Macromolecules in Solution, Wiley-Interscience 1975. portant concepts and methods are given at apc. Tanford, Physical Chemistry of Macromolecules, propriate points. The course has been offered preWiley, 1961. viously with the order of topics as in Table 2 and H. Yamakawa, Modern Theory of Polymer Solutions, with the configurational statistics preceding the Ha r per and Row 1971. thermodynamics. The former approach works Ch.E. 217 is a review of the principal methods much better, perhaps because student familiarity of polymer synthesis with emphasis on molecular with classical thermodynamics allows a more polymerization mechanisms and reaction kinetics gradual transition into thinking about macromoleand their roles in influencing polymer composicules. Extensive reference to the original and tion, structure and ultimate properties. Topics current literature is made throughout the course. include: condensation, radical and ion initiated There is no required text for Ch.E. 212. Howchain polymerizations; heterogeneous and stereoever, the two books by P. J. Flo r y, P ri nciples of regulated polymerizations; copolymerization; Polymer Chemist r y Cornell University Press, bulk, solution emulsion and suspension polymeri1953 and Statist i cal M e chan i cs of Chain Molezation; and application of the principles of synTABLE 1 Course Outline-ChE 170 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 M n by osmotic pressure 3. Determination of M w by light scattering 4. Determination of M v 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. Macro s copic crystallization kinetics B. Amorphous polymers (2) 1. Phenomenological observations of the glass transition 2. Theoretical approaches to the glass transition 3. Structure-property relationships for transi tion temperatures III. Rheology (1) 1. Introduction to non-Newtonian and time dependent flow 2. Power law con s tituti v e relation 3. Effect of temperature on zero shear viscosity 4. Effect of molecular weight on zero shear viscosity IV. Linear viscoelasticity 192 A. Phenomenological treatment using mechanical models (2) 1. Stre s s relaxation and the Maxwell model 2. Creep and the Voigt Model B. Dynamic response (2) 1. Frequency respon s e of the standard linear solid 2. Complex variable notation for modulus and compliance 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 strain 4. Strain in v ariants B. Stres s -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 polymetr chains 2. Gau s sian distribution function 3. Entrop y of deformation D. Thermodynamic analysis of network elasticity (1) 1. Force-extension relations for a Gaussian network 2. Stress-temperature relations 3. Internal energy and volume changes CHEMICAL ENGINEERING EDUCATION

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TABLE2 Course Outline-ChE 212 I. Introduction to polymeric materials A. Molecular architecture (1) 1. Relpeat 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 propeirty 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 parameter 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 thry 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 3. The equivalent chain B. Excluded volume (1) 1. Mean field model 2. Probability of binary encounters 3. Probability of alteration of chain configuration 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 chains C. Configurational partition function (1) 1. Fundamental concepts of statistical mechanics 2. Geration of configurational partition functions by matrix multiplication 3. Evaluation of rotational state probabilities 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 vector 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. 1 3 C nuclear magnetic resonance E. Fluorescence spectroscopy -------------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 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) REFERENCES 1. R. L. Rawls, Chemical and Engineering News, May 23, 1977, p. 19. 193

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THE STRUCTURE OF THE CHEMICAL PROCESSING INDUSTRIES* T. W. F. RUSSELL University of Delaware Newark, DE 19711 THIS COURSE WAS INITIATED at the University 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 197 4 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 soine 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 presideint 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. 194 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) TABLE 1 Course Outline 0 Reader's Guide 1 Introduction 2 Basic Economics 3 Basic Accounting 4 Input-Output Analysis 5 Products and Companies of the CPI 6 Specific Chemical Products 7 Specific Companies 8 General Characteristics of the CPI 9 International Aspects of the CPI 10 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 tion. (ii) It outlines how to use the book, current literature and supplementary information for Copyright ChE Div i si
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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 society. 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 studies. 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. USE OF CASE STUDIES 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. FALL 1979 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 business. 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. SPEAKERS FROM OUTSIDE THE UNIVERSITY 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 vided. 195

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TABLE 2 Typical product Assignments Precipitated calcium carbonate Titanium dioxide Carbon black Yellow iron oxide Penicillin Aspirin Vitamin C Caustic soda Ammonia Sulfuric acid Nylon Polyester fiber Rayon ASSIGNMENT OF STUDENT SPECIALISTS Carbon dioxide Nitrogen Oxygen DDT Pesticides Herbicides 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 THIS ASSIGNMENT REQUIRED each student to become 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 following: Facts and Figures issue of Chemical and Engineering News. 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.) TABLE 3 Planning schedule MONTHS BEFORE COURSE BEGINS 12-10 6-4 4-2 2 1 1 196 PHASES TO BE COMPLETED Collect articles which will expand upon and complement text; decide on reprints students should have Order text 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 COMMENT Begin to rough out in-class course schedule Not knowing class registration can be troublesome; class enroll ment should have an upper limit to ensure adequate class dis cussions and interaction In-class schedule should now be fairly well decided The last bit of information needed to firm up the class schedule CHEMICAL ENGINEERING EDUCATION

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PLANNING To PREP ARE 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. CHAP. HOURS 1 1-2 2 5-7 3 1-3 4 2-4 CO NC LUSI O NS TABLE 4 Class schedule CHAP. HOURS CHAP. 5 1-2 9 6 1-2 10 7 1-2 Guest speakers 8 4-6 Case st udies HOURS 2-4 2-4 3-5 3-5 The course has been w ell 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. Jift:I book s rece iv e d "A n 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 p rese ntation 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-Teachin g Guide de sig ned as a supplement to an o rgan ic 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 organi c chemistry "What Every Engineer S.hould 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 product s This book s hows how the process of designing safer products is a natural ex tension of traditional engineering aptitudes and pro cedures. "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. FALL 1979 POSITIONS AVA ILABLE Use CEE'!, reasonable ratea to advertise. Minimum rate page $50; e ach additional column inch $20. OKLAHOMA STA T E U NIVERSITY Assi s tant or Ass o ciate Pr o f e ss o r 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-investig ation 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 int erests 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 commens urate with qualifica tions and experie nc e If you are interested in joining an established School of Chemica l Engineering (in the pleasant Southwest) that offers exciting professional growth opportunities, please send your resume and list of three references to : Profe ssor Billy L. Crynes, Head, School of Chemical En g in eering, 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 r eferences for further study. It was written for safety specialists, re presentatives and studnts, 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 Fried ric h Loh se John Wiley & Sons, N ew York, 1979, 297 pages, $34.50. The chemistry of macromolecular compounds is pre sented under the topics of synthesis and isolation; character ization 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," Hir o yuk Tad o kor o John Wiley & Son s New York, 1979 465 pages, $35.00. Under s tanding the properties that distinguish o ne 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. 1 9 7

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INTRODUCTION TO THE MOLECULAR THEORY OF THERMODYNAMICS H. TED DAVIS 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. Co pv right ChE D iv i sion ASEE, 19 7 9 198 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 l 00 publications in scientific and engineering journals and edited books. His research interests include statistical mechanics of equi librium and transport processes, experimental and theoretical i nvesti 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. DILUTE GAS KINETICS THE 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 CHEMICAL ENGINEERING EDUCATION

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molecular velocity. In 1845, Waterston [l] 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 "'( ) ( m ) a/~ [ mv 2 ] 't' v 21rkT exp 2kT (2.1) where cp(v)d 3 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 gases. The pressure P exerted by a dilute gas cal culated from the momentum exchange between a wall and particles rebounding from the wall is 2.2) where < mv 2 > 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 < mv 2 > 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 = y8kT/1rm, a result demonstrating the connection between the speed of sound, c = y (dP / mdn)T = ykT / m, and the movement of molecules in a dilute gas. The average flux of dilute gas molecules against a wall is 1 1 / 8kT = 4 n = Tnv 7/"m (2.4) FALL 1979 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 var y inversel y 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 d ensities 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 1 and n 2 occupy the same container, and escape from the same pinhole, then the gas densi ties ni' and n / of the escaping stream obeys the relation I [ ] 1 / 2 n 1 n 1 m 2 -, --. n 2 n 2 m 1 (2.5) 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 U 235 from U 23 8 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 uranium. 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 A (average distance travelled between collisions) are given by v = y21rd 2 n and 1 (2.6) The probability that a particle will travel a distance x (or time t) without collision is q = e -x P (or e -t ) (2.7) The average particle separation l == n 1 1 3 mean free path, collision frequency, and width X of a vessel for which the probability is 0.95 that a 199

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TABLE 1 Dilute nitrogen at 300K. The molecular diameter d is assumed to be 2 x 1 o -s cm. P(atm) Z(cm) A.(cm) v(sec1 ) X(cm) 108 1 3.46 X 10 6 2.34 X 10 2 2.03 X: 10 6 1.20 X 103 3.46 X 107 2.34 X 10 -5 2.03 X 10 9 1.20 X 106 particle can cross without collision are illustrated in Table 1 1:or 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 THERMODYNAMIC FUNCTIONS AND THE PARTITION FUNCTION If an isotropic fluid is subject to a conservative external force, whose potential energy is u (r), then the equation of hydrostatics is VP = -n'\,lu. (3.1) In an isothermal ideal gas, P= nkT, so that Eq. (3.1) can be integrated to yield the barometric formula P(r) = P(r 0 ) exp (-[u(r)-u(r 0 )]/kT). Or, eliminating pressure in favor of density, we obtain [u(r) u(r 0 ) ]/ kT n(r) = n(r 0 )e (3.2) The density n(r) can be interpreted statistically: n (r) d 3 r is the probable number of particles in the volume d 3 r, so that if p(rr)d 3 r is the proba bility that a particle is located in the volume d 3 r 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 (3.3) where e =-mv 2 + u (r) is the energy of the par200 ticle. Thus, the probability that particle 1 of the gas is in d 3 r with velocity in the range V 1 to V1 + dv 1 particle 2 is in d 8 r 2 with velocity in the range V 2 to V 2 + dv 2 etc., is e -E/k T = ----::::::-d 3 v 1 d 8 r 1 ... d 3 v N d 3 r N (3.4) Q N where E = l [ + mv / + u(r 1 )] is the i=l total energy of the particles of the medium and ----Q is the normalization constant for P N i.e., ,-...., ; Q = 5 ... 5 e -E/kT d 3 V 1 ...... d 3 v N d 3 r 1 ... d 3 r N ----= (~) SN/2 Z 21rkT (3.5) Q is called the partition function and Z is called the configuration partition function. In Eq. (3.5), U N == N l u(r 1 ). i=l The formula for P N 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 P N 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, central forces u N = With this generalization, the thermodynamic energy of the system is (3.6) and the pressure is (3.7) where F w 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 expresCHEMICAL ENGINEERING EDUCA.TION

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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 Zn Q, (3.8) where F is the Helmoholtz free energy and '-Q Q / N !h 3 N for a pure system or Q '--""' II Q / 7T (N a !h 3 N a) for a system of v coma=I ponents. From Eq. (3.8), all the thermodynamic functions of interest can be generated as ap propriate derivatives of the partition function (S = -aF / aT, P = -oF / 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 Zin 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 integrations 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 1 (T) J N Z/N !, where q1 (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 n,onideal part is determined by Z. PHASE EQUILIBRIA OF FLUIDS A LMOST 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 FALL 1979 Waals' equation, known variously as the Redlich K wong [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(r 1i ) and a long ranged attractive part u A (r 1 i). Then, supposing that the repulsive forces restrict the configurations allowed to the particle centers, one assumes that the total attractive energy, u = 2 1 .~. u A (r1i), is never !L,J far from its average value in the integrand of Z. Thus, the approximation l kT u : / k T Z e { v ... e d 3 r 1 ... d 3 r N (4.1) is introduced. Since pair potentials are assumed, 1 = 2 N(N 1) , N(N-1) /2 being the number of interacting pairs and u A (r 12 ) the potential of a typical pair. Let p (r 1 ,r 2 ) d 3 r 1 d 3 r 2 denote the probability of a pair of molecules being in a configuration such that one is in d 3 r 1 and the other is in d 8 r 2 If r 1 and r 2 are far apart, then p(r u r 2 ) =p(r 1 ) p(r 2 ), i.e., the particles are statistically independent. Since the molecules cannot overlap, p(1\,r 2 ) must go to zero as I r c r 2 I becomes small. Thus, p (ri,r 2 ) = g(1\,r 2 ) p(r 1 ) p(r 2 ), where g(1 \ ,r 12 ) 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(ri,r ) = g( j rcr 2 I) so that 1 = 2 N(N-1) J J p(r 1 ,r 2 ) u A (lr 1 r 2 1) d 3 r 1 d 3 r 2 1 N(N 1) = 2 J J g( / r 1 -r 2 / ) u A ( / r 1 -r 2 / ) d 3 r 1 d 3 r 2 (4.2) Introducing the coordinate transformation 1'h,r 2 r, r = r 1 -r' 2 we can integrate over one of the volumes in Eq. ( 4.2) to obtain N 2 1 = V a;a = 2 { g(r) uA(r) d 3 r. (4.3) 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. 201

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... 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, yield ing with Eq. (4.3), the configura tion partition function N Z a Z = exp (Vk.T) (V-Nb) N (4.4) and therefore the free energy expression N 2 a F = N, + (T) -NkTZn(V-Nb) + --V-' (4.5) where + (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 N 2 a p = V-Nb V2 ( 4 6 ) In terms of the molecular diameter, d, the excluded volume is b = ;1r 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) = a 2 P /aVz, the relations a = 27k 2 T / / 64P c and b = kT /8Pc 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 fr = 3 i~~l -i, 2 (4.7) where the reduced temperature and volume are Tr= T/T c and Vr = V / V e 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. 202 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 /a Nhv, of the liquid and vapor phases be equal. This is equivalent to finding the pressure such that JVd P = 0, i.e., that the area the pressure isotherm makes with the Maxwell tie-line from below equals the area it makes from above. 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 p :$ Nap.,a + (T) and the parameters band a bea=l p come composition dependent, b = :$ xaba a=l p and a = :$ XaX13a a13. a,/3= 1 X a and ba denote the mole fraction and excluded volume of species a. a a 13 is defined as in Eq. ( 4.3) for the potential of interaction between particles of species a and /3. The equation of state, Eq. (4.6), unchanged in form. A useful empiricism, a a13 = yaaaa1313, 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 a and aa a Liquid-vapor phe nomena result largely from a balance between CHEMICAL ENGINEERING EDUCATION

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P0 r= o.32 0.06 0.04 0.02 0 20 25 30 35 -0.01 -0.02 I v -0.03 I I I 1 r=o.20 -0.06 FIGURE 1. Pressure-volume isotherms of a Van der Waals fluid. P* = Pb 2 / 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 (aaa/ a{l{l). 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 tions. CONCLUDING REMARKS 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 princiFALL 1979 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. *This will be the subject of a subsequent paper by Pro fessor Davis in GEE. Editor REFERENCES CITED 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 (1962) 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 (1949). 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 (1966). 11. V. Bongiorno, L. E. Scriven, and H. T. Davis, J. Coll. Int. Sci,. 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. A1 2 2213 (1976). 14. B. S. Carey, L E. Scriven, and H. T. Davis, AIChEJ. 2 4, 1076 (1978). 15. B. S Carey, L. E. Scriven, and H. T. Davis, J Chem. Phys. 69, 5040 (1978). [iJ;j?I news ZWIEBEL APPOINTED CHAIRMAN 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. RICE APPOINTED HEAD 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. 203

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MITCHEL SHEN 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 ti o n officially which he exercised unofficially through his academic career. He was an assistant editor of T r ans. Soc. Rheol. (1970-75), co-editor of Re v Macromol. Chem. (1969) and editor-at-large for J. Macromol. Sci Part A (1971) The volume of high-quality work he was able t o publish in such a short career was astonishing. In addition to the book "Introduction to Polymer Viscoelasticity" (Interscience, 1972), which he c o authored with J. J. Aklonis and W J. Mac Knight, he edited five other volumes and published 107 research papers (with 24 more in 204 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. R O BERT E. TREYBAL 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 leagues. 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 Island. 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. CHEMICAL ENGINEERING EDUCATION

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AWARD LECTURE Continued from page 158 pect to avoid explosion. However, often another cons ideration 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 sults. 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, w hile 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. CHEMICAL REACTION LIMITS 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. E E 1000 100 10 No explosion Explosion -._-first limit -----440 480 520 560 Temperature, c FIGURE 3. Ignition limits for stoichiometric hydrogen oxygen mixture in a 15-cm spherical vessel (after Lewis and Von Elbe) FALL 1979 Figure 3 is a classic diagram of the ignition limits for H 2 with 0 2 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, 450 C), and move upward in pressure, we start in a zone of slow, measurable reaction advance through the "first explosion limit" into a region of hi gh 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 "seco nd explosion limit" into the same high.temperature fast.reaction region we had previously encountered. Starting again at 1 atm. and increasing the presIt 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 reaction. 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: (Initiation, H 2 + 0 2 (at wall) 2OH (1) weakly) (Propagation) OH + H 2 H 2 O + H (2) H + 0 2 OH + 0 (3) 0 + H 2 OH + H (4) (Net reaction) 3H 2 + 0 2 = 2H 2 O + 2H (2, 3, 4, 2) (Termination) H (at wall) 1 / 2H 2 (5) At steady state, then, the net production of radicals is k1 (H 2 ) (0 2 ) + k a (H) (O 2 )2[K s/ (P r 2 )] (H) = 0. where the parenthesis denote gas-phase concen205

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trations for partial pressures, (if the coefficients are adjusted appropriately), and K 5 / 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: k1k a (H 2 ) (0 2 )i ~ P 2[K 5 / r 2 ] k a (0 2 ) P Because (0 2 ) 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 H0 2 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 2 0 2 + T 20H + T (11) (Propagation: H 2 0 2 as product) H + 0 2 + T H0 2 + T (12) H0 2 + H 2 H 2 0 2 + H (13) (Propagation: H 2 0 as product, by addition of Step 2 above) H + H 2 0 2 H 2 0 + OH (14) (Termination) H + H0 2 + T H 2 0 2 + T (15) We now identify a steady-state reaction condition involving three independent relations. First, the rate of oxygen consumption ( ex cluding step 3) is k 1'2 (H) (0 2 )P = k 1a (H0 2 ) (H 2 ) Second, the rate of H 2 0 production is k 2 (OH) (H 2 ) = k 14 (H) (H 2 0 2 ) Third, the net production of radicals is k 11 (H 2 0 2 ) p + k s (H) (0 2 ) k1 s (H) (H0 2 ) p = 0 Excluding step 3, we have (H0 2 ) = k 11 k 12 P[ (H 2 0 2 ) (0 2 ) ] k1 a k1 5 (H 2 ) :::::: K (H 2 0 2 ) P This relation indicates that the H 2 0 2 concen tration is controlled by the termination reaction. 20 6 It will grow rapidly, ahead of the steps producing H 2 0 2 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 H 2 0 2 a different termination step may predominate (2H0 2 H 2 0 2 + 0 2 ), but this will produce v ery little change in the kinetic relations. Finally, the total rate (including step 3) is approximately (k 11 P + k a ) k 11 (H 2 0 2 ) ( 0 2 ) P k 1 s K (H 2 0 2 ) P 31 2 -k s (0 2 ) z [ k n ~ :: k ia] [ ir 2 0 2 ) ( 0 2 ) 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 Exp]osion 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 w hich 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 bet w een 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. THE THERMAL RUNAWAY LIMIT THE 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 CHEMICAL ENGINEERING EDUCATION

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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 a t the surface temperature. The effect of temperature on rate is approximated by a linear exponential term: k = k exp (w8). Here 8 is the fractional temperature rise, with 8 = 1 at the adiabatic maximum temperature and 8 = 0 at the vessel surface ; e increases from 0 at the surface to B e at the center of the sphere. The coefficient w is related to effective activation energy E by the relation w = EJ / RT .2 where J is the adiabatic maximum temperature rise. Also k H 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 sion. Following Frank-Kamenetskii and Damkohler, we may now equate the integral for heat release over the entire vessel to the heat-transfer rat~ from the mixture to the vessel wall : A i 1T R a k f !r 2 dr = 47T R k H J ( ~:) 8 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 e vs. r, and substi tute the result into our present equation. The temperature gradient de / dr at the surface increases steadily with B e We find that no steady state exists if \J!B e is greater than 1.6, or exp (wB e ) greater than 5. The corresponding value of the dimensionless group formed from the variables in the equation is !;k s A R 2 / k H J B e] = 2.1 An alternative group can be formed by introduc ing we e : ~ A R 2 w / k H 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 k H 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, w hich is used to calculate the effect of mass diffusivity on the effectiveness factor. For a w ell-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, K 2 / k H 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. TABLE 1 Flammability Limits In Air COMPOUND Hydrogen Methane Ethane Acetone n-Butane n-Heptane iso-Octane FALL 1979 MOLE-FRACTIO{N OF COMPOUND LOWER STOIC MAX. VEL. UPPER .040 .258 .745 .050 .095 .150 .033 .056 .063 .125 .030 .050 .058 .116 .017 .031 .035 .103 .010 .019 023 .084 .008 .017 .019 .059 TEMPERATURE, 0 R. MAX. VEL. IGNITION 1500 1535 404 0 1340 3820 1500 4060 1270 3980 940 4 020 1300 207

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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 stabil i ty. 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 control. 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 flam mability 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 CO 2 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 be208 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. ONE-DIMENSION MODELING OF PREMIXED FLAMES 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 ~, and (4) a dimensionless maximum-temperature rate pa rameter involving the first-order constant kco. The dimensionless length and dimensionless rate constant each contain both the effective diffusivity D and the flame velocity U a 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 NO ::, 8 -'C 0 o c ., ,oz ., 0 c.> I _,:. C 8'. 10 L-L... __ --.1. ____ ....1.... ___ ___, 0 20 40 60 Rote-range parameter ,i,, or ln(kco /ko) FIGURE 4. Effect of rate-range parameter on flame velocity group CHEMICAL ENGINEERING EDUCATION

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1.5-----~----~---o ...... 0 ::, ... 0 !::j 1.0 ::: Q) C .:,,: u Q) E 0.5 (I) (I) Q) c 0 ;;; C Q) E c 20 40 60 Rote-range porometer lj,,or ln(kco/kol FIGURE 5. Effect of rate-range parameter on flame thickness group dimensionless rate constant is used which corre sponds to the right U 0 We let X represent both the fraction con verted f and the dimensionless temperature rise (); 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 zU 0 f.D; and C = Dkcxi/U/. The ordinary differential equation is dX d 2 X Uo dz + D = koo e "' ( l -X) (1-X) a In dimensionless form, dY d 2 Y dZ dZ 2 The results of numerical integration of this equation, for a = 1 and 2, and for different w, are given in two new plots. Figure 4 gives C as a function of w, and can be used to determine the flame velocity Uo from the rate coefficient k 00 or vice versa; Figure 5 gives AZ, also as a function of w, and can be used with U o 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-kro end of these curves once FALL 1979 more represents the point where the solution vanishes-Le., the flammability limit, which may involve a flame speed of only a few feet per second. It is a matter of convenience to use k 00 rather than the starting value k o as the rate constant; Figure 4 would show many more orders of magni tude if C contained k 0 The flame velocity in creases rapidly with increasing w, and sonic velocity is likely to occur in the rate of 25 to 40 for w. 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. REFERENCES 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, 471480, 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). [eJ;j:fl stirred pots THE CREATION And in the beginning there was "Control." And Control created r. And Control saw that this was good, but that r was lonely, so Control created r a mate and Control saw that this also was good. r's mate was called 'TS+ 1. But before long rs+ 1 led r down the path of sustained oscilla tion. Control s aw this and He was troubled. He granted r and rs+ 1 a transfer function to the land of instability where through the wonders of "Control" rs+l begat Gain. And before long rs+l 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 r to wash his B.V.D.'s and read the weekly edition of the "Control Gazette." ChE Class, Auburn University 209

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Individuals are alike. Aren't they? Obviously they re not. Everyone knows that each individual is d i fferent. 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 Haaswedon'tthinkpeopleworkcreatively 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 un i que talents That's why we look tor Chemical Engineering grad uates who are f i rs t of all individuals Engineers whose attitudes and motivation are leading them to excel i n both lite and a career Thei r 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 lite 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 tor our employees. 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. It this sounds like your type of future write to : Rohm and Haas Company Recru i ting and Placement # 3 2 1 Independence Mal l West Philadelph i a Pa 19105 ROHMID iHAAS~ An Equal Opportunity Employer.

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FUNCTIONAL ANALYSIS Continued from page 174 Where Pi is defined by its action on any vector x, viz., Pix = zi (3) where zi is the normalized eigenvector of L cor responding to the eigenvalue AJ ; i.e. L zi = AJZ J ll zi ll = 1 The equality (2) along with the property PiPk=O implies that 00 j=l 00 00 >tin Pi, expi L = e ~ i Pi, j=l L 1 = Aj-1 pi j=l (4) whenever it is meaningful to talk about the left handsides of the above equalities. 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 00 X = Aj 1 Pjy (6) j=l where Psis given by (3). Unsteady state initial value problems of the form dx ----;rr-= L x, x(O) = xi (7) are solved using the second equality in ( 4) to obtain X 00 j=l BOUNDARY VALUE PROBLEMS (8) JN DEALING WITH BOUNDARY value problems 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 r(x) dx rp(x) dx ] + q(x) 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 exFALL 1979 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 1 x,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. 211

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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 _lsl(r oT ) k o 2 T +pC v (r) oT = 0 r or or oz 2 p oz O 0 This problem treated in the usual way (as in the literature) is a nonselfadjoint problem. However 212 by defining what one might refer to as the axial energy flow function, r 5 oT S(r,z) = ~k ~+ pC v (r)T]21rrdr (11) 0 Eq. (10) is readily found to be equivalent to a pair of partial differential equations written in terms of a matrix differential expression pCpV z (r) k 2r _Q_ or o 0 T(z,r) S (z,r) T (r,z) S (r,z) (12) 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 = [ f i (r) ] From the boundary conf 2 (r) ditions it can be shown that we must have f 2 (r) 0 faster than r and f 1 (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 R == f [f 1 (r)g 1 (r)2r+f 2 (r)g 2 (r) !r ]dr 0 (13) it implies that our linear space must consist of vectors f such that f 1 (r) must be square-inte grable in [O,RJ with weight 2r and f 2 (r) must be square-integrable with weight 1 / 2r. Moreover, it is readily seen that < f,Lg > = [f1(r)g 2 (r) -f 2 (r)g1(r)] = 0 (14) Thus Lis found to be selfadjoint and the problem has fitted the mold we were talking about. Hence CHEMICAL ENGINEERING EDUCATION

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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. REFERENCES 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 Sy s tems," Springer-Verlag, New York, Inc 1968. 4. Friedman, B., "Principles and Techniqu e s of Applied Mathematics," Wiley, New York, 1956. 5. Feijoo L., Davis, H T. and Ramkrishna, D., J. Heat T r ams/ er (101), 1 3 7-143, 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., Chtim. 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, 1979. MIRROR FOG PROBLEM Continued from page 155 PRELIMINARY DISCUSSION 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. OBJECTIVES AND CRITERIA: To find the time t r when the mirror is completely clear. Part A: since this will be a moving boundary problem, t r 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. FALL 1979 PHYSICAL AND CHEMICAL PRINCIPLES: There 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 condensate film YLJ=O . . fogged X I I .... y ~.-.. I I .. I tdt,' partially clear clear 'FIGURE 3. All surfaces impermeable except front opening. 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 = C s nt u rn t e d) and the opening y = 0 (where C = C r o o m ) 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 indicated already. C A =I= 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 H 2 0 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. 213

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The people behind these products still remember looking for their first job. They were people who wanted a good job with a gooq company A chance to show what they could do And to be r~cognized 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 results. 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 i nterest in marketing f in ance 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 DOW ~~ : ~ '.~~~ ~ .. ~ : ~ ;

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COAL LIQUEFACTION 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. TABLE II Course Reading List (Arranged Under Lecture Headings) INTRODUCTION-COAL RESOURCES AND SUPPLIES, COAL MINING TECHNOLOGY DEVELOP MENT 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 (1976). ORIGIN OF COAL; COAL TYPES AND RANKS; PETROGRAPHY; METAMORPHISM 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). FALI.1979 COAL CHEMISTRY, COAL REACTION, COAL STRUCTURES 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 (1976). 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). PHYSICAL PROPERTIES OF COAL, STATISTICAL APPROACHES AND STRUCTURAL PARAMETERS 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 (1971). COAL PREPARATION COMMINUTION, COAL FEED ENGINEERING PROBLEMS 1. R. C. Neave}, "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. THERMAL PYROLYSIS OF COAL, KINETICS AND MECHANISM OF THERMAL DECOMPOSITION 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. 1975. 4. C. S. Wen and T. F. Yen, "Optimization of Oil Shale Pyrolysis", Chem. Eng. Sci., 32, 346-349 (1977). 215

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CARBONIZATION, MESOPHASE, COKES 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 lOB, AIChE, 61 Annual Meeting, 1968. SOLUBILITY PARAMETERS, SOL VENT REFINING, NATURE OF HYDROGEN DONORS 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). CATALYSIS, CATALYTIC HYDROGENATION 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. FISHER-TROPSCH SYNTHESIS-GENERALIZED GASIFICATION 1. H. Pic~ler 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. Stellgen, "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. COAL LIQUIDS, SEPARATION AND ISOLATION OF ASPHALTENES, CHARACTERIZATIONS l. 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 ?16 Fraction," in Liquid Fuel from Coal, (R. T. Elling ton, ed.), Academic Press, 1977, pp. 233-248. 3. M. Farcasiu, T. 0. 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. REFINING, UPGRADING, DESULFURIZATION, DEMETALLIZATION, DENITROGENERATION 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 (1974). 4. G. A. Mills and H. Perry, "Fossil Fuel Power + Pollution", Chem. Tech., Jan. 1973, pp. 53-63. COAL-DERIVED CHEMICALS AND PRODUCTS, OTHER SYNFUELS 1. A. M. Squires, "Chemicals from Coal", Sci. 191, 689700 (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. NOVEL APPROACHES, IN SITU PRODUCTION 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. ENVIRONMENTAL PROBLEMS IN COAL CONVER SION, ASPECTS OF SAFETY AND HEALTH 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 CHEMICAL ENGINEERING EDUCATION

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2. G. N. Reddy, "E nvironmental 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. PROCESS AND REACTOR DESIGN, MODELS, REACTION CONTROL 1. C. Y. Wen, "Optimization Studies of Various Coal Conversion Systems", ERDA Reports FE-227 4-2, 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 Goal Liquefac tion", ACS, Div. Fuel Chern ., 20(11), 216 (1975). 4. P. Wellman and S. Katell, "The Economics of Coal Conversion Systems", SPE Paper 5097 (197 4). TABLE Ill Supplementary Course Reading List ACS, "Coal Science," Advances in Chemistry Series 55, Washington, D C., 1966. AIChE, "Coal Processing Technology," Chemical Engi neering Progress, AIC hE, "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.), "C hemistry 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, 1976. 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-Chernistry Physics-Constitution," Elsevier, New York, 1961. William, D. A and G. Jones, "Liquid Fuels," Pergamon, Elmsford, N. Y., 1963. FALL 1979 IN MEMORIUM 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.

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UNIVERSITY OF ALBERTA EDMONTON, ALBERTA, CANADA 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 available. Costs. 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. Applications For additional information write to: Chairman 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 sign. 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 Sands. 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 dynamics. J T. Ryan, Ph.D. (Missouri) : Process Economics, Energy Economics and Supply. 218 S. Shah, Ph.D. (Alberta) : Linear Systems Theory Adap tive Control, System Identification. S. E. Wanke, Ph.D (California-Davis): Catalysis, Kine tics. R. K. Wood, Ph.D. (Northwestern): Process Dynamics and Identification, Control of Distillation Columns, Modelling of Crushing and Grinding Circui ts. The University of Alberta One of Canada's largest universities and engineering schools. Enrollment of 20,000 students. Co-ed ucationa I, government-supported, non-denominational. Five minutes from city centre, overlooking scenic river valley. Edmonton 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. CHEMICAL ENGINEERING EDUCATION

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FACULTY THE UNIUEKSITY or flKKON ff kron, OH 4432S DEPARTMENT OF CHEMICAL ENGINEERING GRADUATE PROGRAM RESEARCH INTE RESTS 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. LENCIYK 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. FALL 1979 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 ADDITIONAL INFORMATION WRITE: Dr. Howard l. Greene, Head Department of Chemical Engineering University of Akron Akron, Ohio 44325 219

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THE UNIVERSITY OF ARIZONA TUCSON, AZ 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. THE FACULTY AND THEIR RESEARCH INTERESTS ARE: 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, Biorheology 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 lnterfacial 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 ALAN D. RANDOLPH, Professor 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, Packed Column Distillation, Applied Design 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 Tucson has an excellent climate and many recreational opportunities It is a growing, modern city of 400,000 tha,t retains much of the old Southwestern atmosphere. For further information, write to: Dr. A. D. Randolph Graduate Study Committee Department of Chemical Engineering Univers i ty of Arizona Tucson A riz ona 85721 The University of Arizona is an equal opportunity educational institution / equal opportunity employer Ph.D., University of California-Berkeley, 1972 Reaction Engineering, Kinetics, Catalysis

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AUBURN UNIVERSITY CHEMICAL ENGINEERING GRADUATE STUDIES 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, i s located in Alabama between Atlanta and Montgomery Ala ., with Co lumbus, the second largest city in Georgia, only 35 miles away. The local population i s about 75 000 University -s ponsored activi ties include a lecture series with nationally known speakers, a series of plays and artistic and cultural presentations of all kinds Recreatjonal opportunities include equipment at the University for participation in almost every sport FALL 1979 Research Areas COAL: Coal liquefaction, magnetic de sulfurization and beneficiation, solvent re fining 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 neering 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 liver. For financial aid and admission application forms write: Dr. R. P'. Chambers, Head Chemi~al Engineering Auburn University Auburn, AL 36830 221

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The University of Calgary Program of Study The Department of Chemical Engineering provides unusual opportunities for resea r ch 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. degree. The M.Eng. program is a part-time program designed for those who a re 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 EA 1 690 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 piloit 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 r ecovery 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 rem1ss1on 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 sources. 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 Uni~ersity 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. 222 The Chairman, Graduate Studies Committee Department of Chemical Engineering The University of Calgary Calgary Alberta T2N 1N4 Canada CHEMICAL ENGINEERING EDUCATION

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UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA RESEARCH ENERGY UTILIZATION ENVIRONMENTAL KINETICS AND CATALYSIS THERMODYNAMICS ELECTROCHEMICAL ENGINEERING PROCESS DESIGN AND DEVELOPMENT BIOCHEMICAL ENGINEERING MATERIAL ENGINEERING FLUID MECHANICS AND RHEOLOGY FOR APPLICATIONS AND FURTHER INFORMATION, WRITE: FACULTY 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 UNIVERSITY OF CALIFORNIA Berkeley, California 94720

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UNIVERSITY OF CALIFORNIA, DAVIS UC DAVIS OFFERS A COMPLETE PROGRAM OF GRADUATE STUDY AND RESEARCH IN CHEMICAL ENGINEERING Degrees Offered Master of Science Doctor of Philosophy Course Areas Applied Kinetics and Reactor Design Applied Mathematics Biomedical, Biochemical Engineering Process Dynamics Separation Processes Thermodynamics Transport Phenomena Transport Processes in Porous Media Faculty 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, lnterfacial Phenomena, Transport Processes in Porous Media 224 Program 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 Sacramenito 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 (l l /2 to 2 hours from Davis). These recreational opportunities combine with the friendly informal spiri,t 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 oneand two-bedroom apartments are available. The town of Davis is adjacent to the campus, and within easy walking or cycling distance. Information 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 CHEMICAL ENGINEERING EDUCATION

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UNIVERSITY OF CA LIFORNIA SANT A BARBARA FACULTY AND RESEARCH INTERESTS PROGRAMS AND FINANCIAL SUPPORT H. CHIA CHANG Ph D (Princeton) Chemical Reactor Modeling Applied Mathematics HENRI FENECH Ph D. (M I T.) Nucl e ar Systems Design and Safety Nuclear Fuel Cycles Two Phase Flow Heat Transfer. HUSAMGUROL Ph.D (Michigan) Statistical Mechanics, Polymers, Radiation Damage to Materials, Nuclear Reactor Theory OWEN T. HANNA Ph.D. (Pu r due) Theoretical Methods, Chemical Reactor Analysis Transport Phenomena. GLENN E. LUCAS Ph.D. (M I T ) Radiation Damage, Mechanics of Materials DUNCAN A. MELLICHAMP Ph D. (Purdue) Computer Control Process Dynamics Real-Time Comput i ng FALL 1979 JOHN E. MYERS Ph D (M i ch i gan) ( Dean of Engineering) Bo i ling Heat Transfer G ROBERT ODETTE Ph.D (M I T ) ( V i ce Cha i rman Nuclear Eng i neering) Rad i at i on Effects in So li ds Energy Related Materials Development A. EDWARD PROFIO Ph.D (M 1 T ) Bionuclear Engineering Fusion Reactors, Radiat i on T ransport Analyses ROBERT G. RINKER Ph D (Caltech) Ch e mical Reactor Design Ca t alysis Ene r gy Conver s ion A i r Pollut i on ORVILLE C. SANDALL Ph D (Berkeley) Transpor t Phenomena, Separation Processes DALE E. SEBORG Ph D (Prince t on) (Chairman) 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. THE UNIVERSITY 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 climate. For additional information and applications, write to: Professor Dale E. Seborg, Chairman Department of Chemical & Nuclear Engineering University of California, Santa Barbara, CA 93106 225

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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 strorig 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 th e 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 assis ta ntship, or teaching assistantship appointments during both the academic year and the summer month s A student may carry a full load of graduate study and research in addition to any assigned assi s tantship duties. The Institute gives consideration for admission and financial assistance to all qualified applicants r e gardless of race, religion, or sex. APPLICATIONS Further information and an application form may be obtained by writing Profe s sor L G. Leal Chemical Engineering California Institute of Technology Pasadena, California 91125 It is advisable to submit applications before Fe1'ruary 15, 19 8 0. FACULTY IN CHEMICAL ENGINEERING WILLIAM H. CORCORAN, Institute Professor Ph.D. (1948), California Institute of Technology Kinetics and catal7.sis; biomedical engineering; air and water quahty. GEORGE R GA VALAS, Professor Ph.D. (1964), University of Minnesota Applied kinetics and catalysis; process control and optimization; coal gasification. ERIC HERBOLZHEIMER, Assistant Profe s sor Ph.D. (1979), Stanford Uni v ersity Fluid mechanic s 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. CORNELIUS J. PINGS, Professor, Vice-Provost, and Dean of Graduate Studies Ph.D. (1955), California Institute of Technology Liquid state physics and chemistry; statistical mechanics. 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. GREGORY N STEPHANOPOULOS A ss i s tant Pro fes s o r Ph.D. (1978) Un i versit y of Minne s ota Bio c h e mical e n gi n e e r ing; c h e mic a l re a c t i on engineering. NICHOLAS W. TSCHOEGL, Professor Ph.D. (1958), University of New South Wales Mechanical properties of polymeric materials; theory of viscoelastic behavior; structure property relations in polymers. W. HENRY WEINBERG, Professor Ph.D. (1970), University of California, Berkeley Surface chemistry and catalysis.

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Ever think of Grad School as an Adventure? -write .. Graduate Chemical Engineering Carnegie Mellon University Pittsburgh.Pennsylvania 15213

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228 IS THERE LIFE AFTER GRADUATE STUDY? Want to find out? Heaven can't wait! Write to : Graduate Coordinator Chemical Engineering Department Case Western Reserve University Cleveland Ohio 44106 CHEMICAL ENGINEERING EDUCATION

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Graduate Study in Chemical Engineering Clclrkson M S. and Ph D Programs Fri e ndly Atmosphere Freedom from Big City Problems Personal Touch Vigorous Res e arch Programs Supported by Government and Industry Faculty with International Reputation Skiing Canoeing Mountain Climbing and Other Recreation i n the Adirondacks Variety of Cultural Activities with Two Liberal Arts College s nearby Faculty W L Baldewic z Der Tau Chin Robert Cole David 0 Coone y Joseph Estrin Sandra Harris Richard J McClusk e y John B McLaughlin Richard J Nunge D. H. Rasmussen Herman L Shulman R Shankar Subramanian Peter C Sukanek Thomas J. Ward William R Wilcox Gordon R Youngquist Research Projects are available in : Energy Materials Processing in Space Multiphase Transport Processes Health & Saf e ty Applications Electro c hemical Engineering and Corrosion Polymer Processing Particle Separations Phase Transformations and Equilibria Reaction Engineering Optimization and Control Crystallization And More .... Financial aid in the form of fellowships, research assistantships, and teaching assistantships is available. For more details, please write to: DEAN OF THE GRADUATE SCHOOL CLARKSON COLLEGE OF TECHNOLOGY POTSDAM NEW YORK 13676

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Chemical Engineering at CORNELL UNIVERSITY A place to grow ... with active research in: biochemical and biomedical engineering computer simulation environmental engineering heterogeneous catalysis surface science polymers microscopy reactor design fluid flow and coalescence physics of liquids thermodynamics 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 chemistry biochemistry microbiology 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 Streett, Raymond G Thorpe, Robert L. Von Berg, Herbert F. Wiegandt. FOR FURTHER INFORMATION: Write to Professor Michael L. Shuler Cornell University Olin Hall of Chemical Engineering Ithaca, New York 14853.

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FALL 1979 UNIVERSITY OF DELAWARE 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 time) C. E. Birchenall K. B. Bischoff (Chairman) M. M. Denn C. D. Denson B. C. Gates J. R. Katzer S. I. Sandler G. L. Schrader G. C. A. Schuit( time) J M. Schultz L. A. Spielman A. B. Stiles( time) R. L. McCullough A. B Metzner Visiting Faculty J. H. Olson M. E. Paulaitis R. L. Pigford T. W. F. Russell F. Gioia A. L. Gordon M C. Marti de Gordon M. A. Streicher 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, singleand two-phase systems 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, chemotherapy 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 Homogeneous catalysis, organometallic chemistry 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 chemitherapy, reaction engineering K. F. Wissbrun _____ Polymer physics For information and admissions 1 materials contact: S. I. Sandler, Graduate Advisor 231

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Onlythe Universit~ of Florida's Department of Chemical Engineering gives you both outstanding academic challenge 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 904/392-0881

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Graduate Studies in Chemical Engineering .. GEORGIA TECH Atlanta Ballet 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 Chemical Engineering Air Quality Technology Biochemical Engineering Catalysis and Surfaces Energy Research and Conservation Fine Particle Technology lnterfacia l Phenomena K i netics Mathematical Modeling Mining and Mineral Engineer i ng Polymer Science and Engineer i ng 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

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Graduate Programs in Chemical Engineering at the ... University of Houston 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 A.Jackson D. Luss A. C. Payatakes R. Pollard H. W. Prengle, Jr J. T Richardson F. M. Tiller J. Villadsen F. L. Worley, Jr. The D epartment of Chemical Engineer ing at the University of Houston Central Campus has developed five areas of special research strength : > chemical and biochemical reaction engineering > applied fluid mechanics and transfer processes > 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 mill i on worth of experi mental apparatus 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 appl i cation forms write : Director Graduate Admissions Department of Chemical Engineering University of Houston Central Campus Houston, Texas 77004 (Phone 713/749-4407)

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l Graduate Programs in The Department of Energy Engineering leading to the degrees of MASTER OF SCIENCE and D OCTOR OF PHILOSOPHY Faculty and Research Activities in CHEMICAL ENGINEERING 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 Profes s or John H. Kiefer Ph.D;, Cornell University, 1961 Professor G. Ali Mansoori Ph.D., University of Oklahoma, 1969 Professor Irving F Miller Ph.D., University of Michigan 1960 Professor, Dean of the Graduate College and Ass~iate Vice-Chancellor for Research Sohail Murad Ph.D., Cornell University, 1979 Visiting Assistant Professor Satish C Saxena Ph.D., Calcutta University, 1956 Professor 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: 11111 .... -:--""~ ~.. "-: -, ... :'~ "' ..... -----...... .;., __ ,_ .... -, ..... ... --.... ___ .,. ... ... ~" .. --"' ... .. ;;.;,;::;. :;;;;.._.;,.. .;..; ... --. .. .. ,_ .. .. t. ,. .. ,, __ ,.. ----:: :::: :: -t -_,..,...., ~-------' ~-,,-r,, ~-, -~ JtW~.;, -~~ .: Fluid mechanic s combu s tion turbulence chemically reacting flow s Chemical kinetics mass transport phenomena chemical process design particulate transport phenomena Kinetics of gas reactions, energy tran s fer processe s, molecular lasers Thermodynamics and statistical mechanics of fluid s, solids, and solutions, kinetics of liquid reactions solar energy Thermodynamics, biotransport, artificial organs, biophysics 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

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236 UNIVERSITY OF ILLINOIS URBANA, CHAMPAIGN ACTIVE, RESPECTED, ACCESSIBLE FACULTY 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 p rides 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 EXCEPTIONAL FACILITIES 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 coun t ing the nanosecond range, and pressure and vacuum equipment giving a useful operating range of l 0 5 to l 0 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 i ts 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 e x ample, 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 A DIVERSITY OF RESEARCH INTERESTS Applied Mathematics Heat Transfer Biological Application of High Pressure Chemical Engineering lnterfacial Phenomena Catalysis Mass Transfer Chemical Reactor Dynamics Materials Science and Engineering Colloidal Phenomena Molecular Thermodynamics Computer-Aided Process Phase Transformations Simulation and Design Polymer Crystallization Corrosion Process Control Electronic Structure of Matter Reaction Eng i neering Electrochemical Engineering Resource Management Energy Sources and Conservation Statisti cal Mechanics Environmental Engineering Surface Science Fluid Dynamics Two-Phase Flow FOR INFORMATION AND APPLICATIONS: Professor J. W. Westwater Department of Chemical Engineering 113 Adams laboratory University of Illinois Urbana, Illinois 61801 CHEMICAL ENGINEERING EDUC A TION

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Institute of Technology FALL 1979 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. Faculty D. GIDASPOW J.R. SELMAN B. S. SW ANSON L. L. TAVLARIDES J. S. VRENTAS D.T.WASAN C. V. WITTMANN Heat Trans! er 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 FOR INQUIRIES, WRITE D. T. Wasan, Chairman Chemical Engineering Dept. Illinois Institute of Technology 10 West 33rd St. Chicago, IL 60616 237

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I '! I T 1_ 1 T F '.! I \1 1 I\. C IIH !lt i T K ) li.1/1 I ,11 /1 ,, -,.,,.,11 THE INSTITUTE OF PAPER CHEMISTRY 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 are underway in: process engineering simulation and control surface and colloid chemistry laser, Raman and x-ray diffraction studies 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 OUR GRADUATE PROGRAM is the Number 1 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 industry For further information contact: Director of Admissions The Institute of Paper Chemistry P. 0. Box 1039 Appleton, WI 54912

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IOWA STATE UNIVERSIT'I 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 write to: Chairman OF SCIENCE AND TECHNOLOGY 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 Crystallization Kinetics Maurice A. Larson John D. Stevens Process Instrumentation and System Optimization and Control Lawrence E. Burkhart Kenneth R. Jolls Department of Chemical Engineering Iowa State University Ames, Iowa 50011 GRADUATE STUDY and GRADUATE RESEARCH in Chemical Engineering Transport Pr()Cesses (Heat, mass & momentum transfer) William H. Abraham Renato G. Bautista Charles E. Glatz James C. Hill Frank 0. Shuck Richard C. Seagrave Process Chemistry and Fertilizer Technology David R. Boylan George Burnet Maurice A. Larson

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24 0 Graduate Study in Chemical Engineering KANSAS STATE UNIVERSITY DURLAND HALL-New Home of Chemical Engineering M.S. and Ph.D. programs i n Chemical Engineering and Interdisciplinary Areas of Systems Engineering, Food Science, and Environmental Engi neering Financial Aid Available Up to $7,000 Per Year FOR MORE INFORMATION WRITE TO Professor B. G Kyle Durland Ha ll Kansas S t a t e Un i versi t y Manhattan Kansas 6650 2 AREAS OF STUDY AND RESEARCH TRANSPORT PHENOMENA ENERGY ENGINEERING COAL AND BIOMASS CONVERSION THERMODYNAMICS AND PHASE EQUILIBRIUM BIOCHEMICAL ENGINEERING PROCESS DYNAMICS AND CONTROL CHEMICAL REACTION ENGINEERING MATERIALS SCIENCE SOLID MIXING CATALYSIS AND FUEL SYNTHESIS OPTIMIZATION AND PROCESS SYSTEM ENGINEERING FLUIDIZATION ENVIRONMENTAL POLLUTION CONTROL CHEMICAL ENGINEERING EDUCATION

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Landau Butld1ng Th e new home of Chem1cdl Eng1neer1nq al M I T CHEMICAL ENGINEERING AT M.I.T. GENERAL AREAS OF FUNDAMENTAL AND APPLIED RESEARCH 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 THE FACULTY OF THE DEPARTMENT R. C ARMSTRONG, Ph.D. (1973); Associate Professor POLYMER FLUID MECHANICS TRANSPORT PHENOMENA APPLIED MATHEMATICS R. F. BADDOUR Sc.D. (1951); ProfHIOr, CATALYSIS PLASMA CHEMISTRY, ENZVME TECHNOLOGY J M BEER D Sc (1988); ProfeHor, COMBUSTION FLUIDIZED COMBUSTION OF COAL R. A BROWN Ph D. (1978) ; Assistant Profeasor MATHEMATICAL MODELLING FLUID MECHANICS TRANSPORT AND INTERFACE PHENOMENA R E COHEN Ph.'D (1972) ; Associate Professor PHYSICS AND CHEMISTF.IY OF POLYMERS VISCOELASTIC THEORY C K. COLTON Ph D. (1989); Profeasor, BIOMEDICAL AND BIOCHEMICAL ENGINEERING, MASS TRANSFER W M DEEN Ph D. (1973); Assistant Professor BIOENGINEERING FLUID MECHANICS MASS TRANSFER L B EVANS Ph D. (1962); Professor PROCESS CONTROL OPTIMIZATION COMPUTER AIDED DESIGN C GEORGAKIS Ph D (1975) ; Associate Professor CHEMICAL REACTOR DESIGN PROCESS DYNAMICS AND CONTROL APPLIED MATHEMATICS H. C HOTTEL S.M. (1924) ; Professor Emeritus, RADIATIVE HEAT TRANSFER, COMBUSTION SOLA.fl ENERGY J B HOWARD Ph.D. (1965) ; Professor and Executive Olllcer COMBUSTION .COAL CONVERSION ENERGY TECHNOLOGY J. P. LONGWELL, Sc.D. (1943); Profeasor COMBUSTION FUELS PROCESSING M. P MANNING Sc.D (1978); Aaslstant Profeasor KINETICS AND CATALYSIS SOLAR ENERGY PROCESS DESIGN H. P MEISSNER D Sc. (1938); Profe sor Emeritus, ELECTROCHEMISTRY THERMODYNAMICS PROCESS METALLURGY E. W MERRILL, Sc D. (194n; ProfHIOr, POLYMER CHEMISTRY BIOMEDICAL ENGINEERING MEMBRANE TECHNOLOGY FALL 1979 M MODELL Sc D (1984); Associate Professor T HERMODYNAMICS WASTE TREATMENT CHEMICAL KINETICS AND CATALYSIS C M MOHR, Sc D. (1981); Senior Lecturer, PROCESS DESIGN AND SYNTHESIS INDUSTRIAL CHEMISTRY F. A PUTNAM Ph D (1978) ; Assistant Professor SURFACE PHENOMENA THERMODYNAMICS CATALYSIS R C. REID, Sc D (1954); Professor THERMODYNAMICS PROPERTIES OF MATERIALS LIQUEFl'ED NATURAL GAS A F SAROFIM, Sc D. (1982); Profeasor APPLIED CHEMICAL KINETICS HEAT ,:\ND MASS TRANSFER COMBUSTION C N SATTERFIELD, Sc.D (1948) ; Professor CHEMICAL REACTION ENGINEERING MASS TRANSFER AND HETEROGENEOUS CATALYSIS s M SENKIN Sc.D. (197n ; Assistant Professor, CHEMICAL REACTOR DESIGN MATHEMATICAL MODELLING K A. SMITH Sc D (1982); Profeasor FLUID MECHANICS HEAT AND MASS TRANSFER BIOMEDICAL ENGINEE'llNG C G. VAYENAS Ph D (197n; Aaslslant Professor HETEROGENEOUS CATALYSIS FUEL CELLS P S VIRK Sc D (198n; Associate Profeasor DRAG REDUCTION PYROLYSIS PATHWAYS COAL LIQUIDS J E VIVIAN, Sc D. (1945); Profeasor MASS TRANSFER AND CHEMICAL KINETICS SEPARATION PROCESS J WEI, Sc.D. (1955) ; Professor and Department Head CATALYSIS AND KINETICS CHEMICAL REACTORS TRANSPORT PHENOMENA BIOCHEMICAL ENGINEERING G C WILLIAMS Sc D (1942); Prof11sor and Graduate Officer COMBUSTION CHEMICAL KINETICS AIR POLLUTION 241

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I MCMASTER UNIVERSllY 242 M.ENG. AND PH.D. PROGR4MS PROCESS AND ENERGY ENGINEERING CHEMICAL REACTION ENGINEERING AND CATALYSIS COMPUTER CONTROL, SIMULATION AND OPTIMIZATION POLYMER ENGINEERING BIOMEDICAL ENGINEERING WATER AND WASTEWATER TREATMENT FOR FURTHER INFORMATION, PLEASE CONTACT: CHAIRMAN DEPT. OF CHEMICAL ENGINEERING McMA5TER UNIVERSllY HAMILTON, ONTARIO, CANADA LBS 4L7 CHEMICAL ENGINEERING EDUCATION

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I -I THE FACULTY Dale Briggs Louisville, Michigan Brice Carnahan Case-Western, Michigan Rane Curl MIT Francis Donahue LaSalle, UCLA H. Scott Fogler Illinois, Colorado Erdogan Gulari Roberts, Cal Tech James Hand NJIT, Berkeley Robert Kadlec Wisconsin, Michigan Donald Katz Michigan Lloyd Kempe Minnesota Joseph Martin Iowa, Rochester, Carnegie John Powers Michigan, Berkeley Jerome Schultz, Chairman Columbia, Wisconsin Maurice Sinnott Michigan Henry Wang Iowa State, MIT James Wilkes Cambridge, Michigan Brymer Williams Michigan Gregory Yeh Holy Cross, Cornell, Case Edwin Young Detroit, Michigan FALL 1979 Chemical Engineering At The University Of Michigan THE RESEARCH PROGRAM Laser Light Scattering Reservoir Engineering Thrombogenesis Microemulsions Applied Numerical Methods Dynamic Process Simulation Ecological Simulation Electroless Plating Electrochemical Reactors Polymer Physics Polymer Processing Composite Materials Coal Liquefaction Coal Gasification Acidization Biochemical Engineering Periodic Processes Tertiary Oil Recovery Transport In Membranes Flow Calorimetry Ultrasonic Emulsification Heat Exchangers Renewable Resources THE PLACE Department Of Chemical Engineering THE UNIVERSITY OF MICHIGAN ANN ARBOR, MICHIGAN 48109 For Information Call 313/763-1148 Collect For '. Tomorrows : Engineers ; Today. i 243

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chemical reactor modeling catalysis enhanced oil recovery p olyme r rhe ology biomedical engi neering process synthesis film coating mixed cultures kinetic theory statistical mechanics trans port in blood polymerization nuclear engineering physical metallurgy population dynamics surf ace 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 "WHY MINNESOTA?": .. "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. Ran z L. Schmidt L. E. Scriven J. Sivertsen G. Stephanopoulos M. Tirrell L. Toth H. Tsuchiya J. Wallace S. Wellinghoff 244 WHY MINNESOTA? 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) -----------------I Yes! PLEASE SEND INFORMATION ON 1 YOUR GRADUATE PROGRAM TO: I 1 Name ________ I 1 Address I -------------------------------------I 1 Univ. of Minnesota, Chemical Engr. & Matls. Sci. Dept., 4 2 1 Washington Ave. S. E. I Minneapolis MN 55455 CHEMICAL ENGINEERING EDUCATION

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Department of Chemical Engineering UNIVERSITY OF MISSOURI ROLLA ROLLA, MISSOURI 65401 Contact Dr J. W. Johnson, Chairman Day Programs Established fields of specialization in which re search programs are in progress are: (l) Fluid Turbulence Mixing and Drag Reduction Studies-Dr. G. K. Patterson and Dr. X. B. Reed (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. Yasuda 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. Gaddy (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-Ors. M. E. Findley, R. C. Waggoner, and R. A. Mollen kamp (f) Transport Properties, Kinetics, enzymes and catalysis-Dr. 0. K. Crosser and Dr. B. E. Poling (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 245

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CHEMICAL ENGINEERING AT NORTH CAROLINA STATE UNIVERSITY RALEIGH, N.C. CRYSTALLIZATION Secondary nucleation Crystallization kinetics Selective nucleation CHEMICAL REACTION ENGINEERING Process modeling Pilot plant studies Radiation polymerization ENVIRONMENTAL SCIENCE Stack monitoring Control technology development Biological effects of pollutants B.S. ChE's and Chemists: ADVANCED STUDY AND RESEARCH LEADING TO THE M.S., M.ChE., AND PhD. DEGREES. ALSO Phase equilibrium thermodynamics Heat Transfer Separation Processes Computer Applications COAL GASIFICATION $2.4 Million Pilot Plant completed (1978) in cooperation with EPA Pollutant characterization Process development Sampling and analysis Acid gas cleanup POLYMER SCIENCE Natural and synthetic polymers Glassy state anomalies Advanced membrane processing Controlled drug delivery FOR ADDITIONAL INFORMATION, A CATALOG, AND APPLICATION MATERIALS, WRITE Dr. James K. Ferrell, Head Department of Chemical Engineering North Carolina State University Raleigh, North Carolina 27650 246 CHEMICAL ENGINEERING EDUCATION

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FALL 1979 Graduate Study in Chemical Engineering at NORTHEASTERN UNIVERSITY M.S., Ph.D., and D. Eng. programs are available at Northeastern University to qualified students with B.S. degrees in Chemical Engineering from accredited institutions. The M.S. programs are available on the Coop plan of alternate periods of work and study. Faculty research interests include energy conservation and conversion, process dynamics and control, light induced reactions, environ mental control, process development and modeling simulation. Some financial support is available. location-Northeastern University is located in dynamic Boston close to major cultural, recreational, sports, and learning areas. For further information please contact Dean George W. Hankinson Graduate School of Engineering Northeastern University Boston, Mass. 02115 247

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DRAWING BY DRJAMES L THRONE. ANOCO HSIARCM, NAP'IIIYILLI, ILL 248 Dr john R Collier Chemical Engineering Department OHIO UNIVERSITY Athens, Ohio 4570 I CHEMICAL ENGINEERING EDUCATION

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The Ohio State University Chemical Engineering M.Sc. and Ph.D. Programs The Ohio State University 140 West 19th Avenue Columbus, OH 43210 FALL 1979

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260 CHEMICAL ENGINEERING EDUCATION

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university of pennsylvania chemical and biochemical eng1neer1ng Stuart W. Churchill {Michigan) Elizabeth B. Dussan V {Johns Hopkins) William C Forsman {Pennsylvania) Eduardo D. Glandt (Pennsylvania) David J. Graves (M.I.T.) A. Norman Hixson (Columbia) Arthur E. Humphrey (Columbia) FACULTY Douglas A. Lauffenburger (Minnesota) Mitchell Litt {Columbia) Alan L. Myers {California) Melvin C. Molstad, Emeritus (Yale) Daniel D. Perlmutter (Yale) John A. Quinn (Princeton) Warren D. Seider (Michigan) RESEARCH SPECIAL TIES Combustion Energy Utilization Biomedical Engineering Computer-Aided Design Chemical Reactor Analysis Environmental and Pollution Control Fluid Mechanics Polymer Engineering Process Simulation Solar Energy Surface Phenomena Separations Techniques Thermodynamics Transport Phenomena The faculty includes three members of the National Academy of Engineering and three recip i ents of the highest honors awarded by the American Institute of Chem i cal Engineers. Staff members are act i ve in teaching research, and professional work. Located near one of the largest con centrations of chemical industry in the United States, the University of Pennsylvan i a maintains the scholarly standards of the Ivy League and numbers among its assets a superlat i ve Medical Center and the Wharton School of Business PHILADELPHIA: The cultural advantages h i storical assets, and recreat i onal facilities of a great city are w i th i n walking d i stance of the University Enthusiasts will find a variety of college and profess i onal sports at hand Tlie Pocono Mounta i ns and the New Jersey shore are w i thin a two hour drive For further informat i on on graduate studies i n this dynamic setting, write to Dr A L Myers Cha i rman Department o f Chemical and Biochemical Engineering 220 S 33rd Street, Univers i ty of Pennsylvania Philadelphia PA 19104 FALL 1979 251

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LOOKING 252 WRITE TO Prof. Lee C Eagleton, Head 160 Fenske Laboratory The Pennsylvania State University University Park, Pa. 16802 for a graduate education in Chemical Engineering ? Consider PENN STATE Some Current M.S. & Ph.D. General Research Areas : BIOMEDICAL ENGINEERING Physiological Transport Processes Newborn Monitoring ENVIRONMENTAL RESEARCH Gaseous and Particulate Control Atmospheric Modeling REACTOR DESIGN AND CATALYSIS Heterogeneous Catalysis Cyclic Reactor Operat i ons Catalyst Charac t er iz ation TRANSPORT PHENOMENA Analytical and Numerical Solutions Polymer Rheology and Transport Convective Heating and Mass Transfer Mass Transfer in Cocurrent Flow THERMODYNAMIC PROPERTIES Property Correlations Sta tistical Mechanics PROCESS DYNAMICS AND CONTROL Nonlinear Stability Theory Optimal and Periodic Control APPLIED CHEMISTRY AND KINETICS Industrial Chemical Processes Complex Reaction Systems PETROLEUM REFINING Process Development Product Conversion TRIBOLOGY Properties of Liquid Lubricants Boundary Lub r ication Fundamentals INTERFACIAL PHENOMENA Adsorption Thermodynamics and Kinetics Monolayer and Membrane Processes ENERGY RESEARCH Tertiary Oil Recovery Nuclear Technology CHEMICAL ENGINEERING EDUCATION

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HOW WOULD YOU LIKE TO DO YOUR GRADUATE WORK IN THE CULTURAL CENTER OF THE WORLD? .-... CHEMICAL ENGINEERING POLYMER SCIENCE & ENGINEERING FACULTY R. C. Ackerberg R. F. Benenati J. J. Conti C. D. Han W. H. Kapfer S. H. Lin J. S. Mijovic E. M. Pearce P. F. Schubert E. N. Ziegler Polvtechnic lnsfitute Formed by the merger of Polytechnic Institute of Brooklyn and New York University School of Engineering and Science. Department of Chemical Engineering Programs leading to Master's, Engineer and Doctor's degrees. Areas of study and research: chemical engineering, polymer science and engineering and environmental studies. RESEARCH AREAS Air Pollution Catalysis, Kinetics and Reactors Fermentation and Food Processing Fluidization Fluid Mechanics Heat and Mass Transfer Mathematical Modelling Mechanical Behavior of Polymers Morphology of Polymers Polymerization Reactions Process Control Rheology and Polymer Processing Fellowships and Research Assistantships are available. For further information contact Professor C. D. Han Head, Department of Chemical Engineering Polytechnic Institute of New York 333 Jay Street Brooklyn, New York 11201

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Albright Barile Caruthers Chao Delgass Eckert Emery Franses Greenkom Hannemann Houze Kessler Koppel Lim Malone ~-' ,l. .. An equal access/equal opportunity university __ .. & Peppas Ramkrishna Reklaitis Squires Tsao Wankat Weigand Graduate Information Chemical Engineering Purdue University West Lafayette, Indiana 4 7907

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I --, '------,.r UNIVERSITY OF QUEENSLAND POSTGRADUATE STUDY ~ IN ~ CHEMICAL ENGINEERING STAFF AND RESEARCH AREAS D. J. Nicklin (Cambridge) Two-phase Flow Fluidization P. C. Brooks (M I.T ) Process Dynamics and Control P. F. Greenfield (N.S.W.) Biochemical and Enzyme Engineering, Mass Transfer and Catalysis, Waste Treatment G J. Kelly (Tasmania) Corrosion Electrochemical Technology L. S. Leung (Cambridge) Fluidization, Gas, solid Flow, Thermo dynamics POSTGRADUATE SCHOLARSHIPS AVAILABLE R G. Rice (Pennsylvania) Column Flotation, Mass and Heat Transfer Adsorption R. H Weiland (Toronto) Fluid Dynamics, Mass and Heat Transfer E. T. White (Imperial College) Crystallization, System Analysis Computer Control R. J. Wiles (Queensland) Part i culate Conveying Rheology R Y. K Yang (Princeton) Reaction and Enzyme Engineering Numerical Methods, Stab i lity Analys is THE DEPARTMENT The Department occupies its own new building and is well supported by research grants and modern equip ments incl uding a multi-purpose Varian mini-computer system. It has maintained an active postgraduate pro gramme, which involves course work and research lead i ng to M Eng Stud ies, M Eng. Science and Ph.D degrees. THE UNIVERSITY AND THE CITY The University is one of the largest in Australia with more than 18,000 students Brisbane with a population of about one million enjoys a pleasant climate and attractive coasts which extend northward into The Great Barr ier Reef 0 FURTHER IMFORMATION For further information write to: Co-ordinator of Graduate Studies, Department of Chemical ---Engineering, University of Queensland, Brisbane, Qld. 4067, AUSTRALIA.

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RPI Advanced Study and Research Areas Thermodynamics Heat Transfer Kinetics-Catalysis Fluidization Fluid-Particle Systems lnterfacial Phenomena Process Design & Control Polymer Materials Polymer Processing Biochemical Systems Air Pollution Control Atmospheric Chemistry Water Resources Environmental Studies For full details write Dr. David Hansen, Chairman RENSSELAER POLYTECHNIC INSTITUTE M.S. and Ph.D. Programs in Chemical Engineering The Faculty Michael M Abbott Ph.D. Ren s selaer Elmar R. Altwicker Ph D. Ohio State Yaman Arkun Ph.D ., M i nnes o ta Donald B Aulenbach Ph.D. Rutgers Georges Belfort Ph.D. California Irv i ne Henry R. Bungay Ill Ph.D. Syra c use Chan I. Chung Ph D. Rutgers Nicholas L. Clesceri Ph D ., W i s c ons i n Dady B. Dadyburjor Ph D. Delaware Charles N. Haas Ph D. Illinois David Hansen Ph D. Rensselaer Arland H. Johannes Ph.D ., Kentu c ky Clement Kleinstreuer Ph.D. Vanderb i lt Peter K. Lashmet Ph.D ., Delaware Howard Littman Ph.D. Yale Charles Muckenfuss Ph D. Wisconsin Rajamani Rajagopalan Ph D. Syracuse George P. Sakellaropoulos Ph.D. Wiscons i n William W Shuster D.Ch E. Rensselaer Sanford S Sternstei n Ph.D ., Rensselaer Hendrick C. Van Ness O.Eng ., Yale Peter C Wayner, Jr Ph D ., Northwestern Stephen W Yerazunis D.Ch.E. Rensselaer Department of Chemical and Environmental Engineering Rensselaer Polytechnic Institute Troy, New York 12181 256 C HEMI CA L EN G INEERING EDU CA TION

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Graduate Study in Chemical Engineering at Rice University Graduate study in Chemical Engineering at Rice University is offered to qualified student~ with backgrounds in the fundamental principles of Chemistry, Mathematics, and Physics. The curriculum is aimed at strengthening the studenrs understanding of these principles and provides a basis for developing in certain areas the necessary proficiency for conducting independent research. A large number of research programs are pursued in various areas of Chemical Engineering and related fields, such as Biomedical Engineering and Polymer Science. A ioint program with the Baylor College of Medicine, leading to M-D.-Ph.D and M.D.-M.S. degrees is also available. The Department has approximately 30 graduate students, predominantly Ph.D. candidates. There are also several post-doctoral fellows and research engineers associated with the various laboratories. Permanent faculty numbers 12, all active in undergraduate and graduate teaching, as well as in research. The high faculty-to-student ratio, outstanding laboratory facilities, and stimulating research projects provide a graduate education environment in keeping with Rice's reputation for academic excellence. The Department is one of the leading Chemical Engineer ing Departments in the U.S. ranked by graduate faculty quality and program effectiveness, according to recent evaluations. MAJOR RESEARCH AREAS Thermodynamics and Phase Equilibria Chemical Kinetics and Catalysis Chromatography Optimization, Stability, and Process Control Systems Analysis and Process Dynamics Rheology and Fluid Mechanics Polymer Science BIOMEDICAL ENGINEERING Blood Flow and Blood Trauma Blood Pumping Systems Biomaterials Rice University Rice is a privately endowed nonsectarian, coeduca tional university It occupies an architecturally attrac tive, tree shaded campus of 300 acres, located in a fine residential area, 3 miles from the center of Houston. There are approximately 2200 undergraduate and 800 graduate students. The school offers the benefits of a complete university with programs in the various fields of science and the humanities, as well as in engineer ing. It has an excellent library with extensive holdings The academic year is from August to May As there are no summer classes, graduate students have nearly four months for research The school offers excellent recreational and athletic facilities with a completely equipped gymnasium, and the southern climate makes outdoor sports, such as tennis golf, and sailing year round activities FALL 1979 FINANCIAL SUPPORT Full-time graduate students receive financial support with tuition remission and a tax-free fellowship of $450-550 per month. APPLICATIONS AND INFORMATION Address letters of inquiry to: Houston Chairman Department of Chemical Engineering Rice University Houston Texas 77001 With a population of nearly two million, Houston is the largest metropolitan, financial, and commercial center in the South and Southwest It has achieved world-wide recognition through 'its vast and growing petrochemical complex, the pioneering medical and surgical activities at the Texas Medical Center, and the NASA Manned Spacecraft Center. Houston is a cosmopolitan city w it h many cultural and recreational attractions It has a well-known resident symphony orchestra, an opera, and a ballet company, which perform regularly in the newly constructed Jesse H Jones Hall. Just east of the Rice campus is Hermann Park with i ts free zoo, golf course, Planetarium and Museum of Natural Science, The a i r cond i tioned Astro dome is the home of the Houston Astros and Oilers and the site of many other events 257

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~(\~ RUTGERS THE STATE UNIVERSITY OF NEW JERSEY College of Engineering M.S. and Ph.D. PROGRAMS IN THE DEPARTMENT OF AND CHEMICAL BIOCHEMICAL ENGINEERING AREAS OF TEACHING AND RESEARCH CHEMICAL ENGINEERING FUNDAMENTALS THERMODYNAMICS TRANSPORT PHENOMENA KINETICS AND CATALYSIS CONTROL THEORY, COMPUTERS AND OPTIMIZATION POLYMERS AND SURFACE CHEMISTRY SEMIPERMEABLE MEMBRANES BIOCHEMICAL ENGINEERING FUNDAMENTALS MICROBIAL REACTIONS AND PRODUCTS SOLUBLE AND IMMOBILIZED ENZYMES BIOMATERIALS ENZYME AND FERMENTATION REACTORS ENGINEERING APPLICATIONS BIOCHEMICAL TECHNOLOGY CHEMICAL TECHNOLOGY WATER RESOURCES ANALYSES INDUSTRIAL FERMENTATIONS ENZYMES IN THERAPEUTIC MEDICINE, PHARMACEUTICAL PROCESSING AND WASTE TREATMENT FOOD PROCESSING FELLOWSHIPS AND ASSISTANTSHIPS ARE AVAILABLE 258 FLAMMABILITY OF MATERIALS OCEANS AND ESTUARIES PACKAGING QUALITY MANAGEMENT POLYMER PROCESSING WASTES RECOVERY PLANT DESIGN AND ECONOMICS For Application Forms and Further Information Write To : Graduate Admissions Ofllce 542 Georg Street Rutgen, The State Univenity New Brunswick, N.J. 08903 CHEMICAL ENGINEERING EDUCATION

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University of south Carolina The College of Engineering offers M S., M.E. and Ph.D degrees in Chemical Engineering Graduate students have the opportunity to work closely with the faculty on research projects. Research and teaching stipends are available from $3000 to $8000 The University of South Carolina, with an enrollment of 23,800 on the Columbia campus, offers a variety of cultural and recreational activities Columbia is part of one of the fastest growing areas in the country. The Chemical Engineering Faculty B.L. Baker, Distinguished Professor Emeritus, Ph.D., North Carolina State University, 1955 (Process design, environment problems, ion transport) M.W. Davis, Jr., Professor, Ph D., University of California (Berkeley), 1951 (Kinetics and catalysis chemical process analysis, solvent extraction, waste treatment) J.H. Gibbons, Professor Ph D University of Pittsburgh, 1961 (Heat transfer, fluid mechanics) F.P. Pike, Professor Emeritus, Ph D., University of Minnesota, 1949 (Mass transfer in liquid-liquid systems, vapor-liquid equilibria) T.G. Stanford, Assistant Professor, Ph D., The University of Michigan, 1977 (Chemical reactor engineering mathematical modeling of chemical systems process design, thermodynamics) V. Van Brunt, Associate Professor, Ph D University of Tennessee, 1974 (Mass transfer computer modeling fluidization). For further Information contact: Prof J H Gibbons Chairman, Chemical Engineering College of Engineering University of South Carolina Columbia, South Carolina 29208

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Chemical Engineering at Stevens Institute of Technology ., ;;.."!.:,,. ... /-t!..~,~~::-'!':. Master's-Chemical Engineer-Doctoral Degrees Programs in Chemical Engineering Science Process and Polymer Engineering Research in Transport Processes: Fluid Dynamics, Mass Transfer Separation Processes: Membranes, Absorption, Extraction Reaction Engineering: Catalytic, Polymerization, Coal Liquefaction, Solid Waste Gasification Polymers: Kinetics, Rheology, Processing, Structure-Property Relation For further information contact: Dean of Graduate Studies Stevens Institute of Technology Castle Point Station Hoboken, New Jers ey 07030 201 420-5234 ~;f;~nti I~~!it:J~~~!:~r:n~l its d:;ic~~~:l~~r;;~::.e s~{:o{!~~;s!~:: o:a:~r~~!~~s:e:~da::w~:fc~~!~ o;~:;i~~;t~~tf programs.

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Everything's up to date in Tennessee THE UNIVERSITY OF TENNESSEE, KNOXVILLE Graduate Studies in Chemical, Metallurgical, and Polymer Engineering Programs Programs for the degrees of Master of Science and Doctor of Philosophy are offered in chemical engineering metallurgical engineering and pol ymer engineering. The Master s pro gram may be tailored as a terminal one with emphasis on professional development or it may serve as preparation for more advanced work leading to the Doctorate Financial Assistance Sources available include graduate teaching assistantships, research assistantships and industrial fel lowships Write Department of Chemical Metallurgical and Polymer Engineering The University of Tennessee Knoxville Tennessee 37916 Faculty William T. Becker Donald C. Bogue Charlie R Brooks Duane D Bruns Edward S Clark Oran L Culberson John F Fellers George C Frazier Hsien-Wen Hsu Homer F Johnson Department Head Stanley H Jury (Emeritus) Carl D. Lundin Peter J Meschter Charles F Moore Ben F Oliver Professer-in-Charge of Metallurgical Engineering Joseph J Perona Joseph E Spruiell E Eugene Stansbury James L White Professor-in-Charge of Polymer Engineering Research Process Dynamics and Control Sorption Kinetics and Dynamics of Packed Beds Chromatographic and Ultracentrifuge Studies of Macromolecules Development and Synthesis of New Engineering Polymers Fiber and Plastics Processing Chemical Bioengineering X-Ray Diffraction Transmission and Scanning Electron Microscopy Solidification, Zone Refining Welding Cryogenic and High Temperature Calorimetry Flow and Fracture in Metallic and Polymeric Systems Corrosion Solid State Kinetics

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262 M.S. and Ph.D. Programs in Chemical Engineering Faculty research interests include Aerosol Technology, Bioengineering, Combustion, Computer-Aided Design, Energy, Enviromental, Kinetics and Catalysis, Materials, Optimization, Polymer Engineering, Process Control, Process Engineering, Process Simulation, Surface Phenomena, Transport Processes /or additional information: Graduate Advisor Department of Chemical Engineering The University of Texas Austin, Texas 78712 CHEMICAL ENGINEERING EDUCATION

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TEXAS A&M UNIVERSITY Texas A&M is a land-grant and sea-grant university, and the oldes t public inst i tution of higher learning in Texas. The current enrollment is about 30,000. The uni versity location is Bryan / College Station, Texas twin cities with a combined population of 122,000 (including students). The surrounding country is deciduous forest Houston is 95 miles Southeast and Dallas is 160 miles North. CHEMICAL ENGINEERING DEPARTMENT The ChE department has an enrollment of about 850 undergraduates and 70 graduates. ChE has excellent facilitie s in the Zachry Engineer i ng Center. All gradu ate students have desk space Graduate stipends are Currently $604 / month Admission to The Texas A&M University System and any of its sponsored programs is open to qualified individuals regardless of race, color, religion, sex, national origin or educationally handicaps. FALL 1979 FA CUL TY AND RESEARCH INTERESTS C. D. Holland (department head)-distillation R. G Anthony catalys i s J. A. Bullin pollution R Darby rheology R. R. Davison solar energy L. D. Durbin-control P. T. Eubank-thermodynamics C. J Glover oil recovery K. R. Hall-thermodynamics D. T. S. Hanson-biochemical W. B Harr i s methanol fuel J C. Holste-polyme r s A. D Messina heat transfer R. D. Ostermann bio mass G B Tatterson A. T Watson-simulation R E. White-electrochemical FOR INFORMATION CONTACT: Graduate Advisor Chemical Engineering Dept. Texas A&M University College Station, TX 77843 263

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p109 :s 1 oqwn5 1s1wa4 => J'v' 1 a "l'S 1addO:) SJoMO J::J il lllN :i uiz aw17 JOU)lf\ 1eqeuu1:) 264 Chemical Engineering at Virginia Polytechnic Institute and State University applying chemistry to the needs of man. Study with outstanding professors in the land of Washington Jefferson, Henry and Lee .. where Chemical Engineering is an exciting art. Some current areas of major and well-funded activity are, Renewable Resources chemical and microbiological processing, chemicals and polymers made from renewable resources Coal Science and Process Chemistry chemistry of prompt intermediates reaction paths in coal liquefaction fate of trace elements Coal Combustion Workshop small -sca le systems fate of trace elements, environ ment a l co ntrols Microcomputers Digital Electronics, and Control digital process measurements, microcomputer interfacing, remote data acquisition, digital controls Polymer Science and Engineering pro cess ing morphology synthesis, surface science biopolymers, membrane science Engineering Chemistry c h emica lly pumped lasers multiphase catalysis, c h em i ca l micro-engineering Biochemical Engineering synthetic foods, food processing, antibiotics, plant cell tissue c ulture f er mentation processes and instrumentation, environmental engineering VPI&SU is the state university o f Virginia with 20 000 students and almost 5,000 engineer ing students .. located in the beautiful mountains of sout hwestern Virginia. White water canoeing, skiing, backpacking, and the li ke are all nearby, as is Washingt on, D C. and historic Willi amsburg. Stipends to $8,000 (tax free) plus all fees. Write to: Dr. H. A. McGee, Jr., Department Head, Chemical Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, or call collec t (703) 961-6631. CHEM ICAL ENGINEERING EDUCATION

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Chemical Engineering Energy Engineering Coal Conversion Combustion Conversion of Solid Wastes to Low BTU Gas Environmental Engineering Sludge and Emulsion Dewatering S0 2 Scrubbing River & Lake Modeling Economic Impact of Environmental Regulations West Vlrg1n1a Un1vers1ty Other Topics Optimization Chemical Kinetics Separation Processes Surface and Collaid Phenomena Polymer Processing Fluidization Biochemical Engineering Transport Phenomena Utilization of Ultrasonic Energy Electrochemical Engineering M.S. and Ph.D. Programs For further information on financial aid write: FALL 1979 Dr. J. D. Henry Department of Chemical Engineering West Virginia University Morgantown, West Virginia 26506 265

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CHEMICAL ENGINEERING DEGREES: M.S., Ph.D. RESEARCH AREAS INCLUDE: HEAT AND MASS TRANSFER REACTION KINETICS AND CATALYSIS PROCESS DYNAMICS AND CONTROL PROCESS MODELING IN: COAL GASIFICATION, CHEMICALS FROM WOOD, ECOSYSTEM ANALYSIS AND THEORETICAL STUDIES 266 CONTACT: DR. WILLIAM J. HATCHER, JR., HEAD P.O. BOXG University, Alabama 35486 ASU Tempe, Arizona FACULTY James R. Beckman Lynn Bellamy Neil S. Berman William J. Dorson, Jr. Eric J. Guilbeau James L. Kuester Castle 0. Reiser Vernon E. Sater lmre Zwiebel For information contact: Graduate studies in CHEMICAL AND BIO ENGINEERING leading towards MS and Ph.D. degree RESEARCH ENERGY CONVERSIONS PROCESS ENGINEERING ENVIRONMENTAL CONTROL ADSORPTION / SEPARATION BIOMEDICAL ENGINEERING TRANSPORT PHENOMENA REACTOR ENGINEERING lmre Zwiebel, Chairman Chemical and Bio Engineering Arizona State University Tempe, AZ 85281 C HEMICAL ENGINEERING EDUCATION

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CINCINNATI DEPARTMENT OF CHEMICAL AND NUCLEAR ENGINEERING M.S. AND PH.D DEGREES FALL 1979 -Major urban educational center -New, prize-winning laboratory building and facilities-Rhodes Hall -National Environmental Research Center (EPA) adjacent to campus -Major computer facilities: digital, analog, hybrid -Gri!duate specialization in-process dynamics & control, polymers, applied chemistry, systems, foam fraction ation, air pollution control, biomedical, power gen eration, heat transfer. Inquiries to: Dr. David B. Greenberg, Head Dept. of Chemical & Nuclear Engineering (0620) University of Cincinnati Cincinnati, Ohio 45221 Graduate Study in Chemical Engineering Degrees Offered M S and Ph.D. Pr ograms are available for persons in Chemical Engin eering or related fields. Research Areas Energy Storage and Conservation Polymer Processing Environm ental P o lluti on Control Chem ical Reaction Kinetics and Reactor Design Pro cess Dynamics Non-Newtonian Fluid Mechanics Mem brane Tran sport Pro cesses Thermodynamics Faculty F.C. Alley W.B. Barlage J.N. Beard W.F. Beckwith D.D. Edie J.M. Haile R.C Har s hman S S. Melsheimer J.C. Mullins R.W Rice W.H. Talbott Clemson University Clemson University is a state coeducational land grant univer si t y offering 78 undergraduate fields of study and 54 areas of graduate study in its nine academic units which include the College of Engineering Pre sent on-campus enrollment totals about 10 ,300 students which include s about 1 500 graduate s tudent s. The campus, which com prises 600 acres and represents an investment of approximately $139 million in permanent fa c ilities is loca ted in the northw es tern part of South Carolina on the shores of Lake H artwell. For Information For further information and a descriptive brochure, write D.D. Edie, Graduate Coordinator, Department of Chemical Engineering, Clemson University, Clemson, SC 29631 267

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THE CLEVELAND STATE UNIVERSITY DOCTOR OF ENGINEERING MASTER OF SCIENCE PROGRAM IN CHEMICAL ENGINEERING AREAS OF SPECIALIZATION Transport Processes Porous Media Bioengineering Reaction Engineering Simulation Processes Zeolites The program may be designed as terminal or as preparation for further advance study leading to the doctorate. Financial assistance is available. 268 FOR FURTHER INFORMATION, PLEASE CONTACT: Department of Chemical Engineering The Cleveland State University Euclid Avenue at East 24th Street Cleveland, Ohio 44115 The University of Colorado offers excellent opportunities for graduate study and research leading to the Mas.ter of Science and Doctor of Philosophy degrees in Chemical Engineering Air Pollution Bioengineering Catalysis Cryogenics Design Energy Applications Environmental Applications Fluid Mechanics Heat Transfer Kinetics Polymers Process Control Thermodynamics Water Pollution For application and information, write to: Chairman, Graduate Committee Chemical Engineering Department University of Colorado Boulder, Colorado 80309 CHEMICAL ENGINEERING EDUCATION

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raculty T. F ANDERSON J P. BELL C. 0. BENNETT R. W. COUGHLIN M B. CUTLIP A. T. DiBENEDETTO programs M.S. and Ph.D. programs covering most aspects of Chemical Engineering. Research projects concentrate in four main areas: KINETICS AND CATALYSIS G M HOWARD H. E KLEI M T SHAW R. M. STEPHENSON L. F. STUTZMAN POLYMERS AND COMPOSITE MATERIALS PROCESS DYNAMICS AND CONTROL WATER AND AIR POLLUTION CONTROL BIOCHEMICAL ENGINEERING FUEL PROCESSING D. W. SUNDSTROM SEPARATION THERMODYNAMICS financial aid Research and Teaching Assistantships, Fellowships location Beautiful setting in rural Northeast Connecticut, convenient to Boston, New York, and Northern New England We would like to tell you much more about the opportunities for an education at UCONN, please write to: Graduate Admissions Committee Department of Chemical Engineering The University of Connecticut Storrs, Connecticut 06268 DREXEL UNIVERSITY M.S. and Ph.D. Programs in Chemical Engineering Faculty D. R. Coughanowr E. D. Grossmann Y. Lee R Mutharasan J. A. Tallmadge J. R. Thygeson X Verykios C. B. Weinberger Consider: High faculty /student ratio Excellent facili ties Research Areas Biochemical Engineering Chemical Reactor / Reaction Engineering Coal Conversion Technology Mass and Heat Transport Polymer Processing Process Control and Dynamics Rheology and Fluid Mechanics Systems Analysis and Optimization Thermodynamics and Process Energy Analysis Outstanding location for cultural activities and job opportunities Full time and part time options Write to: Department of Chemical Engineering Drexel University Philadelphia, PA 19104 FALL 1979 269

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CHEMICAL ENGINEERING M.S. and Ph.D. PROGRAMS University of Idaho L L EDWARDS R. R. FURGASON W.R. HAGER K. L. HOLMAN M. L. JACKSON R. A. KORUS J. J. SCHELDORF G. M. SIMMONS W. J. THOMSON FACULTY -Computer Aided Process Design, Systems Analysis, Pulp / Paper Engineering -Heat Transfer, Process Design and Economics -Environmental Systems, Alternative Energy, Engineering Education -Transport Phenomena, Process Analysis Re source Recovery -Mass Transfer in Biological Systems, Particulate Control Technology -Polymers, Biochemical Engineering -Heat Transfer, Thermodynamics -Geothermal Energy Engineering, Energy Re covery, Pyrolysis Kinetics -Applied Kinetics and Catalysis, Oil Shale Tech nology, Fluidization A concentrated program of study in an informal atmosphere allows completion of a M.S. program in one calendar year. The region has an invigorating climate with excellent outdoor recreation including fishing, hunting, skiing, hiking boating and camping. The university community provides access to a variety of cultural activities and events. FOR FURTHER INFORMATION & APPLICATION WRITE : Graduate Advisor Chemical Engineering Department University of Idaho Moscow, Idaho 83843 University of Kentucky M.S and Ph D. Programs Faculty and Research Areas: W L. Conger, Ph.D ., Pennsylvania G R. Crewe. Ph.D. West Virgin ia Thermochem ica l Hydroge n Production ; 2nd Law Analysis of Proc esses Catalytic Hydrocrack ing of Poly aromatics ; Coal Liquefact ion For details write to: R. B. Grieves, Ph D ., Northw este rn C E Hamrin Ph D ., Northw estern R I. Kermode, Ph.D ., Northwestern L. K Peters, Ph D Pittsburgh Foam Fractionation ; Physi coche m ical S e p arations Coal Liquefaction Catalysis ; Non isot he r m a l Kinetics Proc ess Control and Economic s 270 R. B Grieves, Cha ir man Chemical Engineering Dept. University of Kentucky Lexington. Kentucky 40506 E D Moorhead Ph D Princ et on J T Schrodt Ph D ., Louisville A. H P Skelland, Ph D ., Birmingham J Yamanis, Ph D Windso r Atmospheric Transp ort; Aerosol Phenomena Electrochemical Processe s; Novel Measur e ment Techniques Simultaneous Heat and Mas s T ra nsfer ; Fuel G as Desulfurizat io n Liquid Extraction Phenomena ; Non Newton ian Fluid Mechanics Heterogeneous Catalysis and Applied Ch e m ical Kinetics ; Chem ic al Reactor Design Department of Chemical Engineering CHEMICAL ENGINEERING EDUCATION

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FACULTY Hugo S. Caram Marvin Charles Curtis W. Clump Mohamed EI-Aasser Andrew Klein William L. Luyben William E. Schiesser Cesar Silebi Leslie H. Sperling Fred P. Stein Leonard A. Wenzel LEHIGH UNIVERSITY Department of Chemical Engineering Whitaker Laboratory, Bldg. 5 Bethlehem, Pa. 18015 RESEARCH CONCENTRATIONS Polymer Science & Engineering Fermentation, Enzyme Engineering, Biochemical Engineering Process Simulation & Control Catalysis & Reaction Engineering Thermodynamic Property Research Energy Conversion Technology Applied Hea,t & Mass Transfer Fluid Mechanics SPECIAL PROGRAMS M.Eng. Program in Design M.S. and Ph.D. Programs in Polymer Science & Engineering FINANCIAL AID Of course. WRITE US FOR DETAILS Bioengineering Pollution Control Process Dynamics Graduate Enrollment 70 Faculty 15 Computer Control Kinetics and Catalysis Thermodynamics Ecological Modeling Write: Chemical Engfneering Department Sugar Technology Louisiana State University Baton Rouge, Louisiana 70803 FALL 1979 271

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UNIVERSITY OF MAINE at Orono GRADUATE STUDY IN CHEMICAL ENGINEERING M.S. and Ph.D. Programs Pulp & Paper Processing Polymers Energy Sources & Conversion Fluid Dynamics Programs of Study: Cost of Tuition: The Community: Financial Aid: 272 Process Control Instrumentation Food Processing Wood Conversion Reactions Applied Surface Chemistry Heat & Mass Transfer Graduate Study Brochure Available on Request CHEMICAL ENGINEERING DEPARTMENT WRITE: A. L. Fricke, Chairman Department of Chemical Engineering 115 Jenness Hall University of Maine at Orono Orono, ME 04473 UNIVERSITY OF MARYLAND The Department offers a broad program of graduate studies leading to the MS (with or without thesis) and the PhD degrees Areas of research emphasis include Biochemical Engi neering, Coal Technology, Process Analysis, Simulation, and Control, Polymers, and Aerosol Mechanics. Tuition for the 1979-80 academic year is $66 per credit hour for Maryland residents and $111 per credit hour for nonresidents. The College Park campus is located a few miles from Washington, D.C. and thirty miles from Baltimore and Annapolis, Maryland. Because of its location, the University community enjoys advantages found nowhere else in the country The variety of scientific, political, educational, cultural and athletic activities in the area enhances the life of all graduate students at Maryland. Fellowships Graduate Research and Teaching Assistantships. For further information on the programs and aid available, contact Dr. T. W. Cadman, Chairman, Department of Chemical and Nuclear Engineering, University of Maryland, College Park, Maryland 20742 Phone (301) 454-2431. CHEM ICAL ENGINEERING EDUCATION

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~~:~~~~tru;~~~NEERING AT MICHIGAN STATE UNIVERSITY The Department of Chemical Engineering of Michigan State Univers i ty has assistantships and fellowships available for students wishing to pursue advanced study With one of these appointments it is possible for a graduate student to obtain the M S. degree in one year and the Ph.D. in two additional years ASSISTANTSHIPS: Teaching and research assistantships pay $600 per month to a student studying for the M.S. degree and approximately $650 per month for a Ph.D candidate. A thesis may be written on, the subject covered by the research assistantship. Students must pay resident tuition, but the additional non-resident fee is waived. FELLOWSHIPS: Available appointments pay to $8,500 plus tuition and fees CURRENT FACULTY AND RESEARCH INTERESTS K. Jayaraman D. K. Anderson, Chairman Ph.D ., University of Wash i ngton Transport Phenomena B i omedical Engineering Cardio vascular Physiology C. M. Cooper Sc.D., Massachusetts Institute of Technology Thermodynamics and Phase Equilibria Modeling of Trans port Processes A. L. DeVera Ph.D., University of Notre Dame Chemical & Catalytic Reaction Engineering Transport Properties of Random Heterogeneous Med i a and App li ed Mathematics E A. Grulke Ph.D. Ohio State University Food Engineering, Polymer Science, Polymer Engineering M. C Hawley Ph D Michigan State University Porous Media Transport, K i netics Catalysis, Plasmas and React i on Engineering Ph D ., Princeton Un i versity Proces s Dynamics and Control, Nonlinear Rheological Models of Polymeric Materials Nonlinear System Theory C A. Petty Ph.D Univers i ty of Florida Turbulence Stability and T r ansport in Fluidized Beds, Separations B. W. Wilkinson Ph.D Ohio State University Energy Systems and Environmental Control Nuclear Re actor and Radioisotope Applications P E Wood Ph D. California Institute of Technology Turbulent Transport Phenomenon, Mathematics Modeling Appl i ed Mathem atics and Numerical Methods For additional information write: Dr. Donald K. Anderson, Chairman Department of Chemical Engineering 197 Engineering Building Michigan State University East Lansing, Michigan 48824 DO YOUR GRADUATE WORK AT MICHIGAN TECH ... WORK AND STUDY .. with a select faculty .. the best equipment .. surrounded by forests and lakes DEGREES OFFERED : M.S in Chemical Engineering studies in advanced thermodynamics, reaction kinetics transport phenomena, instrumentation, unit operations, and chemical processing. M.S. and Ph.D. in Chemistry special i zation in organic, inorganic physical and analytical chemistry, and in biochemistry. Financial assistance available in the form of fellowships and assistantships. For more information write: H. El Khadem, Head Department of Chemistry and Chemical Engineering Michigan Technological University Houghton, Michigan 49931 Michigan Technological Univers i ty i s an equal opportunity educat i onal institut i o n/ equal opportunity employer. FALL 1979 273

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UNIVERSITY OF MISSOURI COLUMBIA DEPARTMENT OF CHEMICAL ENGINEERING Studies Leading to M.S. and PhD. Degrees Research Areas Air Pollution Monitoring and Control Biochemical Engineering and Biological Stabilization of Waste Streams Biomedical Engineering Catalysis Energy Sources and Systems Environmental Control Engineering Heat and Mass Transport Influence by Fields Newtonian and Non-Newtonian Fluid Mechanics Process Control and Modelling of Processes Single-Cell Protein Research Themodynamics and Transport Properties of Gases and Liquids Transport in Biological Systems WRITE: Dr. George W. Preckshot, Chairman, Department of Chemical Engineering, 1030 Engineering Bldg., University of Missouri, Columbia, MO 65201 274 UNIVERSITY OF NEBRASKA OFFERING GRADUATE STUDY AND RESEARCH I N THE AREAS OF: air pollution bio-mass conversion coal tar utilization energy conversion kinetics micro-processor applications and digital control polymerization thermodynamics others FOR APPLICATION AND INFORMATION ON FINANCIAL ASSISTANCE PLEASE WRITE TO: Prof. L. C. TAO, Chairman, Department of Chemical Engineering, University of Nebraska, Lincoln, Nebraska 68588 CHEMICAL ENGINEERING EDUCATION

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FALL 1 979 THE UNIVERSIT'I OF NEW MEXICO M.S. and Ph.D. Graduate Studies in Chemical Engineering Offering Research Opportunities in Coal Gasification Desalination Synthetic Fuels-In Situ Technology Aerosol Physics Catalysis Mini Computer Applications to Process Control Multi Phase Flow Process Simulation Hydro-Metallurgy Radioactive Waste Management .. and more Enjoy the beautiful Southwest and the hospitality of Albuquerquel For further information, write: E. James Davis, Chairman Dept. of Chemical and Nuclear Engineering The University of New Mexico Albuquerque, New Mexico 87131 Graduate study toward M.S. degrees in chemical engineering Major energy research center: solar petroleum bioconversion geothermal Financial assistance available Special programs for students with B.S. degrees in other fields. For applications and information: Dr. John T. Patton, Head, Department of Chemical Engineer ing, Box 3805, New Mexico State University, Las Cruces, New Mexico 88003 New Mex i co State University is an Equal Opportunity Affirmative Action employer. 275

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NORTHWESTERN UNIVERSITY GRADUATE PROGRAMS IN CHEMICAL ENGINEERING Faculty and Research Activities: S G Sankoff G. M. Brown J B. Butt S. H. Carr W C Cohen B. Crist J. S Dranoff T K. Goldstick W W Graessley H M Hulburt H. H. Kung R S. H Mah J C Slattery W F Stevens G Thodos Boiling Heat Transfer Two-Phase Flow Thermodynamics Process Simulation Chemical Reaction Engineering Applied Catalysis Solid State Properties of Polymers, B i odegradation Dynamics and Control of Process Systems Polymers in the Solid State Chemical Reaction Engineering Chromatograph i c Separations Biomedical Engineering Oxygen Transport Polymer Rheology, Polymer Reaction Engineering Analysis of Chemical and Physical Processes Catalyst Behavior Propert i es of Oxide Surfaces Computer-Aided Process Planning Des i gn and Analysis Transport and lnterfacial Phenomena Process Optimization and Control, Computer Applicat i ons Properties of Fluids Coal Processing Solar Energy Financial support is available For information and application materials, write : Professor J. S. Dranoff, Chairman Department of Chemical Engineering Northwestern University Evanston, Illinois 60201 e1te111ical 8HpiHeeriHfl at /vPtre :Dame RESEARCH AREAS The University of Notre Dame offers programs of graduate study leading to the Master of Science and Doctor of Philosophy degrees in Chemical Engineering. The requirements for the master's degree are normally completed in one calendar year. The doctoral program usually takes three to four y ears of full-time study beyond the bachelor's degree Catalysis Reaction Engineering Phase Eq uilibria Thermodynamics Energy Conversion Applied Mathematics Process Dynamics and Control Modeling and Simulation FACULTY R. A. Schmitz, Chairman J. J. Carberry J.P.Kohn K. D. Luks W. C. Strieder A. Varma E. E. Wolf J. T. Banchero, Emeritus A variety of financially attractive fellowships and assistantship s are available to outstanding students pursuing eithe r program. For further information, write to Director of Graduate Studie s Department of Chemical Engineering University of Notre Dame Notre Dame, Indiana 46556 t---------------------------------------------276 CHEMICAL ENGINEERING EDUCATION

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M.S. and Ph.D. Degrees in Chemical Engineering [[][[] Oklahom a State University For information and applications write: Dr. Billy L. Crynes Head School of Chemical Engineering 423 Engineering North Oklahoma State University Stillwater, Oklahoma 74074 Areas of Research Specialization Thermodynamics Transport properties Stagewise operations ~ Heat transfer and fluid mechanics Computer applications Process design, synthesis and analysis Energy production, conversion and conservation Catalysis The Physical Properties Laboratory (Dr. R. N. Maddox, Director) cooperates closely with the School i, of Chemical Engineering in its research programs. OREGON ST A TE UNIVERSITY Chemical Engineering M.S. and Ph.D. Programs FACULTY T. J. Fitzgerald Control, Fluidization, Mathematical Models F. Kayihan Process Systems Simulation and Analysis J. G. Knudsen -Heat and Momentum Transfer, Two Phase Flow 0. Levenspiel Reactor Design, Fluidization R. E. Meredith Corrosion, Electrochemical Engineer ing R. V. Mrazek Thermodynamics, Applied Mathe matics C. E. Wicks Mass Transfer, Wastewater Treatment An informal atmosphere with oppor tunity for give and take with faculty and for joint work with the Pacific Northwest Environmental Research Laboratory (EPA), Metallurgical Research Center of the U.S. Bureau of Mines, Forest Product Laboratory, Environmental Health Science Center and the School of Oceanography. The location is good-in the heart of the Willamette Valley-60 miles from the rugged Oregon Coast and 70 miles from good skiing or mountain climbing in the high Cascades. FALL 1979 For further information, write: Chemical Engineering Department, Oregon State University Corvallis, Oregon 97331 277

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UNIVERSITY OF OTTAWA FACULTY CHEMICAL ENGINEERING OTTAWA ONTARIO, CANADA KlN 9B 4 phone (613)231-3476 J A. Golding, Ph.D (Toronto) W. Hayduk, Ph.D (UBC) V. Hornof, Ph.D. (SFU) M.A.Sc. and Ph.D. programs in: W. Kozicki, Ph D. (Caltech) B.C. Y. Lu, Ph.D. (Toronto) R. S Mann, Ph.D (Hull) energy storage ... extraction .. process control ... enhanced oil recovery .. reverse osmosis ... kinetics and catalysis .. porous media ... non Newtonian flow ... thermodynamics solar energy .. experimental design polymer modification ... pulp & paper ... phase equilibria D D Mclean, Ph.D. (Queens) G. H. Neale, Ph.D. (Alberta) S. Sourirajan Ph.D (Bombay), D Eng. (Yale) F. D. F. Talbot, Ph.D. (Toronto), Chairman who should be contacted for further information. COME AND JOIN US IN THE EXCITING ENVIRONMENT OF CANADA'S NATIONAL CAPITAL GRADUATE STUDY IN CHEMICAL AND PETROLEUM ENGINEERING .. 278 University of Pittsburgh Today, approximately 2,000 undergraduates and 600 graduate students are enrolled in the School of Engineering. Student s have access to the George M. Bevier Engineer ing Library of 38,000 volumes; University libraries of over 2 500,000 volumes: librari e s in 50 industrial re s earch centers and unive rs ities nearby. University of Pittsburgh has a comprehensive computer system with both batch and time-sharing facilities to use in academic and research investigations. FACULTY Charles S Beroes Alfred A. Bishop Alan J Brainard Shiao-Hung Chiang James T. Cobb, Jr. Paul F. Fulton George E Klinzing Alan A. Reznik Yatish T. Shah Edward B. Stuart John W. Tierney James G Goodwin Gerald D Holder PROGRAMS AND SUPPORT Master of Science and Doctor of Philosoph y degrees in Chemical Engineer ing and Master of Science degree in Petroleum Engineering are offered. While obtaining advanced degrees, students may specialize in Biomedical, Energy Resources Nuclea r and Environmental areas. A joint Master of Science degree with the Department of Mathematics is offered. Teaching and Research Assistantships and Fellowships are available. Si x t y graduate student s alon g with 300 undergraduate s pursue their education on three floors of Ben e dum H a ll The facilities are modern and excellently equipped. Graduate applicants should write : Graduate Coordinator, Chemical and Petroleum Engineering School of Engineering University of Pittsburgh Pittsburgh, PA 15261 CHEMICAL ENGINEERING EDUCATION

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Princeton University M.S.E. AND Ph.D. PROGRAMS IN CHEMICAL ENGINEERING RESEARCH AREAS Atmospheric Aerosols; Biochemical Engineering; Ca,talysis; Chemical Reactor /Reaction Engineering; Computer-Aided Design; Energy Conversion and Fusion Reactor Technology; Engineering Physiology; Environmental Studies; Fluid Mechanics and Rheology; Mass and Momentum Transport; Molecular Beams; Polymer Materials Science and Rheology; Process Control and Optimization; Surface Science; Thermodynamics and Phase Equilibria. FACULTY Ronald P. Andres, Robert C. Axtmann, Jay B. Benziger, Joseph M. Calo, John K. Gillham, Carol K. Hall, Ernest F. Johnson, Jeffrey Koberstein, Morton D. Kostin, Bryce Maxwell, Robert G. Mills, David F. Ollis, Robert K. Prud'homme, Ludwig Rebenield, William B. Russel, Dudley A. Saville, William R. Schowalter, Chairman. WRITE TO Director of Graduate Stvdiff Chemical Engineering Princeton Univenity Princeton, New Jeney 08540 Qgeen's University Kingston, Ontario, Canada Graduate Studies in Chemical Engineering MSc and Ph D Degree Programs D. W. Bacon PhD {Wisconsin) H. A. Becker ScD (MITI D. H. Bone PhD (London S. H. Cho PhD (Princeton) R.H. Clark PhD (Imperial College) R. K. Code PhD (Cornell) J. Downie PhD (Toronto) E. W. Grandmaison Ph.D. (Queen's) C. C. Hsu PhD (Texas) B. W. Wojciechowski PhD (Ottawa) FALL 1979 Waste Processing water and waste treatment applied microbiology biochemical engineering Chemical Reaction Engineering catalysis statistical design polymer studies Transport Processes combustion fluid mechanics heat & mass transfer Write: Dr. Henry A. Becker Department of Chemical Engineering Queen's University Kingston, Ontario Canada 279

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The Faculty UNIVERSITY OF ROCHESTER ROCHESTER, NEW YORK 14627 MS & PhD Programs H. Brenner, Eng Sc. D., 1957, New York Fluid Mechanics, Transport Processes G. R. Cokelet, Sc. D., 1963, MIT Blood & Suspension Rheology, Biotechnology B. E. Dahneke, Ph.D., 1967, Minnesota Aerosols, Surface Phenomena, Biotechnology T. L. Donaldson, Ph.D., 1974, Pennsylvania Enzymes, Biotechnology, Mass Transfer R F. Eisenberg, M.S., 1948, Rochester Corrosion, Physical Metallurgy M R Feinberg, Ph.D ., 1968, Princeton Complex Reaction Systems, Continuum Mechanics J. R. Ferron, Ph.D 1958, Wisconsin Molecular Transport Processes, Applied Mathematics J. C. Friedly, Ph.D., 1965, California (Berkeley) Process Dynamics, Control, Cryogenics R H. Heist, Ph.D., 1972, Purdue Nucleation, Solid State, Atmospheric Chemistry K. C. D. Hickman, Ph.D., 1925, London Boiling & Condensation Phenomena, Distillat i on H.J. Palmer, Ph.D., 1971, Washington (Seattle) lnterfacial Phenomena, Mass Transfer H. Saltsburg, Ph.D., 1955, Boston Surface Phenomena, Catalysis, Molecular Scattering W. D Smith, Jr., D.Eng., 1963, Yale Catalysis & Reactor Design, Computer Applications G. J. Su, Sc. D., 1937, MIT Colloidal & Amphorous States, Glass Science For information write: H. Brenner, Chairman UNIVERSITY OF SOUTHERN CAUIFORNIA Los Angeles Graduate Study in Chemical Engineering FACULTY WENJI VICTOR CHANG (Ph.D., Ch.E ., Caltech, 1976) Rheological properties of polymers and composites, adhesion ; polymer processing JOE D. GODDARD (Ph D ., Ch E. U C Berkeley, 1962) Rheology and mechanics of non Newtonian fluids and composite materials transport processes LYMAN L HANDY (Ph.D. Phys Chem U of Wash ., 1951) Fluid flow through porous media and petroleum reservo i r eng i neer i ng THEODORE T TSOTSIS (Ph.D., Ch E U. of Ill., Urbana 1978 ) Chemical reaction engineering, process dynamics and control JAMES M WHELAN (Ph.D., Chem ., U.C. Berkeley, 1952) Thin Films 111-V, heterogenous catalysis, sintering processes TEH FU YEN (Ph D ., Organic and BioChem ., V.P.I. 1956) 8iomater i als energy resources, environmental science, fossil fuels Interested in advanced studies for the M S. Eng. or Ph D degree i n Chemical Engineering ? FRANK J LOCKHART (Ph.D., Ch.E U. of Mich., 1943) Distillat i on air pollution design of chemical plants oil shales, coals and petroleum, biochemical engineering chemical comminution Interested in a dynamic and growing depart ment in one of the world 's great climates and metropolitan areas? If so, write for further informat i on abou t the program financial support, and applica tion forms to: Graduate Admissions Department of Chemical Engineering University of Southern California University Park, PCE Building 205 Los Angeles, CA 90007 280 CHARLES J. REBERT (Ph.D. Ch E ., Ohio State U., 1955) High pressure vapor-liquid equil i bria, t wo phase flow liquid thermal conducticity RONALD SALOVEY (Ph.D. Phys Chem. Harvard 1958) Physical chemistry and i rradiation of pol ymers, characterization of elastomers and polyu r ethanes VANIS C. YORTSOS (Ph D., Ch E Caltech, 1978) Mathematical modelling and transport processes flow in porous media and thermal oil recovery methods C HEMICAL ENGINEERING EDUCATION

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Chemical Engineering at Stanford Stanford University offers programs of study and research leading to master of science and doctor of philosophy degrees in chemical engineering with a number of financially a,ttractive fellowships and assistantships available to outstanding students pursuing either program For further information and application blanks, write to: FACULTY: Andreas Acrivos (Ph.D., 1954 M i nnesota) Fluid Mechanics Michel Boudart (Ph D ., 1950 Princeton) Kinetics and Catalysis Curtis W. Frank (Ph.D ., 1972 Illinois) Polymer Science George M. Homsy (Ph.D., 1969, Illinois) Fluid Mechanics and Stability Admissions Chairman 0 Robert J. Madlx (Ph D ., 1964, U Cal Berkeley) Surface Reactivity Department of Chemical Engineering Stanford University David M. Mason (Ph.D. 1949 Cal Tech) Applied Thermodynamics and Chemical Kinetics Stanford, California 94305 Alan S. Michaels (Sc.D 1948, M 1.T.) Closing date for applications is January 15, 1980. Membrane Separation Processes Channing R. Robertson ( Ph D ., 1969 Stanford) Bioengineering FALL 1979 Chemical Engineering LECTURERS AND CONSULTING FACULTY: Richard E. Balzhiser, Electric Power Research Institute Palo Alto California Heat Transfer and Thermodynamics Floyd L. Culler, Electric Power Research Institute Palo Alto California Nuclear Energy Robert M. Kendall, Acu rex Corporation Mounta i n View California Combustion Robert H. Schwaar, S R I., Internat ional Menlo Park California Technological Development and Process Design State University of New York at Buffalo, AMHERST, NY Academic programs for MS and PhD candidates are designed to provide depth in chemical engineering fundamentals while preserving the flexibility needed to develop special areas of interest. The Department also draws on the strengths of being part of a large and diverse university center. This environment stimulates interdisciplinary interactions in teaching and re search. The new departmental facilities offer an exceptional opportunity for students to develop their research skills and capabilities These features combined with year-round recrea tional activities afforded by the Western New York country side, and numerous cultural activities centered around the City of Buffalo make SUNYAB an especially attractive place to pursue graduate studies. Faculty and Research Interest G F. Andrews ______________ B i ochemical engineering, wastewater treatment D R. Brutvan ________________________ Staged operations P Ehrlich __ ___________________ Polymeric materials, polymerization W. N. Gill --~-,---------Reverse osmosis, dispersion, fluidization R. J. Good _______________ Surface phenomena, tertiary oil recovery, adhesion K M Kiser-----------------------Fluid mechanics, turbulence E Ruckenstein __ ___________ Catalysis, interfacial phenomena, bioengineer i ng M Ryan -----------~--Non-Newtonian fluid mechanics, polymer processing P Stroeve _____________ ___ Transport surface science, biomedical engineering J. J. Ulbrecht __________________ Rheology of dispersed systems, mixing T. W. Weber ----------------Process control, dynamics of adsorption S. W Weller ----------------------Catalysis, coal conversion R T. Yang ___________ ______ Catalysis coal conversion chemical kinetics Further information may be obtained by writing Professor J. Ulbrecht Chairman, Department of Chemical Engineering, State University of New York at Buffalo, Amherst NY 14260 281

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282 CHEMICAL ENGINEERING GRADUATE STUDY IN SYRACUSE UNIVERSITY RESEARCH AREAS FACULTY Allen J. Barduhn George C. Martin Water Renovation Biomedical Engineering Membrane Processes Desalination Transport Phenomena Polymer Characterization Mathematical Modeling Fluid-Particle Separation Philip A. Rice S. Alexander Stern Gopal Subramanian Chi Tien Chiu-Sen Wang Syracuse University is a private coeducational university located on a 640 acre campus situated among the hills of Central New York State. A broad cultural climate which encourages interest in engineering, science, the social sciences, and the humanities exists at the university. The many diversified activities conducted on the campus provide an ideal environment for the attainment of both specific and general educational goals. As a part of this medium sized research oriented university, the Department of Chemical Engineering and Materials Science offers graduate education which continually reflects the broadening interest of the faculty in new technological problems confronting society. Research, independent study and the general atmosphere within the Department engender individual stimulation. FELLOWSHIPS AND GRADUATE ASSISTANTSHIPS AVAILABLE FOR THE ACADEMIC YEAR 1979-1980 For Information: Stipends: Contact: Chairman Department of Chemical Engineering and Materials Science Stipends range from $3,100 to $6,750 with most students receiving at least $4,400 per annum in addition to remit ted tuition privileges. Syracuse University Syracuse, New York 13210 The University of Toledo Graduate Study Toward the M.S. and Ph.D. Degrees Assistantships and Fellowships Available. EPA Traineeships in Water Supply and Pollution Control. For more details write: Dr. Leslie E. Lahti Department of Chemical Engineering The Univenity of Toledo Toledo, Ohio 43606 CHEMICAL ENGINEERING EDUCATION

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CHEMICAL ENGINEERING M.S. AND Ph.D. PROGRAMS TUFTS UNIVERSITY CURRENT RESEARCH TOPICS Metropolitan Boston RHEOLOGY OPTIMIZATION CRYSTALLIZATION POLYMER STUDIES MEMBRANE PHENOMENA CONTINUOUS CHROMATOGRAPHY BIO-ENGINEERING MECHANO-CHEMISTRY PROCESS CONTROL FOR INFORMATION AND APPLICATIONS, WRITE: PROF K A VAN WORMER, CHAIRMAN DEPARTMENT OF CHEMICAL ENGINEERING TUFTS UNIVERSITY MEDFORD, MASSACHUSETTS 02155 STUDY WITH US AND ENJOY NEW ORLEANS TOO! CHEMICAL AND MANAGEMENT ENGINEERING TULANE UNIVERSITY Specialize through options in: 1. The Polymers and Reaction Engineering Laboratory. 2 The Energy and Environmental Laboratory 3. The Health and Ecology Laboratory 4. The Management and Control Laboratory Established Internships with Industry and Government Agencies For Additional Information, Please Contact Robert E. C. Weaver, Head Department of Chemical Engineering Tulane University New Orleans, LA 70118 FALL 1979 THE FACULTY: R V Ba i ley Ph D (LSU ) _______ Systems Engineer i ng Applied Math, R W Fre e dman Ph.D (M I T ) Energy Conversion ____ Numer i cal Methods Control Theory Mathemat i cal S i mulation L. J Groome Ph D (Florida) ______ .. olecular Thermody n amics, Biophysics Biomedical Engineering T. R. Hanley, Ph D. (Virginia Polytechnic Kinetics and Reactor Design, Polymer Institute and State Un iv e r sity) ___ __, ystems Membrane Transport, Energy Recove r y System s J M Henry Ph.D. (Prince t on) _____ Chemical Eng i neering in Energy and Environmental Studies D W. McCarthy Ph.D (f ulane ) Compu t er Control Optimization Deterministic Modeling S L. Sullivan, Jr Ph D (Te x as A&M) __________ Separation Processes Transport Phenomena Numerical Methods R. E C Weaver Ph D. (Pr i nceton) ___ Opera t ions Research and Control, Energy and Environmental Mgmt. Biomedical Engineering 283

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GRADUATE PROGRAMS IN CHEMICAL ENGINEERING The University of Tulsa THE FACULTY FURTHER INFORMATION M.S., Master of Engineering Management, Ph.D. R. L. Bunn Coal conversion, heat transfer A. P. Buthod Petroleum refining, petroleum phase behavior, heat K. D. Luks F. S. Manning W. C. Philoon E. H. Snider N. D. Sylvester R. E. Thompson transfer Thermodynamics, phase equilibria Industrial pollution control, enhanced oil recovery, environmental protection Corrosion, process design Environmental engineering, kinetics Enhanced oil recovery, environmental protection, fluid mechanics, reaction engineering Oil and gas processing, computer-aided process design If you would like additional information concerning specific research areas, facilities, and curriculum contact the Chairman of Chemical Engineering (Prof. Thompson). Inquiries concerning admissions and financial support should be directed to the Dean of the Graduate School. The University of Tulsa 600 S. College Tulsa, OK 74104 (918) 939-6351 The University of Tulsa has an Equal Opportunity/ Affirmative Action Program for students and employees. VANDERBILT UNIVERSITY GRADUATE STUDIES IN CHEMICAL ENGINEERING M.S. AND Ph.D. DEGREE PROGRAMS W. Wesley Eckenfelder Kenneth A. Debelak Thomas M. Godbold Thomas R Harris Knowles A. Overholser John A. Roth Karl B. Schnelle, Jr. Robert D. Tanner Biological and Advanced Waste Water Treatment Processes Gasification and Liquifaction of coal,, Energy-Environmental Systems, Mathematical Modeling of Chemical Processes. Process Dynamics and Control, Mass Transfer Physiological Systems Analysis, Transport Phenomena, Biomedical Engineering, Tracer Analysis Combustion Physics, Biorheology Reaction Kinetics and Chemical Reactor Design, Gas Chromatography, Industrial Waste Management and Control Air Pollution, Instrumentation and Automatic Control, Dispersion Studies Enzyme Kinetics, Fermentation Processes and Kinetics, Pharmaco kinetics, Microbial Assays W. Dennis Threadgill Unit Operations, Food and Dairy Industry Waste Treatment FURTHER INFORMATION: W. Dennis Threadgill, Chairman Chemical Engineering Department Box 1821, Station B, Vanderbilt University Nashville, Tennessee 37235 284 CHEMICAL ENGINEERING :IIDUCATION

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UNIVERSITY OF WASHINGTON Department of Chemical Engineering BF 10, Seattle, Washington 98195 GRADUATE STUDY BROCHURE AVAILABLE ON REQUEST WASHINGTON UNIVERSITY ST LOUIS, MISSOURI GRADUATE STUDY IN CHEMICAL ENGINEERING Washington University is located on a park like campus at the St. Louis City limit Its location offers the cultural and recreational opportunities of a major metropolitan area combined with the convenience of a Univers i ty surrounded by pleasant residential areas with many apartment houses where single and married graduate students can obtain housing at reasonable rates The Department of Chemical Engineering occupies a modern building with well-equipped laboratory facilities for research in a large variety of areas. There i s close interaction with the research and engineering staffs of major St. Louis chemical companies and also ex tensive collaboration with the faculty of the Washington University School of Medicine in the biomed i cal engineering research activities PRINCIPAL RESEARCH AREAS Biomedical Engineering Process Dynamics and Control Chemical Reaction Engineering Reinforced Plastics Computer Aided Process Engineering Modeling and Simulation Rheology Thermodynamics Polymer Science Transport Phenomena For application forms, a catalog, and a brochure which describes faculty research interests, research projects and financial aid write to: FALL 1979 Dr R. L. Motard, Chairman Department of Chemical Engineering Washington University St. Louis, Missouri 63130 285

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I I I l 286 AIR POLLUTION: ENERGY: TRANSPORT PHENOMENA: WASHINGTON STATE UNIVERSITY Graduate Study in Chemical Engineering M.S. and Ph.D. Programs Submicron Particulate Collection/High Temperature Catalysis/ Global Monitor ing & Meteorological Interaction/Atmospheric Chemistry & Trace Analyses/ Odor Perception/Phytotoxicity Combustion & NOx, SOx Control/Coal Minerals Recovery/ Petrochemical Substitutes From Coal/Process Development & Design Laser-Doppler Velocimetry /Single& Multi-Phase Flow & Heat Transfer/ Foam Flow NUCLEAR ENGINEERING: Radioactive Waste Management/Fuels Reprocessing/LMFBR Technology / Radiocarbon Dating/Neutron Activation Analyses POLYMER ENGINEERING: Electroiniated Polymerization/Polymeric Encapsulation BIOMEDICAL ENGINEERING: Biorheology BIOCHEMICAL ENGINEERING: Fermentation Kinetics Several Fellowships, Assistantships and Full-time Summer Appointments Available Contact: Chairman, Department of Chemical Engineering, Washington State University, Pullman, Wa. 99164/Tel. 509-335-4332. WAYNE STATE UNIVERSITY GRADUATE STUDY in CHEMICAL ENGINEERING D. A. Crowl, PhD combustion-process control H. G. Donnelly, PhD thermodynamics-process design E. R. Fisher, PhD kinetics-molecular lasers J. Jome, PhD electrochemical engr.-fuel cells R. H. Kummler, PhD environmental engr.-kinetics C. B. Leffert, PhD energy conversion-heat transfer R. Marriott, PhD computer applications-nuclear engr. J. H. McMicking, PhD process dynamics mass transfer R Mickelson, PhD polymer science-combustion processes P. K. Roi, PhD molecular beams-vacuum science E. W. Rothe, PhD molecular beams-analysis of experiments S. K Stynes, PhD multi-phase flows-environmental engr. E. Gulari, PhD transport-laser light scattering FOR FURTHER INFORMATION on admission and financial aid contact: Dr. Ralph H. Kummler Chairman, Department of Chemical Engineering Wayne State University Detroit, Michigan 48202 CHEMICAL ENGINEERING EDUCATION

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Graduate Studies CHEMICAL AND BIOCHEMICAL ENGINEERING THE UNIVERSITY OF WESTERN ONTARIO LONDON, ONTARIO, CANADA The Chemical and B i ochem i ca l G r oup offers M E.Sc ., M.Eng ., and Ph D. degrees for Eng i neer i ng and Science graduates Graduate ass i stantsh i ps (teaching and / or research) are available for highly qualified candidates who wish to pursue studies toward the M E.Sc., and Ph.D deg r ees i n Engineering. The minimum stipend for outstanding candidates is $7 500 per annum. The Department A medium sized Chemical and Biochemical Engineering Department with 10 professors 6 post doctoral fellows, 9 Ph.D students, 18 M.E Sc students, 6 M.Eng students and 95 undergraduates Well equipped laboratories with excellent computing and machine shop facilities are available. Areas of Research Areas of research in Chemical Eng i neering include : fluidization and particulate studies environmental studies air and water pollution, catalysis and reactor design systems control engineering, process simulat i on and optimization mass transfer and mixing in reactors, process development studies. Research areas in B i ochemical Engineering include: food engineering new products development, food perservation, pro tein production, microbial process and product development, microbial surfactants for oil extraction enzyme engineering, bio energy product i on, microbial kinetics bacterial aerosol studies, bioleaching of minerals, extracellular protein production enzymatic hydrolysis of cellulose, novel b i oreactor design industrial waste utilization and wastewater treatment, design of wastewater treatment facilities, etc Applications and Enquiries-For more information write to: FALL 1979 Dr. N. Kosaric, Chairman Chemical and Biochemical Engineering The University of Western Ontario London, Ontario, Canada Telephone: (519) 679-3309 287

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IIIPI WORCESTER POLYTECHNIC INSTITUTE "The Innovative School" The WPI Chemical Engineering Department enjoys an excellent reputation for its research under the direction of ten full time faculty members in: ADSORPTION DIFFUSION CATALYSIS MOLECULAR SIEVES BIOCHEMICAL ENGINEERING ENERGY CONVERSION GAS SOLID REACTION Extensive technical and cultural opportunities within the ten-college Worcester Consortium for Higher Education and the facilities of a medium sized city in Central Massachusetts. Attractive assistantships available. Address inquiries to: Dr. Y. H. Ma, Chairman Chemical Engineering Department Worcester Polytechnic Institute Worcester, Massachusetts 01609 UNIVERSITY OF WYOMING Take a moment and write for more information. We offer exciting opportunities for research in many ENERGY related areas, such as coal and oil shale. We also offer research relating to ENVIRONMENT such as in situ processes and water resources. These and many other opportunities are avai I able to those with ENERGY who wish to work in a pleasant ENVIRONMENT both academically and geographically Dr. D. L. Stinson Mineral Engineering Department University of Wyoming P.O. Box 3295 University Station Laramie, Wyoming 82071 Admission, employment, and programs of the University of Wyoming are offered to all eligible people without regard to race, color, national origin, sex, religion, or political belief. 288 Financial aid is available, and all aid recipients obtain full fee waivers. CHEMICAL ENGINEERING EDUCATION

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DUC LL BUCKNELL UNIVERSITY Department of Chemical Engineering MS R. E. Slonaker, Jr C hair man ( Ph .D., I o wa S t ate) Grow t h and p ro p e rti es o f single c r ys t a l s hig h t e mp e r a tur e c a lo r imet r y v ap o r li qu i d e quili bria in te rn a r y sys t e m s M E Hanyak Jr ( P h D ., U nive r s i ty of Pen n s yl vania) Co mput e r a i d e d desi g n and i n s tru c ti o n p ro bl em-o r ien t ed lan g u a g es n um e ri ca l ana l ysis F W Koko, Jr. ( Ph D ., Lehi gh Unive r sity) O p timization a l gori thm s fluid mec h anics and rheo l ogy di r ect digital c o ntrol. IM J M Pommersheim ( Ph D ., Unive r s it y o f Pi tt sb ur gh) Ca t a l ys t deactiva ti o n reac ti o n analysis mat h ematical modeling and di ffu sion with r e acti o n and phase chang e. W J Snyder ( P h D ., Pe n nsylvania S t ate U nive r sity) Ca t alysi s, po l y m e r iza t ion t h e r mal ana l ysis development of specific ion e l ec tr o d es micro p rocesso r s, and instr u mentation w h o h o l d und erg r ad u a t e degrees in one of the natu r al sciences o r math e ma tics s h o u ld contact the de p artment c h ai rm a n re g ar d i n g e l igi b i lit y for gradua t e study F e ll ows hip s and teac h i n g and r esea r c h assis t an t s h i p s a r e a va il a bl e L ew i s b urg l oca t ed in the ce nt e r of Pe n nsy l va n ia pr o vid es th e a ttr ac t io n of a rural se tting w hil e co nv e n ie ntl y l oca t ed wi t h i n 200 mil es o f N ew Y o rk Ph i l a d e lph ia Washing t on D C. and Pittsb u rgh For further information write or phone : Coo r di n a t or of G r ad u at e Studie s Bu cknell U niversity Lewis burg PA 17837 '---------7 1 7 52 4 1 30 4 ______ __, FALL 1979 L a ke Huro n Canada's largest Chemical Engineering De partment offers regular and co-operative M.A.Sc., Ph.D. and post-doctoral programs in: Biochemical and Food Engineering Chemical Kinetics, Catalysis and Reactor Design Environmental and Pollution Control Extractive and Process Metallurgy Polymer Science and Engineering Mathematical Analysis Statistics and Control Transport Phenomena, Multiphase Flow, Petroleum Recovery Electrochemical Processes, Solids Handling, Microwave Heating Financial Aid: M i nimum $8 500 per annum Academic Staff: E Rhodes Ph.D (Manchester) Chair man ; T Z. Fah i dy Ph.D (Illino i s) Associate Chairman, (Graduate) ; G S Muelle r, Ph.D (Manchester) Associ a t e Cha i rman (Undergraduate) ; T L. Ba t ke, Ph.D. (To ronto) ; L. E Bodnar Ph D. (McMaster); C. M. Burns, Ph D (Polytech. Inst Brooklyn ); J J Byerley, Ph.D (UBC) ; K. S Chang Ph D (Northwestern) ; F. A. L Dullien, Ph.D (UBC ); K E Enns Ph D (Toronto) ; J D. Ford, Ph D (Toronto) ; C E Gall, Ph D. (Minn ) ; R. Y. M. Huang Ph D (Toronto) ; R. R Hudgins Ph.D. (Prince ton); I. F. Macdonald Ph.D (Wisconsin) ; M Moo-Young, Ph D (London) ; K F. O Driscoll Ph D (Prince t on) ; D. C. T Pe i, Ph D ., (McGill) ; P M Re i lly, Ph D. (London); G L. Rempel Ph D ( UBC) ; C W. Robinson, Ph D. (Berkeley ); A. Rud i n, Ph D. (Northwestern); J M. Scharer Ph.D. (Pennsylvania) ; D S Scott, Ph.D. (Illinois); P L. Silveston, Dr. Ing. (Munich) ; D R. Spink Ph.D (Iowa Sta t e) ; G. A. Turner, Ph.D (Manchester); B M. E. van der Hoff I r. (Delft); J. R. Wynnyckj Ph.D. (Toronto) To apply, contact : The Associate Chairman (Graduate Studies) Department of Chemical Engineering University of Waterloo Waterloo, Ontario Canada N2l 3G1 Further information: See CEE, p 4 Winter 1975 289

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BRIGHAM YOUNG UNIVERSITY Ph.D., M.S. & M.E. RESEARCH EMPHASIS Biomedical Engineering Fluid Mechanics Catalysis Fossil Fuels Recovery Coal Gasification High Pressure Chem. Combustion Thermochemistry If you are interested in a small, high quality, research active, ChE department (l l dedicated Faculty & 35 funloving graduate students), a beautiful campus in the rugged Rocky Mountains, and a uniquely friendly campus in which students adhere to high moral standards, contact Professor Richard W. Hanks Department of Chem. Engr. 350F CB Brigham Young University Provo, Utah 84602 FINANCIAL AID AVAILABLE THE UNIVERSITY OF IOWA Iowa City M.S. Ph.D. Research in Flow through microporous media Separations using permeation through membranes Mass transfer operations Characterization of particulate materials Materials science Materials processing Plasticity Fracture mechanics 290 Write: Chairman Chemical and Materials Engineering University of Iowa Iowa City, Iowa 52242 THE UNIVERSITY OF BRITISH COLUMBIA GRADUATE STUDIES IN CHEMICAL ENGINEERING The Department of Chemical Engineering invites applications for graduate study from candidates who wish to proceed to the M.Eng. M A Sc. or Ph.D degree For the latter two degrees, Assistantsh i ps or Fellowships are available which pay over $7 000 per annum AREAS OF RESEARCH Air Pollution Biochemical Engineering Biomedical Engineering Coal Gasification Electrochemical Engineering Electrokinetic Phenomena Fluid Dynamics Fluidization Heat Transfer Kinetics Liquid Extraction Magnetic Effects Mass Transfer Modelling and Optimization Particle Dynamics Process Dynamics Pulp & Paper Rheology Rotary Kilns Separat i on Processes Spouted Bed s Sulphur Thermodynamics Water Pollution Enquiries should be addressed to: Dr. Richard M R. Branion Graduate Advisor Department of Chemical Engineering THE UNIVERSITY OF BRITISH COLUMBIA Vancouver B C V6T 1W5 MONASH UNIVERSITY CLAYTON, VICTORIA Department of Chemical Engineering Applications are invited for Monash University Research Scholar ships tenable in the Department of Chemical Eng i neering The awards are i ntended to enab l e scholars to car ry ou t under supervision a programme of full-time advanced s tudies and research which may lead to the degrees of Master of Engineer ing Science and/or Doctor of Philosophy Facilities are available for work in the general field s of: Biochemical and Food Engineering Chemical Reactor Engineering Extractive Metallurgy and Mineral Engineering Process Dynamics, Control and Optimization Polymer Processing and Rheology Transport Phenomena Waste Treatment and Water Purification Hydrogen and Drying of Brown Coal Scholarships carry a stipend of $4 200 per annum. Detailed information about the awards and the necessary application forms may be obtained from the Academic Registrar Technical enquiries should be addressed to the Chairman of Department, Professor O E. Potter Postal Address: Monash University Wellington Road Clayton, 3168 Victoria, Australia CHEMICAL ENGINEERING EDUCATION

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MONT ANA ST A TE Degrees earned, 1970-78 M.S 58 Ph.D. 23 Current Projects: Clean Distillate Fuels from Coal Coal Liquefaction Extractive Distillation Extractive Crystallization Fluidized Bed Heat Transfer NO x Abatement Pumping Properites of Coal Slurries Separations with Membranes Food Processing \ Parametric Pumping Hydrometallurgy 1 Column Flotation Department of Chemical Engineering Montana State University Bozeman, MT 59717 NEW JERSEY INSTITUTE OF TECHNOLOGY NEWARK COLLEGE OF ENGINEERING GRADUATE STUDY FOR M.S., ENGINEER AND Sc.D. DEGREES IN CHEMICAL ENGINEERING Biomedical Engineering Basic Studies-Chemical Engineering Biochemical Engineering Environmental Engineering Basic Studies-Applied Chemistry Polymer Science and Engineering Process and Design Studies For details on applications and financial aid, write: FALL 1979 Dean Alex Bedrosian Graduate Division New Jersey Institute of Technology 323 High Street Newark, New Jersey 07102 ECOLE POL '(TECHNIQUE AFFILIEE A L'UNIVERSITE DE MONTREAL GRADUATE STUDY IN CHEMICAL ENGINEERING Research assistantships are available in the following areas: POLYMER ENGINEERING RHEOLOGY RECYCLING OF WASTE MATERIALS FLUIDISATION REACTION KINETICS PROCESS CONTROL AND SIMULATION INDUSTRIAL POLLUTION CONTROL BIOCHEMICAL AND FOOD ENGINEERING PROFITEZ DE CEITE OCCASION POUR PARFAIRE VOS CONNAISSANCES DU FRANCAISI VIVE LA DIFFERENCE!* Some knowledge of the French language is required. For information, write to: M. R. C. Mayer, prepose a !'admission, Departement du Genie Chimique, Ecole Polytechnique C.P. 6079, Station A Montreal H3C 3A7, CANADA UNIVERSITY OF NORTH DAKOTA Graduate Study in Chemical Engineering PROGRAM OF STUDY: Thesis and non-Thesis programs leading to the M.S. degree are available. A full-time student can com plete the program in a calender year. Research and Teaching assistantships are available. LIGNITE LIQUEFACTION PROJECT: UND's Chemical Engineer ing Department is engaged in a major research program under the U.S. Department of Energy on conversion of lig nite coal to upgraded energy products Students may partici pate in project-related thesis problems, or be employed as project workers while taking course work in the department. ERDA: The Department of Chemical Engineering and the Grand Forks Energy Technology Center offer a cooperative program of study related to coal technology. Course work is taken at the University and thesis research performed at the Center under DOE staff members. Fellowships are available to U.S. citizens. FOR INFORMATION WRITE TO: Dr. Thomas C. Owens, Chairman Chemical Engineering Department University of North Dakota Grand Forks, North Dakota 58201 291

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University of Rhode Island Graduate Study Chemical Engineering MS, PhD AREAS OF RESEARCH Adsorption Biochemical Engineering Catalysis Corrosion Desalination Dispersion Processes Distillation Fluid Dynamics Heat Transfer Kinetics Liquid Extraction Mass Transfer Materials Engineering APPLICATIONS Membrane Diffusion Metal Finishing Metal Oxidation Metallurgy Modeling and Optimizatior. Nuclear Technology Phase Equilibria Two Phase Flow Process Dynamics Thermodynamics Water Resources X-ray Metallography Apply to the Chairman, Dept. of Chemical Engineer ing, University of Rhode Island, Kingston, Rhode Island 02881. Applications for financial aid should be received not later than February 15. Appointments will be made about April. UNIVERSITY OF UTAH ENERGY RESEARCH This is a small ad, directed at people who under stand that bigger isn't necessarily better. The Uni versity of Utah has a small chemical engineering department (11 faculty members), where the empha sis is on quality, not quantity. Our state is a major source of coal, oil, gas, and uranium and will be a source of oil shale and tar sands. Active research is being conducted in our department in coal, oil-shale, and tar-sand extrac tion, utilization, and environmental control tech nology. If you are interested in a small, high-quality chemical engineering department with a variety of research interests and a strong and growing energy research area, located in one of the world's most pleasant cities, write for more information to: 292 Professor Noel de Nevers Director of Graduate Admissions Department of Chemical Engineering University of Utah Salt Lake City, Utah 84112 CHEMICAL ENGINEERING AT TEXAS TECH Join a rapidly accelerating department (research funding has increased an average of 26% per year for the last three years) Graduate research projects available inBIOMASS UTILIZATION PROCESS ENGINEERING POLYMER SCIENCE & TECHNOLOGY ENVIRONMENTAL CONTROL ENERGY COMPLEX FLUID FLOWS Texas Tech Chemical Engineering graduates are among the most sought-after by industry in the country. Be one of them! For information, brochure and application mate rials, write Dr R. W. Tock Graduate Advisor Department of Chemical Engineering Texas Tech University Lubbock, Texas 79409 UNIVERSITY OF VIRGINIA CHEMICAL ENGINEERING GRADUATE STUDIES M S., and Ph.D. Programs in Chemical Engineer ing. Chemical Engineering with a Biomedical /Biochemical Minor is available. RESEARCH INTERESTS : Mass transfer phenomena, surface chemistry, fluid mechanics and rheology, fluidiza tion, parameter estimation, process dy namics and control, solar energy conversion, crys tallization, air pollution control, fermentation proc esses, immobilized biomolecules, biological mass transfer and disease, and modeling of biological processes. FOR ADMISSION AND FINANCIAL AID INFORMATION Graduate Coordinator Department of Chemical Engineering University of Virginia Charlottesville, Virginia 22901 CHEMICAL ENGINEERING EDUCATION

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TO DEPARTMENT CHAIRMEN: Chemical Engineering at YALE The staff of CHEMICAL ENGINEERING EDUCA TION wishes to thank the 109 departments whose adve r tisements appear in this eleventh graduate issue W e also appreciate the excellent response you gave to our request for names of prospective authors. We regret that, because of space limitations, we were not able to include some outstanding papers and that certain areas are not represented In part our selection of papers was based on a desire to comple ment this issue with those of the previous years. As indicated in our letter we are sending automatically to each department for distribution to seniors inter ested in graduate school at least sufficient free copies of this issue for 20 % of the number of bachelor's degrees reported in "ChE Faculties." Because there was a large response to our offer in that letter to s upply copies above this basic allocation we were not able to fully honor all such reauests. However, if you have definite need for more copies than you re ceived, we may be able to furnish these if you write us We also still have some copies of previous Fall issues available. J. W. Gibbs PhD-Engrg. 1863 1983 You? PhD-Engrg. We would like to thank the departments not only for their support of CEE through advertising, but also throu g h bulk subscriptions. We hope that you will be a bl e to continue or increase your support next year. Ray Fahien Editor Specific factual knowledge starts today ... for solutions to tomorrow's engineering problems Process Fluid Mechanics Mor t on M. D enn, University of D e l aware Process Fluid Mechanic s pro vi d es an or d er l y tr ea t ment of th e esse nt ia l s of b o th th e m acro a nd mic ro p r o bl ems of flu i d mec h a n ics. It presen t s a l ogica l ap p roac h t o th e so lut io n of macrosco p ic b a l a n ce eq u ti ons. Pro bl e m s a nd a ppl ica t io n s d ea l w ith real en g in eer in g si tu a t io n s. 1980 464 pp. Est. $22. 95 Reaction Kinetics and Reactor Design John B Buff, Northwe s tern Univer s ity T h is b ook provides a b a l anced int ro du ction to c h emical reac ti o n kinetics in h omogeneo u s ph ases, b o th descriptive a nd th eore ti cal. I t a l so covers th e a n a l ysis a nd design of i d ea l a nd nonide a l c h emical reac t o r sys tem s, a nd th e ki n e t ics of c hem ica l reac t io n s in more th a n o n e p h ase The emp h asis th ro u g h o u t i s on analysis, n o t c h ar t d erived calcu l a t ions 1 98 0 464pp Est. $21 95 Prentice-Hall Deformation and Fracture of Solids Rober t Caddell, Universi t y of Michigan This b ook b r i dges th e ga p b tween th e tra dit io n a l a ppli e d mec h a n ics ap p roac h a nd th e m ore h eav il y e m p h asiz ed ma t eria l s ap p roac h. E xa m p l e pro bl ems are i nt erwov en th ro u g h ou t. 198 0 30 4pp. Est. $ 24. 95 For more i n for m atio n or t o _reserve examination copies of any of th ese t exts p l ease write: R o b e r t Jordan, P r en t1 ce -H a ll In c., Dept J -140, Eng l ewood Cliffs, N J. 07632

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PROCTER & GAMBLE is looking for in R&D / Product Development This organization is responsible for the creation and improvement of new and existing products, together with developing the associated technology advances and solving technical problems While this organization encompasses the full range of scientific and engineering backgrounds, the primary need at the BS/MS level is for Chemical Engineers and MBAs with a chemical or engineering undergraduate degree Your initial responsibilities in the organization would be primarily technical, with varying degrees of interactions with P&G's Engineering, Manufacturing and Marketing divisions As you advance, your career could evolve along technical and/ or management routes This evolution will include progressive assignments exposure to other divisions and in many cases a transfer to another R&D/Product Development division, or where appropriate to an Engineering Manufacturing or Marketing division The R&D/Product Development organization is headquartered in Cincinnati, consists of over 20 divisions, focuses on U.S. consumer and industrial products, conducts P&G's basic research, and provides technical support for our international operations and technical centers (This technical support includes international travel by certain of our U S .based division personnel.) RESPONSIBILITY NOW! If you are Interested In this area please send a resume to: The Procter & Gamble Company R&D BS/ MS Recruiting Coordination Office lvorydale Technical Center Spring Grove and June Avenues Cincinnati, Ohio 45217 PROCTER & GAMBLE AN EQUAi. OPPORTUNITY EMPLOY E R