Chemical engineering education ( Journal Site )

Material Information

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


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


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

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
oclc - 01151209
lccn - 70013732
issn - 0009-2479
sobekcm - AA00000383_00026
lcc - TP165 .C18
ddc - 660/.2/071
System ID:

Full Text


Excellent Text
that can be warmly recommended as an introduction to balances, for it
takes proper account of the nature of the subject -and at the same time
leads to the use of the proper tools."
-Professor Rutherford Aris
Department of Chemical Engineering
University of Minnesota
By ERNEST J. HENLEY, University of Houston; and
EDWARD M. ROSEN, Monsanto Company, St. Louis, Missouri.
This is the first book to bring material and energy balance into modern
focus. An excellent introduction for one- or two-semester engineering
courses, the book stresses the problem of seeking and applying the physical
and mathematical principles of material and energy techniques. The subject
is approached from two viewpoints-covering the material for the engineer
who will do his work with a slide rule, and for the engineer who will work
with a computer-and the differences between the two approaches are
emphasized. A Volume in the Chemical Engineering Outline Series.
1969 577 pages $14.95

Another important text for electrical engineering students-
all of Oregon State University.
On an introductory level, this textbook presents the traditionally separate fields of
momentum transfer (fluid mechanics), heat transfer, and mass transfer (diffusion)-
all from a unified viewpoint. The similar means of describing the various processes
are stressed; and it is shown how information on one area may be extrapolated to
provide an understanding of the other types of transfer.
1969 Approx. 672 pages $16.50
The only text focusing on the sociology of engineering-
Edited by ROBERT PERRUCCI, Purdue University; and
JOEL GERSTL, Temple University.
The only book of its kind, this text provides a detailed examination of the engineer-
ing profession within the social and historical context of American society. The
authors study the social origins, values, and career patterns of members of the
profession, occasionally contrasting the facts with data from other countries.
1969 344 pages $9.95

605 Third Avenue, New York, N.Y. 10016
In Canada: John Wiley & Sons Canada Ltd.
22 Worcester Roard, Rexdale, Ontario

Department of Chemical Engineering
University of Florida
Gainesville, Florida 32601

Editor: Ray Fahien

Associate Editor: Mack Tyner

Business Manager: R. B. Bennett

Publications Board and Regional
Advertising Representatives:

CENTRAL: James H. Weber
Chairman of Publication Board
University of Nebraska
Lincoln, Nebraska 68508
WEST: William H. Corcoran
California Institute of Technology
Pasadena, California 91109
SOUTH: Charles Littlejohn
Clemson University
Clemson, South Carolina 29631
University of Houston
Houston, Texas 77004
EAST: Robert Matteson
College Relations
Sun Oil Company
Philadelphia, Pennsylvania 19100
E. P. Bartkus
Secretary's Department
E. I. du Pont de Nemours
Wilmington, Delaware 19898
Peter Le'derman
Brooklyn Polytechnic Institute
Brooklyn, New York 11201
NORTHEAST: George D. Keeffe
Newark College of Engineering
Newark, New Jersey, 07102
NORTH: J. J. Martin
University of Michigan
Ann Arbor, Michigan 48104
NORTHWEST: R. W. Moulton
University of Washington
Seattle, Washington 98105
MIDWEST: Richard S. Mayer
Ohio University
Athens, Ohio 45701
J. A. Bergantz
State University of New York
Buffalo, New York 14200
D. R. Coughanowr
Drexel University
Philadelphia, Pennsylvania

Chemical Engineering Education

Articles on Graduate Courses

174 Applied Mathematics N. R. Amundson
178 Energy Transport S. W. Churchill
184 Momentum Transport T. J. Hanratty
190 Particulate Systems H. M. Hulburt
194 Mass Transport E. N. Lightfoot
200 Optimal Control Leon Lapidus
204 Molecular Thermodynamics J. M. Prausnitz
212 Classical Thermodynamics J. J. Martin
218 Chemical Reaction Engineering
Dougharty, N.A., & Smith, J. M.


163 Editorial

165 Division Activities
James H. Weber

167 Letters

168 A Founder of the Profession
Allan P. Colburn remembered by Olaf Hougen
173 Biographical sketch.

222 Views and Opinions
Graduate Engineering and Technological
Accreditation, L. E. Grinter

228 The Curriculum
The Chemistry-Chemical Engineering
Merry-Go-Round, R. A. Morgen

199 Book Review
Boudart: Kinetics of Chemical Processes
by J. R. Butt

216 Problems for Teachers

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 DeLand, Florida. Correspondence
regarding editorial matter, circulation and changes of address should b- addressed
to the Editor at Gainesville, Florida 32601. 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., 137 E. Wisconsin
Ave., DeLand, Florida 32720. Subscription rate U.S., Canada, and Mexico is $10 per
year to non-members of the ChE division of ASEE, $6 per year mailed to members,
and $4 per year to ChE faculty in bulk mailing. Individual copies of Vol. 2 and 3
are $3 each. Copyright () 1969, ChE Division of ASEE, Ray Fahien, Editor. 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.

FALL 1969


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Should you go to graduate school?
Through this special issue on graduate educa-
tion, Chemical Engineering Education invites you
to consider graduate school as an opportunity to
further your professional development. We be-
lieve that you will find that graduate work is an
exciting and intellectually satisfying experience
that greatly enhances your ability to obtain re-
sponsible and challenging positions in industry
and teaching. We also feel that graduate study
can provide you with insurance against the
increasing danger of technical obsolescence.
Furthermore, we believe that graduate research
work under the guidance of an inspiring and
interested faculty member will be important in
your growth toward confidence, independence, and
What is taught in graduate school?
In order to familiarize you with the content of
some of the areas of graduate chemical engineer-
ing we are including in this issue articles describ-
ing graduate courses that have been taught by
professors who have specialized in these fields.
In doing so we wish to make clear the following:
1) that there is some variation in the content of
individual graduate courses in the same area as
taught at various schools (e.g., many schools
teach transport phenomena sequences, while
others teach individual courses in fluid mechanics,
heat transfer, and mass transfer), 2) that we
have not included all of the areas in which grad-
uate courses are taught (e.g., we have not in-
cluded a design course, per se), and 3) that the
professors who have written articles for us are
by no means the only authorities in those fields,
nor are their departments the only departments
which emphasize that particular area of study.
What is chemical engineering research?
We are dedicating this graduate education issue
to an outstanding chemical engineering researcher
and teacher: the late Allan P. Colburn. Although
Dr. Colburn's career included work in education,
industry, and government, he is best known
among educators for his pioneering research in
many areas of chemical engineering. This re-
search, while based on fundamentals, was directed
toward the ultimate attainment of an engineer-
ing answer, usually in the form of the many Col-

burn equations or correlations that are still used
by practicing engineers. As an example of some-
one to emulate in your own graduate career, we
urge you to read the article by Professor Olaf
Hougen on Allan Colburn's activities as a grad-
uate student. (Incidentally Professor Olaf Hougen
was himself featured by CEE (Summer 1968)
and is also worthy of emulation).
Where should you go to graduate school?
It is common for a student to broaden himself
by doing graduate work at an institution other
than the one from which he receives his bachelor's
degree. Fortunately there are many very fine
chemical engineering departments in the United
States, each of which has its own "personality"
with special emphases and distinctive strengths.
For example, in choosing a graduate school you
might first consider which school is most suitable
for your own future plans to teach or go into
industry. Or if you have a specific research pro-
ject in mind, you might want to attend a univer-
sity which emphasizes that area and where a
prominent specialist is a member of the faculty.
On the other hand if you are unsure of your field
of research, you might consider a department
that has a large faculty with widely diversified
interests so as to ensure for yourself a wide
choice of projects. Or you might prefer the atmos-
phere of a department with a small enrollment of
graduate students. In any case, we suggest that
you begin by writing the schools that have pro-
vided information on their graduate programs in
the back of this issue. You will probably also wish
to seek advice from members of the faculty at
your own school.
But wherever you decide to go, we hope that
you make the decision to continue your education
in graduate school.


Chemical Engineering Education
University of Florida
Gainesville, Florida 32601
ies of this Graduate Education Issue are available at no
charge (while supply lasts) to your seniors who are in-
terested in graduate work. Please write the Editor at the
above address, stating the number of copies needed.

FALL 1969

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Fellow Division Members:

Chemical Engineering Education is completing
its second year with its new format. Under the
able Editorship of Ray Fahien-assisted by his
colleagues Bob Bennett and Mack Tyner-CEE
has drawn praise from chemical engineers in in-
dustry, teaching and government. We of the
Publication Board believe we have a good thing
going and feel a strong obligation to continue to
seek the necessary financial support.
The financial support for CEE has come chiefly
from two sources-industrial concerns and the
departments of chemical engineering. A grant
from NSF (to the Summer School) helped us
during our first year. Our financing method ap-
pears sound; we have balanced our budget. Never-
the less, we have to abolish free subscriptions to
CEE members. Cost is one reason, another is
duplication-most Division members are also
faculty members. Furthermore, our present sys-
tem of sending each department 10 copies regard-
less of size, has meant that in the large depart-
ments some faculty members seldom saw the
journal, while some small departments received
an over-supply.
Consequently, the Publication Board recom-
mended, and your Executive Committee approved
the following plans for CEE distribution:
1. Chemical Engineering Departments will be
asked to request a definite number of copies at
$4/year for each of the four issues in 1970, with
a minimum contribution of $25/year. (They may
pay for these through departmental funds or
faculty contributions or both.)
2. ASEE-Chemical Engineering Division mem-
bers may request (on the attached form) indi-
vidually addressed copies to any address and pay
$6/year starting in January 1970.
3. Libraries and other subscribers that are not
members of the Chemical Engineering Division
of ASEE may subscribe as before at $10/year.
As a matter of interest, we are attempting to
make arrangements with ASEE to have our sub-
scription fee collected with the annual dues. This
may be in effect in June 1970 for payment of 1971
subscriptions. Again, this applies only to those
desiring individual subscriptions.

Jim Weber is Regents' Professor and Chairman of the
Department at the University of Nebraska. He has been
at Nebraska since 1948 when he received the PhD from
the University of Pittsburgh. Jim is the author or co-
author of fifty articles and serves as an industrial con-
sultant. Besides ASEE, he is a member of AIChE., ACS,
and AAAS, and a registered professional engineer.

We wish to continue to give you a first rate
publication and thank you for past support. We
hope for your continued support and that you
appreciate the need for this change.
Very truly yours,
James H. Weber
Chairman, Publications Board

R. Br. Bennett, Bus. Mgr. CEE
Department of Chemical Engineering
University of Florida
Gainesville, Florida 32601
Please send our department copies of
CEE during 1970 at $4/year each (Minimum $25/
[ Payment enclosed D Please send invoice

Please find my check (made out to
for my 1970 subscription to CEE. I (am, am not)
a member of the ChE Division, ASEE.

FALL 1969





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from our READERS
Lynn responds to Fredrickson
Sir: Dr. A. G. Fredrickson's essay "The Dilemma of
Innovating Societies" (CEE, Summer 1969) points out a
number of the problems facing our society today. The
effects of increasing pollution, exploiting wilderness areas,
and a rapidly expanding population are steadily making
the world a less pleasant place to live. It was therefore
a disappointment to see Dr. Fredrickson weaken the
strength of his message substantially by overstating it in
an emotional tirade against straw villains of his own
It is, for instance, unconvincing to denounce the effects
of man's activities on our environment by proclaiming a
higher-than-human set of values. There is no reason to
think that nature prefers alligators to algae, condors to
crickets, or any of these to mankind. Such preferences
are human value judgments and should be defended as
such. The holier-than-thou stance only beclouds the issue.
If Dr. Fredrickson really questions the relative happi-
ness of today's farmer astride his air-polluting tractor I
would suggest that he try spending a summer of 12-hour
days plowing behind a mule. A good look at Van Gogh's
"The Potato Eaters" might also be instructive. The issue
clearly is not one of slowing down technological innova-
tion but rather of directing innovative efforts to the solu-
tion of the problems that are now becoming pressing.
It may be that society should have foreseen the urgency
of these problems one or two generations ago. However,
one should remember that 20-20 hindsight is a common
virtue and also that no amount of castigation will change
the events of the past. Emotional polemics directed
against over-simplified whipping boys are highly favored
today by political extremists of the left and the right,

super-conservationists, gung-ho developers, and many
others with a Cause. The trouble with such tactics is that
they alienate those whose support might be won by a
rational approach.
If the need to solve the problems arising from the
growth of population and technology is real, and I believe
that it is, then well reasoned arguments to this effect
can surely be found. It is clear that we have or can
develop the technology to solve these problems if we
can get general agreement within our society that they
need to be solved. Attaining such agreement will require
persuasive leadership, factual knowledge, and consider-
able persistence. I submit that very few will be persuaded
by being told that they are simpleminded votaries of the
Cult of the Product, believers of the Creed of Technology,
and preachers of the Gospel of Growth.
Scott Lynn
University of California, Berkeley
Corrections from Lee
Sir: Enclosed please find a corrected copy of the short
article entitled Transport Phenomena: Equations of
Change, which was printed in the summer, 1969 issue of
CEE. Please note that equations 7, 9, 11, 15, 16, 17, 19, 20
are corrected, where originally either a small p (for
pressure) is missing or is mixed up with p (for density).
V. J. Lee
University of Missouri
Editors Note: CEE regrets that Professor Lee did not
correct this error on the galleys he received.
Praise from the Veep
Sir: I certainly appreciate receiving the copy of Chemi-
cal Engineering Education and was particularly interested
in seeing the articles involving Stu Churchill.
A. L. Conn
Vice-President, AIChE
(Letters Continued on page 207)

FALL 1969


N founder

In this issue, CEE begins a new depart-
ment that will feature some of the found-
ers of our chemical engineering profession.
This article deals with the graduate (and
earlier) university career of Allan P. Col-
burn, who has been described by Professor
Olaf Hougen of the University of Wiscon-
sin as "one of the most inspiring friendly
and intellectual teachers and leaders in
chemical engineering." The article is writ-
ten by Professor Hougen, who was his
Ph.D. advisor.


OLAF A. HOUGEN, Professor Emeritus
University of Wisconsin
Madison, Wisconsin 53706

ALLAN PHILIP COLBURN was my first stu-
dent in graduate research directed towards a
doctorate degree in chemical engineering.
Allan was born in Madison, Wisconsin, on June
8, 1904. His father, Willis P. Colburn*, at that
time, after twelve years of high school teaching,
was enrolled as a student in philosophy at the
University of Wisconsin. Upon graduation in 1905
Willis accepted a position as principal of the high
school in Rhinelander, Wisconsin. It was here that
Allan spent his childhood and received his ele-
mentary and high school education. In June 1922
the Colburn family moved to Wauwatosa, a subur-
ban city adjoining Milwaukee, where Willis was
employed as principal of a local high school.
In June 1922 Willis Colburn came with his son

*The records of Platteville Normal School (now Wis-
consin State University-Platteville) show that Willis
Paul Colburn, a resident of Grant County, Wisconsin,
attended Platteville Normal School in three school years
1886-87 and 1889-91 receiving a diploma in 1891. After
graduation he served as high school principal at Potosi,
Cassville and Viroqua, Wisconsin. He married Jennie
Grimm of Cassville. In 1903 he attended the University
of Wisconsin in Madison as a student in philosophy re-
ceiving a bachelor of philosophy degree (BPh) in June
1905. In later life he returned for graduate courses in
Education in 1914 and in the summer session of 1929.
**This sketch was prepared for the dedication cere-
monies of the Allan Philip Colburn Chemical Engineering
Building at the University of Delaware, Sept. 20, 1968.

Allan to my office to consider enrolling him in
the College of Engineering of Marquette Uni-
versity in Milwaukee for a period of two years
prior to enrollment in chemical engineering at the
University of Wisconsin. [The chemical engineer-
ing building was then located on the south shore
of Lake Mendota at the foot of Park Street.] From
Allan's superior high school record and his un-
usual intelligence, I readily agreed that this plan
had much merit not only in the economy of living
at home but also in the cultural advantages asso-
ciated with a sectarian school of high repute. At
Marquette University Allan received undergrad-
uate instruction in general chemistry, mathema-
tics, physics, English, shopwork and surveying.
Imagine! Surveying was a required course in
many curricula of chemical engineering 44 years
ago. On September 12, 1924 Allan enrolled as a
Junior at the University of Wisconsin. I served
as his adviser in his junior year; and Professor
Otto L. Kowalke in his senior year.
The period 1920 to 1930 was critical and transi-
tional in the development of chemical engineering
education. The year 1923 marks the beginning of
the American system of education in chemical
engineering with the publication of the text,
"Principles of Chemical Engineering" by William
H. Walker, Warren K. Lewis, and William H. Mc-
Adams. At Wisconsin the curriculum was at that
time predominant in conventional engineering
courses with instruction in chemical engineering
slowly emerging from descriptive courses in in-
dustrial chemistry supplemented by laboratory
experiments largely empirical in nature.


A humanitarian goal in life was manifest in his selection
rounded citizenship.

-professional level not only towards advanced
studies and research leading to the doctorate
degree but also in seeking a career of high pro-
fessional and civic responsibility. A humanitarian
goal in life was manifest in his selection of liberal
elective courses essential for a well rounded citi-
zenship. In this selection Allan was guided by his
father whose own major college studies had been
in philosophy and by Professor Kowalke. In lib-
eral courses he was fortunate in choosing five of
the most popular and inspirational professors at
Wisconsin, namely, William H. Kiekhofer in Eco-
nomics, Louis Kahlenberg in the History of Chem-
istry, Max Otto in Philosophy, A. A. Vasiliev in
Hellenistic Civilization, and Daniel W. Mead in
Contracts and Specifications. Mead's course was
essentially one in engineering ethics based upon
Mead's world wide experiences in the construction
of dams and power plants. Professor Kiekhofer
was the campus spark plug of enthusiasm in his
animated lectures on conventional principles of
economics injecting life into an otherwise dull
subject. Professor Max Otto held a similar posi-
tion in philosophy and logic. The course in Hel-
lenistic civilization described the Golden Age of
Greece, the causes of its origin and decline. With
a delightful sense of humor Kahlenberg portrayed
the joys and frustrations of scientific discovery
in the lives of great chemists. These five profes-
sors, combined with parental influence and that
of Professor Kowalke gave Allan an altruistic
outlook on life and in his dedication to highly
ethical and benevolent standards. This served him
well in his later administrative responsibilities
and projects of community welfare. The present
day stress on the importance of liberal courses
in training of engineers was met by Colburn 40
years ago. In his college years, Allan became a
proponent of the Single Tax theory of economist
Henry George. This typified student protest forty
years ago in contrast to the violence of today.
The professional staff of the Chemical Engi-
neering Department in 1924 consisted of Profes-
sors Otto L. Kowalke, Oliver P. Watts and myself.
Courses in industrial chemistry and unit opera-
tions were given by Professor Kowalke, applied
electrochemistry by Watts and a calculation
course, applied thermal chemistry, by myself.
Allan was graduated in June 1926 with a

of liberal elective courses essential for a well

bachelors degree in science (BS) and high honors.
An Engineering Fellowship was awarded him for
continuation in graduate studies and research.
This fellowship was later renewed for two addi-
tional years. At this time a new dormitory system
for men was established at the University of
Wisconsin. Allan was one of the first graduate
students to be appointed as House Fellow. The
responsibilities of this position entailed living
with undergraduate students as counsellor, guide
and friend.
Allan received his MS degree in 1927 and
PhD degree in 1929.
In his graduate years Allan's two closest friends
were Kenneth M. Watson and Louis F. Warrick.
The former became a prominent chemical engi-
neer in his contributions to education and indus-
trial practice and the latter became the young
State Sanitary Engineer of Wisconsin in 1927.
A recent letter from Louis Warrick restores an
intimate insight into Allan's zest for living and
some of the extra curricular activities he enjoyed
during student days.
Before accepting a position with du Pont,
Warrick and Colburn had made enthusiastic plans
to form a partnership as consultants in solving
problems in the abatement of water pollution and
disposal of industrial wastes. Already forty years
ago these two young men were aware of the dire
consequences of water pollution, the irrevocable
evils of which are so strikingly evident today.

T HE RESEARCH PROJECT assigned to Allan
for his doctorate thesis was to obtain experi-
mental data on heat and mass transfer coefficients
in the condensation of water vapor from saturated
air streams in a tubular gas condenser and to
formulate correlations based thereon useful for
design and operation. This project differed from
conventional dehumidification in that it involved
air saturated with water at high temperatures
with great reductions in volumetric and mass flow
rates of the gas-vapor stream during cooling and
The Committee on Condensing and Scrubbing
of the American Gas Association had collected
operating data on tubular gas condensers used for
refining crude coal gas with its high initial con-
tent of water vapor, hydrogen sulfide, ammonia,
cyanogen, naphthalene and tar. These data were

FALL 1969

gathered from commercial plants scattered widely
throughout the United States. Professor Kowalke,
as a member of this committee, assigned to me
the task of trying to calculate and correlate the
overall heat transmission coefficients from these
data in terms of operating variables, physical
properties and gas composition. I was unsuccess-
ful in making any meaningful correlations. In-
deed, correlation in terms of the geographical
location of the plants seemed to be better than
any rational attempt. The decision was made to
establish data from carefully controlled operation
of a laboratory scale tubular condenser using
saturated air-water vapor mixtures under indus-
trial conditions of operation.
In the period 1926-29 few graduate students
were enrolled in chemical engineering at the Uni-
versity of Wisconsin. Prior to 1929 only three
doctorate degrees had been granted. In guiding
research towards a doctorate degree Allan was
the only student assigned to me.
A preliminary study of the condensation of
water vapor from air saturated at high initial
temperatures in a tubular condenser revealed
many complexities. Three fluid stream resistances
were involved, the air-vapor stream, the con-
densate layer and the stream of cooling water,
besides the resistance of the metal barrier. The
heat transfer coefficients of these three streams
were to be established each in terms of its inde-
pendent variables. Because of large variations
along the length of the condenser it was evident
that coefficients of the individual streams should
be determined at short intervals of condenser
length. Calculations of average heat transmission
coefficients of the vapor stream from usual log-
arithmic mean values of temperature drops at
terminal conditions were meaningless, indeed, the
temperature drop at the midsection of the con-
denser was usually greater than at either ter-
minal. In retrospect, considering the primitive
status of scientific information and the com-
plexity of the problem, this investigation would
at that time justify three projects with inde-
pendent approach to each.
A vertical tubular condenser, six feet long, was
constructed of three concentric pipes, 3, 7 and 10
inches nominal diameters, well insulated on the
outer shell. Cooling water flowed through the
inner pipe and saturated air flowed downwards
through the two annular channels; the outer
outer annular space served as a guard ring to-
gether with external insulation to minimize the

Colburn's genius consisted in his extraordinary
capacity for intensive concentration with a mind
unusually well organized for retention and

outward flow of heat. With only $100 available
for mechanical help and additional apparatus over
a span of three years, the equipment and instru-
mentation had to be assembled from supplies
available in the stock room or borrowed from dis-
tressed laboratories, including piping, pumps,
thermocouples, orifice meters and potentiometers.
Allan constructed and calibrated all thermo-
couples and orifice meters. The construction and
location of thermocouples were critical for mean-
ingful measurements. Multijunction couples were
constructed for measuring average temperatures
of the gas stream at each level of cross section.
Single couples were located in isothermal areas to
avoid errors by conduction. A traveling thermo-
couple was constructed and installed for measur-
ing the temperature of the cooling water. Tem-
peratures of the three adjoining fluid streams
and the central pipe wall were measured simul-
taneously at successive short intervals of length.
Under commercial conditions of operation natural
convection predominated in the stream of cooling
water; both laminar flow and turbulence occurred
in the gas stream; the condensate accelerated
from laminar flow to turbulence with rippling at
the bottom of the tube.
of heat transmission coefficients of fluid
streams was in a primitive stage in 1926 when
Colburn began his experimental and theoretical
studies. Most published experiments had been
conducted within the preceding ten years. The
most significant work had been carried out in
Germany. This appeared in the German language
without published translation in English. In the
United States chemical engineers required that
formulations of transfer coefficients be expressed
in terms of molecular properties and operating
variables. Other engineers were still satisfied with
specific values of overall coefficients and physicists
had virtually abandoned the field upon discover-
ing the empirical nature involved. Principles of
heat conduction in solids had been well known for
over a century starting with the mathematical
theory of Fourier in 1822 for the unsteady state.
These formulations were extended in the texts
of Ingersoll and Zobel in 1913 and by Carslaw
and Jaeger in 1921.


Colburn was an ideal student, scientist, and engineer. . he had an unusual capacity for clarity of expression
. . (and promoted) self confidence and ambition in others.

The analogy between mass, heat and momen-
tum transfer in flowing fluids was presented by
Prandtl in 1910 based in part upon pressure drop
formulations of Reynolds in 1874. In England
work was reported in 1916 by Pannel for air flow-
ing through tubes and by Stender in Germany for
water flowing through tubes. A theoretical equa-
tion for the transfer of heat by free convection
in fluids was developed by Lorenz in 1881 and
greatly improved by Nusselt in 1915. Nusselt in
1910 also pioneered in deriving theoretical equa-
tions for the transmission of heat through con-
densate layers flowing over vertical surfaces and
horizontal cylinders.
At the time of Colburn's studies and just prior
thereto five books on general heat transmission
appeared in Germany, namely, by Grober (1921
and 1926), by Merkel (1927), Bosch (1927) and
Schack (1921). These were then without English
translation. The first authoritative book on heat
transmission printed in English and applicable to
general engineering processes was that of Mc-
Adams in 1933 but this book did not appear until
seven years after Colburn started his research.
McAdams' text and researches generated wide
attention to research in heat transmission
throughout the United States and among other
branches of engineering besides chemical.
Allan proceeded at once to read intensively the
German sources relying on his high school in-
struction and his preparation for absolving the
German language requirement of the doctorate
degree. The extraction of complex theoretical
principles from lengthy German dissertations re-
quired exceptional capacity for intensive concen-
tration. Allan studied the original German sources
with intense concentration over long intervals of
time to the point of pain and fatigue. Colburn
had exceptional capacity for retaining the argu-
ments and voluminous observations of previous
investigators with subsequent instant recall. Col-
burn's genius consisted in this extraordinary ca-
pacity for intensive concentration with a mind
unusually well organized for retention and re-
In his graduate years Allan devoted fully half
of his time to theoretical studies and experimenta-
tion related to his thesis over a period of three
years. In his efforts to establish simultaneously
the principles of heat and mass transfer in fluid

streams, condensate layers and water streams
with free convection, Allan suffered many periods
of despair and frustration especially in his efforts
to reconcile his data with the formulations of
others. But he always bounced back with a zest
for scientific discovery and to infuse the same
spirit in others.

FROM HIS BOYHOOD DAYS in the recrea-
tional area of Northern Wisconsin with its
forests and lakes, it was natural for Allan to seek
relaxation from his strenuous intellectual pur-
suits and frustrations in out-of-door sports the
year around, in tennis, canoeing, golf, fishing,
skating, and iceboating.
In connection with recreation his friend Lou
Warrick records a vivid and humorous account of
Allan's discovery of 'hot ice'. In iceboating to-
gether on Lake Mendota their speeding boat
struck rough ice and Allan was projected there-
from at high speed over the rough surface on
the seat of his pants. Upon recovery Allan feel-
ing his posterior exclaimed, "Gee, Lou, this is
the first time I realized that ice can get hot!"
Because of the great tragedy in health which be-
fell Allan a few years later few people were
aware of his early athletic prowess.
Colburn's computational facilities were limited
to the use of the slide rule, to laborious calcula-
tions and plotting by hand. In experimental work
he received some aid from two seniors working
for academic credit, namely Robert E. Zinn and
George F. Hrubesky. Today Allan's monumental
task would be greatly facilitated by electronic
computers with generous financial subsidies for
experimental and computational aid. It should be
recalled again that Allan had only $100 available
for research aid.
In his graduate years Allan restricted his ad-
vanced studies to scientific work related to his
thesis. Liberal reading became extra curricular.
His advanced studies included a course in heat
conduction under Professor Leonard R. Ingersoll,
higher mathematics under Professor R. W. Bab-
cock, and advanced chemistry courses under Pro-
fessors J. Howard Mathews, Farrington Daniels,
and John W. Williams. Allan was also fortunate
in taking courses under two visiting professors,
with the Russian chemist A. M. Frumkin in col-
(Continued on page 193.)

FALL 1969






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A LLAN PHILIP COLBURN was born in Madi-
son, Wisconsin, on June 8, 1904. He grad-
uated from Rhinelander High School and attended
Marquette University for two years before com-
pleting his education at the University of Wiscon-
sin, where he received his bachelor's degree in
chemical engineering in 1926, his master's degree
in 1927 and his doctorate in 1929. From 1929-
1938, he was engaged in chemical engineering
research at the Du Pont Experimental Station in
On May 1, 1938, he became associate professor
of chemical engineering and acting head of the
University of Delaware's Department of Chemical
Engineering. As chairman of the department, he
was responsible for developing a wide research
program in cooperation with industry and govern-
mental agencies. In 1947 he became Assistant to
the President with his chief responsibility that of
assisting in the development of research through-
out the University. Dr. Colburn was Acting Presi-
dent of the University from April 1, 1950, to No-
vember 1950 and, upon the arrival of former
President John A. Perkins, he was appointed
Provost. At the time of his death in 1955 he was
Provost and Coordinator of Scientific Research.
During World War II, Dr. Colburn was instru-
mental in directing the use of the chemical engi-
neering laboratories at the University on solving
war research problems for the National Defense
Research Committee, the National Advisory Com-
mittee for Aeronautics, the Office of Rubber Re-
serve, and for various war industries. He further
assisted in the direction of war research else-
where. With Dr. B. F. Dodge of Yale, he prepared
the curriculum on chemical engineering for the
Army, which was taught in the A.S.T. Program
throughout the war years.
In 1948 he was honored as the first recipient
of the Professional Progress Award in Chemical
Engineering. The award was the first major, gen-
eral award in the field of chemical engineering.
Twelve years earlier the AIChE had given him
the Walker Award for outstanding publications.
Active in professional societies, Dr. Colburn
was director and chairman of the Awards Com-
mittee and chairman of the Publications Com-
mittee for the AIChE, on whose council he also
served. His memberships included the ASME, for

whose Heat Transfer Division he was an advisory
associate and former chairman; the ACS, the
NEA, ASEE, AAUP, the AAAS, and the Newco-
men Society of England. He was a member and
former chairman of the Committee on Coopera-
tion with the Military Services for the Engineer-
ing Colleges Research Council of the ASEE. In
the Delaware Section, ACS, he served as both
councilor and member of the education committee.
He was an alternate member of the Committee on
Chemical Warfare of the Research and Develop-
ment Board of the DOD.
Honorary societies of which he was a member
were Phi Kappa Phi, Phi Lamba Upsilon, Tau
Beta Pi and Sigma Xi. He was director of the
Delaware Chapter of the American Red Cross,
and was a member of the research committee of
the Delaware Branch, American Cancer Society.
He also served on the research committee of the
Delaware Academy of Medicine and was a mem-
ber of the Delaware Section of the Anti-Tuber-
culosis Society and the Sigma Phi Eplison social
A nationally recognized authority in chemical
engineering, Dr. Colburn was the author of many
publications. His papers dealt with heat transfer,
fluid flow, distillation, absorption and extracting,
and various other technical subjects. He also
wrote several textbooks.
While his original interest was in engineering
and basic science research, Dr. Colburn appre-
ciated the importance of developing research in
the social science area and in broadening the edu-
cational programs of students so that they might
better understand human relations and interna-
tional affairs. He was active in developing the
University's Institute of Inter-American Study
and Research, the Institute for Human Relations,
the Marine Laboratories and the evening pro-
grams of the Division of University Extension.
As his longtime friend and associate, Dr.
Robert L. Pigford, aptly stated, "He was the
'man of all seasons' at the University of Dela-
ware, the prime example for some of us of the
uses of scholarship in the fullest way, the best
administrator I have seen, the truest friend of
student and colleague, the man who makes me
remember best that teaching engineering can be
just plain fun."
Reprinted from University of Delaware News, Fall 1968.

FALL 1969

A osoie in Applied MAwemaUaS


University of Minnesota
Minneapolis, Minn. 55455

chemical engineers are relatively recent addi-
tions to graduate programs, although some go
back about twenty-five years. Often such courses
were initiated because of a certain dissatisfaction
with pure mathematics offerings and the reluct-
ance of mathematicians to teach topics in applied
mathematics. Courses with purely mathematical
content should be taught in mathematics depart-
ments, while those offered in chemical engineer-
ing departments should contain something else.
That something else is usually associated with
the name "model building," although if the course
is primarily that, it should probably be given as
a part of one of the regular engineering science
courses. In short, we seem to be speaking here of
an offering which neither fits into the regular
framework of a mathematics department nor into
the regular kinetics, reactor, transport, control,
and thermodynamics scheme of the conventional
department. In addition to model building, the
course must provide instruction in a number of
techniques and actually show the student how to
solve problems, a feature that is often anathema
to the pure mathematician. In this seems to lie
the reason for its being. Early courses were
primarily exercises in elementary ordinary differ-
ential equations with applications to chemical
kinetics and oversimplified models of the unit
operations. The emphasis is still on differential
equations but other topics with a more recent
origin are now included.
Our own course has gone through almost a
continuous change in the last twenty years and is
taken by almost all graduate students throughout
their first year in residence. The purpose of such
a course is not to make mathematicians of engi-
neers but rather to give the student enough ex-
perience that he can better cope with the other
graduate courses in the department. Such a course

Neal Amundson is Regents' Professor and Head of the
Department at the University of Minnesota. His dis-
tinguished career as educator includes assignments as
Fulbright Scholar and Guggenheim Fellow at Cambridge
University and Institute Lecturer for AIChE. He received
the Industrial and Engineering Chemistry Award of ACS
in 1960 and the William H. Walker Award of AIChE in
1961. His research interests include the application of
mathematics to chemical engineering processes.

is valuable for the MS student since he may take
little other physically motivated mathematics
during his one year of course work. For the PhD
student it can serve as the first course where
significant and complex problems may be solved
by advanced techniques and if he has theoretical
inclinations frequently urges him on to take more
abstruse and rigorous courses from a proper
mathematician. As mentioned earlier, our own
course has changed considerably through the
years and this was forced on us by the fact that
new graduate students now enter with a consid-
erably better background than formerly. The
average entering student has now had about
three years of undergraduate mathematics, some
have had four years, and only a few the minimum
required for the BS degree. This creates a prob-
lem for the instructor, for the class is very hetero-
geneous not only in terms of quantity of mathe-
matical experience but also because of the fact
that in terms of coverage junior and senior
mathematics courses can be much more variable
than those of the first two undergraduate years.
Because of the former I have attempted to give
material which will overlap as little as possible
with what I think they may have been exposed to.
There is an additional problem since many of
them are taking advanced mathematics courses
concurrently. A number of theoretical and numer-
ical problems are assigned and these seem to be a


It is important that a student understand the engineering g significance of these concepts (linear dependence of
solutions, existence and uniqueness, and continuous dependence of the solutions on the data) and what they tell
him about a mathematical model . .

departure from mathematical experience of most
of the students, and I believe may be the most
valuable part of the course. These are graded and
returned to the student. For the most part the
problems are long and an attempt is made to com-
plement the lectures, bring out points not cov-
ered, and to illustrate the numerical procedures
and difficulties. Over half of the students do the
numerical problems on the University Computer
(CDC 6600) although no time in the course is
spent on programming. Usually a student will do
between 25 and 40 problems in each ten-week
quarter. The course is run from 8:00 to 10:00 on
Tuesday and Thursdays (with a five-minute
break) and largely as a lecture, although because
of the small class size (15-25 students) there are
frequent interruptions for questions.
The fall quarter for some years has covered
essentially the content of my book on matrices1,
although not all of the book is covered in any
single offering. Sections of the book may be
skipped and assigned as reading. Other sections
are omitted entirely and this varies from year to
year. Chapters 1, 2, and 3 are covered almost
entirely along with Chapter 4, through section
4.8; occasionally section 4.12 is presented. Chapter
5 through section 5.14 is in many respects the
most important part of the course. A choice is
usually made among the sections in Chapter 6,
not all of it being given. Chapter 7 through sec-
tion 7.13 is almost always presented. On rare
occasions a shortened version of sections 8.1-8.12
is included. The two volumes of Gantmacher2
serve as a reference for the course.
All of the material presented in this quarter
has a sort of nineteenth-centuryish ring about it
and I have thought for some time that it should
be modernized, probably in the direction of
Shilov" "Theory of Linear Spaces" and with in-
troduction of material on tensor analysis (covered
at Minnesota in the first graduate course in fluid
mechanics). This has not come to pass yet, but
probably will since the transition to functional
analysis would be much easier.
The winter and spring quarters are devoted to
an organized exposition of ordinary and partial
differential equations with related topics. It is
assumed that the student understands the gen-
eration of solutions of simple differential equa-

tions. Some time is spent on the theory of differ-
ential equations covering linear dependence of
solutions, existence and uniqueness, and continu-
ous dependence of the solutions on the data. It is
important that a student understand the engi-
neering significance of these concepts and what
they tell him about a mathematical model, for in
the qualitative theory of differential equations
these ideas play a central role. A good bit of time
is spent on seeking to extract as much informa-
tion as possible about the solution from the model
without recourse to numbers. It is surprising how
much information one can obtain for stirred re-
actors, tubular reactors4, simple distillation
schemes, heat conduction, diffusion, etc., from the
equations by using qualitative but rigorous argu-
ments such as existence and uniqueness and the
various maximum principles for both ordinary
and partial differential equations. Often all of the
intuitively obvious qualitative physical properties
of the system can be drawn from the equations
and this is the ultimate test of a model. For ex-
ample, it should not be necessary to compute a
solution to prove that a mol-fraction lies between
zero and one in a distillation calculation, that in
an adiabatic tubular reactor there can be no tem-
perature maximum, or that in an absorption
column the transient cannot oscillate.
After this qualitative theory a brief discussion
of numerical methods for ordinary differential
equations is given covering predictor-corrector
schemes and Runge-Kutta methods with applica-
tions. The question of numerical stability is
briefly discussed since anyone who does a sig-
nificant amount of computer work eventually runs
into stability problems.
At this time a general discussion of the nth
order linear differential operator is begun. Most
of the interesting problems in ordinary and par-
tial differential equations are boundary value
problems. The concept of the adjoint operator and
adjoint boundary conditions is introduced and the
general idea of a self-adjoint boundary value
problem is presented. For example, given the nth
order operator L

d"y d"-ly d"-2y
Ly=ao + a, + a2
dxn dx"-1 dxn-2

. +any

the adjoint operator L* operating on z is

FALL 1969

Nature operates on inputs to give outputs while mathematical operators, couched in the language of differential
equations, operate on outputs to give inputs.

d- d(-1
L*z = (-1)n (ao) + (-1)-1 (a z) + ... +

dx (a._lz) + anz

and it may then be shown if the region of interest
of x is (a,b) that

S(zLy yL*z) dx = 7r(z,y)
where 7r(z,y) is called the bilinear concomitant
and contains the functions z and y and their first
(n-1) derivatives evaluated at a and b. In most
physical problems we are given n boundary condi-
tions on y, n is even, and we have n/2 boundary
at x=a and n/2 at x=b which we assume are
homogeneous. Suppose these boundary conditions
are denoted collectively by
A fundamental theorem says that there exists a
set of boundary conditions on z, called adjoint,
unique except for linear combinations such that

so that


H (z, y)=0

The system made up of the operator L and the
boundary condition Y is said to be self-adjoint if

S(zLy-y*z) dx=0
L can only be self-adjoint if its order is even.
This equation is a form of Green's Theorem and
is the key formula in much of that which follows.
Our aim is to study linear differential equations
on finite domains. In most applications these are
second or fourth order operators, the former aris-
ing in heat conduction and diffusion problems and
the latter in elasticity and fluid mechanics. We
assume that the students know how to find solu-
tions of ordinary differential equations either by
inspection, expansion in series, or numerically.
(A pamphlet on series solutions is handed out to
the students but is not discussed.)

We consider a self-adjoint eigenvalue problem
Lw = -Xpw; a W (w) = 0; x=a and/or x=b
where p is a function of x and p(x)>0. W(w)
stands collectively for the n boundary conditions.
There are a number of theorems on the existence
and character of the eigenvalues and eigenfunc-
tions of such a system. To be brief, however, there
exists a discrete sequence of real eigenvalues Xi, X2,
,, ... and a corresponding set of eigenfunctions
w, (x), w2 (x), Wa (x),... with an orthogonality prop-

p w jwi dx=0 ; i== j
Provided the set of functions [wn(x)] is complete
with respect to a certain class of functions f(x)
we can expand f (x) into a series
f(x) = cjwj(x)

c(j) = p (x)f(x)wj(x)dx
provided the eigenfunctions have been normal-
ized. These two relations play an important role,
for if we write

c(j) = bpfwj dx
f a

f(x) = S cj wj(x)

then c (j) is called the finite Fourier transform of
f(x) and f(x) is the inverse Fourier transform of
c(j). Without laboring the point here this pair of
formulae may be used to solve a number of partial
differential equations in an almost automatic way
once one recognizes the operator L and its asso-
ciated boundary conditions. If a partial differen-
tial equation has the form
Ly = p(x) M(y)
with boundary conditions


All of our problems are physically motivated and the translation of the problem into mathematical terms is
not mathematics.

Y(y) = 0
where M is an operator not containing x explicitly
and having its own boundary or initial conditions.
We can write
Wn Ly = pWn M(y)
and integrate with respect to x
Sb b
Wn Ly dx = pwn M (y) dx
a a
Using the Green's formula we obtain

-Xn p (x) w (x) y(x) dx=M P pw nydx
a a
-Xn C = M cn
This is a system which is simpler since all refer-
ence to x has been removed and may be solved
(hopefully) to give cn and hence y(x) by using
the inverse transform. In the course this idea is
exploited to obtain solutions of a wide variety of
diffusion, heat transfer, and reactor problems,
and, while, in principle, it is no different than
separation of variables, it possesses an automatic
quality which appeals to the students.
At this point we also discuss Duhamel's
Theorem and the relationship among solutions for
impulse, step function, periodic, random, and gen-
eral inputs, thereby solving the nonhomogeneous
problems which have been avoided up to this time.
A qualitative discussion ensues showing the dif-
ference between mathematical operators and
natural operators. Nature operates on inputs to
give outputs while mathematical operators,
couched in the language of differential equations,
operate on outputs to give inputs. For example, a
distillation column operates on inputs (feeds) to
give outputs (products). The model for a distilla-
tion column in the steady state is a system of
algebraic relations (which must be inverted)
among the outputs. Some mention of non-self ad-
joint problems is also made showing how the bi-
orthogonal set of eigenfunctions can be used to
generate finite Fourier transforms for these
problems. However, because of the extreme diffi-
culty of numerical work the problem is not pur-
sued in detail.
Using solutions to problems on finite domains

standard limiting procedures may now be used to
find Fourier transforms for a variety of boundary
conditions on semi-infinite domains (infinite hol-
low cylinders, etc.). The bag of the student has
thus been equipped with a technique which will
produce solutions with ease and his confidence is
increased. A discussion of the Laplace transform
is also included with applications to partial dif-
ferential equations. This discussion usually takes
until about the sixth week of the spring quarter
(a total of approximately fifteen weeks).
One of the difficult things about differential
equations is that there are no textbooks available
intermediate in level between the elementary
undergraduate books and books such as Codding-
ton and Levinson5, Ince6, Hartman7,, etc. The book
by Weinbergers is an excellent intermediate book
on partial differential equations but there is no
corresponding treatment for ordinary differential
equations. I have used some parts of Kaplan9 and
Ross10 but it is surprising that with the number
of books on differential equations and the age of
the topic there are none that are really suitable.
The remainder of the quarter (5 weeks) is
spent in a variety of ways, but for the past two
years first order partial differential equations
have been presented with applications to chrom-
atography. This is a topic not well-presented in
the literature (a lacuna which Professor Aris and
I hope to fill). At other times topics such as
dynamic programming and calculus of variations,
stochastic processes, numerical solution of partial
differential equations with stability considera-
tions, continuous models for discrete processes
and many others have been presented.
The question arises as to how much rigor should
be presented in such a course. The writer has a
simple answer to this. Rigor is presented when-
ever the student feels the need for it. The solution
of a partial differential equation involves a series
of arbitrary operations and the bright student
should ask whether what one obtains really is a
solution to the problem. Such a proof requires the
introduction of some rigor and it is not avoided.
Different representations of a solution frequently
arise and the student should wonder whether they
are the same; a uniqueness proof is in order here
and it is given. Expansions of functions into
series require completeness of the set of functions
(Continued on page 203.)

FALL 1969

I eoa4" in Mame4ntu a.d ta"" Tda4^t 4




University of Pennsylvania
Philadelphia, Pa. 19104

The students in the class have done their
baccalaureate work in a large number of other
schools. Therefore a primary consideration of the
course must be the diversity of their preparation,
which on each topic ranges from zero through
superficial acquaintance to real understanding.
The individual students shift between these posi-
eions as the topics change. Those who are under-
prepared must be given sufficient encouragement
and guidance and time for remedial self-study.
Those who are over-prepared must at the same
time be kept challenged. Ideally each lecture
begins from a position of security for the least-
prepared and ends at a level which temporarily
distresses even the best-prepared. Problems with
progressively more difficult parts are assigned.
Special readings and problems are suggested for
those "who have the time and inclination." The
class is at first surprised that these optional prob-
lems are discussed as well as the assigned ones,
but soon gets the intended message.
Students appear to learn most readily by first
examining very simple phenomena and models
and then considering the effect of added com-
plexities. Hence the equations, algebraic or differ-
ential, for one-dimensional, limiting cases are first
derived. Then terms and dimensions are gradually
added. Reduction of unsteady state, three-dimen-
sional partial differential equations to simple cases
does not appear to achieve the same rapidity or
degree of understanding.
I consider it an obligation to demonstrate a
convincing and significant application for every
model, theory or solution which is presented and

Stuart W. Churchill became the first Carl V. S. Patter-
son Professor of Chemical Engineering at the University
of Pennsylvania in 1967. He received the BSE in both
chemical engineering and engineering mathematics in
1942, the MSE in 1948 and the PhD in 1952, all from the
University of Michigan. From 1942 to 1947 he worked
for the Shell Oil Company and the Frontier Chemical
Company. He became an Instructor at the University of
Michigan in 1950, rose to Professor in 1957 and served
as Chairman of the Department of Chemical and Metal-
lurgical Engineering from 1962-1967. He is currently
directing research in combustion, natural convection,
freezing, fluid mechanics and drying.

to point out the deficiencies and limitations of
each model and the uncertainties in the support-
ing data.
Home problems are assigned corresponding to
each class meeting. In addition the students are
frequently asked to complete or extend the deriva-
tions presented in the lectures. Several longer and
optional problems, e.g., to be done on the com-
puter or to be considered as part of the final
examination, are assigned during the semester.
The students are sometimes asked to prepare an
examination question and solution. The problems
are a major ingredient of the course and may
illuminate a matter barely the lec-
tures. The aim is therefore for completion and
good comprehension by all students. Teamwork is
encouraged with the admonition that anyone who
fails to participate as a full partner will ultimately
injure only himself.
Incredibly, a few graduate students still arrive
without digital computing experience. Hence it
is difficult to make full use of the computer in this
first course. Optional and group .problems are
assigned and discussed in terms of computational


S. a textbook . is probably not desirable
in any graduate course . .

methods when appropriate. The students are en-
couraged to elect hard-core courses in numerical
methods as well as to develop the capability to use
the University's computing systems.
The entire semester could easily be spent on
any one of the general subjects indicated by the
headings below. Some departments of chemical
and mechanical engineering do indeed offer up to
eight courses on this subject matter-resulting
in more complete but not necessarily deeper cover-
age. However my general objective is neither to
describe the art and equipment nor to cover the
literature of heat transfer and fluid mechanics,
but rather to present a methodology for inter-
preting and using data and concepts for the an-
alysis and prediction of chemical and physical
processes. The technology of momentum and heat
transfer provides convenient and stimulating ex-
amples. If a scientific and operational point-of-
view is the objective, specific subject matter is of
secondary importance and can be chosen primarily
for illustrative and motivational purposes. It is
amazing how much material becomes redundant
when the emphasis is shifted to methods of an-
alysis and solution.
My specific objectives are (1) to give an idea
of the character and current state of knowledge
in fluid mechanics and heat transfer, (2) to show
how to construct and test first-order and better
models and (3) to develop capability, motivation
and confidence for future self-study.
A textbook is not used in the course. Indeed a
textbook in the classical sense is probably undesir-
able in any graduate course in engineering. It
gives the false impression that the subject is
well-known and completely covered. Books at this
level, with the exception of a few monograms,
invariably purport to cover a wider range of
material than the authors have mastered. The
students arrive with the false notion that the
equations, data and statements in the standard
textbooks are almost sacred. Sometimes I use
these familiar books as a foil, pointing out errors,
inconsistencies and misinterpretations to encour-
age them to read critically and skeptically.
Readings are assigned in a variety of books and
journals. Reference lists are distributed on each
topic for optional and future reading to make the
students feel that they are scholars rather than
mere receptors. I accept and try to implement

John W. Gardner's precept that "the ultimate
goal of the educational system is to shift to the
individual the burden of pursuing his own educa-
tion." A significant fraction of the lecture mate-
rial and problems is taken from the very current
literature. Notes are distributed in advance for
much of the lecture material in order to discour-
age the frantic transcription of everything written
on the blackboard.
A course should evolve from semester to semes-
ter in reflection of new developments and concepts
in science, engineering and computation and also
in response to the changing attitudes and inter-
ests of the students. Currently they are concerned
about the relevance of their studies. Insofar as
possible a response is provided to this demand in
the choice of topics and home problems and also
by the allocation of some time to the discussion
of professional matters. My absences are gener-
ally used for quizzes. On returning I usually ex-
plain why I was away. This often provokes a
discussion of extra-curricular topics.
Tom Baron says a lecture should, like a bull-
fight, combine grace and excitement. An attempt
is made to keep the lectures lively, even at the
expense of organization. The students are encour-
aged to flag me down if they are lost and to chal-
lenge me if they are disbelieving.
Inertial (Non-Viscous) Flows
Inertial flow is chosen as a first topic because
of simplicity (one-dimensional, algebraic equa-
tions are adequate for a first approximation) and
because much of the subject is new to most of
the students.
Adiabatic and isothermal, reversible expansions
and their application to orifices, venturi meters
and nozzles are reviewed rapidly. The equations
for weak pressure waves (acoustic waves) are de-
rived and applied to the problem of maximum
flow through nozzles, including over-expansion
and under-expansion, then to the behavior of
rocket motors and finally to choked flow in pipes
(here including viscous losses).
The equations for gravity, shock and detona-
tion waves, each with reflection, are next devel-
oped and applied to open-channel flow, chemical
shock tubes and the failure of process equipment,
Viscous Flows
The models and data for the viscosity of gases
(including kinetic theory) and of liquids (includ-

FALL 1969

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. a lecture should, like a bull
fight, combine grace and
excitement . (Tom Baron)

ing non-Newtonian behavior) are examined. One-
dimensional material and momentum balances are
first derived for laminar flow down inclined
planes, inside tubes, etc., then the integral equa-
tions for the boundary layer, emphasizing the
fortunate insensitivity of the drag to the pos-
tulated velocity distribution.
The three-dimensional, unsteady state, partial
differential equations for the conservation of mass
and momentum are next derived with emphasis
on the physical significance of the various terms.
Although most students have previously been ex-
posed to this material, they readily admit that
they attained no real understanding as under-
These equations are simplified to some of the
cases of laminar flow previously derived in one
dimension, and are simplified and solved for a
few more complex problems. The Blasius problem
is used to introduce the Hellums-Churchill tech-
nique for the reduction of partial differential
equations. This technique is also used to demon-
strate that the equations do indeed describe tur-
bulent flow and that some information on tur-
bulent flows can be obtained by dimensional an-
alysis alone.
Some of the empirical models for the time-
averaged turbulent shear stress are examined in
a historical framework with emphasis on their
success in generalizing the data for the velocity
distribution and drag. The various ways of plot-
ting the data for drag in pipes are examined as
an illustration of correlation.
Other topics in momentum transfer are con-
sidered depending on the available time. (The
schedule and hence some of these extra topics
are frequently sacrificed for comprehension or
for professional diversions which interest the
class). Usually flow through porous media and
the drag of particles are retained with applica-
tions to fluidization, filtration, etc.

Models and data for thermal conduction and
thermal diffusivity are first examined, including
kinetic theory, heterogeneity and mean-free-path
effects. The usefulness of the Van Dusen trans-
formation for variable conductivity is noted.
Conduction between plates, concentric cylinders

and concentric spheres, and outside spheres and
cylinders is reviewed. The equations for three-
dimensional, unsteady state conduction are de-
rived. The comparative usefulness of various
exact methods such as conformal mapping, the
Laplace transform and separation of variables,
and approximate methods, such as mapping,
bounding and patching, are discussed. The use of
Duhamel's formula both analytically and numeri-
cally is described.
Numerical methods for both steady and un-
steady state problems are developed in limited
depth primarily in the hope of whetting the appe-
tite for a complete course in numerical analysis.

Laminar Convection
The integral equations and solutions for the
laminar boundary layer and the Graetz solution
for fully developed laminar flow in a pipe are
examined. (The detailed evaluation of the co-
efficients and the eigenwerte are deferred to the
algebraically eager student as an extra-curricular
exercise). The analog of the Graetz solution for
a power-law fluid is an example of an extension
of a derivation which is assigned as a home prob-
lem. Other solutions for laminar flow in a channel
under different conditions are examined and com-
The equations for laminar, free convection are
used as an illustration of the power of generalized
dimensional analysis to produce the correct form
of the solutions and empirical correlations for
large Pr, small Pr, uniform heat flux and even
fully developed turbulent motion. The success of
asymptotic methods in producing first-order solu-
tions of great generality is noted.
The Nusselt equation for condensation is de-
rived and the effects of finite heat capacity,
curvature and non-Newtonian behavior are con-
sidered in home problems.
Emmon's generalization for condensation, film
boiling, free convection and melting is presented
as an illustration of the analogous nature of these
four gravitational processes and of the great
power of first-order analysis.

Turbulent Convection
The one-dimensional empirical models and
analogies for turbulent forced convection are
compared with each other, with the two-dimen-
sional solutions and with the data. Again, the
insensitivity of the solutions to the several pos-

FALL 1969

tulates is emphasized as the reason for the sur-
prising success of all of the models.


The models and data for emission, absorption,
transmission and scattering by solids and fluids
are first examined. The integral and differential
properties are contrasted.
Interchange between black, gray, adiabatic and
specular surfaces is considered. Analytical
methods and results (including differential ex-
tensions), numerical methods and results, the
electric circuit analog and the radiosity formu-
lation are included.


The character and scope of a course are per-
haps most evident from the problems which are
assigned. Hence, a few representative problems
are given below. Because of space limitations
these problems are somewhat atypical in that
they are restricted to those with very short state-
ments and hence are simpler, involve less input
data and are less applied than most of those
assigned in the course.
1. A shock wave is generated in a tube containing air
at an initial pressure of 0.10 atmosphere and 600F.
The measured velocity of the wave is 7200 ft/sec. If the
wave reflects off the closed end of the tube to what pres-
sure and temperature will the wall be subjected? Note all
2. Will adding to the length of the diverging section of
a rocket nozzle increase the thrust? Explain.
3. A planar shock wave propagates indefinitely, pro-
ducing an increase in temperature, pressure and density.
What is the source of energy for this compression and
4. Water and n-pentane are pumped at equal volumetric
rates between two horizontal parallel plates. Determine the
location of the interface for fully developed laminar flow.
5. In cylindrical coordinates the Coriolis force is
pu u /r and the centrifugal force is pu2 /r. Show
r 0
whether or not each of those terms has a zero or finite,
time-averaged value for fully developed turbulent flow
in a straight pipe. Do these terms affect the pressure
gradients? Explain.
6. On a dry, 700F day with a barometric pressure of
740 mm. Hg, a pitcher is able to throw a baseball with
sufficient force so that it arrives at the plate 60 feet away
with a velocity of 90 miles per hour. Assuming that he
throws with the same force, what would be the maximum
and minimum velocities at the plate if all combinations
of weather from 400F to 1000F, zero to saturated hu-
midity and 730 to 760 mm Hg were encountered during
the season? Neglect the effect of ambient conditions on
the ball itself.
7. A large block of copper at 1000F is brought in

contact with a large block of steel at 2000 F along two
plane faces of the blocks. Calculate the temperature of
the interface as a function of time.
8. The mean monthly air temperature at Detroit
varies as follows in OF: J, 29; F, 28; M, 37; A, 48;
M, 57; J, 63; J, 65; A, 65; S, 62; 0, 54; N, 43; and D, 32.
Assuming that the surface temperature equals the air tem-
perature and that moisture, curvature and geological ef-
fects may be neglected, calculate the temperature at a
depth of 10 feet as a function of time. The soil may be as-
sumed to have a specific gravity of 1.75, a thermal conduc-
tivity of 1.4 x 10-3 cal/cm-sec-C and a specific heat of
9. Starting with the general integral formulation, de-
rive a numerical value for the asymptotic Nusselt num-
ber for fully developed laminar flow and a fully developed
temperature field in a circular tube with a uniform heat
flux density at the wall.
10. Determine by dimensional analysis alone the mini-
mum functional relationship between the local heat trans-
fer coefficient and the other variables for laminar, steady,
free convection of a power-law fluid to a vertical plate
at uniform temperature. The usual assumptions of boun-
dary layer theory may be employed and the inertial terms
may be neglected.
11. Experimental data are to be obtained for con-
vective heat transfer and pressure drop in smooth pipes.
Experience suggests that for the chosen conditions,
(hD/k)/(Cp/k)l/3 and (-dP/dL)(Dp/G2) can be ex-
pected to be different functions of DG/u only. Suggest
dimensionless coordinates for a graphical correlation of
the measured heat transfer coefficient as a function of
the measured pressure gradient such that neither coordi-
nate contains the velocity.
12. A reaction in a very viscous material is to be
carried out in a scraped-surface heat exchanger. The heat
of reaction and heat of viscous dissipation may be
neglected. It is proposed to double both the length of the
exchanger and the flow rate. Will be conversion be
greater, equal or less? Why? Will the outlet temperature
be greater, equal or less? Why?
13. Calculate the error resulting from the following
approximation for the interchange factor between a
square surface and a parallel differential surface at a
normal distance equal to the side of the square. Subdivide
the square into four square elements and sum the inter-
change factors for these elements using the center points
14. A cloud reduces the radiant flux from the sun by
40%. Estimate the reduction to be obtained if the thick-
ness of the cloud were tripled (a) assuming absorption
and negligible scattering (b) assuming scattering and
negligible absorption.


Many colleagues, including particularly
R. R. White, J. O. Wilkes and D. A.
Saville, and many, many students at both
the University of Michigan and the Uni-
versity of Pennsylvania have contributed
to the development of the philosophy and
details of this course.


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e Qow"Us in Moamentnm T4a4Mdp04t


University of Illinois
Urbana, Illinois 61801

Fluid dynamics plays a central role in many
problems of interest to chemical engineers. Be-
cause of this, the semester course in the area pre-
sented by the ChE Division of the University of
Illinois has been one of the most durable offerings
in its graduate curriculum. I have taught this
course since 1953 and one similar to it had existed
many years prior to my involvement.
My goal is to present a unified treatment of fluid
dynamics to students who have had courses in
differential equations and transport phenomena
and who have some knowledge of vector notation.
The content reflects the philosophy within the
Division that the more advanced and more current
aspects of any field are covered in our Special
Topics courses and in our seminars. (For example,
in recent years I have conducted seminars on tur-
bulence, hydro-dynamic stability, continuum me-
chanics, water waves, numerical solutions of the
equations of fluid mechanics, rheology and in
modern aspects of boundary layer theory.) As a
result, the fluid dynamics course is largely based
on material available in a number of textbooks. It
is intended that it be a starting point for ad-
vanced studies of the current literature, which
are best done in an informal fashion.
At present, the course is in transition because
of the introduction by most schools of more ad-
vanced topics in fluid dynamics at the under-
graduate level. One of my chief difficulties is to
assess properly the background of the students
since I find that the courses offered at different
universities in transport phenomena vary consid-
erably in content and depth. Therefore, at the
risk of losing the interest of the better prepared
students, I give a rapid treatment of key physical
notions that should be covered in a basic course in
transport phenomena. I also give the students a
chance to do some reviewing of their own by
assigning at the beginning of the course a num-
ber of problems from the book "Transport Phe-
nomena" by Bird, Stewart, and Lightfoot.

Thomas J. Hanratty is professor of chemical engineer-
ing at University of Illinois. He was educated at Villanova,
Ohio State, and Princeton University, PhD ('53). His
recent professional honors include the Curtis W. McGraw
Award (ASEE) and the William H. Walker and the Pro-
fessional Prograss Awards of AIChE.

I have been experimenting with the contents of
the course and, as a result, the outline accompany-
ing the article is meant to represent the types of
topics treated and not the total material covered
in a semester. For example, this past year I did
nothing with topic 10 and only partially covered
the notes I have prepared under topic 9. One of
the ideas that is not sufficiently developed is that
of hydrodynamic stability. I am currently giving
some thought to ways of working it into the

The course is initiated by reviewing the con-
cept of a fluid particle and of a continuum and,
in particular, by pointing out circumstances,
such as the settling of fine particles, where the
continuum model is invalid. It is then indicated
that an Eulerian framework is usually more con-
venient than a Lagrangian framework for solving
fluid dynamical problems. The second law of
motion and the first law of thermodynamics are
reformulated so that they are applicable to an
arbitrary fixed volume in space rather than to a
fixed mass. Difficulties that sometime can be en-
countered in applying thermodynamics, which is
formulated for an equilibrium system, to flow
fields are pointed out.

The concepts of a shear stress and the sign con-
vention to be associated with it are introduced by
considering fully developed flow in a pipe. New-


ton's law of viscosity is initially presented by
assuming that the shear stress is directly pro-
portional to the velocity gradient. Through the
momentum theorem it is pointed out that the
shear stress may also be interpreted as a flux of
momentum. Through this concept kinetic theory
can be used to interpret fluid viscosity. Flow be-
tween circular cylinders is considered because it
is a convenient way to introduce concepts which
are used later to extend Newton's law of viscosity
to three-dimensions. It is pointed out that viscous
effects will not depend on that portion of the
velocity gradient that gives rise to solid body
rotation but will depend on that portion which
distorts the shape of fluid area elements.

Experiments are described which illustrate non-
Newtonian behavior and which yield definite prop-
erties characterizing the theological behavior of
fluids. These include nonlinear dependence on the
rate of strain of the fluid, normal stress effects
caused by shear flow, and elastic effects. The
Rabinowitsch equation is developed either in class
or in a homework problem because of its import-
ance in interpreting nonlinear effects in steady
flows. Methods for calculating normal stress co-
efficients and the use of small amplitude sinusoidal
oscillations and relaxation tests to determine
elastic properties are discussed. The Maxwell
equation for linear viscoelastic fluids is applied to
a few simple flow problems.

The differential equations describing the three-
dimensional flow of a Newtonian fluid are now
developed in a cartesian coordinate system. This
is not done in general curvilinear coordinates be-
cause the small number of new physical concepts
introduced by this generalization does not seem to
warrant the added complexity. The equation of
conservation of mass and the momentum theorem
are applied to a differential volume. The use of
cartesian tensors to simplify the notation is intro-
duced. The physical interpretation of the sub-
stantial derivative arising from the momentum
terms is presented. It is pointed out that in order
to describe the force acting on the surface of a
volume the location as well as the orientation of
each surface element is needed. The problem of
representing these surface forces is greatly sim-
plifid by showing that the stress on any arbi-

S. a theory for turbulent flows is still to be
developed. My goal ... is to introduce some of
the language used in correlating turbulence
measurements and in characterizing the turbulent

trarily oriented surface element can be described
in terms of the nine stress components needed to
specify the stress vectors acting on three mutually
perpendicular planes. Cauchy's equation of motion
can then be derived. The properties of the stress
components are now explored in order to facilitate
the development of constitutive relations. It is
shown that the nine stress components are a
second order symmetrical cartesian tensor. The
concepts of principle axes and principle stresses
are introduced. The invariants of the stress tensor
are defined.

The constitutive equations relating the stress
components to the velocity field are now devel-
oped for a Newtonian fluid. The problem of doing
this for more general fluids is discussed briefly.
The velocity gradient is shown to be a second
order cartesian tensor which can be represented
as the sum of a symmetric and an antisymmetric
tensor. The stress components can be related only
to the symmetric part of the stress tensor (rate
of strain tensor) since this is the part that gives
rise to the distortion of fluid volume elements.
Newton's law of viscosity is generalized to three
dimensions by assuming that the components of
the stress tensor are linearly related to the com-
ponents of the symmetric part of the velocity
gradient tensor. This produces eighty-one co-
efficients of viscosity. Only two of these coeffi-
cients are independent, because the fluid is
isotropic and because the stress and rate of strain
tensors are symmetric. The assumption of a linear
relation between the stress tensor and the rate
of strain tensor is now relaxed and the most
general relation is developed for an isotropic
fluid for which the components of the stress tensor
are only functions of the components of the rate
of strain tensor. This relation predicts normal
stress effects and non-Newtonian behavior for
steady flow in a channel. The work of Oldroyd,
Rivlin and Erickson, and Colman and Noll aimed
at developing constitutive relations which exhibit
elastic effects as well as nonlinearity and normal
stresses is discussed only qualitatively.
The Navier-Stokes equations are now derived

FALL 1969

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by introducing the constitutive equations for a
Newtonian fluid into the Cauchy equation. The
solutions of these equations for the case of an
incompressible fluid are developed for three very
general assumptions: creeping flow, perfect fluids,
and boundary layers.

According to the creeping flow approximation
the inertia terms of the equations of motion can
be neglected at small Reynolds numbers. Creeping
flow around a sphere is worked out in much detail
since it illustrates the use of a stream function,
the method of eliminating the pressure term from
the equations of motion, and the calculation of
body forces and skin friction on a solid body. The
case of flow around a bubble is worked out in a
homework assignment. It is shown that the creep-
ing flow approximation does a good job in predict-
ing the force on a sphere but a poor job in predict-
ing the flow field at distances far from the sphere.
For flow around a cylinder it doesn't even predict
the force on the cylinder. Regular perturbation
methods are shown to yield poor higher order
approximations to the creeping flow solutions.
The method of Oseen is discussed. The singular
perturbation method, as outlined by Proudman
and Pearson, is then shown to be a proper way
of getting higher order approximations.

A perfect fluid is defined as one for which the
viscosity and thermal conductivity are zero and
for which the entropy of fluid particles is con-
stant. The Euler equations then describe the flow
field. The conditions under which one might ex-
pect an irrotational flow field are discussed. The
velocity vector is then describable as the gradient
of a potential function and the velocity field is
given by the equation of conservation of mass.
The integration of the Euler equation using the
assumption of irrotational flow yields the Ber-
noulli equation. The Bernoulli equation can also
be obtained for rotational flows by applying the
momentum theorem to flow of a perfect fluid along
a stream tube. The constant of integration then
varies from stream tube to stream tube. The
solution for the flow of an irrotational perfect
fluid around a sphere is obtained. The predicted
pressure distribution around the surface is dis-
cussed. The concept of virtual mass is introduced
by considering the unsteady motion of a sphere in

a perfect fluid and is applied to some problems of
interest. Two-dimensional flows of irrotational
perfect fluids are then considered. A stream func-
tion can be defined for a two-dimensional flow
from the equation of conservation of mass and
complex variable theory can be used to solve flow
problems. A number of examples are considered
including the lift of solid bodies and free stream-
lines. The treatment of small amplitude, waves
at an interface is one of the more successful
applications of the theory for irrotational perfect
fluids. Some of the problems considered in this
area are progressive two-dimensional waves,
standing waves, group velocity, wave resistance,
Kelvin-Helmholtz instability, and Taylor insta-

Boundary layer theory attempts to correct per-
fect fluid theory for viscous effects by assuming
the existence of a viscous layer close to a solid
surface. If this viscous layer is thin compared to
the dimensions of the body a simplified version of
the Navier-Stokes equation applicable to bound-
ary layers on flat plates and curved surfaces is
obtained. The concept of separation is discussed
and it is pointed out that boundary layer theory
is only applicable up to the point where the bound-
ary layer separates from the solid surface. The
difficulties of applying the theory are discussed,
and, in particular, the problems associated with
determining the external inviscid flow or the pres-
sure distribution around the body are emphasized.
Dimensional analysis is applied to the boundary
layer equations to determine the functional rela-
tion between the skin friction coefficient and the
Reynolds number. Similarity solutions are briefly
discussed. The series methods of Blasius and of
Gbrtler and the integral methods ofKPohlhausen
and of Bohlen and Walz for solvifig the boundary
layer equations for some general pressure dis-
tribution are introduced. I find that the best way
to present these methods is to give a homework
problem which requires the application of bound-
ary layer theory to a solid body for which the
pressure distribution is known.

This treatment of boundary layers concludes
my discussion of laminar flows. It might seem
anomolous that even though most flows in nature
are turbulent I don't introduce the topic of tur-

FALL 1969

bulence until this point in the course. The reason
for this is simply that a theory for turbulent
flows is still to be developed. Therefore my goal
in treating turbulent flows is to introduce some
of the language used in correlating turbulence
measurements and in characterizing the turbulent
field. The increased apparent shear stress in tur-
bulent flows is explained in terms of the momen-
tum transport caused by the fluctuating velocity
field. The concepts of eddy viscosity and mixing
length are introduced. They are found not to be
as useful for turbulent flows as were molecular
viscosity and mean free path for laminar flows
because the scale of the turbulent motion respon-
sible for transport is of the same order as the
dimensions of the field. A general discussion is
given on the character of fully developed velocity
profiles and, in particular, on the roles of fluid
viscosity and of the viscous sublayer. The varia-
tion of the average velocity and the eddy viscosity
with location is correlated through dimensional
analysis and the "law of the wall", the "velocity
defect law", and the "overlap law". It is then
shown how the definition of eddy conductivities
for heat transfer are useful in explaining meas-
urements and in particular the effect of Prandtl
number on temperature profiles. The interpreta-
tion of fully developed velocity profiles and Cole's
"law of the wake" are used to develop predictive
methods for general turbulent boundary layer
flows. Taylor's treatment of point source diffusion
in homogeneous turbulent fields is presented as
one of the few successful theories in turbulence.
It is used to explain the gross aspects of turbulent
mixing and to interpret the observed variation of
eddy conductivities. Statistical methods for de-

K01 news

The following item on CACHE was sub-
mitted by Professor Warren D. Seider,
University of Pennsylvania, Philadelphia,
Pennsylvania 19104.

The CACHE (Computer Aids for Chemical
Engineering Education) Committee has been
organized to coordinate the development of com-
puting systems for use in chemical engineering
education. The committee includes twenty educa-
tors from sixteen universities. The principal goal

scribing turbulent flows are discussed and in par-
ticular the concepts of correlation, scale, and
spectrum are introduced. A very brief summary
is given of theoretical attempts to deal with tur-
bulence through the use of the concept of isotropy
and the definition of a turbulence structure.

The last topic in the outline is a one-dimensional
treatment of compressible flows. It is usually pre-
sented after the material on perfect fluid theory
but appears here in my outline because in recent
offerings of the course I have deleted it. Most of
this material with the exception of that on finite
amplitude waves and shock tubes are more prop-
erly treated in undergraduate courses.

I should conclude this article by saying that
the course that I have discussed is only one way,
and not necessarily the best way, of introducing
graduate students in chemical engineering to
basic concepts in fluid dynamics. My own intro-
duction to and interest in fluid dynamics devel-
oped from a course in reactor design.

1. Basic Equations
2. Unidirectional Viscous Flows
3. Non-Newtonian Fluids
4. Equations of Motion for a Viscous Fluid
5. Constitutive Relations
6. Creeping Flow Approximation
7. Perfect Fluid Theory
8. Boundary Layer Theory
9. Turbulence
10. One-Dimensional Compressible Flows

of the CACHE Committee is to accelerate the in-
tegration of computing into the chemical engi-
neering curriculum by sustained inter-university
cooperation in the preparation of curriculum and
course outlines and in the specification and crea-
tion of computing systems.
The CACHE Committee's curriculum sub-
committee has organized a session for the AICHE
Annual Meeting in Washington, D.C., entitled
"Computers in Chemical Engineering Education."
The session will emphasize topics relating to
short and long range plans for the integration of
computers into the curriculum. Ten members of
the CACHE Committee will participate in the
panel discussion after brief presentations.


. A Celanese c





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If you, or your students, have any questions about Celanese, we will be
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Relations, Celanese Corporation, 522 Fifth Avenue, New York, N.Y. 10036.


An equal opportunity employer

$4 Semifnaz GCanue:


Northwestern University
Evanston, Illinois 60201

The theory of transport processes in the past
twenty years has been developed into a compre-
hensive scientific basis for the description of the
essential operations of chemical engineering in
any arbitrary differential volume element. The
theory is essentially a continuum theory which
poses differential equations which must be inte-
grated over the domain pertinent to each particu-
lar process unit under consideration. Two major
difficulties arise in application. The less onerous
is the fact that continuum theory does not pro-
vide the values of the transport properties, equa-
tions of state and constitutive relationships for
specific systems. Molecular statistical mechanics
or experimental measurements, or both, must
provide this data. The more serious is the ex-
tremely intricate forms often taken by the solu-
tions of the transport equations, for example,
in turbulent flow. Although turbulence has been
studied intensively for nearly 100 years, we
still lack a sound theoretical connection with
the Navier-Stokes equations and still less a pre-
dictively useful one. The principles of fracture
under stress are equally important in crushing
and grinding operations and are even less well
understood in terms of elasticity theory. Aggrega-
tion, coagulation and agglomeration are likewise
processes which cannot as yet be usefully de-
scribed by fundamental transport theory.
All of these processes have in common the cir-
cumstance that they occur under conditions which
permit a large variety of solutions of transport
equations and which select no one of this variety
uniquely. The flow paths in a stirred vessel, each
of which we are confident is a solution of the
Navier-Stokes equations, are so various that we
must describe them as a statistical aggregate of
paths having some probability distribution. In
most applications, the residence times determined
by each path are of less interest than the mean
residence time, or some other statistical property
of the residence time distribution. In some cases,
however, the distribution itself is of direct in-
terest, as in a crystallizer, since here the crystal

Hugh M. Hulburt is Professor and Chairman of the
Chemical Engineering Department at Northwestern Uni-
versity. After receiving his PhD in physical chemistry at
the University of Wisconsin in 1942, he was National
Research Fellow in Chemistry at Princeton University
for one year. He has taught at Hunter College, and the
Catholic University and he has held positions with Shell
Oil Company, Chemical Construction Corporation, and
American Cyanamid Company-at the latter firm as
Director of Chemical Engineering (1958-59) and Direc-
tor of Physical Research (1959-63) at their Stamford
Laboratories. In 1963 he joined the faculty of North-
western University, and became Chairman of the De-
partment of Chemical Engineering in 1964. His current
research interests include reaction design, chemical kine-
tics, and electrochemical engineering.

size distribution is a direct consequence of the
residence time distribution.
Thus, there is a class of unit operations for
which the basic transport equations are insuffi-
cient to provide the theory for engineering design.
The first stage of improvement over direct em-
piricism and analysis by dimensionless groups is
to pose a theory based on a statistical distribution
of possible transport processes. The system in
question is defined by a number of properties (or
state variables) whose values are subject to
stochastic variation. We visualize the possibility
of making a simultaneous observation of these
properties and believe that, in any sufficiently
large set of replicated observations there will be
a definite frequency with which any specified set
of values will be observed. The function of the
state variables which associates this probability
with the specified set of values is the probability



The flow paths in a stirred vessel, each of which is a solution of the Navier-Stokes equations, are so various

that we must describe them as a statistical aggregate

For example, in an ideal gas the velocity of any
particular molecule might (in thought at least) be
observed. Repeated observations will not give the
same result, but the observations will tend to
cluster about a central value. We can define a
function P(v) which is the probability that the
observed value, v', be at most equal to v, i.e.,
P(v) = {Probability that v' < v} = F(v) (1)
Our fundamental physical hypothesis is that re-
peated observations define in the limit a definite
function F(v). In general, of course, F(v) may
be multi-dimensional, even continuously infinite
dimensional, but the conceptually simple cases of
one to three dimensions are often of real utility.
Our knowledge of the probability P(v) is not
limited solely to the results of empirical observa-
tion. We remain convinced that the transport
equations hold for sufficiently local phenomena
just as any one molecule in a gas obeys New-
tonian (or quantum) laws of motion. Hence, the
variations in the values of the state-variables
must be consistent with the local transport laws
and their distribution function, P(v), is not
purely random. There must be correlations im-
posed by the local laws which lead to functional
relationships between the statistical properties of
the system and which account for the central ten-
dencies of the distribution of state-variables.
Indeed, they should determine the functional
form of F(v) itself.
The role of statistical theory is to discover and
define those classes of distribution function which
are consistent with the local transport laws and
whatever other conditions are required and can
be defined by the physical nature of the process
under study. These additional conditions are
usually such physically obvious requirements as,
for example, that the system is confined to a
finite volume, or contains a fixed mass, or has a
definite average velocity and/or energy. Since
local velocity is a distributed variable, the re-
quirement that the system have an average
energy requires that F(v) have a form that will
produce a definite mean square velocity

= f 00

v'dF (v)

Thus physical considerations will restrict the
class of admissible distribution functions to those

of paths having some probability distribution.

possessing at least one and usually two moments,
or more.
In addition, the effect of the local transport
laws on the distribution functions can be ex-
pressed very generally. For the simple case of a
single stochastic variable, q, whose local rate of
change is q(q, t), a continuity equation holds in
the form

3f a (qf)
S+ aq = H(f,q,q,t) (3)

Here H (f,q,q,t) is a function that expresses the
effect of random sudden interactions upon the
distribution density f. Two classes of system are
met with in applications. In one, the elements of
the system interact only rarely, as in kinetics, or
not at all, as in collisionless plasmas or non-
agglomerating crystallizers. Changes in f are
then brought about by the influence of external
fields on the motion of the non-interacting par-
ticles, modified by occasion strong interactions
(or collisions) between particles. In the second
class of system, a particle interacts frequently
with others, but weakly, so that each collision
produces only an infinitesimal modification of its
properties, as in Brownian motion, or in plasma
In the first case, one estimates the change in q
produced by the strong interaction in a collision
and sums over the distribution of target particles
and impinging particles. The function H then is
the net probability that in unit time a particle
acquire a value of q = q' + dq by interaction with
other particles. It will usually be expressible as a
collision frequency multiplied by a cross-section
and integrated over the distributed property, q.
In the second case, the effect of collisions is to
produce an infinitesimal change in f and the H
function is expanded in series of derivatives of f
with coefficients which depend upon the collision
This equation or its equivalent is called vari-
ously the particle balance equation10 the Liou-
ville equation, the Kolmogoroff equation, the
Fokker-Planck equation, the Boltzmann equation,
or possibly other names in specific contexts. In
recent engineering applications, physical particles
have been envisioned and the "particle balance
equation" has has been a descriptive term.1,2 In

FALL 1969

general probability theory, the Chapman-Kolmo-
goroff equation is studied, usually under restric-
tions slightly more limiting than desirable for
engineering applications.3
Physicists have studied the Fokker-Planck or
Boltzmann equations5 (or for aerosols,6 the
Smolichowski equation) in theories of molecular
statistical mechanics.7
The Liouville equation clearly applies to any
stochastic system for which one can define the
weakly interacting entities, or generalized par-
ticles, and the significant state-variables, q, and
their local laws of motion, q=Q(q,t). When
physical particles are the elements of the system,
f can be interpreted directly as the particle num-
ber distribution in q, which may be taken to be
location, size, mass, residence time or other meas-
urable or significant property. However, in
polymers," one can define chain segments and a
distribution of chain lengths which obeys the
balance equation. For all termination schemes ex-
cept radical recombination, or branching transfer,
the collision term, H, vanishes and the chain
length distribution is determined by the rate of
growth in a monomer field, modified by catalysts
and transfer agents. Chemical kinetic laws thus
give us forms for q=Q(q) and where required,
for H(q,t). In comminution9 the same equation is
obeyed, but now q (size) is altered only by impact
collision. The present problem here is discover the
appropriate fracture equations for individual par-
ticles so that an expression can be given for
H(q). In aerosol coagulation, the collision mechan-
isms are well defined but the effects of boundary
conditions and external fields have been explored
only partially.
That there is a pedagogically useful common
base for this wide variety of applications was evi-
dent in a seminar conducted recently at North-
western University in the Winter Quarter,
1968-69. Graduate students and faculty inter-
ested in crystallization, polymerization, aerosol
coagulation, hydrosol coagulation and reaction
kinetics in dispersed two phase media par-
ticipated. The ostensible outline of the seminar
was afforded by Beran, "Statistical Continuum
Theories," but it soon became apparent that some
background in basic probability was required and
several weeks were spent by the author develop-
ing the basic probabilistic notions, the Chapman-
Kolmogoroff equations and the Liouville or
Fokker-Planck Equations as applied to simple

The role of statistical theory is to discover and define
those classes of distribution function which are
consistent with local transport laws and . other
conditions . and can be defined by the physical
nature of the process under study.

Markov processes. The books by Feller, "Introduc-
tion to Probability Theory," Vol. I and especially
Vol. II were invaluable in this phase of the semi-
nar. Blanc- LaPierre and Fortet, "Theory of Ran-
dom Functions," was also very helpful in pro-
viding physically motivated treatments of proba-
bility theory. Loeve, "Probability Theory," is a
standard reference on matters of rigor and mathe-
matical detail.
The following topic headings suggest the scope
of the course. Each occupied three to five lecture
1. Heuristic motivation-stirred tank crystallizer-prob-
abilistic model building.
2. Concepts of probability theory-distribution, mean,
conditional probabilities, set functions, combination of
3. Characteristic functions, moments.
4. Random functions, indicator function.
5. Law of Large Numbers-Tchebycheff inequality,
Poisson distribution-Central Limit Theorem.
6. Standard probabilistic models-Bernoulli trials, com-
pound events, normal distribution.
7. Random processes-waiting time distributions-pro-
cesses with independent increments-gamma distribution-
Poisson processes.
8. Kolmogoroff equations-Markov processes, convolu-
9. The Agglomeration Equation-collision processes.
The final eight days were devoted to reports on
specific applications to fields of interest to the
As the seminar developed, it became increas-
ingly apparent that much of the engineering lit-
erature in probabilistic models consists of redis-
covery or reinterpretation of some basic concepts
and models which have been thoroughly studied
in general theory, but which need to be made
explicit and in some cases extended to cover fields
of engineering interest. Most discussions of ran-
dom processes are based on Markov processes, yet
many engineering models are non-Markov. Some
may be considered to be superpositions or con-
volutions of Markov processes, and this represen-
tation is often illuminating when one discovers it.
Of greatest value, perhaps, was the exercise in
the use of probabilistic concepts and the demon-
stration of a common logical structure in a wide
range of seeming independent physical phe-
nomena. An initial insight was gained into the


identification of properties of a system which are
purely consequences of its being an assembly of
weakly interacting parts or particles as distin-
guished from those which reflect the intrinsic
physical nature of the isolated particles.
It seems to the author that while such insights
depend upon understanding the general theory
of stochastic processes, they do not come without
deep study and comparison of specific processes.
Therefore, the statistical theory of particulate
systems is truly an engineering science, approach-
able in a useful way from the base of the analysis
of engineering problems.

1. Randolph, A. D., and M. A. Larson, AIChE Journal
8, 639 (1962).
2. Hulburt, H. M. and S. Katz, Chem. Eng. Sci. 19, 555
3. Feller, W., Introduction to Probability Theory, Vol. I
and II., John Wiley and Sons Co., New York 1966.
4. Blanc-LaPierre, A., and R. Fortet, Theory of Random
Functions, Vols. I and II, Gordon and Breach, New York.
5. Chandrasekhar, S., Rev. Mod. Phys., 15, (1943).
6. Fuchs, N. A. Mechanics of Aerosols, Macmillan, New
York (1964).
7. Cercignani, C., Mathematical Methods in Kinetic
Theory, Plenum Press, New York, 1969.
8. Bamford, C. H. and H. Tompa, Trans. Farad. Soc. 50,
1097 (1954).
9. Austin, L. G., "Equations of Grinding", ACS Christ-
mas Symposium, Cambridge, Mass., 1967.
10. Himmelblau, D. and K. B. Bischoff, Process Analysis
and Simulation, John Wiley and Sons, New York, 1968.

HOUGEN ON COLBURN (from p.171.)
loidal chemistry and Peter Debye in the kinetic
theory of gases.

in 1929, Colburn was employed in the Engi-
neering Experiment Station of the E. I. Du Pont
de Nemours Company under Thomas H. Chilton.
The du Pont Company very generously supported
Allan in his undertaking to derive independently
the mathematical formulations for mass and heat
transfer in fluid streams covering a wide variety
of industrial devices and conditions. These formu-
lations appear in Chapter VII of the pioneer bul-
letin "Studies on Heat Transmission" by Colburn
and Hougen [Bulletin 70 of the Engineering Ex-
periment Station, College of Engineering, Univer-
sity of Wisconsin, October 1930]. Otherwise this
bulletin is based on Colburn's doctorate thesis.
The rough draft was improved by the critical
review of K. M. Watson.

Colburn was an ideal student, scientist and en-
gineer. In conversation and public lectures he had
an unusual capacity for clarity of expression. He
met unsound criticisms and arguments of his
audience with patience and encouragement, never
with disparagement, seeking not p-rsonal acclaim
but rather promoting self confidence and ambition
in others. My technical correspondence with Allan
continued for fifteen years following his academic
career but terminated when I no longer could keep
pace with his ever expanding scientific specula-
My last meeting with Allan occurred in London
in September 1951-an unexpected meeting at the
time of the Festival of Britain. Mrs. Hougen and
I met Mrs. Colburn accidentally on a London bus
on our way to the Tate Art Gallery. Allan arrived
in London one week later while we were awaiting
boat reservations for a return trip to the United
States. The four of us spent a pleasant summer
evening together at the amusement section of the
Festival of Britain. We enjoyed watching the
teenagers on the roller coasters and whirligigs.
In turn the British teenagers enjoyed our strange
use of the English language.
As an epilogue to this sketch I should add one
additional incident. In the fall of 1963 a young
coed, Miss Nancy Hall, a graduate student and
research assistant in the Department of Oncology
at the University of Wisconsin came to my office
to inquire about the possibility of a young man,
Willis Colburn, entering the University of Wis-
consin as a Senior in Electrical Engineering. This
was easily arranged. When Willis appeared on the
campus, his similarity to his father 43 years
previous was most striking and brought a surge
of nostalgic memories. And thus this account re-
turns full circle to its beginning, starting with a
meeting with Allan and his father Willis in 1922
and ending with the enrollment of his son Willis
42 years later. Nancy and Willis were soon
married. Both continued as research assistants
and graduate students for two or three years in
their respective fields. And thus three generations
of Colburns have touched my life over 46 years
of time. I understand the fourth generation has
recently arrived.
I shall close with one sentence from the letter
of his college friend Louis Warrick "How proud
the parents (of Allan Colburn) would be to know
of this latest honor to the memory of an out-
standing son." This applies to all who knew Allan

FALL 1969

4 Comase in Mat 't7anapodt


E. N. Lightfoot
University of Wisconsin
Madison, Wisconsin 53706

This is an introduction to heat and mass trans-
fer for graduate chemical engineers and others
seriously interested in transport phenomena. It is
normally given in the spring semester to provide
entering students an opportunity to take inter-
,mediate transport phenomena or fluid mechanics
by way of preparation. It can be followed to ad-
vantage by special topics courses offered on an
irregular basis and by Professor Curtiss' course,
The Transport and Other Properties of Fluids,
given in our Chemistry Department.
The organization of the course is indicated in
the idealized outline of Table 1, but the actual
coverage has changed substantially from term to
term ever since its original ancestor in 1944 was
introduced by Olaf A. Hougen. Emphasis is
normally given to those topics in greatest need
of reorganization. Thus in 1965-66 and 1966-67
emphasis was put on the formulation and solution
of multicomponent diffusion problems and the
estimation of transport properties of low-density
gases. During the last two years the highest prior-
ity has been given to applications of boundary-
layer theory, with particular emphasis on mass
transfer across mobile interfaces. This current
bias shows clearly in this paper. It is now our
hope to decrease the emphasis on transport prop-
erties, and, if possible, to put this material in a
separate course. If this goal is realized, more
attention will be given to applications of current
interest, to demonstrate the utility of the tech-
niques introduced.
The direction in which this course changes will,
however, be strongly influenced by the instructor
in charge since course content and the instructor's
research program have always been closely inter-
related. Until recently the coverage was heavily
influenced by Mr. Lightfoot's interests in bio-
medical mass transfer and fluid-fluid contacting
devices. With the increasing involvement of Mr.
T. W. Chapman more emphasis on electrochemical
applications can be expected.

Professor Lightfoot was educated at Cornell University,
BchE and PhD. In 1953 he joined the Wisconsin depart-
ment, became active in curriculum revision, and colla-
borated with Bird and Stewart on the text Transport
Phenomena. His major research interests are in mass
transfer and separation processes and in the application
of transport phenomena to environmental and biomedical

There is no one reference on which this course
is based. However, the text Transport Phenomena
provides a good introduction to much of the ma-
terial covered, and The Molecular Theory of Gases
and Liquids is used very heavily for both the
phenomenological aspects of diffusion and the
prediction of transport properties. It has also
been the custom in recent years to distribute
copies of the lecturer's notes, and a substantial
portion of these is now available in printed form
as Chapter Two: Estimation of Heat and Mass
Transfer Rates in Volume 4, Lectures in Trans-
port Phenomena of the AIChE continuing educa-
tion series.

I. The Equations of Change and the Transport
The purpose of this first section of the course
is to lay a sufficiently firm theoretical foundation
for the foreseeable needs of the students. It has
been found desirable to spend six to eight weeks
on these topics, or eighteen to twenty-four 50-
minute class periods, and even then only a partial
coverage can be achieved. In the spring of 1968-69
most of the material on transport properties was
omitted to permit greater coverage of boundary-
layer theory. However, it is felt by the author
that this material should not be slighted.
Our introduction of the conservation equations


TABLE 1-Topical Outline for Diffusional Operations
I. The Equations of Change and the Transport Prop-
A. Conservation Relations for Multicomponent Systems
1. The equations of continuity and energy
2. The equations of motion
3. The equation of entropy conservation
B. Relations between Fluxes and Driving Forces: The
Transport Properties
1. A thermodynamic basis for the formulation of
rate equations
2. Prediction of transport properties on the basis of
kinetic theory
3. Semi-empirical correlations of the transport
4. Experimental determination of transport proper-
C. The Requirements of a Quantitative Description
1. Review of the equations and boundary conditions
needed to describe mass-transfer systems
2. Dimensional analysis
3. The approximate description of multi-component
non-isothermal systems in terms of binary
isothermal solutions
II. Estimation of Heat and Mass-Transfer Rates
in Well-defined Systems
A. Intraphase Transport in Systems of Fixed Geometry
1. The film model: unidirectional transport
2. Convective heat and mass transfer through
laminar boundary layers
a. Forced convection
b. Free convection
3. The effects of operating conditions on intraphase
transfer coefficients
a. Net mass transfer across bounding surfaces
b. Homogeneous chemical reactions
c. End effects
B. Intraphase Transport in Systems with Mobile
1. The boundary-layer equations of energy and con-
tinuity near a deformable surface
2. Description of model systems
3. Effects of operating conditions
C. Interphase Transport
1. Addition of intraphase resistance: the two-resist-
ance theory of Whitman and its limitations
2. Effects of heat and mass transfer on hydro-
dynamic stability: Marangoni effects
III. Approximate Descriptions of Complex Systems
A. Mass Transfer to Rippling Laminar Films
1. The effect of surface mobility on mass-transfer
2. The effects of surface-tension gradients on heat
and mass transfer
B. Mass Transfer across Free Turbulent Surfaces
C. Mass Transfer in Dispersed Systems: Performance
of a Model Liquid Extractor
is a straightforward extension of the treatment
in Chapter 18 of Transport Phenomena and hence
is largely a review. This discussion is short, and
it is a convenient vehicle for reviewing vector-
tensor operations.

The rate equations require a much more exten-
sive discussion, however, and neither the coverage
nor the approach of Transport Phenomena is con-
sidered adequate for our purposes. We begin with
a careful description of the postulates and predic-
tions of irreversible thermodynamic analyses and
put major emphasis on the mass-transfer aspects.
The most important single result of this discus-
sion is the generalization of the Stefan-Maxwell
equations which for isothermal transport take
the form:

with i

j = 0

These equations define* the multicomponent dif-
fusivities. Equation 1 forms a very convenient
and flexible basis for discussion of diffusional
transport in both free solution and mechanically
constrained membranes. It is particularly useful
for systems containing electrolytes.
Discussion of kinetic theory is largely a conden-
sation of the pertinent sections of the Molecular
Theory of Gases and Liquids, and its purpose is
to explain the origins of the low-density gas ex-
pressions summarized in Chapters 1, 8, and 16 of
Transport Phenomena. This is difficult material
to explain in a short time, particularly in the later
highly mathematical stages of the development
of expressions for the transport properties.
We are still looking for easier ways to "tell the
story". Nevertheless this portion of the course
has proven useful to the students and has stimu-
lated a number to take Professor Curtiss' course
in transport properties referred to above.
Subsection C is rather heterogeneous and in-
cludes such topics as the specification of boundary
conditions at gas-solid and fluid-fluid interactions,
development of scale-up criteria, and solution of
multicomponent diffusion problems by matrix
techniques. Here too it is important for the lec-
turer to focus attention on carefully selected
areas rather than to attempt encyclopedic cov-

*Here .j is the molar chemical potential of species j, and
except as noted the nomenclature of this article is that
of the text Transport Phenomena.

FALL 1969

II. Estimation of Heat and Mass Transfer Rates
in Well Defined Systems
Accurate prediction of heat and mass transfer
rates in applications of practical interest is still a
formidable problem. This is due in part to the
complex geometry and flow conditions encoun-
tered but also to the large number of parameters
affecting system behavior. Fortunately it is often
possible to determine the functional dependence,
and even the magnitude, of heat and mass-trans-
fer coefficients from highly simplified models of
the real system. This section of the course is
devoted to discussion of the most widely useful
physical models.

A. Intraphase Transport in Systems of Fixed
We start by discussion of intraphase transport
in systems with fixed boundaries and concentrate
on asymptotic boundary-layer models. In each
case we begin our discussion with a simple proto-
type to illustrate characteristic behavior and then
proceed to generalize our discussion to the degree
possible. After discussion of convective transfer
at zero interfacial velocities we consider the com-
plications introduced by chemical reactions and
high net mass transfer rates.
We first consider film models of heat and mass
transfer and concentrate our attention on tur-
bulent transport in duct flows. In this discussion
we compare available expressions for the turbu-
lent transport properties and show that the best
of these yield simple asymptotic correlations sim-
ilar to the Chilton-Colburn relation for the Rey-
nolds and Schmidt (or Prandtl) number ranges
of most interest. Since adequate empirical corre-
lations already exist for long ducts this discussion
is most useful as a preparation for analysis of
transfer in short ducts and mass transfer accom-
panied by chemical reaction.
We next consider forced-convection transport
through laminar boundary layers and use as our
prototypes penetration into a stagnant liquid and
dissolution of a sparingly soluble duct wall. These
are then generalized using the techniques pio-
neered by Acrivos and Stewart to systems of
arbitrary geometry as suggested in Fig. 1. The
key results of these analyses are:

SF(4/3) (" d.]
Sg.r '(2)

a 1d N,,-= (R.A)'4 -I o 5 fal e t )

Here* h,, hy, h2 = scale factors for the locally orthogonal
S co-ordinates of Fig. 1.
yz the dimensionless shear rate at the system
u*o = dimensionless tangential velocity component at the
X = Schmidt or Prandtl number.

Equation 2 is essentially that given by Stewart
in his boundary-layer analysis of heat and mass
transfer about three-dimensional solid bodies at
high Sc or Pr. Equation 3 is a straightforward
generalization of Acrivos' development for two-
dimensional and axi-symmetric bodies at very low
Sc or Pr. It is, however, actually most useful for
describing steady transfer about drops and bub-

- -. ',E ATED Z

Fig. 1. Heat or mass transfer from a three-dimensional
surface. The asymptotic analysis applies upstream of the
separated and turbulent flow regions.

*Notation given by Lightfoot, op cit.


bles at very high Schmidt number. It is thus a
special case of the surface-stretch modification of
the penetration model discussed below.
After introduction of these rather general re-
sults the behavior of several real systems is dis-
cussed briefly to demonstrate both their utility
and limitations.
We follow this discussion with introduction to
free-convection transport and the challenging
problems of transfer accompanied by chemical
reaction and high net mass-transfer rates. In
these latter discussions we place particular em-
phasis on the development of geometry-insensi-
tive correlations.

B. Intraphase Transport in Systems with Mobile
This section is devoted largely to extension of
the penetration model to systems with stretching
and shrinking interfaces. We follow here the
approach of Angelo, Lightfoot, and Howard as
refined by Stewart, Angelo, and Lightfoot. In
doing this we make use of a similarity trans-
formation first suggested by Ilkovic in 1934 and
since independently re-introduced many times by
other workers including Acrivos, Lochiel and
Calderbank, and Scriven and Pigford.
We are able to show as a result of our analysis
that the mass-transfer behavior of an extremely
wide variety of fluid-fluid systems is described by
the simple equation

-. i-F4 T)/sct)]2d

where Nu is the temporal mean Nusselt number
for a surface element based on its area so at an
arbitrary reference time, and s (7) is the area as a
function of the dimensionless time t*. The symbol
A is used for Schmidt or Prandtl number. The
term in braces in Eq. 4 is simply the penetration-
theory result for a non-deformable surface ele-
ment, and the correction factor K is just the tem-
poral root-mean-square value of s/So. Equation 4
is useful for drops and bubbles, rippling films,
laminar jets, and many other important systems.
Some of the most important of these are discussed
in detail.

C. Interphase Transport
This discussion is devoted largely to a critical

review of the two-film theory of Whitman and
of Marangoni effects.
Surprisingly relatively few vigorous treatments
of interphase transport are available, and it is
still common practice to estimate overall coeffi-
cients by addition of separately calculated intro-
phase resistances. We review the errors inherent
in this approach and show that improper area
averaging of local coefficients can be a particu-
larly important source of error. In this discussion
we follow much of the original treatment of King.
In fluid-fluid contractors variations in inter-
facial tension over the mass-transfer surface can
have profound effects on both the shape of this
surface and the flow conditions near it. These
so-called Marangoni effects were first shown to
be important in separations processes by Sher-
wood and Wei, and the first significant attempt to
describe them quantitatively for process equip-
ment was made by Sternling and Scriven by
means of a linearized stability analysis. We con-
sider in our course two simple analyses of Maran-
goni effects in falling films due to Ludviksson and
Lightfoot and Wang, Ludviksson and Lightfoot.
In addition to their simplicity these examples
offer the advantage of direct application in sim-
ple process equipment. They can thus be used in
our practical examples.

III. Approximate Descriptions of More Complex
In this section we consider systems too complex
for detailed rigorous analysis but which can be
usefully analyzed in the light of the preceding
sections. This is felt to be a very important part
of the course since in practice engineers must
usually stick their necks out and deal with a con-
siderable amount of uncertainty. The purpose
here is to show what sorts of approximations and
simplifications are likely to be successful and to
encourage the development of "engineering judge-
The specific examples we are presently using
1) Semi-quantitative descriptions of inertial rippling
and Marangoni effects on mass and heat transfer in
laminar falling films. We base these discussions on an-
alyses and measurements performed in our own labora-
tory by Howard, Irani, Ludviksson, Massot, and Wang.
2) Prediction of re-aeration rates of streams using an
extension of the analysis of Fortescue and Pearson.
3) Prediction of the performance of a sieve-tray liquid
extractor from fluid-mechanic measurements, based on
analyses and measurements of Angelo and Howard in
our laboratory.

FALL 1969

The university where classes neverend.

Union Carbide's research centers are in many ways like a university.
In any one of them you'd meet a faculty with advanced degrees in practically every science.
You'd see them scribbling complicated formulas on blackboards and working with complex
scientific instruments.
You'd hear them discussing the uses of tremendous pressures, unearthly heat, intense
cold-as well as problems in oceanography, outer space, atomic energy.
In any one of our many research centers and laboratories which we maintain here and
abroad, you'd sense the vast and diversified scope of Union Carbide technology.
Finding better ways to do things is the aim of this research. And when a better way is found
to revolutionize an industrial process-or simply develop a new product for your comfort or
convenience-our research scientists don't graduate.
They move on to new and exciting challenges created by today's advancing technology.
M Aoom

For additional information on our activities, write to Union Carbide Corporation, Department of University
Relations, 270 Park Avenue, New York, N.Y. 10017. An equal opportunity employer.


We have chosen these for familiarity and because
they are (perhaps fortuitously) successful ex-
amples of the application of fundamentals intro-
duced earlier in the course. We believe that unit
operations should be taught this way when pos-
sible: from personal experience and in the light
of available theory.

Plans for Future Development
It is obvious from this discussion that our
course outline is too long, and each year we must
slight some topics very badly to obtain meaning-
ful coverage of others. We believe we must soon
either expand to a one-year sequence or move
much of Section I to a new course on the estima-
tion of physical properties.
We particularly feel the need of more examples,
both for consolidating the theory presented and
for advertising new fields. We also feel that we
are placing too little emphasis on inventiveness
and ingenuity. This course is therefore far from
satisfactory, even in its philosophy. We hope it
will look very different five years from now.
Bird, R.B., W.E. Stewart, and E.N. Lightfoot, "Transport
Phenomena", Wiley (1960)
Bird, R.B., W. E. Stewart, E.N. Lightfoot, and T. W.
Chapman, "Lectures in Transport Phenomena", Vol. 4.
AIChE Continuing Education Series (1969), Chap. 2,
Estimation of Heat and Mass Transfer Rates, By E.N.L.
Hirschfelder, J.O., C.E. Curtiss, and R.B. Bird, "Molecular
Theory of Gases and Liquids", Wiley (1954)

Book reviews

Kinetics of Chemical Processes
Michel Boudart,
Prentice-Hall (1968), ix+246 pp.
To quote from the jacket of this volume
"... Chemical kinetics, once the esoteric domain
of the theorist, has become a vital tool in the
design, operation and control of reactors . .".
With the emergence over the past decade of
chemical reaction engineering as an active and
vital area in both teaching and research, the need
for a book such as that Professor Boudart has
provided us with here has become almost painful.
To be sure, chemical engineering kinetics (what-
ever that is) is said to be the topic treated in a
number of available texts. Kinetics, however,
generally seems to bow out of the picture after
quick tours through phenomological rate forms,

chain reactions and the steadystate approxima-
tion, numerous integrated rate equations and the
inevitable Langmuir-Hinshelwood discussion. One
is left in these texts with a substantial involve-
ment in reactor analysis and design, which is cer-
tainly worthwhile, but kinetics then appear only
as something taken for granted. Those who have
attempted teaching reaction kinetics as distinct
from reactor analysis or reaction engineering,
know that the assembly of material for such a
course at any level other than the trivial is a
tiresome task of searching through a number
(in my own case, six) of texts and monographs
in the chemical and chemical engineering litera-
ture. No longer! In this admirable introductory
text, Professor Boudart has put all the informa-
tion together for us, clearly and concisely, while
still leaving lots of latitude for us all to incorpo-
rate our own variations.
The approach of the book is straightforwardly
put in the Preface: to develop the single chapter
on kinetics in a physical chemistry text into a
whole course, giving the essence of theory and
experiment without indulging in extreme chemi-
cal detail. The contents include introductory ma-
terial on rate functions and reactor types, theory
of chemical kinetics of elementary steps, steady
state treatments for various systems, chain reac-
tion sequences, the concept of rate determining
steps and stoichiometric numbers, irreducible
(i.e., those arising from the reaction process it-
self) transport effects on kinetics, and correla-
tion methods for both homogeneous and hetero-
geneous reactions. There are a number of points
which demonstrate how well structured and care-
fully written this text is. For example, transition
state theory is developed via the thermodynamic
formulation, which very clearly distinguishes
between energy and entropy contributions to re-
action rates. The development given fbr reac-
tions proceeding via elementary steps involving
active centers chain and catalytic sequences -
provides a useful generalization for a large por-
tion of kinetics, and the chapters on correlations
in homogeneous and heterogeneous reaction ki-
netics provide a nice amalgam of information
from sources which are diverse and perhaps not
the most familiar. There are quite a number of
problems included, and they are generally excel-
lent. In short, this is a book which every chemi-
cal engineer should have in his library.
John B:'Butt
Northwestern University

FALL 1969

74 CaO-we in anttol and OP&inaKtkOn



Princeton University
Princeton, N. J. 08540
In this article we shall briefly outline some of
the major topics covered in a graduate course in
Optimal Control of Reaction Systems at Prince-
ton. This course was originally started in 1955
as a full year of Numerical Analysis and has
gradually evolved into its present form. This was
achieved by the inclusion in 1959 of selected items
(3 and 6 in Table II below) and the subsequent
addition of more and more material until the
present coverage resulted.

I- 1. Athans, M., and Falb, P. L., "Optimal Control",
McGraw-Hill (1966).
I- 2. Bryson, A. E., and Ho, Y., "Applied Optimal
Control", Blaisdell (1969).
I- 3. Koppel, L. B., "Introduction to Control Theory",
Prentice-Hall (1968).
I- 4. Lapidus, L., and Luus, R., 'Optimal Control of
Engineering Processes", Blaisdell (1967).
I- 5. Larson, R. E., "State Increment Dynamic Pro-
gramming", Elsevier (1968).
I- 6. Lee, E. S., 'Quasilinearization and Invariant Im-
bedding", Academic Press (1968).
I- 7. Luenberger, D. G., "Optimization by Vector Space
Methods", Wiley (1969).
I- 8. Ogata, K., "State Space Analysis of Control Sys-
tems", Prentice-Hall (1967).
I- 9. Roberts, S. M., "Dynamic Programming in Chemi-
cal Engineering and Process Control", Academic
Press (1964).
1-10. Sage, A. P., "Optimum Systems Control", Prentice-
Hall (1968).
I-11. Wilde, D. J., and Beightler, C. S., "Foundations of
-Optimnization", Prentice-Hall (1967).

Table I lists a number of recommended texts
which are used through the year and Table II
gives some details on the explicit topics covered
in the course. The main text references are I-2
and 1-4, but all those shown in Table I are con-

Leon Lapidus is professor and chairman of the chemi-
cal engineering department at Princeton University. He
was educated at Syracuse University (BS and MS) and
the University of Minnesota (PhD, '50). He teaches
courses in analysis of transport phenomena and com-
putational techniques and in numerical techniques in
engineering analysis. His research interests lie in the
areas of optimization, optimal control and stability of
chemical reaction systems.

sulted at various points. Recent references have
been included in Table II so that the reader or
student has a convenient starting point for pub-
lished material.
The course is devoted to the mathematical and
numerical-computational aspects of the state-
space or time-domain approach as distinguished
from the frequency or transform domain. In
general it covers deterministic problems although
some stochastic control and the effects of noise
are briefly treated near the end of the course.
Extensive numerical and computer problems are
given as exercises to allow the students to try
their hand at applying the theory. As an example,
the optimal control of a series of CSTR will be
discussed in class and the same problem but with
control delay will be given to the students to
solve by a variety of algorithms. However, em-
phasis on complex physical reactions systems for
complexity sake is kept to a minimum.
To give some perspective to the course objec-
tives we present Figure 1 which is taken from
an article of Kalman, Lapidus and Shapiro pub-
lished in 1959 in the Instn. Chem. Engrs. Journal.
Here we show an on-line adaptive (learning) com-
puter connected directly to a process or system.
Within the computer there are three main pro-
grams designated A, B and C. The function of
program A is to carry out the optimal control of



*1. Numerical Concepts. Vector-matrix manipulation,
solution of O.D.E. and P.D.E., iteration methods and
accelerating convergence and functional analysis. Refs.:
Amundson, "Mathematical Methods in Chem. Eng.",
Prentice-Hall (1966); Lapidus, "Digital Computation for
Chem. Eng.", McGraw-Hill (1962); I-7 and I-8 of Table
I.; Kantorovich, "Approximate Methods of Higher An-
alysis", Interscience (1958).*
*2. Necessary and Sufficient Conditions for Minimum.
Hessian matrix, constraints, Lagrange multipliers and
penalty functions. Refs.: I-2 and I-11 of Table I.
3. Optimal Control Problem. Definitions of systems,
constraints, performance index and selection of optimal
control. Refs.: I-1 and I-4 of Table I; Lapidus, Chem. Eng.
Prog. 63, No. 12, 64 (1967).
4. Minimum Principle. Continuous and discrete form
of Minimum Principle, extensions, simplifications, numeri-
cal difficulties and advantages. Refs.: 1-2, I-4 and 1-10 of
Table I; Gurel and Lapidus, IEC Fund. 7, 617 (1968).
5. Dynamic Programming and Invariant Imbedding.
Continuous and discrete form of dynamic programming,
numerical solution of full nonlinear control problem,
numerical solution of 2-point B.V. problems and numerical
questions. Refs.: 1-4, 1-5, I-6 and I-9 of Table I; Seinfeld,
IEC Proc. Design and Devel. 7, 475, 479 (1968); Rothen-
berger, AIChE Jrn. 13, 114 (1967).
6. Linear-Quadratic Problem. Solution of special con-
trol problem via Minimum Principle, dynamic program-
ming and variational calculus. Continuous and discrete
problems, Riccati equation and numerical questions. The
ASP computer program. Refs.: I-4 and 1-10 of Table I;
Lapidus, Chem. Eng. Prog. 63, No. 12, 64 (1967).
7. Minimum Time Problem. So ution via Minimum
Principle, concept of switching times, bang-bang control
and singular control. Connection to linear and nonlinear
programming. Refs.: Lesser, AIChE Jrn. 12, 143 (1966);
Flynn,AIChE Jrn. 15, 308 (1969); 1-2, I-3 and I-4 of
Table I.
8. Optimal Control Algorithms. Numerical algorithms
Depending on the background of the students.

for iteratively solving the full nonlinear control problem.
First (gradient) and second variation methods including
quasilinearization, neighborhood extremals, and the use
of the linear-quadratic procedure. Constraints and penalty
functions. Open and closed-loop solutions. Refs.: I-2 and
I-4 of Table I.
9. Suboptimal control. Generation of closed-loop feed-
back approximate control of nonlinear systems. Refs.:
Internal work only.
**10. Sensitivity Analysis. Performance and trajectory
sensitivity, adaptive systems, parameter compensation,
closed and open-loop algorithms. Refs.: Kokotivoc, Int.
Jrl. Cont. 9, 111 (1969); Sobral, Proc IEEE 56, 1644
(1968); Seinfeld, Canad. Jrn. Chem. Eng. 47, 212 (1969).
11. Stability. Single and multiple equilibrium points,
limit cycles, lumped and distributed systems and Liapunov
functions. Refs.: Storey, Brit. Chem. Eng. 13, 1585 (1968) ;
Aris, Chern. Eng. Sci. 24, 149 (1969); Luss, Chem. Eng.
Sci. 23, 1237 (1968); Gurel, IEC 61, No. 3, 30 (1969);
Berger, AIChE Jrn. 14, 558 (1968), 15, 171 (1969).
12. Control and Stability. Linear quadratic problem and
Liapunov functions, lumped and distributed systems,
time-optional control and control algorithms. Refs.: I-3
and I-4 of Table I; Denn, AIChE Jrn. 13, 926 (1967);
Chant, Canad. Jrn. Chem. Eng. 46, 376, (1968); Wang,
AIChE Jrn. 14, 934, 976 (1968).
**13. Control of Distributed Parameter Systems. Mini-
mum Principle, dynamic programming, finite differencing,
method of lines and control algorithms. Refs.: I-3 of
Table I; Seinfeld, Chem. Eng. Sci. 23, 1461 (1968) ; Denn,
IEC Fund. 7, 410 (1968); Seinfeld, AIChE Jrn. 15, 57
**14. Filtering, Parameter Estimation and Identification.
Linear and nonlinear systems determination of para-
meters, black box representation and computational ques-
tions. Refs.: Bard, Cat. Reviews 2, 67 (1968); Harris,
AIChE Jrn. 13, 291 (1967); Peterson, Chem. Eng. Sci. 21,
655 (1966); I-6 of Table I.
** If enough time is available.

the process (issue commands to the various in-
puts) using the latest process measurements and
taking into account the control objective and the
dynamic model of the process. Program B con-
tinually analyses the process measurements to
identify an accurate model of the process. Pro-
gram C is used to generate and inject special
calibrating signals into the process such that they
do not significantly disturb the process; yet they
perturb the process in such a way that useful
information can be obtained by means of sophis-
ticated data evaluation techniques. Feedback be-
tween the programs is also allowed to increase
the efficiency of the overall operation.
Within this simple appearing arrangement we
have all of the features of the publicized learning
computer which can build its own mathematical

model of a process and then carry out any pre-
scribed form of control. The present course is
directed, as much as feasible, to detailing the
mathematics of these different features. Because
of the current state of technology, Program A
receives the major emphasis although Programs
B and C are discussed (14 of Table II).
ConLrol Feedback Informative Feedback

Optimal Con ir e l rDeter ilnint Systep m 'Ini ellggenteS turning

... .. H g .L .

Figure A possible Adpt---- Digital Control System.

FALL 1969

The course is devoted to the mathematical and numerical-computational aspects of the state-space or time

domain approach as distinguished from the frequency


Because of the wide background of students
who take this course it is necessary to first pre-
sent certain introductory topics which are then
used throughout the year. These include the com-
plete vector-matrix notation and its uses such as
evaluating the transition matrix and the pseudo-
inverse, the numerical solution of ordinary and
partial differential equations, the fundamental
properties of convergence algorithms and some
basic material on functional analysis. The solu-
tion of equations and the numerical stability of
these solutions is necessary because they are an
integral portion of all control algorithms and
must be done correctly. Further, convergence
algorithms are used throughout the entire course
to actually obtain the optimal control.
In addition to these numerical concepts it may
be necessary to present some preliminary details
on the necessary and sufficient conditions for an
unconstrained minimum of a multivariable func-
tion, the influence and effects of constraints and
the use of Lagrange multipliers and penalty
functions to handle constraints. These items,
which can be developed for a simple two-variable
function, can be carried over directly to the most
complicated control problem. As such the con-
cepts are absolutely necessary throughout the


1. General Form
1. x(t) = f(x,u) System Model
2. x(to) Initial State
4. CFinal Time Conditiate Constraints
4. Final Tine Conditions (tf )


2. Linear-Quadratic Form.
1. x(t) = Ax + Bu

Linear System

2, 3, and 4 are same
5. I = x(t )'Sx(t) + f/ x'Qx + u'Rudt Quadratic
Sto Scalar Index
Find u(t), toSt-tf, such that I is minimized subject to constraints
of 1-4.

With these preliminaries in hand the next step
in the course is to define the optimal control
problem (see 1 of Table III) and to detail the


minimum principle and the techniques of dynamic
programming and invariant imbedding as general
methods of solving the problem. Here it is very
important to give numerical examples and to illus-
trate both the positive and negative features of
these solution methods.
The linear-quadratic problem (see 2 in Table
III) is then treated in detail using the minimum
principle, dynamic programming and variational
calculus. This is important because the techniques
developed form the basis for all 2nd order
algorithms for solving the full nonlinear control
problem. Because of the availability of the ASP
computer program (see I-4) to numerically solve
this linear-quadratic problem a number of differ-
ent exercises are given to the students.
The minimum-time problem is then solved via
the minimum principle and the connection to
linear and nonlinear programming detailed. Com-
putational considerations and the singular case
are stressed. This area is interesting since it con-
nects to programming methods and is applicable
to the analysis of many reactor systems.
Next we discuss a wide variety of computa-
tional algorithms for solving the nonlinear control
problem without and with constraints. These
methods include the gradient (first variation)
approach and the second variation including
quasilinearization. Much of this analysis can be
connected directly to the special linear-quadratic
case already treated. In addition, consideration is
given to a form of suboptimal control which is
easily developed and yields a closed-loop type of
approximate control. At the same time sensitivity
considerations are employed to indicate the influ-
ence of parameter uncertainties and to generate
iterative methods for the optimal control.
Since many reaction systems exhibit the fea-
tures of stability and instability we then turn
to a detailed discussion of the concepts of trajec-
tory paths in the neighborhood (or global) of an
equilibrium point. This leads directly into an
analysis of multiple equilibrium points, non-
uniqueness of solutions of nonlinear equations,
limit cycles and Liapunov functions. In particular
the Liapunov function approach is extended to
distributed parameter systems and to provide
convenient algorithms for minimum-time and
suboptimal control.
The extension of many of the above ideas may


now be used advantageously to analyze the con-
trol of distributed parameter systems. Here we
treat the control problem in its normal form or
carry out a partial type of lumping (finite differ-
encing) to convert the system to sets of ordinary
differential equations. In both cases a variety of
possible control algorithms following from the
minimum principle and dynamic programming
are developed.
Finally we consider the identification problem
either in its full complexity where no apriori in-
formation about the reaction system is known or
where a model is available but the parameters
must be adjusted to fit experimental data (para-
meter estimation). Here we turn to the linear-
quadratic case treated as a filtering problem,
carry out nonlinear last-square regression and fit
the system data with generalized orthogonal
polynomials. Questions such as the noise involved
in the inputs and on the measurement are of im-

AMUNDSON on Math (Cont'd from p. 177)
and some comments must be made and analogies
are drawn with finite vector systems.
The object of such a course should be to pre-
sent methods for new problems. If a problem has
been solved once then the engineer should use it.
But with a new problem there is no one to tell him
when the problem is properly posed. Has the
model been drawn so it makes mathematical sense
and how does one test whether it does? Whether a
solution fits certain physical and chemical require-
ments will be determined by comparison with
experiment, but this comparison is meaningless if
the model is not self-consistent.
There is frequent confusion in the minds of
beginning graduate students on what is mathe-
matics and what is not mathematics, and, if such
a course serves no other function, this question
should be answered for him. All of our problems
as engineers are physically motivated and the
translation of a problem into mathematical terms
is not mathematics. The generation of the appro-
priate mathematical model is the job of a good
engineer and whether conclusions drawn from the
model agree with experiment is the test of how
good an engineer he is. If the model does not
agree with the experiments, one of two things
may be at fault. Either the model was poorly
drawn in that it does not describe the physical
situation or the model is incomplete or incon-
sistent. Once the model is put to paper a mathe-

If the model does not agree with the experiments . .
either the model was poorly drawn . or it is
incomplete or inconsistent.

matical problem must be solved. The engineer
must somehow convince himself either by intui-
tion or rigorous mathematical argument that the
mathematical problem is properly posed. The old
argument that the problem is a physical one and
therefore possesses a unique solution is a useful
argument but not infallible, since only nature
solves physical problems and she is quite capable
of giving a non-unique solution. The argument
also betrays an unrealistic confidence in the engi-
neer for it assumes that he has translated the
physical problem into mathematical language
exactly, a most unlikely event. This is really a
very complicated problem, for in the course of the
solution certain changes or approximations in the
model, both physical and mathematical, are made
and these should be examined in some detail to
insure that the structure has not been destroyed.
In conclusion, such a graduate course should
not only teach techniques but it should also give
the student a feel for what he is doing and what
is involved. It has been frequently asserted that
we teach only mathematics and neglect engineer-
ing. On the contrary, we are trying to teach the
student the proper place and function of mathe-
matics, showing not only its strengths but also
the pitfalls which may befall the unwary and the

1. Amundson, Neal R., "Mathematical Methods in
Chemical Engineering," Prentice-Hall, Inc., Englewood
Cliffs, N. J. (1966).
2. Gantmacher, F. R., "Theory of Matrices," Vols.
I and II, Chelsea Publ. Co., New York (1959).
3. Shilov, G. E., "Theory of Linear Spaces," Prentice-
Hall, Inc., Englewood Cliffs, N. J. (1961).
4. Amundson, Neal R., and Dan Luss, Canad. J. Chem.
Eng. 46, 424 (1968).
5. Coddington, E. A., and Norman Levinson, "Theory
of Ordinary Differential Equations," McGraw-Hill, Inc.
6. Ince, E. L., "Ordinary Differential Equations,"
Longmans, Green & Co., London (1927).
7. Hartman, Philip, "Ordinary Differential Equa-
tions," Wiley, New York (1964).
8. Weinberger, Hans, "Partial Differential Equa-
tions," Blaisdell Co., New York (1965).
9. Kaplan, W., "Ordinary Differential Equations,"
Addison Wesley, Inc., Reading, Mass. (1968).
10. Ross, S. L., "Differential Equations," Ginn-Blaisdell,
Waltham, Mass. (1964).

FALL 1969

74 o4w4ue iW Te',zmemadnatdmci



University of California, Berkeley
Berkeley, Calif.

Chemical thermodynamics started with J.
Willard Gibbs nearly 100 years ago but its sig-
nificant influence on chemists and chemical engi-
neers in the United States, starting about 50
years ago, is due in large measure to the work
of G. N. Lewis, who introduced fugacity and
activity. For many years Lewis' strong personal-
ity dominated the College of Chemistry at the
University of California at Berkeley; he served
as its dean from 1912 until shortly before his
death in 1946. It is therefore not surprising that
Berkeley's College of Chemistry (which includes
the Department of Chemical Engineering) has
retained a tradition of strong interest in the
application of thermodynamics to chemical prob-
While Lewis' early work in thermodynamics
was along classical lines, in his middle and later
years he devoted much attention to relations be-
tween molecular physics and thermodynamic
properties. Classical thermodynamics establishes
broad relations between macroscopic equilibrium
properties but, by itself, it cannot generate
numerical values of these properties; further, it
is limited in its ability to suggest useful tech-
niques for interpreting and correlating them. For
such purposes, we must call on the insights pro-
vided by statistical mechanics and molecular
physics. Lewis' efforts in this area were accom-
panied and continued by various collaborators,
including W. F. Giauque (who won the Nobel
prize for his low-temperature work) and later,
Leo Brewer and K. S. Pitzer (now president of
Stanford University). But, with respect to chemi-
cal engineering education and research in thermo-
dynamics, the most important of Lewis' collabora-
tors was (and is) Joel H. Hildebrand, who at age
88 is still active in research on the properties of
liquid solutions.
Hildebrand's numerous publications have
shown that when thermodynamics is coupled with

J. M. Prausnitz (BChE Cornell, PhD Princeton) has
been a member of the Chemical Engineering faculty at
the University of California, Berkeley since 1955. His
research interests are concerned with the application of
thermodynamics and molecular physics to chemical en-
gineering design. He has published extensively in this
area and serves as a consultant to petroleum, petro-
chemical and cryogenic industries. He has been honored
with a Guggenheim fellowship, Miller Research Professor-
ship, ACS Honor Scroll and with the Colburn and Walker
Awards of the AIChE.

simple (often semiempirical) molecular models,
many practical phase-equilibrium problems can
be solved with a minimum of effort, and what is
more important, with a minimum of experimental
data. It is this feature of Hildebrand's work that
has become the major influence on the course
"Phase Equilibria" in the Chemical Engineering
Department at Berkeley.
The course is normally taken by graduate stu-
dents in their first quarter at Berkeley. It meets
twice a week; each meeting is for one and a half
hours. Prerequisites for the course are a one-year
course in undergraduate physical chemistry and
at least a one-quarter course in undergraduate
chemical engineering thermodynamics; almost all
entering graduate students satisfy these pre-
requisites. The two main purposes of the course
are: (1) to give students the background needed
to apply thermodynamics and molecular physics
toward the solution of practical phase equilibrium
problems as required in typical chemical engi-
neering design practice, and (2) to provide an
introduction to applied molecular science for
tackling new problems on the frontier of modern
chemical engineering. The student acquires some
feeling for the physical (as opposed to the merely
mathematical) significance of thermodynamic
functions and some insight into the intermolecular
forces which determine the magnitude of these


Table 1. Berkeley's Course in Phase-Equilibrium
1. The Phase Equilibrium Problem
2. Classical Thermodynamics of Phase Equilibria
3. Thermodynamic Properties from Volumetric Data
4. Intermolecular Forces
5. Fugacities in Gas Mixtures
6. Fugacities in Liquid Mixtures; Excess Functions
7. Fugacities in Liquid Mixtures: Theories of Solutions
8. Solubility of Gases in Liquids
9. Solubility of Solids in Liquids
10. High-Pressure Equilibria

functions. He gains practice in reduction and in-
terpretation of experimental data and in devising
efficient and physically meaningful methods for
data correlation. Most important, he achieves
some perspective on what kind of experimental
information he requires for a given problem and,
lacking that information, he gains experience in
quantitatively estimating desired phase equili-
brium relations from a minimum of experimental
data. Finally, he becomes acquainted with some of
the literature on phase equilibrium thermo-
dynamics and learns, often to his great surprise,
that he must be critical of what he reads since
this literature, unfortunately, is not free of
The course is divided into ten somewhat arbi-
trary sections which are given in Table 1. These
sections correspond to the ten chapters of a
recent textbook*. The lectures summarize, focus
and illustrate the material in the text which the
student reads concurrently.
The first section introduces the student to the
phase equilibrium problem: what are we trying
to do and what connection is there between
thermodynamics and the distribution of several
components between two (or more) phases? The
importance of this problem is discussed not only
with respect to typical chemical engineering
operations (distillation, extraction, etc.) but also
with respect to physiology, meteorology and
everyday experiences such as brewing coffee or
dry cleaning a piece of clothing. The second sec-
tion reviews the classical work of Gibbs and
Lewis: the concept of open systems; definition
and utility of the chemical potential; fugacity and
activity; a worked-out simple example (Raoult's
law as a special case of the general equation of
equilibrium). The third section deals with the
calculation of thermodynamic functions (espe-

*J. M. Prausnitz, "Molecular Thermodynamics of
Fluid-Phase Equilibria," Prentice-Hall, Inc., Englewood
Cliffs, N. J., 1969.

cially fugacity) from experimental P-V-T data
(or empirical equations of state) for pure gases,
for gas mixtures and for pure liquids and solids.
Attention is given to the general procedure of
calculating vapor-liquid equilibria using only an
equation of state assumed to be valid for both
gas and liquid phases (e.g., the Benedict-Webb-
Rubin equation).
After the third section the student begins to
understand that for finding successful solutions
to phase equilibrium problems, the important
bottleneck has little to do with thermodynamics;
the real problem is not thermodynamics, which is
(essentially) all worked out, but molecular
physics: How do we obtain, with a minimum of
experimental work, the various constants in the
equations? The student recognizes the need for
constants which appear because real substances,
unlike ideal gases, consist of finite-size molecules
which attract and repel one another. He is made
aware of the main difficulty in applied thermo-
dynamics: to use thermodynamics for obtaining
numerical results we must add physical under-
standing to our thermodynam'c formalism. And
while the thermodynamic formalism is beautiful,
exact and complete, our understanding of molecu-
lar behavior is still very limited.
Section four presents a simplified survey of
what is known about intermolecular forces. The
nature and origin of intermolecular forces is pre-
sented along with the concept and significance of
potential energy functions and the microscopic
law of corresponding states. A brief discussion is
given of such "chemical" forces as hydrogen
bonding and charge-transfer complex formation.
Emphasis is given to qualitative and semiquanti-
tative relations between intermolecular forces
and macroscopic properties.
Section five begins with a critical discussion of
the virial equation of state: its theoretical sig-
nificance, its utility and limitations for calculat-
ing fugacity coefficients in gas mixtures. Atten-
tion is given to the exact relations between virial
coefficients and intermolecular potential functions
and to the composition dependence of virial co-
efficients. The 'chemical" theory of gas imperfec-
tions is discussed. Semiempirical methods (e.g.,
the Redlich-Kwong equation) are presented for
finding fugacity coefficients at high densities, and
it is shown how these are used to calculate solu-
bilities of liquids and solids in compressed gases.
Excess functions and their application to liquid
mixtures are considered in section six. Various

FALL 1969

if YOU can

answer "YES" to any

of these

questions, Rohm and Haas

can make your life


Do you enjoy being responsible
(and the rewards that go with it)
for developing a project and
carrying it through to completion?
Do you like a job that gives free
rein to your imagination and
tests your skills?
Do you like the satisfaction of
making a contribution to society
by improving a wide range of
industrial and consumer products
or by protecting natural resources
or improving farming efficiency?
Would you like to work for a
company that is concerned with
problems of social responsibility
and encourages its employees to
be active in urban affairs?

We are not altruists. We are a
strong and growth oriented
chemical company that needs
engineers of all types-chemical,
mechanical, electrical and
industrial-who want to make a
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same time advance themselves in
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and you can move with us into
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There's just one thing-you'll be
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Write to Manpower &
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An equal opportunity employer.

equations for representing activity coefficients
(van Laar, Margules, Wilson, NRTL, etc.) are
discussed. Consideration is given to multicom-
ponent mixtures and to systems with partial mis-
cibility. The significance and uses of the Gibbs-
Duhem equation are given special attention.
Section seven is an introduction to the theory
of liquid solutions. Brief attention is given to
the lattice theory of simple mixtures and of
polymer solutions; emphasis is placed on the
theory of regular solutions, on applications of
corresponding states theory, and on the "chemi-
cal" theory of associated and solvated solutions.
All theories are regarded critically; advantages
and disadvantages are pointed out.
Sections eight and nine are concerned with the
solubilities of gases and solids in pure solvents
and in solvent mixtures. Physical and chemical
effects on solubility are pointed out and special
attention is given to the importance of the stan-
dard-state fugacity of the solute.
The course ends with a brief discussion of the
uses of thermodynamics to describe systems at
high pressure. Special emphasis is given to the
important role of the partial molar volume. Vapor-
liquid, liquid-liquid and gas-gas equilibria are
As outlined above, the course appears to con-
tain a lot of material. However, experience has
shown that well-prepared first-year graduate
students can handle the course without difficulty
provided their total course load is not large.

LETTERS (Cont'd from p. 167.)
Sir: During a recent conversation one of my graduate
students described a course he was taking. The professor
wrote everything down on the blackboard. He defined each
symbol of every equation. Definitions were given of each
technical word. Discussion was limited to students asking
for clarification of the professor's handwriting. And then
he added, "It wasn't like the Rate Processes course you
taught last year". That had been an exciting learning
experience for him. It had been the same for me.
I was teaching the second quarter of Rate Processes to
first-year graduate students of varied backgrounds. In
the first quarter we had covered the Momentum Transport
section of "Transport Phenomena" by Bird, Stewart, and
Lightfoot (BSL). This quarter I decided to teach Energy
and Mass Transfer by the "row" approach. As the authors
point out in the preface this alternate approach is suitable
for graduate students. It emphasizes the type of transport
and the analogies between the transport phenomena.
Realistically it also eliminated the possibility that only

Typical first-year graduate students at Berkeley
usually take only a total of two lecture courses
plus one seminar course per quarter. Careful
reading of the text (which was available in
mimeographed form until its recent publication)
is augmented with reading of "classical" original
articles which are kept on reserve in the College
of Chemistry library. Eight problem sets give the
student practice in applying what he has learned
to the solution of practical phase equilibrium
problems. All problem sets are corrected by a
teaching assistant and the more difficult problems
are discussed in class.
The course provides a good partial foundation
for subsequent graduate courses in separation
operations, in process design and in medical en-
gineering. For those students interested in doing
research in molecular science and engineering it
provides background and perspective for subse-
quent courses in statistical mechanics and in
advanced chemistry, physics, and materials
The often-praised versatility of the chemical
engineer, his ability to tackle a wide variety of
new problems, is in large measure due to his
knowledge of applied physical chemistry. Berke-
ley's course in phase equilibrium thermodynamics
aims to contribute to that knowledge while at
the same time providing the student with some of
the skills for the practice of conventional chemical

a week or two at the end of the quarter would be left for
Mass Transport.
The first topic covered was methods for predicting
thermal conductivities and binary diffusivities. Since this
touched on the area of my doctoral research, I added
current literature methods to the text material and the
students evaluated:
Variation of thermal conductivity for sulfur dioxide,
carbon tetrafluoride, and tungsten hexafluoride
over the temperature range of 0 to 10000C.
Comparison of thermal conductivities of ammonia,
carbon tetrafluoride, and hydrogen at three
elevated pressures with experimental values.
Variation of the binary diffusivities of tungsten
hexafluoride and hydrogen fluoride over the tem-
perature range of 0 to 10000C.
Three lessons were learned from this exercise. First,
beware of phase changes when computing transport
properties (melting point of tungsten hexafluoride is
20C and critical point is 1780C). Second, use of available
sources of or estimation techniques for intermolecular
force parameters. Finally, a feel for the accuracy of gen-
eralized correlations for transport properties.

FALL 1969

Shell balances for simple energy and mass transfer
problems (Chapters 9 and 17) came next. This was
followed by the equations of change for nonisothermal
systems and also the equations of change for multi-
component systems. The latter topic stirred everyone's
interest. On3 of the reasons, I guess, was because it was
so difficult. Another reason was that we had finally
arrived at equations which encompassed all of the fluxes
that would normally be encountered in any problem. In
other words these equations presented the whole story.
Up to this point the course had been interesting but
very conventional. All of us had learned some new ideas.
But the real breakthrough was to come. Unscheduled.
Unexpected. A real example of serendipity in teaching.
An AIChE meeting was scheduled for St. Louis in
approximately the middle of the quarter. I was planning
on attending and was trying to figure out what the
students should do in my absence. Sounds familiar,
doesn't it? What I hit upon was to assign each student
a paper to review. Since mass transfer seemed to be the
area of highest interest, most of the papers were in this
area. (See list of papers assigned). Some related to the
students interests as I was aware of them. None were
by BSL because this would have been unfair in the light
of the review I requested. Here are the things I wanted
them to include in a written review and also in a fifteen
minute presentation before the class:
Put the important equations and boundary conditions
of the paper in BSL notation. Are these equations
in BSL or what equations in BSL are they related
What are the basic assumptions in the starting
equations and do the authors clearly state them?
What are the unstated assumptions?
Prepare a clear diagram showing problem solved.
Show concentration, velocity, or temperature pro-
files in diagrams.
State the three most important contributions of the
Should BSL include results in revision of the text-
book and why?
What a surprise I had in store when I returned from
St. Louis! Fifteen minutes turned out to be woefully
inadequate for any of the students to discuss their papers.
I extended the time limit to an half hour. Even this
proved inadequate. Discussion on some of the papers
lasted as long as an hour after the formal presentation.
This was exciting, I finally had to limit discussion so
that all of the papers could be discussed within the
From this experience I gained new insight into what
constitutes effective teaching. First, teaching was not my
exclusive domain in the classroom. Students could teach
one another and also they could teach me. In other words,
teaching can be listening. How foreign that concept is
among professors I've known. How foreign it was to me.
Also, how threatening! Prior to this I felt that everything
depended on my performance in the classroom. If I pre-
sented a well-prepared lecture, including good examples
to illustrate the material, then students could learn. But
I always had a gnawing feeling that there must be other
ways and probably better ways of teaching. One of these
is embodied in the concept of teaching is listening.

Secondly, students can evaluate themselves. Each stu-
dent graded (anonymously) each talk. The average was
their letter grade for the presentation. I was so awestruck
by the talks I probably would have given them all A's.
The students were more objective and gave an equal
number of A's and B's. Grades which I gave on the written
reports agreed very closely with those of the students.
Relevancy is an overworked word in today's student
vocabulary. It denotes that classroom learning has mean-
ing in or can be applied to the real world and its problems.
Unexpectedly, this teaching adventure touched on some-
thing that was relevant to the students. We had all pro-
gressed to a common ground of understanding transport
phenomena. With this each student attacked a paper in
the literature and found that what we had learned applied
to that paper. And each student could do his own thing
within the guidelines laid down. Further each student
had the opportunity to experience that greatest satisfac-
tion of teaching; namely, to teach is to learn. Frankly,
we need to share this sense of fulfillment with our stu-
dents more often. In a future paper I'll tell how I did this
with undergraduate students.
In closing let me share one of the other things my
graduate student told me. He said that one of the students
finished his report while I was away. He then cornered
each of his classmates individually and went over his
report with them soliciting questions and comments. As
I recall his lecture was the best. More importantly, I
know he had experienced an adventure in teaching.


Arnold, K. R. and H. L. Toor, Unsteady Diffusion in
Ternary Gas Mixtures, A.I.Ch.E.J. 13, 909 (1967).
Evans, E. V. and C. N. Kenney, Gaseous Dispersion in
Laminar Flow Through a Circular Tube, Proc. Roy Soc.
(London) 284A, 540 (1965).
Getzinger, R. W. and C. R. Wilke, An Experimental Study
of Nonequimolal Diffusion in Ternary Gas Mixtures,
A.I.Ch.E.J. 13, 577 (1967), also Ind. Eng. Chem. 47,
1253 (1955).
Grimsrud, L. and A. L. Babb, Velocity and Concentration
Profiles for Laminar Flow of a Newtonian Fluid in a
Dialyzer, Chem. Eng. Progr. Symp. Series No. 66, 62,
20 (1966).
Lever, R. F. and F. P. Jona, Chemical Transport in Non-
convective Systems A.I.Ch.E.J. 12, 1158 (1966).
Lyczkowski, R. W. et al, Simultaneous Convective Dif-
fusion of Reactants, Products, and Heat with a Surface
Reaction, Chem. Eng. Progr. Symp. Series No. 77, 63,
1 (1967).
McCall, D. W. and D.C. Douglass, Diffusion in Binary
Solutions, J. Phys. Chem. 71, 987 (1967).
Satterfield, C. N. and R. C. Yeung, Diffusion and
Heterogeneous Reaction in a Tubular Reactor, Ind.
Eng. Chem. (Fundamentals) 2, 257 (1963).
Toor, H. L. Diffusion in Three-Component Gas Mixtures,
A.I.Ch.E.J. 3, 198 (1957).
Walker, R. E., and Westenberg, A. A., Molecular Diffusion
Studies in Gases at High Temperatures, J. Chem. Phys.
29, 1139 (1958).
Charles E. Hamrim, Jr.
University of Kentucky
(Continued on page 233.)


Shell is a pair of sneakers-made from
our thermoplastic rubber.
Shell is a milk container-we were a
pioneer in the all-plastic ones.
Shell is a clear, clean country stream
-aided by our non-polluting detergent mate-
Shell is a space capsule control-ener-
gized by Shell's hydrazine catalyst.
Shell is food on the table-made more
plentiful by Shell's fertilizers.
Shell is mileage gasoline-developed
through Shell research.
Shell is a good place for Chemical
Engineers to build a career.

Shell is an integrated research, engineering, marketing and product application methods;
exploration and production, manufacturing, and carrying out research and development
transportation, marketing organization with to support all of these. Information about
diverse technical operations and business openings throughout Shell may be obtained
activities throughout the United States. by signing at the Placement Office for an
Chemical Engineers are vital to the Com- interview with our representative, or by
pany, applying their knowledge to recover- writing to Recruitment Manager, The Shell
ing oil from the ground; designing and Companies, Department C, Box 2099,
operating oil, chemical and natural Houston, Texas 77001. Shell is an
gas processing plants; developing new equal opportunity employer.

Shell Oil Company/Shell Chemical Company/Shell Development Company/Shell Pipe Line Corporation.

FALL 1969







.LI~ .









Purify water

with the fiber

that made

men whistle.

Nylon. Reverse osmosis.
A fiber that started making girls'
legs more beautiful some 30 years
And a process that's been around
a lot longer.
But when Du Pont scientists and
engineers look at them in a new
way, they combine into an idea that
can change the world.
Reverse osmosis is a purification
process that requires no phase
change. It's potentiallythe cheapest
way to desalinate water.
Du Pont's innovation? Hollow,
semipermeable nylon fibers much
finerthan human hair. Symmetrical,

with an outer diameter of .002 inch
and a wall thickness of .0005 inch,
with an accuracy of manufacture
maintained at close to 100%.
Twenty-five to 30 million of them
encased in a precisely engineered
unit 14 inches in diameter by 7 feet
The result: a semipermeable sur-
face area of about 85,000 square
feet-the size of a 2-acre lot-and
up to 10,000 gallons of desalted
water per day.
So far "Permasep" permeators
have been used experimentally to
purify brackish and polluted water,
and in various industrial separa-

tions. But the potential to desalt
seawater, too, is there.
So Du Pont scientists and engi-
neers are even now working to-
ward improved fibers, units and
plant designs that should make it
possible to get fresh water from salt
at a price that any town or nation
can afford.
Innovation-applying the known
to discover the unknown, inventing
new materials and putting them to
work, using research and engi-
neering to create the ideas and
products of the future-this is the
venture Du Pont people are now
engaged in.

Ventures for better living.

74 Cas'ze in T'slwwo.a4namiaii



University of Michigan,
Ann Arbor, Mich.

Thermodynamics has the reputation, enviable
or not, of being a worthy adversary for those who
dare to engage it in battle. For most young pro-
teges there are many rounds of rough in-fighting
before mastery of the subject can be claimed.
This is not because of its sheer logic, for mathe-
matics is undoubtedly the queen of the sciences
in this respect, and mathematics does not seem
to offer the same degree of difficulty. Rather, it is
more probably due to the extreme range of
application of thermodynamic principles. Although
Webster says that "thermodynamics is the
science which treats of the mechanical action or
relations of heat," it is much more appropriate
to say that thermodynamics is the science of
energy and entropy which is involved in every
equilibrium state of matter and every process or
change that occurs in the real ponderable uni-
As an undergraduate the young protege is ex-
posed to the so-called "laws of thermodynamics,"
of which there are just four as follows:
Zeroth. If a thermometer shows the same reading when
in separate contact with two objects, no change occurs
when the two objects are touched to each other.
First. Energy and mass are simultaneously conserved
(accountable) in all processes and individually con-
served in most cases.
Second. Actual processes occur in one direction and the
initial conditions will never be restored without the
aid of some outside agent.
Third. The entropy of a pure substance in perfect crys-
talline form vanishes at the absolute zero of tempera-
The zeroth and second laws are quite acceptable
to the undergraduate because he has had some
experience with thermometers and because he
has learned the irreversible ways of mother
nature from the time of his first broken dish or
balloon to the time he has burned the last drop
of gasoline in his car many miles from a service
station. The first law is palatable because energy
and mass balances are mathematically neat, but
the protege is often shaky on the general concept

Joseph J. Martin was educated at Iowa State, Rochester,
and Carnegie-Mellon University (Sc.D. '47). He is pro-
fessor and associate director of Institute of Science and
Technology at University of Michigan. Presently he is a
vice-president of ASEE and a Director of AIChE.

of energy. He finds it difficult to explain the
nature of internal energy or to tell just where
energy is stored when a weight is lifted in a
gravitational field. The third law makes sense to
him only insofar as he understands the abstract
quantity, entropy, and the absolute temperature
It is generally not the laws of thermodynamics
which present the greatest difficulty to the novice
in the field, but the hundreds of equations which
have been developed to permit quantification of
the elementary principles embodied in the laws
themselves. Fortunately, however, there are just
four basic equations from which all others are
derived by suitable mathematical manipulation.
These four questions do not have a one to one
correspondence with the four laws, but collectively
they incorporate the first three laws within their
structures. The fourtequations are:

The Fundamental Property Relation of Matter
(Gibbs Equation),

dU = TdS PdV + P i dmi
The Energy Balance on a System,**

d(U+mu2/2 + mgz) sys = 6Q 6W + 6 + (H+u2/2 + gZl.d m (2)
j =1 -

*See the Nomenclature at the end for the definition of
**A system is any portion of the universe chosen for
analysis, and may have many distinct parts.


The Entropy Balance on a System,
M. K
days = T (60/T), + 6LW/To + S- sj6
i=1" j=1

Thermodynamics is the science of energy and entropy
which is involved in every equilibrium state of matter
(3) and every process that occurs in the real universe.

The Mass Balance on a System,
m, = T 6m (4)
sys j= ()
Although it may appear to be an oversimplifica-
tion of the subject, there is little question but
what complete understanding of the four basic
equations amounts to a mastery of classical
thermodynamics. The equations are, therefore, in-
troduced to the protege at an early stage, even
though it is quite unlikely that in a single
course he will perceive all of their underlying
implications. The graduate student who is ex-
posed to one or more succeeding courses will grad-
ually gain a more complete understanding of the
extreme power and utility of the four equations
to describe the thermodynamic character of all
processes and all equilibrium states of matter.
The first of the basic equations is probably the
most important and the protege learns that a
uniform mass of matter has the extensive thermo-
dynamic properties, internal energy, entropy,
volume, and mass of each component, and the
intensive properties (potentials), temperature,
pressure, and chemical potential of each com-
ponent.* The point to be emphasized is that these
properties are not completely independent, but
are interlocked through Eqn. (1). Any change in
the condition or state of matter will cause changes
in the thermodynamic properties, but the changes
cannot occur indiscriminately; they must occur in
accordance with this differential equation. In the
deduction of the several terms in the equation,
the inclusion of entropy is paramount. It is done
in one approach by saying that for a simple heat
transfer to the exclusion of any other effect the
change of entropy is the change of internal en-
ergy divided by temperature, or dS=dU/T. This
makes S extensive in the same manner as U. The
desirability of defining entropy this way is best
understood by noting that, for example, when a
hot object is touched to a cold object in isolated
conditions, the energy balance shows nothing is
lost since dUBoth=dUH+dUc=0. Yet experience
and intuition tell us that something has changed
and the ability to do work has been lost. Calculat-
*Equation (1) is the ordinary version of the funda-
mental property relation. Additional terms of the form,
(intensive) d (extensive) may readily be added to it to
account for the more unusual effects such as surface,
elongation or tensile, electric, and magnetic.

ing dU/T (i.e., entropy change) for both objects
shows (dU/T)Both = (dU/T) + (dU/T)o =
dSBoth > 0 because dU = -dUc and T1 > Tc.
The change in entropy, dS, provides a quantita-
tive measure of the irreversibility of the heat
transfer. Its relation to the work lost is given by
Eqn. (3).
The unusual mathematical character of Eqn.
(1) being an exact differential and homogeneous
of the first degree permits it to be integrated to
U = TS PV + p.m. (5)
and then differentiated to
0 = SdT VdP + Z midpi (6)
which is the Gibbs-Duhem equation that is worthy
of extended contemplation by the protege. Be-
cause U, TS, and PV often occur together as in
(5), it is convenient to define H = U + PV, A = U
- TS, and G = H TS, but it is obvious that
although very handy and efficient, H, A, and G
are not fundamental properties. By rules of partial
differentiation and the definition of heat capacity
Cx = T(dS/dT)x (7)
it is possible to put Eqn. (1) in such seemingly
unrelated forms as
dS = O(dT/T (dV/dT) dP (8)

AH = TAV(dP/dT) (9)
and many others. In fact, the bulk of thermo-
dynamics involves the application of Eqn. (1) in
different ways to a wide variety of situations in-
volving ponderable matter.
In the second basic equation, the energy bal-
ance, the protege notes how heat and work are
introduced with arbitraary signs, and the reason
for distinguishing flows of energy to the system
by "8", and changes of energy within the system
by "d". The most common applications of the
equation are in three integrated forms:
Closed System,
Q W = AUsys (10)
Steady-Flow System,
Q W = AH + A(u2/2) + gAZ (11)

FALL 1969

Single-Flow System,
fsHm + Q W = [(Un) (Um)ys (12)

Of course, the energy balance may take many
other forms by proper specialization of Eqn. (2)
for particular cases.
The third basic equation, the entropy balance,
is useful for calculation of the work lost in real
irreversible processes and for analysis of idealized
reversible processes. The protege is quite aware
that a tank of compressed air can do useful work
by connecting it to an expansion engine and that
such work can be forever lost by allowing the air
to leak out instead of flowing through the engine.
He is equally aware that an outside agent must
do work on the air that leaked out in order to
get it back into the tank. He will readily appre-
ciate that this work of restoration under certain
ideal conditions is the work lost during the irre-
versible leaking process.
For many applications the entropy balance is
applied to closed systems as a simple integral,
fTdSys = Q + LW (13)
In this form it is seen that for a non-flow rever-
sible process (no lost work) the heat transfer
equals the S Tds. If in addition there is no heat
transfer (adiabatic as well as reversible), the
STds vanishes and the process is isentropic.
When Eqn. (3) is applied to a reversible heat
engine operating in a steady state (no lost work,
no change of entropy of the system-the engine,
no mass flow-only heat and work flow),
1i(8Q/T)i = 0 = 8Qi/TT + 8Qi/T,,
This may be combined with the energy balance,
8Qh +68Q 8Wr = 0, to give

6Wr = 6Qh (Th -
r h Th

-"> "

which is the Carnot relation that is utilized in
the analysis of heat engines and heat transfer
processes. Here it is desirable that the protege
become familiar with heat engine cycles that are
used in steam plants, gas turbines, and reciprocat-
ing internal combustion engines. The concept of
available energy should be included also.
The energy and entropy balances may be com-
bined in another manner by eliminating Q be-
tween Eqn. (11) and Eqn. (13) applied to a unit
mass of flowing material, and utilizing the defini-
tion of
G = H TS or AG = AH JTdS /SdT, so that
-LW W = AG + JSdT + A (u2/2) + gAZ (15)

By using the property relation, AG = S VdP -
I SdT, which is just a case of Eqn. (1) for the
unit mass, another energy-entropy balance form
-LW W = JVdP + A(u2/2) + gAZ (16)
which is Bernoulli's equation. This equation has
proven extremely useful in the treatment of a
wide variety of fluid flow problems, particularly
those in which there is friction lost work. For a
reversible process no work is lost and (16) be-
-_r I vdP + A(u2/2) + gAZ (17)
while (15) becomes
-r= AG + SdT + A(u2/2) + gZ (18)
The last two equations find applications in the
flow work concept of equilibrium between two
states. By this concept if two states are in equili-
brium, no work can be obtained from a transfer
or flow of mass between them. Direct use of the
equations furnishes an analysis of non-isothermal
equilibrium, which is equilibrium superimposed
on a steady-state irreversible heat transfer. Most
applications, however, are to isothermal equilib-
rium so that Eqn. (18) is written
0 = AGT + (u2/2) + gz = AGT + m(u2/2) + mgAZ (19)
If component A in a mixture is free to move be-
tween two states in equilibrium, (19) may be
0 = AG + A(u2/2) + gAZ (20)
This is the key equation of phase equilibrium and
to understand its implications, it is necessary to
become familiar with partial extensive properties
as derivatives of any extensive property with
respect to mass of component A at constant T, P,
and masses of all other components. For free
energy, as an example, GA = (dG/dmA)T,P m (21)
This may be compared with the property relation
(1) to show that GAx =/ (22)
Further comparison with (5) shows that
G = mA GA + mB GB + ... (23)
When one has gained confidence that a partial
property of a component of a mixture is essen-
tially the same as the unit mass property of a
pure substance, he sees how most of the equations
for pure and mixture components are inter-
changeable. For example, by proper manipulation
of the fundamental property relation (1) he can
get both
d(GIT) -H (24)
dT P p 2


The entropy balance is useful for calculations of the

L-dT- (25)
which are Gibbs-Helmholtz equations.
The protege's level of sophistication in thermo-
dynamics is advancing rapidly if he fully compre-
hends the definition and use of fugacity and activ-
ity through the equations,
dGA = RTdlnTA where -A pA as P 0 (26)


G= GA + RT In G + RT In a (27)
Here integration has been conducted isothermally
from a chosen standard state* to any state. When
Eqns. (23) and (27) are applied to a reaction,
aA + bB= cC + dD, at a given temperature and
no kinetic or potential effects, Eqn. (18) yields
c d
aC aD 0
-Wr = AGO + RT n aC g = AGO + RT In J (28)
aAa a
At equilibrium where W, = 0, this becomes

AGo = -RT In K

(K = Ja ) (29)

Then substituting Eqns. (8) and (25) into the
temperature derivative of (29), and integrating
between two temperatures, the following equation
for situations without appreciable latent heat
effects can be obtained by a person who has a
good grasp of the subject,

aK A 2 f ( C )dT
in a2 A 1 1 + o Prod React dT (30)
Kal R T1 TR2

At the same time this move is made, it is desir-
able that the protege learn how to use certain
tabular values of thermodynamic functions so
that he can evaluate
A 0 AHo 0
(A). =- E (GOT o -G + ) (31)
T a T _T Prod R T T React(1
The protege's knowledge should extend to elec-
trochemical reactions, so that he understands the
relations involving electrical work and voltage,
such as

work lost in real irreversible processes and for
analysis of idealized reversible processes.

NSY- = Nf 0 RT1nJ
r r a


By defining the activity coefficient, yi = i./xif i,
it is desirable to be able to proceed from Eqn. (6) to get
xAdlnyA + xBdlnYB = 0 (36)

In dx = 0
0 B

lny =j XB dlYB (38)
vBl xA

Rewriting Eqn. (20). for simple phase equilibria.
Ua -5
A g (39)
and utilizing (27), the extremely useful relation,

- a = 7A
fA A

is obtained. From the definition of the activity
coefficient the equation for liquid-vapor-equili-
brium is often shown as

(YAXAfAo)li = IAYAfAO) vapor


For ideal solutions the protege learns that if he
appreciates the significance of assuming VA = ,A' he can derive
TA = YAfA (42)

ideal = RT(nAlnx + nnlnXg) (43)
Equally useful relations for enthalpy and entropy
may be obtained.
For non-ideal solutions it is desirable to see how
GEx= AGix AGideal= RT(nAlnyA + nBlnYB) (44)
and for regular solutions how

AGr = XA(1-XA)w + RT(xAlnxA + xBlnxB)

d (E,/T) AHO
dT N- T ( ,2 (33)

NE or = RT1nK (34)
r a

*Standard state is a state of the material at the tem-
perature of interest and usually at a given pressure or
other conditions that determine the state.

The empirical and semi-theoretical techniques for
obtaining activity coefficients or required PVT
behavior or an empirical constant such as a must
be introduced at each step in which real problems
are considered. Calculation of actual situations
leads to the application, employment, and even
development of correlations of the properties of
matter. It behooves the protege to master many
of these in the course of mastering the funda-
mentals of thermodynamics.

FALL 1969

W = N_3


(45) -


Nothing has been said about the fourth basic
equation since it is generally used directly as is.
Clearly, however, if an application is contem-
plated to an extremely high energy process, such
as a nuclear reaction or high velocity particles,
the Einstein relation, E = mc, must be employed.
In such a case the individual mass and energy
balances must be modified to allow for the equival-
ence of mass and energy.

A Helmholtz free energy, U-TS
a Activity, f/fo
C Heat capacity, T(dS/dT)
3 Faraday number
f Fugacity
G Gibbs free energy, H-TS
g Acceleration of gravity
H Enthalpy
J. Ratio of activities aca4/aaB
Ka Equilibrium ratio of activities
LW Lost work
m Mass
N,n Number of moles
P Pressure
p Partial pressure
a Quatity of heat

U Internal Energy
u Velocity
V Volume
W Work
x Mole fraction
y Male fraction
Z Height above datum plane
a,8 Phases
y Activity coefficient
a Chemical potential
u Constant for regular solutions
- Below an extensive property makes
it per unit mass
Above an extensive property makes
it a partial property of a mixture.
In case of fugacity, shows that
component is in a mixture.
o Denotes vapor pressure, as P0.

S Entropy
Several example problems and solutions are
presented in the following section.

[ N a problems for teachers

The following problems with solutions were
submitted by Professor J. J. Martin.
No. 1. One hundred million standard cubic feet (600F,
1 atm) per day of radioactive waste gas at 10000F must
be released at a height of 400 ft. above the ground to
avoid contamination of the surrounding area. A circular
stack of uniform diameter is to be used. A draft at the
,0 base of the st('ck of 1 in. of water will be required (pres-
sure inside stack base is 1 in. HzO less than barometric
pressure). The barometric pressure at the base of the
stack is 740 mm Hg and the ambient temperature 600F.
The gas has a molecular weight of 32 and may be con-
sidered an ideal gas. What diameter will be required?
The lost work of gas flowing through the stack may be
approximated by the equation:

0.032 lu2
LW = gD

LW = lost work in ft-lbF/lbM

1 = height in ft

D = diameter in ft

u = velocity in feet per sec

g, = conversion factor from lbM to IbF
Solution: For barometric pressure at top consider a stag-
nant column of air outside the stack. Since it is at
equilibrium (no flow) with no kinetic effects, Eqn. (17)
applies as
0 = fVdp + gAZ = dP + gAZ

RT In Poa = -gAZ

so (10.73) (520)ln PEt = (40

and p = 729.41 mm Hg

The pressure inside the base of the stack is

p = 740n- (25.4) (1)
in base = 740 = 78.13 mm Hg
The gas velocity inside the stack at an average pressure of
734 nm Hg is
S= 108(760) (1460) (4) 4290 ft
24(3600) (520) (734) nD2 D2 sec
For flow inside the stack with no kinetic effects and no work,
Eqn. (16) applies as

-LW = VdP + gAZ = fT dP+ gAZ

Thus, (0.032) (400) (4290)2 (10.73) (1460)(144) n 729.41 + 400
32.17 D D (32) 738.13


D = 7.2 ft

No. 2. A Ranque-Hilsch vortex cylinder is a device to
expand a stream of air in steady flow from high pressure
and ambient temperature down to two streams at atmos-
pheric pressure, one of which is at low temperature and
the other at high temperature. Air enters the cylinder
through a tangential tube, creating a vortex from which
the hot air is withdrawn from the outer periphery and
the cold air is withdrawn from the central region, as
shown below. In a certain test of the equipment the tem-
peratures and pressures were measured and reported to
be as indicated on the diagram. The mass flow rate of the
hot air was stated to be 1.35 times that of the cold air.
Show by calculations whether the reported measurements
are possible.

nlet Air
Surroundings P = 20 psia
at 80*F and 1
14.7 psia ti = 80o
End view

,' Cold air
Hot air <- outlet
outlet o. tlet = -l90a P
th= 280-J t = -1900F

Solution: Apply the energy balance Eqn. (2) to the whole
device. Assuming negligible kinetic and potential effects,

6Q = 6W = dE = 0,
E = 0 or (H6m)i = (Hm)h + (H6m)

Let 6mh = 1.35, 6m = 1.0, 6mi = 2.35

Taking the reference state of air at 800F and 20 psia,
and assuming ideal gas behavior with C, = 7.0 Btu/lb

H = 0, -h = 7(280-80) = 1400, and H = 7(-190-80) = -1890

Substituting in the energy balance
0 = (1400)(1.35) + (-1890)(1)= 0. So energy balance OK.
Apply the entropy balance as
dS = + ES 6m. = 0 for steady state
S 0 j-3 :I

6- = (Sim)i (sim) (6m)c
Tc I h (smC


Integrating Eqn. (8), AS = Cplln -R lnPJ
Using this to calculate entropies with respect to the refer-
ence state,

Si = 0, Sh = 7 in -4 1.99 in 147 = 2.815 and S =
270540 20

7 In 1.99 in 14.7 4.24
540 20
Putting these into the entropy balance gives
S6L = 0 (2.815)(1.35) (1)(-4.24) = 0.44
or 6LW = 0.44 T

To is the temperature at which heat may be rejected to the
surroundings, 540, so
6LW = (-0.44) (540) = 237
This, however, is impossible because the minimum value
of lost work in a perfect process (reversible) is zero.
There is no such thing as negative lost work (gained
work). Thus, the data from the experiment must be in
error. In other words, do not invest in this device if suc-
cessful exploitation is dependent upon the above data.
No. 3. A mixture consisting of 33-1/3% by volume
methane and 66-2/3% oxygen at 25C and 1 atmos-
pheres total pressure is fed to a combustion chamber
where the methane is burned completely at 18000C. The
combustion products are then cooled and expanded at
constant composition to 250C and 1 atmosphere pressure.
Assume ideal gases and surroundings at 250C and no
condensation of HO.
a) What is the maximum work obtainable from the
above process?
b) What would be the maximum work obtainable if
the combustion! reaction were carried out irrever-
sibly at 18000C, but all other steps were reversible?
DATA: For the reaction at 9 atmospheres pressure,
CH4 + 2 02 + CO2 + 2H20.

At 25*C:

AH = -208,500 cal/gm mole CH4

AS = -1.23 cal/gm mole CH4/K

At 1800*C:

AH = -211,110 cal/gm mole CH4

AS = -4.07 cal/gm mole CH4/K

(a) At 250C, AG = AH-TAS = -208,500 298 (-1.23)
= -208,140
To expand 3 moles of products from 9 atm to 1 atm
AG = /VdP = nflR dP = nRT(lnP) = 3(1.99) (298)ln1

= -3900 cal
From Eqn. (18) -Wr = AGT = -208,140 3900 = -212,040 cal
(b) Irreversible combustion at 18000C means that the
work which could have been produced in a reversible
engine is converted to heat. This could be put through a
reversible heat engine to recover some work.
Thus, AG = -211,110 (2073) (-4.07) = -202,680 cal
Using Eqn. (14) Wr = 202,680( 2073 = 173580 cal

Therefore the lost work due to the irreversible combustion is

LW = 202,680 173,580 = 29,100 cal
Net work by this process is
W = 212,040 29,100 = 182,940 cal
No. 4. One hundred Ib-mole of a solution of 10 mole per-
cent carbon disulfide and 90 mole percent acetone are to
be separated into pure acetone and the azeotrope which
forms at 39.250C under atmospheric pressure. The
azeotrope which forms 61 mole percent carbon disulfide
and 39 mole percent acetone.
It is desired to estimate the minimum work to carry
out the above separation in a distillation column if the
feed solution is all liquid at 39.250C and the products are
withdrawn as liquids at the same temperature.
At 39.250C the vapor pressure of CS, is 604 mm Hg,
while the vapor pressure of (CH,)2 CO at the same
temperature is 400 mmHg. At atmospheric pressure the
vapor phase may be assumed to behave as an ideal gas.
The liquid solution does not behave as an ideal solution,
but its activity coefficients may be represented by the Van
Laar equation,
Iny = 2 and InyB = 2

Solution: Let acetone be component A and carbon disulfide be B.
For the equilibrium between the liquid and vapor, Eqns. (20)and
(27) show that f = "?. For the liquid i = yixif. Taking
the standard state as pure liquid under its own vapor pressure
and since vapor pressure is low this may be taken as the fugacity
f?, f- = yixiPi. Also for the gas, assuming ideality, J = Pi "
yiP. Thus,

ixiPi = yiP
For an azeotrope xi = yi so Yi = -

Thus, 760 760
YA = 0 = 1.900 and B = = 1.258
From equations for Van Laar constants

x lnyBl 2
A = InyA 1 + XAlny
xLAlnY J

= 1.558
xlny' 2
B = nyB 1 + x BlA
^L ''~B11

= In 1.90 1g

0.61 In 1.258 2
0.39 In 1.90

0.39 In 1.90 2
= n 1.258 + 0.61 In 1.25

= 1.787
In feed solution,
Iny or = 1.0202
inyA 1.558(0.9)2 or A 1.0202
+ 1.787(0.1)

nyB = 1.787

+ 1.558(0.9

or yB = 4.08

From AG = AGEx + AGideal and Eqns. (43) and (44),
AG = RT(nAlnxAYA + nBlnxBBg)
So AGfeed (1.99) (561) [901n(0.9) (1.0202) + 10 In(0.1) (4.08)1
= -18,140 Btu

(Continued on page 221.)

FALL 1969

4 GaOwsLe in Cenmical Readcoti Cnwaineetyi


University of California
Davis, California 95616

At the University of California, Davis (UCD)
two quarter-length (3 lectures/week) graduate
courses are available in chemical reaction engi-
neering. The first course, which is required, is a
general treatment. The second is an optional
offering the contents of which are more special-
ized and may vary from time to time. The goal
of the first course is to complete the outline shown
in Table I. However, even though most students
have had an undergraduate kinetics course, our
experience has been that a semester-length offer-
ing would be desirable to cover the subjects
Following each major topic in the outline are
references to appropriate books and papers. To-
gether the book references include all the major
texts in the field. At UCD several of these (3, 24,
27, 29) have been used as the textbook for the
course. On other occasions, the complete list has
been assigned as a set of references. We find that
even graduate students benefit from thorough
familiarity with one reasonably general book.
The course starts out with a review of chemical
reaction equilibria to ensure that the student
understands how to evaluate equilibrium product
distributions. At this time it is also convenient
to introduce the interrelations between kinetics
and thermodynamics.
The differential conservation equations (Sec-
tion II) provide the basis for subsequent design
of whatever degree of complexity. The equations
of motion are generally omitted, to be picked up
in context as needed. The energy equation is
ordinarily simplified to neglect kinetic and poten-
tial energies and shaft work. It is developed care-
fully in terms of both partial molar enthalpies
and temperature, since this seems frequently a
source of confusion.
The point material-balance equations also serve
to introduce the reaction source term or rate ex-
pression. At this point the continuity equation

Joe M. Smith was educated at Cal Tech (BS) and
Massachusetts Institute of Technology (ScD, '43). He
has taught chemical engineering at Maryland, Purdue,
Northwestern, and California (Davis). His research in-
terests are in chemical reaction engineering. Presently
he is chairman of the department at Davis.
Neil A. Dougharty was educated at Lamar Tech (BS)
and University of California, Berkeley (PhD, '65). He
was a NAS-NRC Postdoctoral Fellow at Institut de
Recherches sur la Catalyse, Villeurbanne, France and a
NSF Postdoctoral Fellow at Rice University. His research
interests include heterogeneous catalysis, applied chem-
ical kinetics, and chemical reactor design. Presently he
is an assistant professor at the University of California

for homogeneous reaction is integrated for con-
stant-volume and variable-volume uniform batch
reactors, to stress the nature of the source term
in the material balance as a function of instan-
taneous local properties, independent of the type
of constraints on the reacting volume.
The discussion of chemical kinetics (Section III
of Table I) is necessarily brief. Students will have
had an introduction at least to formal kinetics in
undergraduate physical chemistry and chemical
engineering kinetics courses. We acknowledge
that chemical kinetics in its present state of de-
velopment is only rarely predictive but often
permits more reliable interpolation and limited
The steady-state approximation is discussed
fairly thoroughly (2), and its mathematically
very valuable consequence-that it reduces a
stoichiometrically complex reaction sequence to
a stoichiometrically simple reaction-is stressed.
With the information presented the student
should be able to follow most of the chemical en-
gineering literature insofar as it attempts to
discern reaction mechanisms. On the other hand,




Review of chemical reaction eq.
Conservation equations for
systems with chemical reaction
A. Continuity equations with
homogeneous reaction
B. Continuity equations with
heterogeneous reaction
C. Energy equation

III. Reaction rate expressions ]
A. Material balances with reaction
B. Stoichiometrically simple reactions
C. Stoichiometrically complex
1. Determination of an inde-

7, 26, 29


1, 20

3, 27

pendent set
2. Analysis of extents of
complex reactions
D. Kinetic treatment of reaction
mechanisms 6, 17, 23
1. Molecular reactions
2. Steady-state approximation
for reactive intermediates
a. Open sequences
b. Closed sequences
(1) Initiation-termination
(2) Constancy of number
of reactive intermediates
E. Empirical rate expressions
F. Pseudohomogeneous rate expr. 27
IV. Physical transport and reaction
in heterogeneous systems
A. Pseudohomogeneous rate equa-
tions-global rate
B. Intrapellet transport
1. Isothermal effectiveness
factors 27, 29, 34
a. Pellet geometry
b. Reaction order
c. Criteria for absence of diff.
retardation of rate 27
2. Non-isothermal effec-
tiveness factors 27, 28
3. Physical properties of
porous catalysts 29
a. Surface area
b. Pore volume, porosity
c. Pore volume distribution
4. Diffusion in porous media 27-29, 34
a. Bulk and Knudsen diffusion
b. Surface migration
c. Effective diffusivities
5. Heat transfer in porous media 27-29,
a. Free molecule and
normal conduction
b. Effective thermal conductivity
6. Effect of poisoning on
the global rate 34


6. Autothermal operation
VI. Transport parameters for
packed-bed reactors
A. Velocity profiles
B. Pressure drop
C. Radial mass and heat transfer

4, 9, 16, 21
15, 18, 19

5, 27-29

1. Effective diffusivities and
thermal conductivities
2. Wall heat-transfer coefficients 16
D. Axial mass and heat transfer
VII. Design of fluidized-bed reactors 22, 29, 30
A. Mixing phenomena
B. Models of reactor behavior
VIII. Miscellaneous reactor types
A. Gas-solid non-catalytic reactions 22, 24
1. Global rate equations
2. Reactor design
a. Well-mixed fluid phase
b. Moving fluid, stationary
solid phase
c. Moving fluid and solid phases
B. Slurry reactors 28, 29
1. Global rate equations
2. Reactor design
IX. Non-ideal homogeneous reactors 15, 24, 25
A. Nature of deviations from
ideal flow
B. Measurement of residence-time
distribution functions (RTD)
C. Modeling actual reactors with
PFR and CSTR assemblies
D. Effect on conversion

FALL 1969

7. Effect of intrapellet transport
on selectivity 34
C. External transport 27-29
1. Mass and energy transfer
2. Effect of external trans-
port upon global rate
a. Single reactions
b. Selectivity effects
3. Multiple steady states (stability) 1
V. Reactor design
A. Uniform batch reactor
B. Continuous stirred-tank reactor
1. Steady-state design
2. Multiple steady states and
stability 1, 8, 15
C. CSTR sequences
D. Tubular reactor
1. Plug-flow reactor
2. Tubular reactor with homo-
geneous reaction 12, 13, 31, 32
3. PFR with axial dispersion 24
4. Three-dimensional design
for packed beds 5
5. Stability and parametric

Teaching, understanding, and applying the principles of reactor design will long remain a major challenge . .
students benefit from thorough familiarity with one reasonably general book.

a discussion follows in which the wholly empirical
nature of much practical rate data is noted, deal-
ing as it so often does with complex and un-
analyzed mixtures, empirical parameters such as
research octane number, catalyst deactivation,
trace poisons, etc.
Finally, a brief discussion of rate data for
heterogeneous reactors, usually treated alto-
gether by homogeneous transport models on a
global scale, leads naturally into physical trans-
port questions, that is, Section IV of Table I.
In Section IV effectiveness-factor concepts are
first developed, and then their numerical evalua-
tion is investigated. This approach leads con-
veniently to a discussion of physical properties
of porous catalysts, followed by study of diffusion
and heat transfer with the effective diffusivity
and thermal conductivity the goal. External
transport resistances complete this Section. Here
care is taken to emphasize the relative import-
ance of heat and mass transport effects for
various types of heterogenous environments such
as packed-bed, fluidized-bed, and slurry reactors.
The integral reactor design equations (Section
V) are developed rather quickly and little atten-
tion is given to their application to isothermal
examples. The students are assumed to have had
prior experience with this in an undergraduate
course. Somewhat more attention is given to non-
isothermal cases, since time frequently prohibits
adequate consideration of these at the under-
graduate level. Particular emphasis is placed on
reactor thermal stability. Stirred-tank reactor
sequences are discussed briefly, and their use in
modeling tubular reactors [e.g., ref. (14)] is noted.
Primary emphasis in Section V is placed on the
phenomena which occur in packed-bed reactors.
Again, particular attention is given to thermal
effects, which Denbigh (15) has emphasized as
"undoubtedly the biggest factor of uncertainty in
the design of fixed-bed reactors at the present
time." Quantitative analysis of these effects re-
quires numerical values for radial and axial Peclet
numbers for heat and mass transfer. Empirical
correlations and theories for these quantities are
discussed in Section VI.
Specific, but practically important, types of
heterogeneous reactors are considered in Sections
VII and VIII, with fluidized-bed systems singled
out for particular emphasis. While gas-solid non-

catalytic and slurry reactors are the only ones
listed in Section VIII, it is at this point that other
specialized forms can be introduced.
The final subject is non-ideal flow in homo-
geneous reactors. The time spent here is depend-
ent upon the background of the class. Practical
situations where non-ideal flow has a significant
effect upon conversion are stressed; for example,
the CSTR with one or more internal cooling coils.

A state-of-the-art graduate course will natur-
ally bare the limitations of our present knowledge,
as well as a variety of bypassed problems. A
discussion of fluid-solid processes reveals many
such areas, both for global rates and reactor
design. The role of surface migration, inhomo-
geneity of catalysts, and heat and mass transfer
in real solids are examples, for global rates, of
research problems of chemical engineering inter-
est. Work in this area often encounters unusual
practical consequences. An interesting recent
example is the report of Weisz (33) that catalyst
attrition rates in a fluidized catalytic cracking
unit can be greatly affected by intraparticle dif-
fusion limitations in the cyclic formation and
burnoff of coke deposits. In the design of non-
adiabatic packed-bed reactors, uncertainties in
the calculation of temperature profiles remain a
major source of concern. The scale-up of non-
catalytic fluid-solid reactors such as carbon black
reactors and lime kilns is hindered because of
lack of research on mixing patterns. Many com-
putational difficulties remain in the design of
integral reactors because of the complexity of
boundary conditions in heterogeneous systems.
Research on the design and operation of re-
actors for treating both municipal and industrial
waste water is of literally vital significance. Im-
provement in the operation of biological reactors
for treating primary effluents is an urgent need.
New schemes are needed for the treatment of
secondary effluents, and the chemical-reaction
route offers many advantages. The design of
photochemical reactors, which offer a new kind
of nonuniformity, that of the light intensity, is
an area of active research.
Though by no means exhaustive, these research
areas are illustrative of both the work basic to
reactor design yet to be done and the demanding


practical needs of society which application of our
knowledge of reactor design offers hope of meet-
ing. Teaching, understanding, and applying the
principles of reactor design will long remain a
major challenge to chemical engineers.


1. N. R. Amundson and R. Aris, Chem. Eng. Sci, 7, 121
2. Rutherford Aris, Ind. Eng. Chem., 61, 17 (1969).
3. Rutherford Aris, "Elementary Chemical Reactor
Analysis," Prentice-Hall, Englewood Cliffs, New
Jersey (1969).
4. C. H. Barkelew, Chem. Eng. Progr. Symp. Ser., 55,
(25), 37 (1959).
5. John Beek, "Design of Packed Catalytic Reactors," in
"Advances in Chemical Engineering," Vol. 3, Academic
Press, New York (1962).
6. S. W. Benson, "Foundations of Chemical Kinetics,"
McGraw-Hill, New York (1960).
7. S. W. Benson, "Thermochemical Kinetics," John
Wiley & Sons, New York (1968).
8. O. Bilous and N. R. Amundson, A.I.Ch.E. Jour., 1,
513 (1955).
9. 0. Bilous and N. R. Amundson, A.I.Ch.E. Jour., 2,
117 (1956).
10. R. B. Bird, W. E. Stewart, and E. N. Lightfoot,
"Transport Phenomena," Ch. 18, John Wiley & Sons,
New York (1960).
11. Michel Boudart, "Kinetics of Chemical Processes,"
Prentice-Hall, Englewood Cliffs, New Jersey (1968).
12. F. A. Cleland and R. H. Wilhelm, A.I.Ch.E. Jour., 1,
489 (1956).
13. P. V. Danckwerts, Chem. Eng. Sci., 2, 1 (1953).
14. H. A. Deans and L. Lapidus, A.I.Ch.E. Jour., 6, 656
15. Kenneth Denbigh, "Chemical Reactor Theory," Cam-
bridge University Press (1965).
16. G. F. Froment, Ind. Eng. Chem., 59, 18 (1967).
17. A. A. Frost and R. G. Pearson, "Kinetics and Mechan-

PROBLEMS (Cont'd from p. 217.)
AGproducts = AGazeo + AGacetone AGazeo

Gazeo = (1.99) (561) 3 In(0.39)(1.9) + 10 In(0.61)(1.258)]
= -5,050 Btu
-Wr AG = AGproducts AGfeed
=-5050 + 18140 = 13090 Btu/100 moles feed
No. 5. Badische Anilin and Soda-Fabrik AG of Ludwigs-
hafen am Rhein give this data.
"Water-Gas Shift Reaction--Conversion of the carbon
monoxide proceeds according to the expression:
(1) CO + H20 --CO2 + H2; AH = -9,810 cal
It is an equilibrium reaction with a temperature-
dependent equilibrium constant,
(2) Kp = (CO)(H20)
(CO2) (H2)

ism." John Wiley & Sons, New York (1961).
18. E. A. Grens and R. A. McKean, Chem. Eng. Sci., 18,
291 (1963).
19. C. van Heerden, Ind. Eng. Chem., 45, 1242 (1953).
20. J. C. Jungers, et al., "Cin6tique Chimique Appliqude."
Editions Technip, Paris (1958).
21. H. Kramers & K. R. Westerterp, "Elements of Chemi-
cal Reactor Design and Operation," Academic Press,
New York (1963).
22. Daizo Kunii and Octave Levenspiel, "Fluidization
Engineering," John Wiley & Sons, New York (1968).
23. K. J. Laidler, "Chemical Kinetics," McGraw-Hill,
New York (1965).
24. Octave Levenspiel, "Chemical Reaction Engineering,"
John Wiley & Sons, New York (1962).
25. Octave Levenspiel and K. B. Bischoff, "Patterns of
Flow in Chemical Process Vessels," in "Advances in
Chemical Engineering," Vol. 4, Academic Press, New
York (1964).
26. G. N. Lewis and Merle Randall, as revised by K. S.
Pitzer and Leo Brewer, "Thermodynamics," McGraw-
Hill, New York (1961).
27. E. E. Petersen, "Chemical Reaction Analysis,"
Prentice-Hall, Englewood Cliffs, New Jersey (1965).
28. C. N. Satterfield and T. K. Sherwood, "The Role of
Diffusion in Catalysis," Addison-Wesley, Reading,
Mass. (1963).
29. J. M. Smith, "Chemical Engineering Kinetics," Second
Edition, McGraw-Hill, New York (publication date
30. J. M. Thomas and W. J. Thomas, "Introduction to the
Principles of Heterogeneous Catalysis," Academic
Press, New York (1967).
31. J. P. Vignes and P. J. Trambouze, Chem. Eng. Sci.,
17, 73 (1962).
32. J. F. Wehner and R. H. Wilhelm Chem. Eng. Sci. 6,
89 (1956).
33. P. S. Weisz, Ind. Eng. Chem. Fundamentals, 8, 325
34. Ahlborn Wheeler, "Reaction Rates and Selectivity in
Catalyst Pores," in "Advances in Catalysis," Vol. 3,
Academic Press, New York (1951).

The location of the equilibrium for a given gas composi-
tion is independent of the total pressure of the system."
Also presented with the above statements is a graph
which is reproduced below. Please study this information
and demonstrate (a) by numerical calculations whether
their data are concordant, and determine (b) the free
energy change of the reaction at 5000C.

Temperature dependence of the equilibrium constant Ep
0.401 I

0.30 /

0 53 400 450 500


Assume Kp = Ka


(Continued on page 226.)

FALL 1969

1 '14


mn .views and opinions




University of Florida
Gainesville, Fla. 32601

Perhaps at no time in its history has engineer-
ing education been beset by as many problems
as exist today. It has been said from many direc-
tions that those who left engineering teaching as
much as fifteen years ago would not recognize
much of the course material taught today. Al-
though this may be somewhat of an exaggera-
tion we recognize its broad validity, and we must
look forward to equally rapid changes in the
future. A vice-president of one of the great
electrical concerns mentioned when talking to
students that his company based its long-term
planning on the assumption that one-half of its
business twenty years from now would be in
new products. To transfer this concept to engi-
neering education we might anticipate that one-
half of the courses in the engineering college
catalogs circa 1985 will be totally new subject
matter and the remainder will be considerably
Because college catalogs are revised every
year faculties are used to the concept of new
courses and curricular changes. The picture of a
fifty percent change in course material in fifteen
years is not startling because it represents a
normal evolutionary trend. In fifteen years the
volume of published scientific and engineering
material will at least have doubled. There are
other changes which are just as probable that
appear to produce very severe emotional reac-
tions even when they are merely discussed. Such
questions as, what should represent the first pro-
fessional degree in engineering, and how does
technician training articulate with engineering
education are highly sensitive areas of interest.
These areas require objective analysis which is

Linton E. Grinter is vice-president of the University
of Florida. He was educated at the University of Kansas
and the University of Illinois (PhD, '26). Dr. Grinter
was ASEE Lamme Medalist in 1958. He is a leader in
establishing goals and directions for engineering educa-
tion in this country. The 1955 Grinter report on the
"Evaluation of Engineering Education" was instrumental
in adding an engineering science base to all engineering
curricula. He is active in many professional societies and
has served as president of both ASEE and ECPD.

difficult to achieve because of emotional reactions
based upon the concept of a unified profession
that has never truly existed in engineering. We
wear blinders if we fail to recognize that techni-
cians continually, although in small numbers,
move upward into the engineering profession, and
that scientists move laterally with little resist-
ance into engineering activities. Both groups
achieve the title of engineer in industry. Engi-
neering is a profession in flux that has still not
been defined for the purpose of exclusion either by
words or more importantly by actions.
An agency involved deeply with the need to
define the undefined and perhaps undefinable
profession of engineering is the Engineers' Coun-
cil for Professional Development. Its task of
accrediting engineering curricula and therefore
degrees has successfully placed a floor under the
profession of engineering that has received broad
acceptance. However, this floor, based upon the
amount of engineering education that can be
mastered in four academic years while allowing
for required work in mathematics, science, and
social-humanistic studies is not highly restrictive.
The great majority of institutions that make an


The evidence seems to point to the master's degree evolving rather gradually into the main accredited degree
whether or not it is called the first professional degree.

effort to recruit an engineering faculty of reason-
able quality, who in turn select students of rea-
sonable competency, achieve accreditation. Their
products become engineers by definition, and
those scientists and technicians who retrain or
upgrade themselves to compete with the product
of the engineering schools are accepted as
Under the procedures just described, we seem
to have some 800,000 engineers in this country,
of which about one-half belong to a major en-
gineering society. A 1967 EJC survey deter-
mined that 565,000 individuals belonged to 45
technical and professional societies, of an en-
gineering and applied science nature, of which
438,000 were classified as engineers. The tech-
nical societies that hold membership in ECPD
and EJC do not all restrict their membership
to engineers.

An old refrain in engineering education has
been the five-year undergraduate curriculum. It
has been proposed, urged and tried over a forty-
year period without significant success. At times
it appeared that nearly a majority of faculty
members would favor it. Why then has there been
so much emotional resistance to the concept of
the master's degree becoming the "first profes-
sional degree"? It seems doubtful that the re-
sistance rests upon the concept that future pro-
fessional engineers can attain an adequate edu-
cation in four years. Such is patently not true.
It may be that the terminology of "first profes-
sional degree" applied to the master's degree
raises the specter that a very large fraction of
presently practicing engineers would lose profes-
sional status. Because only a quarter of practic-
ing engineers now have master's degrees a long
transition period would be inevitable. Terminol-
ogy can often mask the most desirable objectives.
It is becoming evident that the Engineers'
Council for Professional Development is gradu-
ally being drawn into graduate accreditation in a
step-by-step fashion. The first step over a decade
ago was to accredit the master's programs of the
Naval Postgraduate School using under-graduate
standards. Then a number, of master's degree
programs or curricula developed in engineering
departments having no undergraduate curricula.

These departments applied for accreditation and
were gradually accepted. Now there are requests
for accreditation of master's level curricula in
colleges that offer bachelor's degrees in engineer-
ing where the bachelor's program is considered
to be pre-professional by the institution con-
cerned. ECPD certainly cannot insist upon ac-
crediting a pre-professional curriculum, and it is
doubtful that it can logically reject the right of
any educational institution to define for itself
what it wishes to call its first professional degree
in engineering.
The evidence seems to point to the master's
degree evolving rather gradually into the main
accredited degree whether or not it is called the
first professional degree. Important influences
are the following: (1) It seems doubtful that a
four-year education in engineering can be made
sufficiently superior to four years of either science
or technology to form the base for a clearly de-
fined profession. (2) An accredited master's de-
gree program based upon student desire and
aptitude for advanced study, with the opportunity
for those whose interests are not highly profes-
sional to accept employment at the bachelor's
level, would aid greatly in defining the profes-
sion of engineering. Quite independent of emo-
tional reactions this seems to be the most prob-
able direction of gradual evolution. This change
will be stimulated by changes in the engineering
college catalog because the course material added
always exceeds the deletions. Additions can be
made at the master's level without gross eco-
nomic waste due to greater motivation of selected
and self-selected students.
A factor that should not be overlooked in the
accreditation of graduate education is its useful-
ness in upgrading the casual offerings at many
off-campus centers. Undergraduate work in the
evening was at one time taught mainly by indus-
trial employees on a part-time basis. Gradually
through the accreditation process evening study
has been upgraded to achieve as nearly as practi-
cal an equivalency with day curricula and day
procedures. At the graduate level there has been
a dissemination of degree work to so-called grad-
uate centers. These centers operate not only un-
der the difficulties of evening programs on an
over-time basis, but they often use part-time
teachers to an excessive degree. Many fail to

FALL 1969

A factor that should not be overlooked in the accreditation of graduate education is its usefulness in
upgrading the casual offerings at many off-campus centers.

provide even the minimum essentials of library
or laboratory resources. Until graduate accredi-
tation in engineering becomes accepted, these
graduate centers will lack standards to guide
their activities. They need and their students
deserve the support that professional accredita-
tion would provide. Unfortunately, we still cannot
provide the upgrading through accreditation that
the off-campus graduate programs so clearly

At the opposite end of the spectrum from
graduate-engineering accreditation is found the
problem of technology curricula accreditation.
Beginning with the Wickenden report in the late
nineteen twenties it has been recognized that the
productivity of engineers depends upon the num-
ber and quality of the technicians available as
engineering assistants. In World War II the
engineering colleges became large scale techni-
cian training agencies for the Federal Govern-
ment and made one of their greatest immediate
contributions to the war effort through this chan-
nel. A post-war surplus of technicians may have
existed for a time, but if so, this could have been
only at the lower levels. The United States has
never developed an educational system that has
produced high-level technicians comparable to
those produced in most European countries. In-
stead, our bachelor degree engineers have per-
formed many technician-level activities.
This country suffers under the status symbol
of the bachelor's degree. Parents make great
sacrifices for their children to attain degrees.
Any degree often appears acceptable. Hence
technician curricula ranging from two to three
years have never attracted sufficient numbers of
students. The result is that new degree-level
programs in technology have been growing in
numbers. They now represent a considerable
group of curricula that carry the same descrip-
tive titles as the branches of engineering, i.e.,
electrical, mechanical, etc. One technological cur-
riculum widely adopted is building construction,
which found a home in colleges of architecture
rather than engineering. It has in part super-
ceded the curriculum of architectural engineering
which was technically too demanding upon the
type of student who was interested in this field.

The curriculum of building construction provides
the degree incentive and the reward of desirable
employment in a status position ultimately di-
rected toward supervision without requiring the
rigor of an engineering curriculum. It has grown
rapidly in popularity and is entirely outside the
control or direction of the engineering profession.
The broad field of industrial technology based
educationally upon degree curricula now seems to
be ripe for a development comparable to the ex-
ample given of building construction. The engi-
neering profession can influence this develop-
ment through its procedures of accreditation or
it can stand aside and observe the uncontrolled
development of a second channel for the prepara-
tion of technological personnel. When this prob-
lem was presented by the establishment of asso-
ciate-degree technician training curricula in the
years immediately following World War II it
was decided to lend a hand toward strengthening
these technical curricula through ECPD accredi-
tation. Of course, the question of terminology
arose, in particular the use of the adjective en-
gineering to describe such curricula. Obviously
ECPD could serve no function in the field of
medical technology or other fields not directly
related to engineering. Our interest had to be
restricted to the training of engineering techni-
cians. To make this clear the curricula eligible
for ECPD accreditation were classified as "engi-
neering technology" curricula. However one may
feel about the terminology chosen, the logic in-
volved seems indisputable. Unless a technical
curriculum is designed to produce technicians
who will work directly with engineers it could
hardly fit within the objectives of ECPD.
The recent action of the Board of Directors of
ECPD to accredit engineering technology curric-
ula of two, three and four years duration upon
the single basis of inspection of about 70 credit
hours of technical course work merely fulfills the
concept described above. Beyond the required
and regulated core of some 70 credit hours the
institution may decide to add additional work
requirements to justify the award of a bachelor's
degree. This additional work may be in liberal
arts, business administration, further technical
courses in the major, or in a second specialty,
or in any combination it may choose. ECPD will
restrict its interest to the core program that


Six Good Reasons To Choose A McGraw-Hill Text


GORDON S. G. BEVERIDGE, Heriot-Watt Uni-
versity, Edinburgh and ROBERT S. SCHECH-
TER, University of Texas. Available Winter, 1970
This text encompasses techniques from all
aspects of mathematical optimization with the
objective of introducing these methods to seniors
and graduate students. It is organized to illus-
trate the interrelationships among optimization
methods, their ranges of applicability, and their
comparative effectiveness. The authors provide
fully worked-out examples throughout the book
to aid the student, and discuss the main tech-
niques in detail to give the student competence in
their applications.

MORTON M. DENN, University of Delaware.
416 pages, $16.50
In order to present a comprehensive examina-
tion of optimal process design and control, the
author has simultaneously developed both ana-
lytical and computational considerations and then
united them with detailed practical applications.
The text utilizes the "variational" approach, in-
corporating traditional differential calculus pro-
cedures and associated computational techniques;
classical calculus of variations; Pontryagin-type
"minimum principles" and related computational
methods; and dynamic programming. Many of
the examples cited are examined at various levels
of sophistication and solved by several different

WILLIAM C. REYNOLDS, Stanford University
and HENRY C. PERKINS, University of Arizona.
Available Winter, 1970
The first half of this book develops the funda-
mentals of thermodynamics using microscopic
insight as the basis for macroscopic postulates.
Disorder, randomness, and uncertainty notions
are used in conjunction with the Gibbs definition
of entropy to provide an intuitive basis for the
second law postulate. The remainder of the book
applies the statistical concepts that have already
been developed to actual engineering systems.
Material on power systems and chapters on com-
pressible flow and heat transfer are included.

ROBERT D. KERSTEN, Florida Technological
University. 224 pages, $13.50
This is the first book to treat both the ana-
lytical as well as the numerical methods in engi-
neering. The author's thesis is that a complete
solution to a given engineering differential system
can be developed by using these approaches to
connect four essential parts of the system: (1)
properly understood phenomena; (2) a correct
mathematical model of the phenomena; (3) a ten-
tative solution; and (4) a proper application of
boundary or initial conditions or both.

WILLIAM E. RANZ, University of Minnesota.
Available Winter, 1970
With the intention of demonstrating how phy-
sical and mathematical models are built, this par-
ticipation textbook discusses states and actions of
physical and chemical systems; shows the detailed
development of material and energy balances; and
includes interactions of simple connected systems
as they are applied to chemical engineering. This
workbook is based on the premise that a student
learns by doing-therefore, numerous questions
and worked-out examples dominate the text.

WEL, JR., both of the State University of New
York at Buffalo. 500 pages, $15.50
This text (1) presents an introduction to the
field of modern computational methods in terms
intelligible to the second- or third-year student;
(2) develops from these various methods the
first principles that are basic and/or in general
usage and indicates the interrelationships among
them; and (3) views the material specifically but
yet generally enough to give the student the
background he will need in numerical methods to
cope with future engineering courses. Through-
out, the emphasis is on the methodology of the
solution process and the universality of its appli-
cation to problems in all fields of engineering and
the applied sciences.

330 West 42nd Street
New York, New York 10036

FALL 1969

relates directly to the title of the curriculum.
The award of a degree will be primarily the in-
terest of the regional accrediting agency. Re-
gional accreditation at the appropriate level (as-
sociate or bachelor's degree) must precede ECPD
inspection. It is believed that this limited ac-
crediting procedure by ECPD will eliminate, to
the maximum degree possible, confusion between
engineering education and engineering technician


tention given to continuing education would
doubtless increase. Because of its extensive ex-
perience with the accreditation process, ECPD
seems to be the logical agency to experiment with
this concept of formal recognition of achievement
in continuing education. It is hoped that an ap-
propriate channel for such recognition may be
devised. It seems to the writer that such recog-
nition is a serious responsibility of the engineer-
ing profession that has been neglected merely be-
cause of its sensitive nature.


The significance of continuing education for Fr,,,,, rA r"SV0
engineers was recognized a few years ago by a A profession may be defined in part by re-
comprehensive report sponsored by EJC. ECPD, quired steps of admission and advancement of its
ASEE and NSPE that emphasizes its great im- members. It can also be defined in part through
portance to the engineering profession. Never- aiding in the recognition of associated groups,
theless, continuing education operates under the who relate clearly to its activities, but by using
handicap that the achievement of the individual distinctly different standards for recognition.
receives no formal recognition. In contrast, a Such a relationship exists between engineers and
reasonable amount of effort directed toward engineering technicians or technologists. There
part-time graduate study can result in a master's is reason to hope that these and other actions of
degree that receives nation-wide acceptance. If engineering societies may aid in defining the pro-
some type of formal recognition of perhaps an fession of engineering which has resisted inclu-
equivalent academic year of effort devoted to sive definition by words alone. Nevertheless, the
continuing education could be developed, the at- writer believes that definitions can be improved.

PROBLEMS (Cont'd from p. 221.) Calculate the reversible voltage to electrolyze water at
Solution: 400C if the products and reactants are at 5 atm pressure.
Assume ideal gas behavior and negligible effect of pres-
(a) Assuming heat capacity effects negligible, use Eqn. (30) inr e t
sure on vapor pressure. For water take the standard
the form H/ \ state to be (a) pure liquid under atmospheric pressure
in a AH 1 1- T and (b) pure gas under its vapor pressure at 180C. Com-
l 1 22 pare the two answers. The reaction is HO0 -> H, + 1/2 02.

From the graph Ka = 0.lat427C and 0.4 at 600 C
Thus (1.99)8 (700) n -9750 cal/gm ole
.00-873 0.1- -9750 cal/gm mole
This agrees well with the -9810 cal given. The slope of the
InKa vs 1/T plot gives the same result.
(b) At 5000C, Ka = 0.19 for CO2 + H2 + CO + H20
For the reverse reaction Ka =
Therefore, from Eqn. (29)
AG = -RTlnKa = -(1.99) (773)1n 1
=-2550 cal/gm mole
No. 6. The heat of combustion of hydrogen with oxygen
at atmospheric pressure and 180C to form liquid water
is 68,300 cal/gm mole HO. The reversible voltage for
the electrolysis of water in a very dilute acid solution
at 180C is -1.23 volts when all products and reactants
are at atmospheric pressure. The latent heat of vaporiza-
tion of water is 10,500 cal/gm mole, and both this and
the heat of combustion vary negligibly with temperature.
The vapor pressure of water at 180C is 15.48 mm Hg
(neglect effect of small acid content), while at 400C the
vapor pressure is 55.31 mm Hg.

(a) Integrating Eqn. (33) assuming little change in AH,

| I H 1
or -,
o -1.23(313) 68,300(313)
40 291 2(23,050) 2
= -1.211 volts
By Eqn. (35)
S0 T 02 "2

-1.211 .99) (313) n)/2() -1.2438 volts

(b) In producing gaseous water AH = 68,300 10,500 57,800 cal/gm mole
u, c =-1.23(313) + (57,800) (313) [ 1 1 BI
Thus, o -+ 2(23,050) 21 = -1,228 volts
Now activity of gaseous water under own vapor pressure is
al20 It-r = 3.57

So -12 (1.s9s9)(313) (5)1/2(5)
So (2( -1.228 3in
-1.2434 volts which agrees well with -1.2438



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kC uvdicuam


Stevens Institute of Technology
Hoboken, N. J.

distinguishes the chemical engineer from all
other engineers is the foundation in chemistry
which is required. There is a generally accepted
statement, the origin of which has been lost in
antiquity, that says "The day mechanical engi-
neers dropped physical chemistry from their cur-
riculum, chemical engineering was born." Since
the birth of the AIChE, the question of chemical
engineering education has been uppermost in the
minds of its members. One of the first acts of the
new Society was to establish a committee on
Chemical Engineering Education, under the
Chairmanship of C. F. McKenna. There was
much debate on the curriculum content for chem-
ical engineering but little consensus until after
World War I, which has been known by many
people as the "Chemists' War." Prior to that
war, there was little chemical industry in this
country. As a matter of fact, the United States
was so dependent on foreign imports of chemicals
that the Germans were encouraged in 1915 to
deliver a supply of dyes to the United States by
submarine to avoid the Allied blockade. Following
the "Chemists' War" there was a major increase
in the chemical industry. Along with the growth
of that industry, there was a demand for chem-
ists and chemical engineers to staff these indus-
The fundamental educational debate at that
time was whether or not there really was such a
thing as chemical engineering. That chemists
were employed in the chemical industry was un-
questioned. That engineers were employed in the
chemical industry was unquestioned. The Ger-
man concept was to have a team of a chemist
and a mechanical engineer perform most of the
functions that are today thought of as chemical
engineering. It remained for the team of William
H. Walker, W. K. Lewis, and W. H. McAdams
* Presented at the Annual Meeting of ASEE, June 19-22,

Ralph A. Morgen is a graduate of the University
of California, Berkeley (PhD '25). He has been active in
research, teaching, and administration in engineering
education for thirty years. His most recent assignments
were President of Rose Polytechic Institute and Dean of
Graduate Studies at Stevens. Currently he is an engi-
neering consultant to Florida Atlantic University.
to publish a textbook "Principles of Chemical
Engineering" in 1923, to clearly and succinctly
delineate, for the first time, the place of chemical
engineering. This book made a clear distinction
between the industrial chemists on the one hand
and all other engineers on the other. The most
significant contribution of Walker, Lewis and
McAdams was to focus the attention of chemical
engineers on the unique place of the unit opera-
tions. While the term 'unit operation' had been
used earlier and is credited to Arthur D. Little,
who based a curriculum study on unit operations
as early as 19151, the concept did not take hold
until after the publication of this book. Dr. Little,
while he was Chairman of the Chemical Engi-
neering Education Committee of AIChE, made
the first steps towards the establishment of ac-
credited chemical engineering curricula. This
initial list appeared in 1925, eight years before
the rest of the engineering profession established
the Engineers' Council for Professional Develop-
ment. Only fourteen institutions appeared on this
list. In 1933, the chemical engineers joined
ECPD, but they retained a certain amount
of autonomy. They were the only ones who,
because of their previous experience, saw the
necessity for greater emphasis on the basic
sciences in the undergraduate curriculum fol-
lowed by advanced work at the graduate level.
This occurred before World War II, commonly
known as the "Physicists' War."
1"Highlights the first 50 years of the American
Institute of Chemical Engineers, pg. 56, (1958 published
by AIChE).


happened to the chemistry content of the under-
graduate curriculum over the past 30 years, the
14 institutions on the original accredited list
augmented by those institutions which were
deemed to have either distinguished or strong
faculties in the American Council on Education
study2 have been reviewed. The conclusions in
this paper have been confirmed by reviewing
what has happened to the chemistry content of
these twenty-four institutions.
From 1925 until accreditation was tempo-
rarily abandoned during World War II in 1943,
there was general hauling and pulling among
the proponents of more chemistry and basic
sciences as opposed to those who preferred more
applied and more practical engineering emphasis
in the curriculum. Dr. Albert B. Newman3 sum-
marized the situation as it existed in the late
1930's very well. Quoting from that paper'
"In modern practice, it seems clear that the chemical
engineer must not only have a working quantitative
knowledge of the unit operations, but he must have a
sound knowledge of chemistry, physics, mathematics,
thermodynamics and economics. He must have facility in
applying physical chemistry to plant processes, particu-
larly in relation to reaction velocities and the graphical
calculus used in the interpretation of laboratory and pilot
plant data on kinetics of chemical reactions."
As a result, in order to try to satisfy the two
opposing views, more engineering and applied
courses versus more chemistry and basic sciences,
the credit content of the undergraduate chemical
engineering course rose to an almost intolerable
level at many of the institutions. In some cases,
an average of 20 semester credit hours for a
total of eight semesters was required for gradua-
tion. The four year curriculum was reaching the
bursting point. Most of the stronger accredited
institutions, in that period, insisted on four years
and a summer session, usually between the junior
and senior years, to lessen this unrealistic load.
The Chemical Engineering Education Committee
was far ahead of the education committees of the
other engineering societies and of the philosophy
of ECPD in two respects in the 1930's. The

2An Assessment of quality in Graduate Education,
Allan M. Cartter, American Council on Education, Wash-
ington, D. C. pg. 70, 1966.
8Development of Chemical Engineering Education in
the United States, Supplement to transaction of the
American Institute of Chemical Engineers, Volume 34,
No. 3A, July 25, 1938.
4Ibid. Pg. 12

chemical engineers did not consider the four
year undergraduate course as terminal education,
but rather "that education5 has just begun at the
end of the four year course. No student should
prepare for chemical engineering unless he is
enthusiastic about the idea of a lifetime of
study." The Committee further believed that re-
search activity by the chemical engineering staff
and graduate students is important and was
usually found in those institutions which quali-
fied for accrediting.

in chemical engineering was one of the close ties
between chemists and chemical engineers which fostered
graduate education in both disciplines following (World
War I). The recommended content of an undergraduate
chemical engineering curriculum in 1938 is shown in
Table I. The percent figures are those taken from New-
man's publication6. There was little dissension regarding
IN 1938
(Normal Credits in)
Percent Semester Hours
Chemistry 25-30 36-44
Chemical Engineering 20-15 30-22
Other Engineering 12 18
Mathematics 12 18
Physics 8 12
Mechanics 6 9
Other Sciences 2 3
Cultural Subjects 15 22
Total 100 148
Development of Chemical Engineering Education in
the United States, Albert B. Newman (Trans. AIChE 34,
3a (1938).
the percentages, but the difficulty arose when such a
curriculum had to be translated into a reasonable number
of credit hours. For convenience, in Table I, the column
of normal credits is given for comparison with present
day curricula, but many of the actual curricula contained
total credits up to 160. It appears, therefore, that in
the 30's, most of the accredited curricula included four
whole year courses and at least one additional one
semester course in chemistry. The year courses were
usually general chemistry, quantitative analysis, organic
chemistry and physical chemistry. The additional courses
varied widely depending on the interests, competence and
backgrounds of the faculty at the various institutions. At
this time, it was generally agreed that the undergraduate
load was too heavy and further that graduate work was
to be encouraged. Quoting again from Newman's paper7
"The Committee is of the opinion that the tendency to
extend chemical engineering study into graduate years,
especially on the part of those students whose special
aptitude in theoretical divisions, is one that should be
5Ibid. pg. 16
6Ibid. pg. 23.
'Ibid. pg. 23.

FALL 1969


encouraged, because of the widely recognized difficulty
of giving adequate instruction within a period of four
years, especially if any attempt is made to teach methods
of research in science or engineering." Thus, it appears
that the Chemical Engineering Education Committee in
1938 reached the conclusion which apparently the rest
of the engineering profession is tentatively approaching
in 19678.
There was general agreement in the thirties
that if the amount of chemistry in the chemical
engineering curriculum is reduced drastically,
then the need for chemical engineering as a sepa-
rate entity becomes academic. This was about
the situation when World War II intervened. A
temporary cessation of the accrediting function
took place between 1943 and 1946. When the
ECPD Education and Accreditation Committee
reconvened after World War II, the effect on the
undergraduate engineering curricula was obvious
to many. The engineering education of the 30's
was found to be insufficient in its content of
mathematics and the basic sciences. The need
for adding large doses of the engineering sciences
(which the chemical engineers had called unit
operations in their area for many years) became
obvious. The physicists became enamored with
sub-atomic phenomena and tended to abandon
classical physics. Thus, the engineering sciences
and much of classical physics tended to merge.
The resulting effect on the chemistry content of
the chemical engineering curricula was serious
and in some cases drastic.
It became obvious that a thorough re-study
of the needs of undergraduate engineering edu-
cation was in order. At the request of ECPD,
ASEE undertook a study which has come to be
known as the Grinter Report9. The report of this
committee reads strikingly similar to the recom-
mendations of the Committee on Education and
Accreditation of AIChE as annunciated by its
chairman in 193810 The obvious difference, how-
ever, is that when most of the members of the
Grinter Committee talked about the basic sci-
ences and the engineering sciences, they were
almost uniformly talking about physics and al-
most uniformly neglecting chemistry. It was
only through the valiant effort of the few chemi-
cal engineering members of the ASEE Commit-

sInterim Report of the Committee on Goals of Engi-
neering Education, E. A. Walker, Chairman, American
Society for Engineering Eduction, April, 1967.
9Report of the Committee on Evaluation of Engineer-
ing Education, L. E. Grinter, Chairman, ASEE Pamphlet,
June 15, 1955.

It appears that the ChE Education Committee in 1938
reached the conclusion which apparently the rest of
the engineering profession is tentatively
approaching in 1967.

teen that some of the normal chemical engineer-
ing unit operations were included as some of the
engineering sciences. The publication of the
Grinter Report was a signal for rather drastic
revisions of engineering curricula throughout the
country. The kind of dichotomy which was men-
tioned previously as occurring among the chemi-
cal engineers in the 30's, now infected all the
branches of engineering, i.e., one group advocat-
ing more mathematics and basic science as op-
posed to those who recommend more applied
courses and practical training. The course con-
tent recommended by the ASEE Committee"1
illustrates the dilemma. (See Table II) The
whole four year curriculum allows less time for
mathematics and all basic sciences than the chem-
ical engineers thought was necessary for chem-
istry along in the 1930's. As a result, the chem-
istry content in 1966 of all of the curricula
studied contains less chemistry than those
same institutions had in the 30's or when they
were first accredited by ECPD.
Proportion of
(1) Humanistic Social Studies About 20%
(2) Mathematics and Basic Sciences
(About equal weight) About 25%
(3) Engineering Sciences About 25%
(4) Sequenceof Engineering Analysis,
Design and Engineering Systems, in-
cluding the Technological Background About 25%
(5) Options or Electives About 10%
Total Four years

aggravate the current situation, the explosion
of scientific knowledge since World War II,
argues for the inclusion of more subject matter
while the ASEE Committee recommends decreas-
ing the total number of credit hours to lighten
the burden on the student. This places engineer-
ing education squarely on the horns of two dilem-
mas: How to increase the science content of the
"Report of the Committee on Evaluation of Engineer-
ing Education, L. E. Grinter, Chairman (ASEE Pamphlet


curriculum on one side, decrease the total number
of contact hours on the other side and still make
an engineering curriculum without going beyond
four years. The conclusion is obvious. Sooner or
later it must be recognized that an adequate four
years curriculum in chemical engineering is a
misnomer. The Goals of Engineering Education
Committee realize that there are many ways to
reach the desired objective of a well educated
professional engineer. However, in each case the
inescapable conclusion must be reached that an
engineer has an insufficient background at the
end of the Bachelor's degree program to fit him
for a productive technical career in engineering.
The report further contends that formal educa-
tion to the Master's level followed by continuing
education throughout his professional life is a
must for the engineer of the future. Equating
the Goals report to chemical engineering it ap-
pears that there is room for various kinds of
chemical engineering curricula, all the way from
a very "light" chemistry content at the under-
graduate level followed by more chemistry at the
graduate level to a "strong" chemistry content
at the undergraduate level followed later by more
engineering at the advanced level. (See Table III)


Light Chem.
Semester cr.
Mathematics 21
Chemistry 24
Other Science 12
Chem Eng Science 34
Other Eng Science 10
Chem Eng Design 9
Other Eng Design (Electives) 6
Humanistic-Social 28
Total 144

Strong Chem.
Semester cr.

engineering is to continue to be the norm for first
accreditation and if the student is not to be given an
intolerable overload, then some compromises must be
accepted. A reasonable compromise can be achieved
among the relative amounts of basic science (in this case
the amount of chemistry), the engineering sciences and
the analysis, synthesis and design sequences. This com-
promise is coupled with the assumption that a course load
greater than 18 credits per semester or 144 semester
credit hours for four years is undesirable.
The "light chemistry" curriculum provides for a year
course each in general, organic and physical chemistry.
This is agreed as the irreducible minimum for a chemical
engineer. The "strong chemistry" program allows for
about three semesters of additional chemistry, but in so
doing some mathematics, chemical engineering science

and chemical engineering analysis, design and systems
must be sacrificed. The twenty-three institutions in Table
II with accredited undergraduate chemical engineering
curricula in 1967 all come within these limits.
Once the young Bachelor's degree recipient from
either of these curricula becomes engaged in technical
work in industry, he will feel his inadequacy in one
direction or the other depending on his needs. He will
be encouraged by his employer to fill the gaps by pro-
ceeding to the Master's degree. A typical program (See
Table IV) illustrates how either man can reach the same
general Master's degree plateau by selecting the appro-
priate courses.
There is considerable question in this writer's
mind whether the graduate from the "strong
chemistry" curriculum (which contains the mini-
mum amount of chemistry recommended by
AIChE in the 30's) has sufficient engineering
content to justify a designated degree (or an
accreditable degree) in chemical engineering.
The "light chemistry" curriculum has a reason-
able engineering content but is shy in chemistry.
The problem has now come full circle. When the
AIChE Committee on Accreditation published its
first accredited list in 1925, the concern was to


Other Science
Ch.E. Science
Other Eng. Science
Ch. Eng. Analysis,
Design and Systems
Other Eng. Analysis,
Design and Systems

Chem Eng Science
Chem Eng Analysis,
Design and Systems
(includes thesis)


22 21 16
28 24 36
16 12 16
22 34 28
18 10 10

4 9















FALL 1969

No student should prepare from ChE unless
he is prepared for a life-time of

distinguish the chemical engineer as an engineer
distinct from the industrial chemist. Now the
problem appears to be to provide the chemical
engineer with enough chemistry to distinguish
him from other engineers.

his Committee recognized that education be-
yond the Bachelor's level was required if the
chemical engineer were to have both sufficient
chemistry and engineering. The intervention of
the Physicists' War showed everyone the need
for basic physics for all engineers. Thus, at the
time of the Grinter Report in 1955, the amount
of basic science in all engineering curricula was
raised for the first time to the level required by
the chemical engineers as early as 1933. The net
result has been that chemical engineering, in
order to increase the physics content, had to
decrease the chemistry content. The Grinter Re-
port recommended that an engineering curricu-
lum include in the more general engineering
science courses much of the material that in the
1930's the chemical engineer covered (less thor-
oughly to be sure) under the unit operations
label. The result is a squeeze in the chemical
engineering sequence in favor of engineering
science courses in other departments, i.e. fluid
dynamics in place of the unit operations fluid
flow. Conversely, some very fine courses in high
temperature chemistry are being conducted by
departments of astronautics and aeronautical en-
gineering and some courses in radiation chemis-
try are being taught by departments of physics
and nuclear engineering rather than depart-
ments of chemistry. Thus, many of the old labels
are being confused.
At this point, it does not seem desirable to
debate the virtues and vices of these changes,
but merely to report them as facts. The result is
similar to the meeting of the immovable body
and the irresistible force. Somebody has to give
or the result is chaos. This writer favors a com-
promise solution in which all engineers will be
given a Bachelor's degree in engineering un-
designated. Each student in the general engi-
neering curriculum (See Table IV) would be given

rlIbid. pg. 23

... it must be recognized that an adequate four year
curriculum in ChE is a misnomer.
... This writer favors a compromise solution in
which all engineers will be given a Bachelors
degree in engineering undesignated.
. the first designated degree would be at the
Master's level.

sufficient latitude in electives so that he can
choose the basic science and the engineering
science that will give him a sufficient flavor of his
proposed major. At the same time, the concen-
tration in his major would be limited so as to
permit his getting a broader engineering educa-
tion than would be the case if there were a des-
ignated degree at the Bachelor's level. With this
type of broad engineering degree, the first desig-
nated degree would be at the Master's level. It
should be a stronger degree with a broader back-
ground than would be the case with a Master's
degree built on either the "light chemistry"
BChE degree or the "strong chemistry" BChE
degree. (See Table IV for comparison).
Nevertheless, it seems perfectly clear that there are at
least three routes toward the Master's level in chemical
engineering, any one of which will produce a satisfactory
product. It is also evident that more chemistry is needed
by the chemical engineer than he is now getting in many
of the "light chemistry" BChE curricula in institutions
listed in Table III. It is further assumed, however, that
the better students are wise enough to get that chemistry
either by taking additional courses after they graduate
or are being exposed to this material by taking courses
otherwise labeled in other departments.
The inevitable conclusion is that the explosion of
knowledge since World War II has emphasized the im-
portance of giving to the present day chemical engineer
at least as much chemistry as he had before World War
II. In addition, his curriculum must include more from
the other basic sciences plus more mathematics as well as
new and expanded engineering sciences. If he is to be
an engineer, he must have his share of courses in analysis,
and design. All this material cannot fit in the old
standardized package.
There will be ample jobs for anyone who
wishes to terminate his formal education at the
traditional Bachelor's level. All three routes, the
"light chemistry" BChE, the "strong chemistry"
BChE and the general engineering with chemical
electives BE, will find many opportunities for
productive careers. But in 1967, as in 1938 the
chemical engineer has just begun at the end of
four years of formal study. No student should
prepare for chemical engineering unless he is
prepared for a life-time of study with a maxi-
mum of chemistry.


LETTERS (Cont'd from p. 208.)
Wills surveys publication frequencies
Sir: Publication of the results of their continuing re-
search is a major responsibility of those holding academic
positions in the field of Chemical Engineering. Frequently,
and at least once a year during salary review, questions
arise concerning these scholarly publications. Presumably
both individuals and departments as a whole are eval-
uated. While it is possible to determine an average per-
formance for an institution, for its component schools
and departments, it is not ordinarily possible to compare
individuals and departments with their peers (i.e., similar
departments and disciplines at other institutions) even
though this would be highly desirable. The deficiency in
the use of peer-comparison is due to the lack of suitably
detailed statistics for each discipline. The purpose here
is to furnish the data necessary for peer-comparison in
the field of Chemical Engineering.
Detailed reporting of publications by departments and
by individuals is available for ChE for the two year
period July, 1965 to July, 1967. The source of this in-
formation is the 'Directory of Graduate Research," pub-
lished by the ACS. The information contained in this
publication was solicited directly from all of the ChE
departments in the United States offering graduate de-
While detailed information concerning publication
records is available in the ACS "Directory of Graduate
Research", there is no statistical correlation of these
data. Given here is a correlation of these data. The pub-
lication records by professional rank are given in Figures



20 UPPER 10%

a 10
0M R
0 0 0.5-1 L5-2 2.5-3 3.5-4 45-5 55-6 >6

1, 2 and 3. Figure 4 gives overall departmental records.
Table 1 gives additional information concerning the pub-
lication data.
It should be pointed out that the estimates of publica-
tions should be considered as slightly inflated due to the
reporting of items that ordinarily would not be considered
publications. However, some editing has been done in this
regard and the distributions and averages shown should
be substantially correct. Also, the data correlated reflect
the period 1965-67. The decreasing graduate enrollments
of the past two years may well result in a reduction in
the current rates of publication.
George B. Wills
Virginia Polytechnic Institute

Table 1. Publication Rates in 78 ChE Departments

Pub. per
Professors Number man-yr.


Assistant 229 0.73 11.3% published 2 or more
Associate 216 1.09 10.2% published 3 or more
Full 308 1.95 10.1% published more than
4 papers/yr.
Avg. 9.0% of all depts. pub. 2.25
(78 depts.) 1.27 or more papers/yr.

n 40-


o I
'. I 1 0 1,

0 05-1 15-2 25-3 35-4 4.5-5 5.5-6 >6

0 0.5-1 15-2 25-3 3.5-4 4.5-5 55-6 >6



-< 20 I UPPER 10%


0 0-.5 5-1 1-1.5 15-2 2:25 >2.5

FALL 1969


2.Berkeley overlooks beautiful
San Francisco__ .
5.The Athens of the West.
9.City on Monterey Peninsula,
3 hrs. south of Berkeley.
11.California State University
12.Telegraph Avenue Is a
veritable__ .
14.Recent Basketball star for
southern branch of U.C.
15.People over 30 are likely
to be _
2O.Princlple item developed
during thesis research.
23.Noted early Californian.
27.French deity.
28.Cal occasionally scores one
in Memorial Stadium.
30.Goes halfway to the stars.
32.Initials of American Conser-
vatory Theater, noted San
Franclso repertory group.
33.Graduate students do spend
some time here.
34.In Berkeley,75 across makes
the weather never .
36.Prominent resident of Carmel
Valley,south of Berkeley.
37.0pen up that Golden-- .
38.Tall tree on Berkeley campus.
41.San Francisco airport.
43.The Queen of England.
45.The_ and fauna of the
Sierra Nevada are famous.
47.At Berkeley, a graduate stu-
dent never feels like a- .
49.Location of notorious steps
oft seen on TV.
S2.Swiss Sierra Nevada.
56.Berkeley Inltials of 1964.
58.Where the action s.
59.In oral exams.graduate
students hope not to -__
61..ame for ancient Troy.
63.Waterfalls, lakes and granite
domes,4 hrs. east of Berkeley
66.First word represented by
initials of 56 Across.
68.The entering Berkeley grad
student Is a11 .
69.Component of cyclotron.
70.Adversary of Bond,Dr.-- .
71.Prominent California politico
73._ Valleylowest spot in US


BRAIN BENDER Sequoia Sempervr,.- s
the largest.
2 Common verb.
Island in San Francisco
75:Cause of pleasant Berkeley 4.See 16 Down.
summers. 51Thlng to do In Berkeley
17.Ernest O.Lawrence first built Chemistry library.
one In Berkeley. 6.Just write EHH here--e.
O0.If you're not looking at the couldn't think of any-
bow, you are looking .._ thing:
83.Object of Berkeley chemi-ts 7.Dutch air line.
research. B. River, Source of gold
64.Opposite of u.v. In 1849.
85.Berkeley electrochemical eng- 10.Honest -- .
Liners are concerned with this. 13.lnollsh suffix.
88.Principal product of valley 14.Same as 33 Across.
Just north of Bay Area. 16.Source of ego.
89.Another West Coast state (abbr) 17.River In Arizona.
90.Where Berkeley students go to 18.Bush with purple flower.
see Willie Mays. common In Sierra Nevada.
93.Et ._ Brutus? 19.Potato.
94.Hippie home. 21.Type of current.
g7.Whltney is the highest one; 22.A lake, gem of the Sierra.
It's In California, too. 24.What this is all about
98.Theme of many a rally. (initials).
99. __ alley, site of 1960 25.Industrial recruiters
Winter Olympics -easy drive pick up the
from Berkeley. 26.Mass_.Heat__.Momentum--.
101.Noted San Francisco hill. 28.Scholarly area stressed
103.At Trader Vic's In San Fran. at Berkeley.
or Oakland you may have a 29.SIltcone queen of North
__ -Ta Beach.
105.We endeavor not to make our 31.Type of record.
oral exams a__ 35.First letter of acronym
107.Shot In tennis, played year- of recent Berkeley move-
round by faculty and students, meant.
O1g. Free ___ 37. t was found at Sutter's
110.A graduate student is never Mill.
__ for very long after he comes 38.After you come to Berk-
to Berkeley. eley, your future is-
112.Noted wine-producing area near 39.Modern art form.
Berkeley. 40.Gol of grad studies at
114.French plane of World War I. Berkeley (degree).
115.French king. 41.Type of food, music.etc.
S116. ___ Cobb. 42.erkeleyc Is .
117. Galahad. 44.It Intersects Ashbury.




46.Last two letters of
acronym begun in 35 Doen.
48.Scottish no.
50.11_ only In wnter In
Berkeley (French).
51 Initials of see water
conversion process,.patents
held bv U.C.
33.All but "he" would
greet you warmly.
54.oted Berkeley faculty
5S.Stat University (abbr)
57.Mhen you go fishing In
the Sierra, you bring
60.What old professors become.
62.Contalner for beer and
ale at LaVal's -near campus.
64.Reciprocal of cosine.
65.Nature of Berkeley faculty.
66.Mr. Manchu.
67.Registered nurse.
68.University of California
72.Length of typical mid-
term quiz.
73.Another result of 75
74.Type of flower.
77.Berkeley's computer isn't
78.Substance of concern to
chemical engineers.
79.Computer- sts sometimes
count In-
82.Attending Berkeley starts
you on the to success.
85.Berkeley Is always free of
snow and__.
86.Desired verdict from
Oualifying E amination.
87.Element No. 93. discovered
It Berkeley.
91. ype of water under research
by Berkeley Chem. E's.
92. F lllar name for Headless
9S.hever regard the faculty
as your .
96.Most classes are held in the
100.The California sun keeps one
from looking-- .
101O.Greek letter.
102.Baghdad the Bay (SF).
105.Component of distillation
106.Curse you._ Baroni
10S.Berkeley chemists found
CH. and NH on __
lO9.Popular musical, now
playing In San. Fran.
Ill.Our graduate students
are ll scholars.
113.Hawailan food.






The Department of Chemical and Nuclear Engineering offers a full program of graduate courses and research
projects leading to the M.S. and Ph.D. degrees in chemical engineering. Eight full-time faculty members direct
research over a wide variety of chemical engineering and related nuclear engineering problems. Modern, well-
equipped research laboratories and computer facilities (IBM 360/75) back up all research programs.

FACULTY . John E. Myers, Ph.D., Univ. of Michigan
1952. Professor of chemical engineering and chair-
man of Department. Research program: Two phase flow
in porous media, mechanisms of boiling heat transfer.
Henri J. Fenech, Sc.D., Massachusetts Institute of
Technology 1959. Professor of nuclear engineering.
Research program: Reactor engineering and reactor
analysis, heat transfer.
Owen T. Hanna, Ph.D., Purdue Univ. 1961. Asso-
ciate professor of chemical engineering. Research pro-
gram: Applications of mathematics in chemical engi-
A. Edward Profio, Ph.D., Massachusetts institute of
Technology 1963. Associate Professor of Nuclear
Engineering. Research program: Reactor experimental
physics, neutron shielding, nuclear interaction with
Robert G. Rinker, Ph.D., California Institute of Tech-
nology 1959. Associate professor of chemical engi-
neering. Research program: Kinetics and reactor de-
sign, energy conversion, air pollution control.
Duncan A. Mellichamp, Ph.D., Purdue Univ. 1964.
Assistant professor of chemical engineering. Research
program: Dynamics of chemical processes, hybrid
computer applications to adaptive and predictive con-
trol problems.
Paul G. Mikolaj, Ph.D., California Institute of Tech-
nology 1965. Assistant professor of chemical engi-
neering. Research program: Thermodynamics and

phase equilibria, structure of liquids and dense gases,
oil pollution control.
Orville C. Sandall, Ph.D., Univ. of California,
Berkeley 1966. Assistant professor of chemical engi-
neering. Research program: Non-Newtonian heat trans-
fer, interphase mass transfer, fluid mechanics of film
CAMPUS . Santa Barbara is located on the Pacific
coast one hundred miles north of Los Angeles. The
campus occupies a 630-acre scenic promontory with
the Santa Ynez mountains immediately behind. Twelve
thousand students are enrolled in programs in diverse
fields of engineering, science, humanities and the arts.
Attractive housing of all kinds is available within
walking distance of the campus.
URES . Teaching assistantships are available to
qualified students; the stipend begins at $3,402 for
the academic year with merit increases as progress is
made towards a degree. A number of University
Fellowships, Research Assistantships and various Train-
eeships are also available for qualified students. In-
formation concerning departmental procedures can be
obtained by writing Professor J. E. Myers, Department
of Chemical and Nuclear Engineering, University of
California, Santa Barbara 93106. Application forms
for admission and financial assistance should be re-
quested from the Dean of the Graduate Division, Uni-
versity of California, Santa Barbara 93106.

FALL 1969



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.
The Ph.D. degree requires a minimum of three years
subsequent to the B.S. degree, consisting of thesis re-
search 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.

APPLICATIONS Further information and an application
form may be obtained by writing
Prof. C. J. Pings
Executive Officer for Chemical Engineering
California Institute of Technology
Pasadena, California 91109
It is advisable to submit applications before February
15, 1970.


WILLIAM H. CORCORAN, Professor and Vice
President for Institute Relations
Ph.D. (1948), California Institute of Technology
Kinetics and catalysis; gas chromatography;
plasma chemistry.
Ph.D. (1954), University of Illinois
Aerosol physics; particle-surface interactions;
interfacial transfer; diffusion and membrane
GEORGE R. GAVALAS, Associate Professor
Ph.D. (1964), University of Minnesota
Mathematical methods applied to problems of
chemical reactions and transport, process dy-
namics and control.
CORNELIUS J. PINGS, Professor and Executive
Ph.D. (1955), California Institute of Technology
Liquid state physics and chemistry; statistical

BRUCE H. SAGE, Research Associate
Ph.D. (1934), California Institute of Technology
Eng.D (1953), New Mexico State College.
JOHN H. SEINFELD, Assistant Professor
Ph.D. (1967), Princeton University
Optimization and systems studies in chemical
process control.
FRED H. SHAIR, Associate Professor
Ph.D. (1963), University of California, Berkeley
Phenomena associated with magnetohydrody-
namic power generation; chemical reactions and
diffusion in electrical discharges.
Ph.D. (1958), University of New South Wales
Mechanical properties of polymeric materials and
dilute polymer solutions.
ROBERT W. VAUGHAN, Assistant Professor
Ph.D. (1967), University of Illinois
Solid state chemistry and physics, particularly
effects of high pressure.

Professor W. N. Gill, Chairman
Chemical Engineering Department
Clarkson College of Technology
Potsdam, N. Y. 13676

Please send further information on your graduate program to


Number and Street

Undergraduate School

State Zip Code

For example, Drexel awards more engineering degrees than any other private university.
PROGRAMS: M.S. and Ph.D. in Chemical Engineering.
RESEARCH: Drying Dynamics Process Dynamics and Control
Atomization Phenomena Fluid Mechanics of Films
Environmental Problems Optimization of Drying Processes
Biomedical Engineering Catalysis of Reverse Flow Reactors
SUPPORT: Fellowships, Research Assistantships, and Teaching Assistantships are awarded to
qualified students. The minimum stipend is $275/month plus remission of
tuition and fees.
LOCATION: In Philadelphia, the hub of the industrialized Delaware Valley. Contact with
many of the chemical and petroleum companies of the area is convenient and

For further details, please send this form to: NAME:
Dr. John A. Tallmadge, Graduate Advisor; or ADDRESS:
Dr. Donald R. Coughanowr, Chairman
Department of Chemical Engineering SCH
Full-Time__ Part-Time_





* Remote IBM 360 Terminals
* Computer Controlled Laboratory
* Individual Student Attention
* A Dynamically Developing Department
* Modern Air-conditioned $1,500,000 Building
* Balanced Department
Faculty of 17: diversified interests
Wide course selection
Four degree programs
* Participation in NSF "Center of Excellence" Grant

Since many of you are interested in industrial
careers in development and design, while others
intend to teach and do basic research our gradu-
ate program is divided into two main areas and
several interdisciplinary activities.
Transport phenomena Fluid dynamics
Thermodynamics Kinetics
Materials science Applied Math
Chemical reaction engineering Process dynamics
Separations processes Process control
Computer aided design Optimization
Energy conversion Polymer science
Biomedical Process economics
Microelectronics Bioengineering

Master of Engineering with project on de-
sign, cost analysis, experimental investiga-
tion, or computer study.
Master of Science with thesis.
Master of Engineering Pre-Ph.D.
Doctor of Philosophy.

New Chemical Engineering Building located at center
of new Engineering Building Complex.

Models and Methods Multidimensional and
Discrete Systems Thermodynamics of Reac-
tion and Phase Equilibria Fundamental
Transport Phenomena Process Dynamics 1 or
Process Dynamics 2 Reactor Design and Op-
timization (Systems Program) or Chemical
Kinetics (Science Program)
Mathematical Methods in Chemical Engineering
* Applied Field Theory Computer Control of
Processes Optimization Techniques Trans-
port Properties and Irreversible Thermody-
namics Applied Statistical Mechanics Sta-
tistical Thermodynamics Interfacial Trans-
port Phenomena Turbulent Transport Phe-
nomena Advanced Transport Phenomena *
Rheology Non-Newtonian Fluid Dynamics *
Chemical Energy Conversion Particulate Sys-
tems Applied Fluid Dynamics Process Engi-
neering Process Equipment Design Process
and Plant Design Process Economy Analysis
* Tensor Fields and Fluid Dynamics Biochem-
ical Engineering

Chairman, Chemical Engineering Department
University of Florida
Gainesville, Florida 32601
Please send information on your graduate program to:

FALL 1969

Iowa State University in Ames, Iowa, the
first school to be established under the 1862
Land Grant Act, has a long tradition of lead-
ership in Engineering and Applied Science.
Today it ranks seventh in the nation in Ph.D.
degrees granted in Engineering and ninth in
degrees in Chemical Engineering. Its College
of Engineering is the largest west of the
Mississippi River.

To those interested in Chemical Engineer-
ing, Iowa State offers a variety of courses and
research areas leading to the M.E., M.S. and
Ph.D. degrees. The Department of Chemical
Engineering is one of the oldest in the United
States and enjoys a rich heritage of excellence
in teaching and research. The staff numbers
22 and the enrollment consists of 300 under-
graduate and 70 graduate students.

In addition to facilities available in a new
Chemical Engineering building, research is

conducted in the Ames Laboratory, a Nation-
al Laboratory of the US Atomic Energy Com-
mission, located on the Iowa State campus. A
staff of nearly 1,000 at the Laboratory con-
ducts basic research of long-range interest to
the nuclear industry.
Ames lies amid the gently rolling hills of
central Iowa. Typical of the picturesque yet
modern campus is the new cultural center
shown above, now half complete. This fall the
Festival of Concerts at the center auditorium
was opened by the New York Philharmonic.
The 14,000-seat coliseum will host many Big
Eight Conference athletic events.
A large variety of assistantships and fellow-
ships are filled each year by new graduate stu-
dents in Chemical Engineering. Living accom-
odations are available for single students in a
new eight-story graduate dormitory, and for
married students in more than 1300 apart-
ments operated by the University.

IGeorge Burnet, Head
IChemical Engineering Department
SIowa State University
Ames, Iowa 50010

Please send application forms and further information on your graduate program.



luate School

Number and Street

City State Zip Code__


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



Kinetics and equilibria of atmospheric reactions
Diffusion in the atmosphere: modelling of urban areas
Air sampling and analysis
Process and system control; air cleaning
Effects of pollutants on man, materials, and environs

Excellent, U.S.P.H.S. Traineeships available

At U.K.-a nine-man faculty, new laboratory and class-
room facilities, a complete graduate curriculum, a variety
of research topics . .

Contact: Robert B. Grieves
Dep't of Chemical Engineering
University of Kentucky
Lexington, Kentucky 40506

FALL 1969


Department of Chemical Engineering

Program of Study

Research Facilities

This department offers work leading to the Master of Science degree in chemical engineering and the Doctor
of Philosophy degree in chemical engineering. The Master of Science degree may be earned under either thesis
option or a course work option. Where practical, the thesis option is encouraged for students planning a
terminal Master of Science. A Master of Science in sugar engineering is also available through the department.
Each of twenty graduate courses is taught at least once each academic year. Undergraduate preparation
should normally be the equivalent of that established as the minimum requirement for accreditation by the
Engineers' Council for Professional Development. Special cases will be considered by the Head of the
The Master of Science degree requires a thesis plus 24 course work credit hours of which a minimum of 12
must be taken in chemical engineering. For nonthesis Master of Science students, 36 credit hours are
For the Ph.D. degree a minimum of 60 credit hours beyond the baccalaureate are required. These must
include 18 to 27 credit hours in chemical engineering, 12 to 15 in one or two minor subjects, 3 to 6 in
cultural electives, and 12 to 15 in technical electives. A maximum of 9 credit hours is allowed for dissertation
research. In addition each candidate must demonstrate a reading knowledge in at least one foreign language.

Within the Chemical Engineering Department are a number of special purpose research facilities which
include a reacting fluids laboratory, thermal fluids laboratory, a high polymers laboratory and a modern
computing laboratory which includes analog, digital and hybrid computers. The department is also serviced
by such University facilities as the Nuclear Science Center, the Computer Research Center, and one of the
most modern libraries in the South with holdings of more than 1,300,000 volumes.

Financial Aid A number of fellowships and assistantships are available for graduate students during the academic year.
Fellowship and research assistantship support is provided by the NSF, NDEA, HEW, NASA, DOD, the
University, and private industry. Typical academic year stipends for half-time graduate assistantships or
fellowships range between $2250 and $2700 (tax-free) plus an additional tuition and fee exemption (not
including an activity fee of $55).
Graduate students have no difficulty in obtaining technical employment during the summer because of the
local concentration of chemical and allied industry in the area. Alternatively, full-time summer research
support is also possible.

Cost of Study For each regular semester (up to 12 credit hours) graduate student tuition includes a general fee of $50, a
University fee of $55, an activity fee of $55, and a nonresident fee (if applicable) of $100.

Cost of Living

For single students, dormitory rooms vary from $81 to $225 for men and $119 to $227 for women per
semester. Unfurrished apartments for married students rent for $65 to $90 monthly. Many reasonably priced
off-campus apartments and residences also are available for students within the University environs.

Student Body Undergraduate enrollment on the Baton Rouge campus averages 14,800, 40 per cent of whom are women.
Graduate and professional enrollment is over 3,500. Students are drawn from every state in the Union and
more than 60 foreign countries. About 730 international students are registered each academic year in both
the undergraduate and graduate programs.
Graduate enrollment within the Department of Chemical Engineering is approximately 90, including
part-time and full-time students. There are 40 full-time graduate students, of whom 19 are doctoral
candidates and 21 are master's or predoctoral candidates. Currently, 38 full-time graduate students in the
department are receiving financial aid.

The Community

LSU, situated within the city of Baton Rouge, has the unique advantages of a growing metropolis of over a
quarter of a million people as well as those of the outlying countryside, a paradise for fishing, boating, and
hunting enthusiasts. In addition the University supports a vast cultural and recreational program in music,
drama, art, and literature as well as fine programs in athletics. Just eighty miles southeast of the main
campus, at the entrance to the Gulf of Mexico, is New Orleans, internationally known for its southern
hospitality, charm and recreational activities.

The University Louisiana State University and Agricultural and Mechanical College is a multicampus, multipurpose system of
higher education, exerting a major influence on the economic, social, and cultural life of all its citizens.
Founded as a land-grant institution in 1860, LSU has grown to become one of the leading universities in the
South. The main campus consisting of 15 colleges and specialized schools is located on a beautifully
landscaped 300-acre plateau just east of the Mississippi River. Although physically retaining the beauty of its
southern heritage, the University is nevertheless a modern facility reflecting the scholarship and culture of the

Applying Applications for admission, although considered throughout the year, should be made as early as possible.
For those seeking financial assistance it should be made preferably by March 1 for a fall appointment and
November 1 for the spring semester. The aptitude portion of the Graduate Record Examination is required
for all applicants.

and Information
Department of Chemical Engineering
Louisiana State University
University Station
Baton Rouge, Louisiana 70803


Manufacture of Pulp and Paper is one of the largest and fastest
growing industries in the United States and the world. A research ren-
aissance in product and process diversification provides exceptional
growth opportunities for men and women in all disciplines of engi-
neering and science. Such talents are in demand for research, indus-
trial engineering, business management, marketing, systems planning
-you name it, this industry offers it.

Train for it at the University of Maine

The Department of Chemical Engineering at the University of Maine,
Orono, pioneered the first paper studies program in the United States,
and continues to lead in teaching multidisciplinary application of engi-
neering sciences to the varied and complex operational decisions of
this forest resources industry. The modern and rapidly expanding
paper industry of this state provides an exceptional opportunity for
cooperative interaction of University based programs with real life
problems of industrial development.
Students with a B.S. degree in most scientific or engineering disci-
plines can program a fifth year extension of their undergraduate cur-
riculum to fulfill requirements for a Certificate of Advanced Study in
Pulp and Paper Management. One half of the fifth year covers basic
fiber science and the technology of pulp and paper production. The
other half can be an elective sequence to develop special interests in:

Systems Engineering Process Control
Environmental Engineering Plant Design
Applied Computer Sciences Operations Economy
Polymer Science Engineering Management
... and others
Students who apply and qualify for admission to graduate school can
/ fit a substantial part of their fifth year Certificate Program to graduate
school requirements for a Master of Science degree in Pulp and Paper
Technology, in Systems Engineering, or in Chemical Engineering.

The University of Maine Pulp and Paper Foundation offers grants
to qualified students who undertake the fifth year program. Such
grants of full tuition plus $1100 cover all essential academic costs.
Fellowships and Assistantships are available also for a limited number
of students beyond the fifth year who aim for a Ph.D. in Chemical
For more detailed information about the pulp and paper programs
at the University of Maine and the financial assistance available write:

Dr. Edward G. Bobalek
Chemical Engineering Department
255 Aubert Hall
University of Maine
Orono, Maine 04473

FALL 1969





What are


looking for

in a



The University of Michigan, Department of Chemical
and Metallurgical Engineering, has operated gradu-
ate degree programs for over 50 years. We have
awarded over 300 doctorates and 1000 master's

The 35 faculty members work in all the traditional
areas of research and also such fields as plasma
reactions, process dynamics, catalyst structure, bio-
chemical processes, electrochemistry, multi-phase
systems, computer-assisted design, non-Newtonian
fluids, and reservoir engineering.

Besides the usual campus activities the University
and the Ann Arbor community offers the students
scores of concerts by famous artists, lectures held
throughout the year, plus the three drama series-
all handy to campus. Ann Arbor is located in a river
valley and is ideal for both winter and summer sports.

Most of our American and Canadian students receive
financial assistance. Also, the University has excellent
employment opportunities for student wives.

Write for information and a special book to:
Robert H. Kadlec, Chairman of the Graduate Committee
Department of Chemical and Metallurgical Engineering
The University of Michigan
Ann Arbor, Michigan 48104






The Department offers graduate work in chemical, materials, and nuclear engineering leading to the M.S. and
Ph.D. degrees. Some of the fields of specialization of the faculty are:

Chemical Engineering

Process Control Systems
Heat and Mass Transfer
Turbulent Transport
Solvent Extraction
Design and Cost Studies
Reaction Kinetics
Multiphase Flow
Process Dynamics
Computer Simulation

Biological and
Environmental Engineering

Aerosol Mechanics
Membrane Separations
Artificial Organs
Environmental Health
Air Pollution Control

Nuclear Engineering
Nuclear Reactor Physics
Nuclear Reactor Design
Nuclear Reactor Operation
Radiation Induced Reactions
System Dynamics
Radiation Shielding
Radiation Engineering
Engineering Materials
Reaction of Solid Surfaces
Solid State Behavior
Composite Materials
Statistical Thermodynamics
Structure of Metallic Solutions
Applied Polymer Science
Polymer Physics
Graft Polymerization
Polymerization Kinetics
Non-Newtonian Flow

The general requirements are set forth in the Graduate Catalog. The chemical engineering program
is designed for qualified bachelors chemical engineering students. The materials and nuclear en-
gineering programs are open to qualified students holding bachelors degrees in engineering, the
physical sciences, and mathematics.

Address inquiries to

Dean, Graduate School or Chairman Department of Chemical Engineering

FALL 1969

Department of Chemical Engineering



Contact Dr. M. R. Strunk, Chairman
Day Programs M.S. and Ph.D. Degrees

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

(1) Fluid Turbulence and Drag Reduction Studies
-Drs. J. L. Zakin and G. K. Patterson

(2) Electrochemistry and Fuel Cells-Dr. J. W.

(3) Heat Transfer (Cryogenics) Dr. E. L. Park, Jr.

(4) Mass Transfer Studies-Dr. R. M. Wellek

(5) Structure and Properties of Polymers-Dr. K.
G. Mayhan

In addition, research projects are being carried
out in the following areas:

(a) Optimization of Chemical Systems-Dr. J. L.

(b) Evaporation through non-Wettable Porous
Membranes-Dr. M. E. Findley

(c) Multi-component Distillation Efficiencies-Dr.
R. C. Waggoner

(d) Gas Permeability Studies-Dr. R. A. Prim-

(e) Separations by Electrodialysis Techniques-
Dr. H. H. Grice

(f) Process Dynamics and Control-Drs. M. E.
Findley, and R. C. Waggoner

(g) Transport Properties and Kinetics-Dr. O. K.

Tuition: Out of state tuition waived for Graduate Stu-
dents. Fees are approximately $200 per semester for
10 credit hours or more.

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








Biochemical Engineering
Computer Applications
Food Processing
Heat Transfer

Laser Applications
Mass Transfer
and other areas


Prof. J. H. Weber, Chairman
Department of Chemical Engineering
University of Nebraska
Lincoln, Nebraska 68508



Engineers working in the areas of control, communications
and reliability have long been familiar with stochastic processes
and have contributed to the development of the theory. The
powerful mathematical tools developed in these contexts, such
as the Theory of Markov processes, Queueing and Renewal
Theory, etc., have till recently found only limited application in
the chemical engineering profession and many research engineers
are still unfamiliar with its use. In the last few years these
methods have gained wider acceptance and their usefulness has
been demonstrated by different workers in a number of fields.

Our department is conducting one of the largest concentrated
research efforts in this field. The research group is headed by
Professors Stanley Katz and Reuel Shinnar and is active in a
wide variety of problem areas endeavoring to demonstrate the
usefulness and power of probability methods when applied to
contemporary chemical engineering problems.

Emphasis is given both to extensions of the theory and
the development of new methods, as well as to new applications
of the methods developed in other fields. Areas of investigation

1) Mixing and turbulence in chemical reactors.
2) Control of process plants.
3) Theory of tracer experiments.
4) Applications of tracer experiments to physiological prob-
5) Behavior of particulate systems, with emphasis on crys-
tallization, polymerization and more recently, meteo-
rological problems.

The program is specially suited for students with a mathe-
matical inclination, providing them an opportunity to enter a
new and growing field in chemical engineering. Research assis-
tantships for students intending to study for the doctoral degree
as well as a few post-doctoral fellowships are available. Inquiries
should be directed to

Professor A. X. Schmidt
Department of Chemical Engineering
The City College of the City University of New York
New York, N. Y. 10031



* Oklahoma, a vigorous state with space to dream and
grow, with a unique heritage and a promising future...
* a friendly city with a tradition of fine arts excellence
and exceptional recreation opportunities. .
* a University where human beings share values and con-
cerns, where innovation and relevance are more than
words ..
* a balanced department oriented to its missions . .
quality teaching for graduate and undergraduate stu-
dents . .providing basic knowledge through research
S.. translating that knowledge to practical use through
public service . .
* bright, young faculty members with energy and dedi-
cation, highly-motivated in teaching, research and
public service, beginning to achieve deserved recogni-
tion. ..
* a curriculum that has produced outstanding doctor of
philosophy recipients, 68 in the past 7 years, 17 of
whom are in professorial positions...
* academic opportunity, intellectual challenge, and an
atmosphere of creativity.

The School of Chemical Engineering
and Materials Science
The University of Oklahoma
Norman, Oklahoma






University of Pittsburgh
:. M.S. and Ph.D. Degrees


< Dr.


. Dr.



'* i / - -** .,. -

I, ,, -~--
(l*u /* -^ -^ -
h'^^--' -/':.^. 4
.,--- -




Charles S. Befoes. ---- pas Dynamics, Process Desigrtn& Oplimiza
,-Unsteady State Heal Transmissi
Alan'J. Brainard...... ..... .Thermodynamics. Mass Trans
George D. Byrne. Applied Manre rati
Shiao-Hung Chiang .... .Mass Transfer, Inleriacial pinS
.Morton Corn .. .. ......... A f
James Coull.. .......... Chemical Kinetics. Catalysis =bLe
Thermogravilalional Separali
Benjamin Gal-Or ... ......... . Transport Phenomer
Relativistic Therrnodynami
Harold E. Hoelscher .......... . ... Reaction Kinetic
Interfacial Phenome
George E. Klinzing .. .......Fluid Dynamics, Transport Phenome
Chung-Chiun Liu . : ............ Electrochemical Engineeri
Yatish T. Shah.. ........ .........Transport Phenome
Edward B. Stuart ... .......... .. .Thermodynamics, Adsorpti
John W. Tierney . .. Process Dynami
Equilibrium Stage Calculatio
Lemuel B. Wingard : .. . Biomedical Engineerir
Enzyme Catalys

Dr. Paul F. Fulton. . ... ......... .... Multiphase Flow in Poro
Media, Wettabil
Prof. James H. Hartsock. ... . ... Computer Applicatio
to Unsteady State Fl
Dr. Joseph J. Taber ................. Interfacial and Surface Phenomer
Miscible Displaceme

Chemical and Petroleum Engi-
neering is one of six School
of Engineeri4n departments
which offer graduate degrees.
Interdisciplinary programs
4-.. with other engineering depart-
S mnts and with other PITT
.- schools and divisions such as
i. Public Health, Natural Sci-
enc and Medicine are en-
SCourses begin in Septem-
ber, January and April; gradu-
ate students may enter in any

Graduate assistantships, re-
S search assistantships, fellow-
fer ships and tuition scholarships
S~ available to qualified stu-

inancal support is pro-
r," -vded by Ihe University, indus-
oit try, and various government
ia, agencies. Among sponsors of
cs current research programs are
cs, Petroleum Research Fund, Na-
na tional Science Foundation,
na U.S. Department of Agricul-
ng ture, National Aeronautics and
na Space Administration, and
on United States Steel Corpora-
cs, tion.
ns For application forms and
9g, detailed information on FEL-
us to:
ity Graduate Coordinator
ns Chemical and Petroleum
w Engineering Department
601 Engineering Hall
la, University of Pittsburgh
nt Pittsburgh, Pennsylvania 15213

*t^ia-. .^


:ORONAT Syracuse University is a private university situated among
S the hills of Central New York State. A broad cultural climate
t which stimulates interest in engineering, science, the social
-ED sciences, and the humanities exists at the university.

Programs leading to Master's and Ph.D. Degrees in Chemical Engi-
neering, Master's Degree in Metallurgy, and Master's and Ph.D. Degrees
in Solid State Science.

Computer Science Mathematical Modeling
Solid Mechanics X-Ray and Electron Diffraction

Separation Processes
Solid State Physics

Water Renovation Optimization of Multistage Processes
Rheology and Viscoelastic Fluid Phenomena

Membrane Processes
Mechanical Behavior of Solids
Surface Science

Metal Physics

Biomedical Applications
Thermodynamics and Kinetics
Electron Microscopy

Graduate Fellowships and Assistantships. Stipends range from $2,000 to $5,000 with most students
receiving $4,000 per annum in addition to remitted tuition privileges.

For Information Contact:
Dr. James A. Luker, Chairman
Department of Chemical Engineering and Metallurgy
Syracuse University
Syracuse, New York 13210
Telephone: Area 315-476-5541, extension 2559

FALL 1969

PROGRAMS for the degrees of Master of Science and Doctor of Philosophy are offered in both chemical z
and metallurgical engineering. The Master's program may be tailored as a terminal one with emphasis on ..
systems and design, or it may serve as preparation for more advanced work leading to the Doctorate.
Interests of the staff include thermodynamics, physical metallurgy, diffusional operations, heat transfer,
fluid mechanics, polymer science, reaction kinetics, information-operations, and systems analysis and A
design as applied to both chemical and metallurgical engineering.
FACULTY AND RESEARCH INTERESTS-William T. Becker, Ph.D., Illinois, Mechanical Properties and Deformation;
Donald C. Bogue, Ph.D., Delaware, Rheology; Charlie R. Brooks, Ph.D., Tennessee, Electron Microscopy, Thermodynamics;
Oran L. Culberson, Ph.D., Texas, Operations Research, Process Design; George C. Frazier, Jr., D. Eng., Johns Hopkins,
Kinetics and Combustion, Transfer with Reaction; Hsien-Wen Hsu, Ph.D., Wisconsin, Thermodynamics, Transport Phenom-
ena, Optimization; Homer F. Johnson, D. Eng., Yale, (Department Head), Mass Transfer, Interface Phenomena; Stanley
H. Jury, Ph.D., Cincinnati, Sorption Kinetics, Hygrometry, Information Operations; William J. Kooyman, Ph.D., Johns
Hopkins, Reaction Kinetics in Flow Systems; Carl D. Lundin, Ph.D., Rensselaer, Physical Metallurgy, Welding; Charles F.
Moore, Ph.D., L.S. U., Process Control and Dynamics; Ben F. Oliver, Ph.D., Pennsylvania State University, Solidification,
High Purity Metals; Joseph J. Perona, Ph.D., Northwestern, Mass Transfer and Kinetics, Heat Transfer; Joseph E. Spruiell,
Ph.D., Tennessee, X-ray Diffraction, Electron Microscopy; E. Eugene Stansbury, Ph.D., Cincinnati, Thermodynamics Kinetics
of Phase Transformation, Corrosion; James L. White, Ph.D., Delaware, Rheology, Polymer Chemistry. REGULAR PART
TIME-Lloyd G. Alexander, Ph.D., Purdue, Fluid Flow, Heat Transfer; Bernard S. Borie, Ph.D., M.I.T., X-ray Diffraction;
Albert H. Cooper, Ph.D., Michigan State, Process Design, Economics; Kenneth H. McCorkle; Ph.D., Tennessee, Colloidal
Systems; Carl J. McHargue, Ph.D., Kentucky, Physical Metallurgy; Jack S. Watson, Ph.D. Tennessee, Fluid Mechanics;
Monroe S. Wechsler, Ph.D., Columbia, Physical Metallurgy, Effect of Radiation on Metals.
LABORATORIES AND SHOPS-Analog computer (Expanded EAI,'PACE 221R) and digital computer (DEC, PDP 15/20
with analog interface), High-speed automatic frost point hygrometer, Mass and heat transfer in porous media, Polymer
rheology (Weisenburg rheogoniometer, Instron theological tester, roll mill, extruder), Polymer characterization (gel per-
meation chromatograph, osmometer), Mass spectograph, Continuous zone centrifuge, Process dynamics, X-ray diffraction
(including single crystal diffuse scattering analysis), Electron microscopes (Phillips EM75 and EM300), Calorimetry (25-
10000C), Electrical resistivity measurements for studies of structural and phase changes, Single crystal preparation facilities,
Mechanical fabrication and testing, (metallograph, optical microscopes and melting, etc.), High purity materials preparation,
Electronic and mechanical shops staffed by thirteen full-time technicians and craftsmen.
FINANCIAL ASSISTANCE from a number of sources is available, including graduate assistantships, graduate teaching
assistantships, research assistantships, industrial fellowships, industrial grants-in-aid, NSF Traineeships, NASA Traineeships,
NDEA (Title IV) Fellowships, and University Non-Service Fellowships.
COST OF STUDY-Full-time students who are Tennessee residents pay $105 per quarter maintenance fee; out-of-state
students pay an additional tuition of $205 per quarter. Holders of fellowships, graduate assistantships, and certain teaching
appointments pay no fees or tuition.
COST OF LIVING-Dormitory rooms costs for single students range from $75 to $100 per quarter; combined room-and-
board arrangements are available at $305 per quarter. Attractive one- and two-bedroom apartments for married students
rent from $60 to $110 per month unfurnished, approximately $15 higher furnished. Privately operated apartments are
available to single or married graduate students at equivalent and higher rates. Food and other living expenses are below
national averages.
STUDENT BODY-About 16,000 undergraduate and 4,000 graduate students are enrolled at the Knoxville campus of
The University of Tennessee. In the College of Engineering there are approximately 2200 undergraduate and 300 resident
graduate students.
KNOXVILLE AND SURROUNDINGS- Knoxville, with a population near 200,000, is the trade and industrial center of
East Tennessee; convenient transportation is available to all parts of the country. The University is located about five
blocks from the downtown business area. In the nearby Auditorium-Coliseum, Broadway plays, musical and dramatic
artists, and other entertainment events are regularly scheduled. Knoxville has a number of points of historical interest,
a theater-in-the-round, an excellent symphony orchestra, two art galleries, and a number of museums. Within an hour's
drive are many TVA lakes and mountain streams for fishing, boating, and water sports; the Great Smoky Mountains
National Park with the Gatlinburg tourist area; two state parks; and the atomic energy installations at Oak Ridge, including
the Museum of Atomic Energy. Avastnumberof cultural, recreational, and social activities are available on the University
A WORD ABOUT U.T.-Founded in 1794 as Blount College, The University of Tennessee has grown to a large multi-
campus, multi-purpose system of higher education covering the entire state. Graduate programs in science and engineering
centered at the Knoxville campus have developed to major size and strength over the past 25 years. A major stimulus to
the growth of these programs has been the proximity of the atomic energy facilities at Oak Ridge and the close cooperation
that has developed between these facilities and the University.




For admission, address
Dr. David S. Ray,
Coordinator of Graduate Studies

Graduate degrees granted: Master of Science in Chemical Engineering
Courses for graduate credit are available in the evenings.
Typical research interests of the faculty include the areas of: mass transfer, particularly
distillation and liquid-liquid extraction; thermodynamics; mathematical applications in
chemical systems; reaction kinetics; process dynamics and control; metallurgy and the
science of materials; nuclear engineering.
Assistantships and scholarships are available.
For the usual candidate, with a B.S. in Chemical Engineering, the equivalent of thirty
semester-hours of graduate credit including a thesis is the requirement for graduation.


Carnegie-NMellon University


Howard Brenner
Duane Condiff
Edward Cussler
Kun Li
Clarence Miller
Carl Monrad
Matthew Reilly
Stephen Rosen
Robert Rothfus
Herbert Toor
Raymond Zahradnik

FALL 1969 25c



SChemical Engineering Department

*ooo....... M.S. and Doctoral Programs

Alley, F. C., Ph.D., U. North Carolina-Air Pollution, Unit Operations
Barlage, W. B., Ph.D., N. C. State-Transfer Processes in Non-Newtonian Fluids
Beckwith, W. F., Ph.D., Iowa State-Transport Phenomena
Bruley, D. F., Ph.D., U. Tennessee-Process Dynamics, Bio-medical Engineering
Hall, J. W., Ph.D., U. Texas-Chemical Kinetics, Catalysis, Design
Harshman, R. C., Ph.D., Ohio State-Chemical and Biological Kinetics, Design
Littlejohn, C. E., Ph.D., V.P.I.-Mass Transfer
Melsheimer, S S., Ph.D. Tulane-Process Dynamics, Applied Mathematics
Mullins, J. C., Ph.D., Georgia Tech-Thermodynamics, Adsorption
FINANCIAL ASSISTANCE-Fellowships, Assistantships, Traineeships
C. E. Littlejohn, Head
Department of Chemical Engineering
Clemson University
Clemson, S. C. 29631


Case Institute of Technology, a privately en-
dowed institution with a tradition of excellence
in Engineering and Applied Science has long
offered a variety of courses and research areas
leading to the M.S. and Ph.D. degrees in Chemi-
cal Engineering. In 1967 Case Institute and
Western Reserve University joined together. The
enrollment and endowment make Case Western
Reserve University one of the largest private
schools in the country.


Chemical Engineering Science Division
Case Western Reserve University
University Circle
Cleveland, Ohio 44106



The Department of Chemical Engineering at
the University of Colorado offers excellent oppor-
tunities for graduate study and research leading
to the Master of Science and Doctor of Philosophy
degrees in Chemical Engineering.

Research interests of the faculty include cryo-
genics, process control, polymer science, catalysis,
fluid mechanics, heat transfer, mass transfer, air
and water pollution, biomedical engineering, and
ecological engineering.

For application and information, write to:
Chairman, Graduate Committee
Chemical Engineering Department
University of Colorado, Boulder





* Research in most areas of current chemical
engineering activity

Recipient of a $420,000 NSF "Center of
Excellence" departmental development

New 4.5 million dollar engineering building

Graduate studies through Ph.D. with a
faculty of 16 and over 90 graduate students

Located in the petroleum and petrochemical
capitol of the world

Year-round recreational activities

Qualified applicants are encouraged to apply.
Fellowships and assistantships are available in
amounts of $3600-$5000 in annual stipends.

For details and applications contact:

Chairman, Graduate Admissions Committee
Department of Chemical Engineering
University of Houston
Houston, Texas 77004.

FALL 1969



Department of Chemical Engineering
Lehigh University,
Bethlehem, Penna. 18015





Simulation, Optimization and
Computer-Aided Analysis
Water & Waste Water Treatment
Chemical Reaction Engineering
Transport Phenomena

Contact: Dr. T. W. Hoffman, Chairman
Dept. of Chemical Engineering




Students seeking a commitment to excellence
in careers in Chemical Engineering will find a
wealth of opportunity at Newark College of En-
The ChE Department at NCE has a well de-
veloped graduate program leading to the degrees
of Master of Science in Chemical Engineering or
Master of Science with major in such interdisci-
plinary areas as Polymer Engineering or Polymer
Science. Beyond the Master's degree, NCE offers
the degrees of Engineer and of Doctor of Engi-
neering Science.
Over sixty on-going projects in Chemical En-
gineering and Chemistry provide exceptional re-
search opportunities for Master's and Doctoral
candidates. Research topics include the follow-
ing areas:

* Fluid Mechanics Heat Transfer
* Thermodynamics Process Dynamics
* Kinetics and Catalysis Transport Phenomena
0 Mathematical Methods
NCE is located on a modern, twenty-acre cam-
pus in Newark, within 30 minutes of Manhattan.
Tuition for New Jersey residents is $24 per
credit; for non-residents, the cost is $35 per
credit. Fellowships and financial assistance are
available to qualified applicants.
Mr. Alex Bedrosian, Assistant Dean
Graduate Division
Newark College of Engineering
323 High Street, Newark, N. J. 07102



The Department of Chemical Engineering of Michigan State University
has assistantships and fellowships available for the academic year 1970-71.

Transport Phenomena
Radiation Engineering
Novel Separations
Biomedical Engineering
Hybrid Computation
Chemical Process Systems
Process Dynamics and
Flow Through Porous FOUNDED
Media 155
Kinetics and Reaction
Engineering VER
Diffusion in Liquids
Applied Chemical Engi-
neering Mathematics


Graduate Program


In The Areas Of

Heat Transfer and
Fluid Mechanics
Mathematical Applications
in Chemical Engineering

Optimization of
Chemical Processes
Process Dynamics

M.S. AND Ph.D.

For application forms and further information address:
Department of Chemical Engineering
360 Huntington Avenue, Boston, Massachusetts 02115

graduate study in ,CHEIALI


Master of Science in Chemical Engineering
Master of Science in Nuclear Engineering
Doctor of Philosophy in Chemical Engineering

programs designed to
S. develop and expand your scientific and engineering background
. equip you to play an effective role in R&D and in production and design
S. prepare you to undertake major responsibilities for scientific and technical
aspects of chemical engineering

A diversified faculty with wide-ranging research interests . .
excellent laboratory facilities especially equipped for graduate
research . modern computing facilities, including a "hands-
on" facility exclusively for engineering students and available
24 hours daily . financial support available

Your inquiries are invited. Address:
Dr. Robert N. Maddox, P.E.
Professor and Head
School of Chemical Engineering
Oklahoma State University
Stillwater, Oklahoma 74074

FALL 1969




Offers the M.S., the M.E. and the Ph.D. in Engineering. Em-
phasis on transport processes and thermodynamics. Strong in-
terdisciplinary support in chemistry, physics, mathematics, ma-
terials and computer science. Small classes taught by professors
with industrial experience.

Research and teaching assistantships, fellowships, and
traineeships are available.

For particulars and application forms write to:
Dr. M. W. Davis, Jr., Chairman
Graduate Studies Committee
College of Engineering
University of South Carolina
Columbia, S. C. 29208

New Mexico

State University

M. S. Program


Chemical Reaction


P. O. Box 3805
Las Cruces, N. M. 88001



Graduate Assistantships, Teaching Assistantships
and Fellowships Available

For Further information and applications for
graduate study in the Land of Enchantment,

Dr. T. T. Castonguay, Chairman
Department of Chemical Engineering
University of New Mexico
Albuquerque, New Mexico 87106

Full Text