Chemical engineering education

f 9 73 4wa4d 24d.,wu

Waterloo Program for High Schools

A Junior Course in ChE Computations

Indirect Measurement of Reaction Rate

The Project Approach to ChE Education

Test to Measure the Ability of Seniors in
the Practical Application of ChE Principles

An Undergraduate Course in Interfacial Phenomena

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to stop looking at life through a tunnel and find ways to protect all forms of it-from our
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EDITORIAL AND BUSINESS ADDRESS
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Chemical Engineering Education

VOLUME 8 NUMBER 1 WINTER 1974

FEATURES

.20 4wcad .Peclie -f'973
The Theory of Diffusion and Reaction-A
Chemical Engineering Symphony
Rutherford Aris

44 Waterloo Program for High Schools
E. Rhodes

48 A Junior Course in Chemical Engineering
Computations, E. M. Rosen

DEPARTMENTS
2 The Educator
James J. Carberry of Notre Dame

6 Departments of Chemical Engineering
University of California-Berkeley

12 Curriculum
Project Approach to Chemical Engineeering
Education Under the WPI Plan
W. Kranich, I. Zwiebel, and Y. Ma

28 Laboratory
Indirect Measurement of Reaction Rate
R. D. Williams

32 Classroom
Interface Phenomena for Engineers
D. O. Shah

16 Views and Opinions
Test to Measure the Ability of ChE Gradu-
ates in the Practical Application of ChE
Principles, E. C. Oden

41 Book Review

CHEMICAL ENGINEERING EDUCATION is published quarterly by the Chemical
Engineering Division, American Society for Engineering Education. The publication
is edited at the Chemical Engineering Department, University of Florida. Second-class
postage is paid at Gainesville, Florida, and at DeLeon Springs, Florida. Correspondence
regarding editorial matter, circulation and changes of address should be addressed
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available from the advertising representatives. Plates and other advertising material
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and $4 per year to ChE faculty in bulk mailing. Write for prices on individual
back copies. Copyright ( 1974. Chemical Engineering Division of American Society
for Engineering Education, 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. Defective
copies replaced if notified within 120 days.
The International Organization for Standarization has assigned the code US ISSN
0009-2479 for the identification of this periodical.

WINTER 1974

Educator

Jame J. Ga44e 4

OF NOTRE DAME

Prepared by the Faculty of the Department of
Chemical Engineering

etW E ARE LIKE DWARFS seated on the
shoulders of giants; we see more things
than the ancients and things more distant, but
this is due neither to the sharpness of our own
sight, nor to the greatness of our own stature, but
because we are raised and borne aloft on that
giant mass." So wrote Bernard of Chartres in the
12th century. Jim Carberry is rather fond of that
quotation. How else could he have risen, in the
words of his friend Rutherford Aris, "from the
low tables of Morries to the high table of Trinity,
Cambridge."*

BROOKLYN BEGINNINGS

A NATIVE OF BROOKLYN, Jim managed to
graduate from the famed Brooklyn Technical
High School at which site he achieved absolute
mediocrity as a single-wing halfback. "Brooklyn
Tech" recalls Carberry "was somewhat more than
absolutely competitive." Several classmates in-
vented radar some eleven months prior to Great
Britain's discovery of that toy. Carberry's qualifi-
cations impressed President F. D. Roosevelt, who
immediately appointed him an Apprentice Seaman
in the U. S. Navy. Japanese intelligence learned of
this and thus they assaulted Midway with supreme
confidence. As Jim was at that moment interned
at Torpedomen's School at Great Lakes, Illinois,
the Japanese lost the Battle of Midway.
Appropriately inspired by the quality of life
aboard a U. S. Navy Light Cruiser, Carberry sur-
rendered unconditionally in 1946 and, armed with
the G. I. Bill, enrolled as a chemical engineering
major at Notre Dame. He notes "there is nothing
quite like sea duty amidst grunting 'deck apes' to
inspire the lowliest of citizens to seek the highest

"Citation in U of Minn. "Semisesquibiennial Wet Test
Meter Award." Carberry was first and last recipient of
this noble award.

Now we must get on with our task-applied Chemistry.

of goals-outside the Navy." At Notre Dame, he
struggled with chemical engineering, played quar-
terback in its intramural tackle football program
(said John Lujack, "a quarterback should hide the
ball, but in Carberry's case, it hides him"), helped
classmate Leon Hart win the Heisman Trophy;
while Leon tutored Jim in Physics I through IV.
Somewhat less than inspired by the traditional
chemical engineering program ("I haven't been
confronted with a plate and frame filter press
since I burned my copy of Walker, Lewis, and
McAdams at a cocktail party in 1949"), Jim
minored in English Literature and, informally,
Italian opera. "I was destined, I believed, to be
a Literary-Musical critic for the now deceased
Brooklyn Eagle-but John Treacy saved literature
and music by introducing me to chemical kinetics
in my senior year. My medieval mind prompts me
to envision my ultimate paper "Nth-Order Adia-
batic Reaction in a Plate & Frame Filter Press."

INDUSTRIAL CONTACTS
IM JOINED THE EXPLOSIVES Department
of the du Pont Company in 1951 as a process
engineer, at which post (Eastern Laboratory,
Gibbstown) he labored happily under the mentor-
ship of Bill Kirst, Bob Cavanaugh, Win Johnson,
and John Vyverberg. Johnson, a former student
of B. F. Dodge encouraged Jim to seek a Ph.D. at
Yale. At Yale Jim worked under R. H. Bretton on

CHEMICAL ENGINEERING EDUCATION

axial dispersion in fixed beds, talked endlessly
with Jon Olson (now at University of Delaware)
on topics ranging from Aquinas to Zeus, presented
numerous impromptu seminars at Smith and Vas-
sar Colleges, confounded B. F. Dodge by attending
Barny's 8 a.m. class clad in p.j.'s, and worshipped
R. Harding Bliss. "He, Harding, was a gentleman
and a scholar." He feels he learned much from
that Yale faculty-a logical consequence of his
student days at Notre Dame under Treacy and
Wilhelm, (then of the chemical engineering fac-
ulty) and Burton and Hamill of Notre Dame's
Chemistry Department. "One likes to think that
the Professor-Student relationship be mutually re-
spectful yet informal, as it was between Wilhelm,
Treacy (of Notre Dame), Dodge, Bliss, Bretton,
Walker (of Yale) and me."
Jim returned to the Engineering Department
of the du Pont Company as a research engineer at
the Engineering Research Laboratory (ERL), a
site famed by Chilton, Colburn, Drew, Pigford,
Marshall, etc. Tom Chilton directed Carberry into
catalysis: du Pont sent Jim to Johns Hopkins to
take Paul Emmett's cosmic course "Catalysis" in
1959-60. "Between Paul's course and numerous
discussions with Sir Hugh Taylor, I felt as would
an altar-boy at the feet of Augustine and
Aquinas." The four years at ERL proved most
stimulating to Carberry. His mentors Von Wett-
berg, Rush, and Roberts, he notes "were most
tolerant and therefore encouraging." His col-
leagues at ERL were most stimulating-humble
Steve Whitaker, placid Forest Mixon. Marty
Wendel shared his office and taught him all man-
ner of things about wit and numerical analysis
(namely there is a synergism there somewhere).
In moments of scientific-technological terror, a
fellow Brooklynite, Sheldon Isakoff, reminded Jim
that "the sun never sets on Sheepshead Bay,
Brooklyn."

RETURN TO ACADEMIA
TAKING THE CLOTH, as it were, Jim re-
turned to Notre Dame in 1961 as Assistant

Professor of Chemical Engineering. Dr. J. T.
Banchero of Michigan had then assumed the
Chairmanship of Chemical Engineering at Notre
Dame and immediately set about the task of de-
veloping a graduate program in chemical engi-
neering. Notre Dame's president, Father Hes-
burgh and then Dean of Engineering, Harry Saxe
and later Norman Gay encouraged and sustained
developments which created the chemical engi-
neering Ph.D. program. "That indeed was a most
fruitful period of maturation for our department.
Without the energetic support of Father Hes-
burgh, Deans Saxe and Gay, Banky, Jim Kohn,
and that wise man, Ernest Thiele, naught would

. . he . . helpedd Leon Hart win the Heisman trophy.

have been reaped. We were, of course, not eligible
for the first Cartter Report rating since we had
not granted a chemical engineering Ph.D. prior to
'59. Yet in the second, our first, evaluation, we
were judged as "Good"-a judgment both en-
couraging and challenging. I attribute this to the
wise vitality of our administration, faculty, staff
and students."
"Since those formative years, we've retained
excellent people in Luks (Minn.) and Verhoff and
Smith (Mich.). One can only hope that the present
Engineering College administration will be cogni-
zant of whose shoulders sustain us now."

"I was destined to be a literary- musical critic for the now deceased Brooklyn
Eagle-but John Treacy saved literature and music by introducing me to chemical
kinetics in my senior year. My medieval mind prompts me to envision my
ultimate paper " 'Nth-Order Adiabatic Reaction in a Plate and Frame Filter Press'."

WINTER 1974

In his twelve years at Notre Dame, Jim has
directed research in Chemical Reaction Engineer-
ing and Heterogeneous Catalysis. The now-uni-
versally employed "swirling basket catalytic re-
actor" or "Carberry Reactor," which Jim prefers
to term the "Notre Dame CSTCR" was conceived
and developed in 1964. The key experimental
work was carried out by then Ph.D. candidate
Dan Tajbl (now at Mobil Oil) who came to Notre
Dame from Northwestern "a year before Ara
made a move equally beneficial to Notre Dame" as
Jim puts it.

ACCLAIM AND ALLEGIANCE
N 1965-66, CARBERRY was awarded an NSF
Senior Postdoctoral Fellowship at Cambridge
University, England where he thrived upon dia-
logues with Danckwerts, Pearson, Davidson,
Turner, Bridgwater, et al. Between "teas" he man-
aged to lecture at various posts between Warsaw
and Haifa. Thus it was that he, the devotee of
Verdi and Puccini, found Italy. "It is asserted that
I am of Anglo-Irish derivation. So be it with re-
spect to my blood chemistry, but I do declare that
my heart is Italian," declares Giacomo Carberri.
This Spring (1974) Commendatori Carberri will
again be in Italy as a Senior Fulbright Scholar at
the University of Rome.
In 1968, Jim received the Yale Engineering
Association Award for Advancement of Basic and
Applied Sciences, and he fondly hopes that in 1974
he will once again be recipient of the Interhall
Football Coach Trophy at Notre Dame. For the
"ole" Brooklyn Tech scrub halfback has been
coaching intramural eleven man contact ("col-
lision") football on the Notre Dame campus for
over a decade. Says he, "oh, for the pre-Ara days
when I could boast as being the only winning foot-
ball coach on campus. But, alas, no threat to Ara
am I."
Off-season, Carberry preoccupies himself with
research in surface catalysis in association with
his solid-state physicist colleague George Kuczyn-

"It is asserted that I am of Anglo-Irish derivation.
So be it with respect to blood chemistry. But I
do declare that my heart is Italian.

i ~t:

fl "
I*r*
J
*r
Ik'

Carberry and his daughters.

ski and teaching both graduate and ("most im-
portantly") undergraduate Reaction Engineering.
He is now co-editor of Catalysis Reviews and a
member of the U.S.-Soviet Working Group on
Catalysis.
He harbors rather firm views regarding the
future of Chemical Engineering and society in
general. A Stevensonian Democrat, in typical
eclectic fashion, Carberry is a devoted admirer of
William F. Buckley, Jr. and his National Review.
Given his studied dedication to Aquinas, Dante,
and Maritain, the seeming paradox may be il-
lusionary. He believes in civilized society, which
signifies civilized discourse amongst civilized men,
phrased in civilized form and spirit. "I am the
enemy of the 'you know' generation, who are
poised before bronze calves, mesmerized by a
cacophony, miscoined by morons and idiotic sooth-
sayers as meaningful, relevent, and true because it
feels right."
Explaining how he views chemical engineer-
ing, Carberry relates "Olaf Hougen put it all in
perspective-our roots reside in chemistry-at a
particular stage the Hougen's, McAdam's, etc. put
order into transport processes. Now we must get
on with our true task-applied chemistry. This
may well mean divorce with respect to general
engineering. Che sara', sara'. Remember those
shoulders which sustain us all." D

CHEMICAL ENGINEERING EDUCATION

�~ L

.'

Find out if the chemistry's right.

At Du Pont, the best chemistry is
people chemistry.
Anything can be achieved if you
have the right people and they talk to
each other.
So we look at you as much as at
your grades.
We look for compatibility as much
as talent.
And that goes for engineers and
chemists as well as business students.
If you want to find out what fields
An Equal Opportunity Employer M/F

have openings, what states you can work
in and more, meet with the Du Pont
recruiter when he comes to your campus.
Or if you've already graduated and
have experience, write Du Pont direct,
Room N-13400, Wilmington, Del. 19898.
And as you know by now, we're
equally interested in women and men of
any color.
The chemistry is what counts.

WINTER 1974

iFJ department

BERKELEY

C. JUDSON KING, THEODORE VERMEULEN
and JOHN M. PRAUSNITZ
UnlirersitU of California
Berkeley, California

THE CHEMICAL ENGINEERING Department
at the University of California's charter
campus celebrated its 25th anniversary in 1971-72.
Starting strong but small just after World War II,
with both The M.S. and the Ph.D. programs pre-
ceding establishment of the B.S. degree, the de-
partment has grown to he one of the largest units
among U.S. universities. Today there is a faculty
of 20 full-time professors, a graduate student body
numbering about 130, and 30 to 40 seniors gradu-
ating annually. The number of Ph.D.'s graduating
in 1971-72 was 22, and in the same year there
were 20 M.S. graduates.
Several distinctive features characterize Berk-
eley chemical engineering-beyond its relatively
recent genesis and its physical location in the
Athens of the West. One characteristic is its close
affiliation with chemistry; in fact, the Depart-
ments of Chemical Engineering and Chemistry
make up the College of Chemistry at Berkeley, one
of very few such college structures. As another
feature, Berkeley's department devotes a larger
fraction of its effort to the graduate program than
is possible in most schools. The M.S. shares center-
stage with the Ph.D., and both degrees require a
thesis. To a great extent graduate education is
built around individual tutorial instruction, car-
ried on for the most part through joint student-
faculty research and design. The spectrum of top-
ics of interest and investigation represented in the
department is extremely wide, ranging from ap-
plied to fundamental. Chemical process design
and engineering are emphasized equally with basic
engineering science.

DEPARTMENTAL HISTORY
At Berkeley, chemical engineering by that
name began in the 1940's but had been anticipated

Berkeley's Campanile dominates the campus skyline and overlooks
San Francisco Bay-an Ivory Tower but not an academic refuge.

from the time the University was founded in 1868.
Frederick Cottrell, Cal's first true chemical engi-
neer, invented electrostatic precipitation here
around 1906. In 1912, Gilbert N. Lewis, as in-
coming Dean of the College of Chemistry, insti-
tuted a chemical technology major, subsequently
directed by Merle Randall. As of 1942 an inter-
departmental Graduate Group offered the M.S.
degree in chemical engineering. September 1946
marked the start of formal undergraduate instruc-
tion, offered in the College of Chemistry with
complementary work in the College of Engineer-
ing. Philip Schutz, the program's first unofficial
chairman, LeRoy Bromley and Charles Wilke
formed the charter group. Succumbing soon to a
tragic illness, Schutz was replaced by Theodore
Vermeulen. This group was then joined by Donald
Hanson and Charles Tobias in 1947, completing

CHEMICAL ENGINEERING EDUCATION

the initial staff. The new program rapidly gained
recognition, achieving formal approval of the
Ph.D. program (1947) and B.S. program (1948),
changing the departmental name to Chemistry
and Chemical Engineering (1949), creating the
sub-departmental Division (1952), creating a sep-
arate Department (1957), renovating and fully
occupying Gilman Hall (1963), and subsequently
expanding into a major portion of Lewis Hall
(1965).

FACULTY GROWTH
W ILKE SUCCEEDED Vermeulen as Chair-
man in 1953, and led a rapid expansion in
numbers of graduate students and faculty, to
serve the fast-growing needs of the State of Cali-
fornia. Eugene Petersen (1953) and John Praus-
nitz (1955) were the next of the present profes-
sorial staff to arrive, and were followed by David
Lyon who had been with the Low Temperature
Laboratory of the College, Alan Foss (1961),
Simon Goren (1962), Edward Grens (1963), Jud-
son King (1963), John Newman (1963), Robert
Merrill (1964), Michael Williams (1965), Robert
Pigford (1966), Scott Lynn (1967), Alexis Bell
(1967), Mitchel Shen (1969), and Lee Donaghey
(1970). Thomas Sherwood, after two previous
visiting appointments here, transferred perma-
nently from M.I.T. in 1970. In 1963, Hanson suc-
ceeded Wilke as Chairman, followed by Tobias
(1967-72) and King (1972-present).
Activities of the department are extended and
supported by a number of other professionally
active engineers, including Lecturers E. Morse
Blue, Gerhard Klein, Arthur Morgan, Rolf Muller,
Charles Oldershaw, and Otto Redlich. David
Templeton, dean of the College of Chemistry, and
Douglas Fuerstenau, Chairman of Materials Sci-
ence and Engineering in the College of Engineer-
ing, participate often. Enrichment of the depart-
ment's work also comes from strong ties with the
Lawrence Berkeley Laboratory and the Sea Water
Conversion Laboratory.

Students and faculty meet at the coffee hour preceding the de-
partment's weekly Colloquium.
Visiting professors have included Shinichi Aiba (To-
kyo), Chandler Barkelew (Shell), Thomas Baron (Shell),
Andre Bellemans (University of Brussels), Thomas Chilton
(DuPont), Lewis Etherington (Esso), Ulrich Franck (Karl-
sruhe), Robert Finn (Cornell), Robert Greenkorn (Pur-
due), Norbert Ibl (ETH Zurich), Lewis Iscol (Chevron),
Robert Johnk (San Jose State), Adriaan Klinkenberg
(Royal Dutch), Herman Mark (Brooklyn Poly), John
Ornea (Shell), Giuseppe Parravano (Michigan), Henrick
Van Ness (Rensselaer), and Fumitake Yoshida (Kyoto).
The work of the department has been sup-
ported generously by the State of California, Fed-
eral agencies and several research foundations.
Present industrial donors include the DuPont
Company, General Electric Company, Shell Oil,
Standard Oil of California, Exxon Companies,
Union Carbide Corporation, Stauffer Chemical
Corporation, Dow Chemical USA, Gulf Oil, Mobil
Oil, and Union Oil.
Many members of the faculty have received
awards from AIChE, ACS, ASEE or the Electro-
chemical Society. In addition, three are members
of the National Academy of Sciences and two are
members of the National Academy of Engineer-
ing.

BERKELEY PHILOSOPHY

A STRONG TENET of the Berkeley faculty is
that education in chemical engineering en-

Several distinctive features characterize Berkeley chemical engineering-its close affiliation
with chemistry .. . it devotes a large fraction of its effort to the graduate program ...
and it puts the M.S. and the Ph.D. on center stage requiring theses for both degrees.

WINTER 1974

ables a graduate to undertake any of an ex-
tremely wide and steadily expanding range of
endeavors. This is reflected in the broad scope of
research and technical interests represented in the
department, by the wide variety of courses and
seminars, and by the diverse occupations filled by
past graduates of the department: process engi-
neers, electrochemical engineers, systems engi-
neers, food engineers, biochemical engineers, ex-
tractive metallurgists, pharmaceutical-device en-
gineers, environmental engineers, nuclear engi-
neers, experts in pure sciences, and managers of
technical enterprises. The program at Berkeley is
designed to give the student extensive competence
and understanding, with abilities to develop fur-
ther knowledge and insight with minimal difficulty
in whatever specialized area he may enter. In
1970, option areas were made available in the
undergraduate program, offering supplementary
study in chemistry, applied physics, systems anal-
ysis and applied mathematics, materials and mole-
cular engineering, space systems, earth-ocean-
atmospheric sciences, environmental balance, ap-
plied biology, food resources and processing, busi-
ness enterprise, or science education.
Research and project engineering are the pri-
mary vehicles for tutorial instruction, which aims
at developing the student's self-reliance, initiative,
and technical maturity. The underlying principle
is that a student learns best the things he does
himself rather than those he hears second-hand.
"Research" is interpreted in a broad sense. In
recent years many theses have dealt with process
synthesis, development, and design. The common
thread of exploration in all these areas, as well as
for research on more fundamental problems, is

Mysteries of catalysis are the focal point for research by professor
Eugene Petersen and graduate student Daniel Kahn.

"Research" is interpreted in a broad sense . ..
In recent years many theses have dealt with
process synthesis, development and design.

that the student undertakes a truly original prob-
lem-something clearly new, for which the answer
has not already been determined. The depart-
ment's attention to chemical process engineering
as well as to fundamentals is reflected in several
problem-oriented graduate courses, and in its
focus upon chemical process engineering (to-
gether with transport phenomena and physico-
chemical principles) in the comprehensive pre-
liminary examination for Ph.D. candidates.

Emphasis upon developing the student's ability to work
on his own is also reflected in the definitive Ph.D. oral
qualifying examination. Here the student presents and
defends a self-generated "proposition" for a significant re-
search advance or process improvement. The proposition
cannot be related to his thesis research; it is conceived on
his own without faculty help, although advance criticisms
may be made by his qualifying committee chairman. This
examination provides a profoundly maturing experience,
and when completed gives the student greatly increased
self-confidence and independence of mind for further engi-
neering studies which culminate his doctoral thesis.

The Berkeley Ph.D. program has proved to be
a major supply of teachers for other universities.
A recent count shows that 39 U.S. professors have
received a Ph.D. in chemical engineering from
Berkeley, most of them within the last 10 years.
These include:

Richard Alkire (Illinois), Byron Anshus (Delaware),
Douglas Bennion (UCLA), John Berg (Washington),
Robert Blanks (Michigan State), David Bonner (Texas
Tech), Ray Bowen (Wisconsin), Robert Chambers (Tu-
lane), Thomas Chapman (Wisconsin), Winston Cheh (Co-
lumbia), Peter Clark (Virginia Poly), Milton Davis (South
Carolina), John Duffin (Naval Postgraduate School),
Charles Eckert (Illinois), John Friedly (Rochester), Joe
Goddard (Michigan), Earl Gose (UI Chicago Circle), Rob-
ert Gunn (Wyoming), James Han (Michigan), Gordon
Harris (Tulane), Thomas Hicks (UCLA), Jacob Jorne
(Wayne State), William Krantz (Colorado), Robert Madix
(Stanford), Thomas Massaro (Wisconsin), Robert Mer-
edith (Oregon State), Reid Mil'er (Wyoming), Alan Myers
(Pennsylvania), John O'Connell (Florida), John Powers
(Michigan), Clayton Radke (Penn State), Peter Rony
(Virginia Poly), Orville Sandall (UC, Santa Barbara),
Fred Shair (Caltech), Lloyd Spielman (Harvard), Darsh
Wasan (Illinois Institute of Technology), Henry Weinberg
(Caltech), Douglass Wilde (Stanford), and William Wilcox
(Southern California).

CHEMICAL ENGINEERING EDUCATION

A corresponding list of Ph.D. graduates teach-
ing at foreign universities would number another
15-20. Also a significant number of Cal's B.S. and
M.S. graduates are serving on university faculties.
These include, among others:
Philip Becker (Penn State), Robert Brodkey (Ohio
State), Sunny Chan (Caltech), Bruce Gates (Delaware),
K. R. Hall (Virginia), George Homsy (Stanford), Marc
LeMaguer (Alberta), Octave Levenspiel (Oregon State),
R. L. Merson (UC Davis), Zuhair Munir (UC Davis), Ken
Nobe (UCLA), Channing Robertson (Stanford), Robert
Sani (Illinois), L. E. Scriven (Minnesota), J. D. Seader
(Utah), Oktay Sinanoglu (Yale) and Steven Whitaker (UC
Davis).

Graduate student Daniel Kahn deals with the mysteries of catalysis
in his research at Berkeley.

The department encourages its own bachelors
to take their graduate work at other schools, based
upon the principle that students should experience
more than one approach to subject matter and to
problem-solving techniques.

RESEARCH PROGRAMS

BERKELEY'S RESEARCH activity and cap-
ability encompass an ever-evolving range, as
twenty full-time faculty and four of the part-tim-
ers in chemical engineering continually reassess
the needs and opportunities for significant innova-
tive work. The fields of research listed in the ac-
companying table include few surprises, as they
almost all show a substantial relevance to eventual
practical applications in physical preparation, sep-
aration, or chemical reaction, with respect to sys-
tems of multicomponent and or multiphase char-
acter. Of the ten main areas, the first five are
fields where Berkeley has an exceptional intensity

of effort, compared with the general average, and
the second five can be considered as nearly uni-
versal.
What "master concepts" underlie this research
activity? The goal already cited-intellectual
growth by the student into the status of a fully
independent professional-is implemented by a
number of operational principles, proven by time
and applied with flexibility.

First, when the interests of different staff members
overlap or coincide, collaboration between them often oc-
curs.
Second, the student's growth is measured by ever-in-
creasing control over the research he (or she) conducts.
A Ph.D. student in his first year typically does about 20%
of the innovation and 80% of the physical and mental
work involved in his research project, the faculty super-
visor providing the remainder directly or indirectly. In his
last year, the student does 80% of the innovation and
95% of the physical and mental work. A student engaged
in research will typically spend two to four hours each
week with his faculty supervisor. However in the period
when the dissertation is being written, reviewed, and re-
vised, many additional hours of intense discussion occur.
Third, graduate students consult widely with faculty
members other than their immediate research supervisor,
with enough opportunity to learn from all of them. They
are expected in due time to become more expert than
their mentors.
Fourth, although of course the professors are expected
to provide the largest primary input into the communica-
tion chain, graduate students are likely to learn even more
from one another than they learn directly from the faculty.
Fifth, the program emphasizes breadth as well as
depth. Graduate students attend a variety of courses and
seminars, including those in neighboring departments, and
frequently carry out a second brief research project with
a faculty member other than their thesis advisor.
Sixth, the student normally is spurred to complete his
master's degree within 12 to 24 months, or his doctorate
in 36 to 54 months, on the basis that graduate study is
preparation for a career and not a career in itself.

WIDER AFIELD

Although the campus is most often identified
by its 310-foot Campanile, Berkeley is no ivory
tower but a bustling reflection of the world at
large. Its scenic setting overlooking San Francisco

The department's attention to chemical process
engineering as well as to fundamentals is reflected
in several problem-oriented graduate courses, and
in its focus upon chemical process engineering.

WINTER 1974

Bay provides a multitude of recreational and so-
cial opportunities for students and faculty. Be-
sides the proximity of supportive industry and
government laboratories, there are all the cultural
attractions befitting this major urban center, as
well as opportunities for hiking and mountaineer-
ing in the Sierra Nevada, sailing in the Bay, other
participatory and spectator sports of all kinds,
and finally a living laboratory of sociological, po-
litical, and philosophical "ferment" for which
Berkeley has attracted international attention. D

RESEARCH ACTIVITIES AT BERKELEY

Process Development, Design, and Optimization

Calculation Techniques and General Strategy. Systematic
procedures for synthesis, arrangement, and improvement
of processes. Computation strategies to define optimum
designs. Computer-implemented simulation of large proc-
ess systems and their individual components. (Foss, Grens,
King).
Process Engineering and Conceptual Design. Development
and analysis of case problems for instruction. Desalination
of sea water by processes involving evaporation, ion ex-
change, reverse osmosis, freezing and/or foam fractiona-
tion. Waste utilization through microbial processes and
other techniques. Hydrogenation and extraction of coal
and oil shale. Electro-refining of metals. Cryogenic separa-
tion, including isotope recovery. (Bromley, Grens, King,
Klein, Lynn, Lyon, Sherwood, Tobias, Vermeulen, Wilke).
Pollution Control. Recovery of solvents from vent gases
by adsorption. Catalytic treatment of automobile-exhaust
components. Removal of SOx and NO, from stack gases.
Water pollution abatement by solvent extraction, foaming,
coalescence, process modification and other approaches.
Radioactive waste disposal. (Bell, Bromley, Goren, King,
Klein, Lynn, Petersen, Pigford, Prausnitz, Sherwood,
Vermeulen).

Biochemical, Food and Biomedical Applications

Techniques for dense culture of bacterial cells, with ap-
plications to fermentation processes, vaccine production
and solid-waste utilization. Reactions involving immob-
ilized enzymes. Food processing by freeze-drying, freeze-
concentration, and other dehydration methods. Polymers
for biomedical applications, including synthesis by glow
discharge. Fluid dynamics, structure, and susceptibility to
damage of blood under flow conditions. (Bell, King, Shen,
Wilke, Williams).

Polymeric and Inorganic Materials

Polymer Systems. Measurement and theory of viscoelastic-
ity of solutions, melts, and multiphase polymer systems.
Thermodynamics of block copolymers and polymer solu-
tions. Polymerization kinetics. (Merrill, Prausnitz, Shen,
Vermeulen, Williams).
Inorganic Solids. Determination of solid-surface lattice
structure, composition, and reactivity. Crystal growth.

Of the ten main areas, the first five are fields
where Berkeley has an exceptional intensity of
effort, compared with the average, and the
second five can be considered nearly universal.

Optical, electronic, and elastic properties of solids. Thin-
film production and epitaxial growth. (Donaghey, Merrill).

Cryogenic Engineering

P-V-T behavior, separations, and heat exchange in the
liquefaction of air, hydrogen, and helium. Adiabatic de-
magnetization with large-volume magnetic fields. Physical
properties of fluids and solids at high pressure and low
temperature. Low-temperature mechanical and dielectric
relaxation and other physical properties of polymers.
(Lyon, Prausnitz, Shen).

Electrochemical Engineering

Development and Design of Electrolytic Cells. Electrode
processes-geometry, current distribution, limiting cur-
rents, gas evolution. Electro-chemical shaping and finish-
ing of metals. Production of surfaces and fibers by elec-
trolysis. (Lynn, Merrill, Muller, Tobias).
Energy Storage and Conversion. Batteries and fuel cells.
Electrolysis in nonaqueous ionizing solvents. (Grens,
Tobias).
General. Electrostatic gas-solid and liquid-solid separations.
Continuous electrophoresis or electrochromatography in
liquids. Electronic and ionic transport in inorganic solids.
Corona- and glow-discharge devices for measurement of
solid-aerosol areas and size distributions. (Bell, Donaghey,
Hanson, Tobias, Vermeulen, Wilke).

Chemical Process Dynamics and Control

Control-systems development for industrial-scale re-
action and separation systems. Dynamic models for large
scale systems including fixed-bed reactors and distillation
systems. Response mode-based synthesis methods for con-
trol system configurations. (Foss, Grens).

Kinetics and Catalysis

Heterogeneous Catalysis. Molecular-scale gas-solid be-
havior over extreme pressure ranges. Chromatographic
reactors. Reactor dynamics and particle configuration.
Process applications. (Bell, Merrill, Petersen).
Simultaneous Heat Transfer, Mass Transfer, and Chemical
Reaction. Combustion. Particle deflagration. Reactor engi-
neering. Kinetics of phase transitions. Photochemical re-
actor design. Plasma chemistry. Homogeneous catalysis.
Kinetics and mass transfer in microbial growth. (Bell,
Donaghey, Grens, Merrill, Petersen, Pigford, Sherwood,
Vermeulen, Wilke).

(Continued on page 41.)

CHEMICAL ENGINEERING EDUCATION

WE ENCOURAGE JOB HOPPING.
In fact at Sun Oil we've just adopted a new system
that promotes it. * Internal Placement System.
* Here's how it works. Say you're in Production
and you decide to take a crack at Marketing.
Next opening in Marketing we'll tell you. You can
apply and be considered. First. You have freedom
to experiment and move around at Sun. You
learn more and you learn faster.

* Why do we encourage job hopping? Because
we happen to believe our most valuable corporate
assets are our people. The more our people
know, the stronger we are. * Now-you want to
know more? Ask your Placement Director when
a Sun Oil recruiter will be on campus. Or write
for a copy of our Career Guide. SUN OIL
COMPANY, Human Resources Dept. CED.
1608 Walnut Street, Philadelphia, Pa. 19103.

An E l Opportunity EOC r M
An Equnl Opportunity Employer M/F

curriculum

THE PROJECT APPROACH

TO CHEMICAL ENGINEERING EDUCATION

UNDER THE WPI PLAN

W. L. KRANICH, I. ZWIEBEL, and Y. H. MA
Worcester Polytechnic Institute
Worcester, Massachusetts 01609

FOR MANY YEARS the faculty and students
at Worcester Polytechnic Institute have been
aware of the great educational value of inde-
pendent projects. This awareness has been fos-
tered by National Science Foundation Undergrad-
uate Research Participation grants, senior theses
(optional in many departments), use of under-
graduates as assistants and participants in sup-
ported graduate research projects, and special
programs such as the Clean Air Car race.
Projects have, in fact, become the cornerstone
of the newly developed educational innovation,
the WPI Plan. Unlike the usual experiments in
education where one variable is altered at a time,
this is a total commitment with changes in just
about every aspect of the college. The central
theme of the program is that the student is pre-
pared for his professional life by an educational
program which emphasizes his independence and
develops confidence and self-reliance through a
strong element of self-education. There is no
formal curriculum and the criteria for graduation
are intended to demonstrate the student's com-
petence to enter his or her chosen profession. The
basic criteria are given in Table 1.

Table 1
GRADUATION REQUIREMENTS
UNDER THE WPI PLAN
1. Satisfactory completion of an independent project in the
major field
2. Satisfactory completion of an independent project which
relates society and technology
3. Successful performance on an examination which tests
the competency of the student to enter his profession
4. Demonstration of sufficient competence in a secondary
field

Students entering as freshmen during the first
two years of operation were permitted to choose
either this program or traditional departmental
requirements (curriculum, minimum grade-point
average, minimum credits). During the second
year more than 95% of the entering freshmen
elected the WPI Plan. This encouraged the faculty
to eliminate the traditional option one year earlier
than planned. As a result, during the current year
the entire freshman class entered under the new
program.
In addition to the new graduation require-
ments there are other innovative features of the
Plan. During each of four or five seven-week
terms the student concentrates on three subject
areas (rather than studying five or six subjects
for a 14-week semester). In the planning of a
student's program the key roles are played by the
student himself and by his academic advisor. De-
partments provide a home base for the faculty,
but need not be of central importance to the stu-
dent. So long as the student can find an advisor
willing to work with him in his desired area, and
that advisor can assemble a faculty committee
willing to examine the student's competence, there
are no constraints on the major area of the stu-
dent. While we expect that for the next several
years at least, most students will choose to major
in the conventional fields of science and engineer-
ing, we expect to find some who will want a major
in such areas as biomedical engineering with an

The central theme ... is that the student is
prepared for his professional life by an educational
program which emphasizes his independence and
develops confidence and self-reliance through . ..
self education. There is no formal curriculum.

CHEMICAL ENGINEERING EDUCATION

emphasis on the chemical point of view, or man-
agement engineering with concentration on the
management of chemical plants. Naturally it will
be one function of the advisor to discourage the
student from too narrow specialization, but in the
end it will be the student's choice.

PROJECT ORIENTED PROGRAM

INDEPENDENT PROJECTS are at the heart
of the new program. The projects may be car-
ried out in groups or individually, as research or
independent study. Up to about 25'/ of a stu-
dent's activities at WPI will be taken up by such
projects; some will be chosen to meet the degree
requirements (i.e., qualifying type), while some
will be exploratory or preparatory to the qualify-
ing projects. They may be executed on campus or
at an off-campus site, but still under full faculty
supervision. Past experience shows that in chem-
ical engineering, far more than half of these proj-
ects will be of experimental, research or develop-
ment type as contrasted to design projects.
While there has been considerable experience
at WPI in project work of the on-campus, senior-
thesis type, until recently we had little operating
know-how on group projects, particularly those
concerned with off-campus, real-world problems
of government and industry. The chemical engi-
neering department has participated in two major
pilot projects of this type-one the Environ-
mental Systems Study Program (ESSP) spon-
sored by the Sloan Foundation and the Environ-
mental Protection Agency, and the other an off-
campus internship center at the U.S. Army Natick
Laboratories in Natick, Mass. One of the authors
of this paper (I. Zwiebel) was instrumental in
developing the former program and another

Y. H. Ma received his bachelor's degree from National Taiwan Uni-
versity, his master's degree from Notre Dame and his doctorate from
M.I.T. (in 1967) all in Chemical Engineering. He has taught at WPI
since 1967. His research areas include diffusion in porous solids and
mathematical simulation. (left)
W. L. Kranich received his B.S. in Chemical Engineering from the
University of Pennsylvania and his PhD. (in 1944) from Cornell Uni-
versity. He taught at Princeton University before coming to Worcester
Polytechnic Institute in 1948, and has been Head of the Chemical En-
gineering Department since 1958. His current research interests are in
reactions on molecular sieve zeolite catalysts and process development.
(left below)
I. Zwiebel did his undergraduate work in Chemical Engineering at
the University of Michigan and his graduate study at Yale, where he
received his doctorate in 1961. He has had industrial experience with
duPont and Esso, and has been on the WPI faculty since 1964. His
research efforts are concentrated in the fields of adsorption and ap-
plied mathematics. (right below)

author (Y. H. Ma) played the key role in the de-
velopment of the latter and serves as Internship
Center Director.

PROJECT EXAMPLES

N THE REMAINDER of this paper we present
examples of student projects of the research
type-associated with on-going sponsored re-
search at WPI-and of the group, off-campus
type under the ESSP program and the Natick
Internship Center.
Both underclassmen and seniors have success-
fully joined teams of graduate students and car-
ried out individual projects on a solid waste con-
version program sponsored by EPA. The overall
effort is concerned with conversion of cellulosic
and other organic wastes to useful oil by hydro-
genation. One undergraduate studied the effects
of some of the process variables. Another devel-
oped an analytical technique for characterizing
the product. A third, using computer-aided design
techniques, developed a flow sheet and preliminary
cost data for a projected large scale application.

WINTER 1974

A NASA-sponsored research program for
long-duration space flight is concerned with con-
version of human wastes into edible sugars via
formose synthesis. One undergraduate looked
into the effect of different catalysts. Another
studied the fermentation of formose sugars with
the objective of protein generation. A third at-
tempted to explain and characterize the observed
instabilities of the continuous stirred tank reactor
in which the formose synthesis occurred.
The educational value of undergraduate proj-
ects cannot always be measured in terms of posi-
tive research results. In one instance an under-
graduate study of the bonding between absorbate
species and adsorbent sites (associated with an
EPA-sponsored air pollution control project) was
not very productive. Infra-red absorption spec-
troscopic techniques with KBr pellets containing
varying amounts of the absorbent were used. The
observed results were inconclusive. While the in-
terpretation of I.R. spectra is a very complicated
skill, the student in consultation with a faculty
member of the chemistry department did a very
fine job analyzing his meager spectra. However,
the student exhibited a case of stubbornness. In
the literature, only a very few instances were gas-
solid interactions successfully investigated by KBr
absorption techniques-most researchers prefer
the reflectance methods. The student refused to

Past experience shows that in chemical engineering
far more than half of these projects will be of
experimental, research or development type as
contrasted to design projects.

try out this technique, stubbornly insisting that a
way shall be found to use the pellet technique. At
the end, in light of the absence of results, he had
to concede that research should not be a sledge-
hammer operation. The student enjoyed his ex-
periments and was satisfied by his experiences; he
went on to graduate school to pursue a career in
biochemical engineering.
A more successful example of a research proj-
ect is illustrated by a sophomore, who tried en-
gineering research because he never had exposure
to large scale facilities. He was facing a choice
between a career in chemistry or chemical engi-
neering. We teamed him up with a Ph.D. candi-
date who was studying the dynamics of adsorption

in fixed bed columns. This sophomore was to be in
charge of the desorption experiments which had
to be carried out before the next adsorption could
be run. In part emulating the graduate student,
the sophomore developed a comprehensive experi-
mental schedule for the desorption runs, devoted
many night-time hours to gather the data, ana-
lyzed his results, and developed sufficient results
to warrant publication. In this case the learning
and direction were very positive. He was gradu-
ally, through participation, introduced to chemical
engineering. He has since graduated at the top of
his class and gone on to graduate school in chem-
ical engineering.

PROJECTS CONTRIBUTE TO SOLUTIONS

THE ENVIRONMENTAL SYSTEMS Study
Program, sponsored by the Alfred P. Sloan
Foundation, was designed to develop team inter-
disciplinary projects in conjunction with indus-
trial governmental sponsors. The intent was not
to teach the subjects of the other disciplines rep-
resented on the team to the chemical engineers, or
vice versa; it was hoped that students would learn
to communicate with specialists from other areas.
It was expected that each person working in his
own field could contribute to the combined solu-
tion of complex real problems. We have had
twelve such projects in the past two years. An ex-
ample in which the chemical engineering contribu-
tion was quite significant was the Salem Harbor
Project.
Salem Harbor power generating plant is lo-
cated in the immediate vicinity of resort towns
and is frequently influenced by local meteorolog-
ical phenomena, i.e., strong but short range winds
off the ocean. The growth of the plant has in
recent years created an environmental concern.
The environmental influences during transient
peak-load operation of the plant were to be evalu-
ated.
First the concepts of transient operations had
to be brought across to the students. Then, fa-
miliarization with the power plant process had to
be covered. This brought into focus the stoichio-
metric calculations.
Initial instinct was to measure SO, emissions.
However, the student team quickly realized that
SO, emissions are directly proportional to fuel
feed rate, and in no way do they represent unique
pollution problems during the transient opera-
tions.

CHEMICAL ENGINEERING EDUCATION

While ... most students will choose to major in the conventional fields of science
and engineering, we expect to find some who will want a major in such areas
as biomedical engineering with an emphasis on the chemical point of view, or
management engineering with concentration on the management of chemical plants.

Next, they zeroed in on NO, measurements.
The various analytical procedures were evaluated;
sampling and remote analyses were compared
with continuous instrumental techniques. They
selected instruments, chose sampling locations,
and ran preliminary measurements under steady
state operating conditions. Then the variation of
NO, concentration with operating load was ob-
served.
A plot of air-to-fuel ratio versus time revealed
that during the transient phase the plant operates
in a fuel-rich regime. This prompted a switch to
the measurement of CO, unburned hydrocarbons,
and particulates.
The final in-depth design will focus upon im-
proved precipitator operating conditions, the in-
stallation of some sort of scrubbing device to re-
move the NO, which is in excess of emission
standards, the establishment of an operating pol-
icy which will maintain reasonably uniform con-
ditions in the combustion chamber, and the re-
placement of existing (old) control devices with
equipment that will quickly respond to the pri-
mary variables.
The systems design will consider the power
generation facilities of the entire plant, consisting
of four units, and the entire New England Power
System, and will attempt to establish a control
policy so as not to burden the vicinity of the
Salem area. Also the development of a regional
simulation program, starting with one of EPA's
air quality display models, is planned.
In industrially sponsored projects the lack of
effective communications between the involved
personnel may create some problems. Occasion-
ally, the liaison-advisors assigned to work with
the students are not involved in the project de-
velopment stages. Then, if the educational objec-
tives are not clearly specified, some of these super-
visors may view the presence of the students with
suspicion. In one instance when this happened,
one meeting with the involved principals on an

ESSP project was sufficient to re-establish a fav-
orable environment to continue the project. In an-
other instance, however, on a project dealing with
a sensitive water pollution problem, comments
were made to the students by an uninformed engi-
neer insinuating that the students were planted
for espionage purposes. Rather than wasting the
students' time while potentially extensive negotia-
tions were being held to clear up a misunderstand-
ing, we decided to terminate the project. The stu-
dents were assigned to another problem.
One of the unique features of the Plan is the
establishment of Internship Centers where WPI
students can go for off-campus project experience.
The WPI Internship Center is different from the
commonly known cooperative program. While the
industrial experience gained by the students
through the co-op programs is undeniable, it must
he recognized that one of the chief purposes is to
extend financial aid to the student. The Colleges
involved have little or no control of the students'
on-site activity. On the other hand, the WPI In-
ternship Center emphasizes the educational merit
of the programs which are closely related to the
student's technological interest. The students
work on problems of their own choice at the off-
campus Internship Center in cooperation with
site personnel and under the overall supervision
of WPI faculty as site directors.

CONTACT WITH GOVERNMENT RESEARCH
N INTERNSHIP CENTER was established
at the U.S. Army Natick Laboratories which
accommodated six groups of students for the year
1971-72. The number of students in each group
ranged from one to three. All were chemical en-
gineering majors except one group of two mre-
chanical engineers. Two typical projects are de-
scribed in the following:

(Continued on page 10.)

WINTER 1974

views and opinions

Test to Measure the Ability of ChE Seniors

In the Practical Application

Of ChE Principles

E. C. ODEN
Mississippi State University
State College, Mississippi

The following test was first given to our plant
design students. It was meant to be part of a rou-
tine test toward the end of the semester in the
practical application of ChE principles to the lay-
out of a typical process flowsheet. When I re-
viewed the answers to the problem, it was very
discouraging to have to accept the fact that our
students had made so very many unexpected mis-
takes. It caused me to wonder how ChE seniors
in other schools compared with ours in the prac-
tical application of chemical engineering princi-
ples. It occurred to me to ask other schools to give
this same test, if their professors would cooperate.
Copies of the same test were submitted to sev-
eral schools having ChE departments in hopes of
making comparisons of our students with theirs.
The professors were promised that I would not use
school names or student names, if the test scores
were analyzed and published. Thus, no effort is
made to compare schools or individual students in
this publication. The test presented below was
given to the schools that agreed to the proposal.

OPEN BOOK PORTION OF TEST
Complete the process flowsheet that has been
started having been given the following data:
Compound A has physical properties comparable
to isobutane. Compound B has properties compar-
able to hexane. The compound B is unsaturated
but when combined with A and I.1, IIi ii "n over a
nickel complex catalyst, a saturated compound AB
is formed with traces of methane and about 2(
tar based on total weight of A + B fed. Reactions
may be represented:

A(4 moles) + B(I mole)-> AB unsaturated + A(excess)
AB unsaturated + H.(4 moles)->
AB saturated + 3 moles H. + 2% tar
The tar boils at about 450�F and 35 to 40 psia.
The reaction is exothermic having about 100,-
000 Btu lb mole of AB formed. Compound AB
has properties equivalent to decade.
Assume impurities in the hydrogen should not
build up above 10'/ before being bled off and there
is a constant supply of make up hydrogen avail-
able as well as A + B.
Assume product AB is to be 95'/; or greater
purity. Showi approximate temperatures, pres-
sures and approximate compositions directly on
vessels on the flow'sheet you complete. Take ad-
vantage of utilities produced where possible. Re-
flux ratios on tower or towers may be taken as
1 /1.
Approximately 100 students took the test, in-
cluding all schools. The names of schools and
names of students are not given to avoid em-
barassing any schools or students. The test results
are summarized below.
This was given as an open book test and equi-
librium data or other needed data were available.

SUMMARY OF ANSWERS
1. 23% of the students used a pump to take the 25 psia
gas from the holder and charge to the reactor at 700
psia.
2. Of those that used compressors to move the gas from

My analysis of the results reveals a very
serious weakness on our part as professors
in teaching our students to think.

CHEMICAL ENGINEERING EDUCATION

pllb

FEEDSTOCKS

REACTOR

DISENGAGING
EQUIPMENT
FRACTIONATOR

- . t

17r% H
I%CO4
25PSIA

IOOIA
100-F

FINISHED
STREAMS

GAS FUEL

400 PSIA
140'F

o00 PSIA STEAM

\ C -.FI, A
q> SUPPORT
CONDENS TE ~'Q -
OENC --- 11- 00F
COILS L SOO-F b660 PSIA
650 PSIA

22. 60% failed to place any type product coolers on prod-
uct lines to storage vessels.
23. 90% failed to show any temperature or pressures rec-
ommended for storage vessels.
24. Only three students took into consideration that it
would be better to store the tar at elevated tempera-
ture.
25. Only about 10% of the students established the correct
design basis for the feed to the reactor-the moles
H., should be in the ratio 9 moles per 1 mole of the
sum of the inerts-10% inerts in the total Hydrogen
feed.
26. Obviously, with the knowledge of the simple mistakes
made as mentioned, it would be too much to expect
them to know how to process the #1 column overhead
in a manner to obtain the proper recycle compositions.
Some students did select the correct type reboilers
and similar considerations.

Process Flowsheet.

TEACHING OUR STUDENTS TO THINK

25 psia to 700 psia, 69% failed to use a knockout drum
ahead of the compressor.
3. 24% of the students used compressors to take liquid
"A" at 100 psia and discharge to reactor at 700 psia.
(Note: Equilibrium temperature and pressure relation-
ships of "A" and "B" could have been consulted, if in
doubt, as to being a liquid or a gas.)
4. 36% of the students used no pump to take liquid "A"
at 100 psia to reactor at 700 psia.
5. 28% of the students used compressors for moving
liquid "B" at 20 psia to reactor at 700 psia.
6. 26% took liquid "B" at 20 psia directly to reactor at
700 psia without any power mover.
7. 20% used no preheater of any type to go from the
vessels as indicated to reactor at 10000F.
8. 12% vaporized liquids then compressed to 700 psia
with a compressor.
9. 46% preheated with 6000F steam only to reach 10000F
feed temperature entering the reactor.
10. 80% failed to recycle steam condensate to reactor.
11. 68% showed no recycle H., from flash vessel to reactor.
12. 82% showed no recycle of product "A".
13. Of those that did recycle hydrogen, only 10% took
advantage of the pressure of gas off the flash vessel
and returned it to one of the higher pressure stages
of the compressor.
14. 80% failed to quote any temperature or pressure what-
ever as requested on the first tower.
15. 60% failed to show any reflux for tower #1.
16. 40% failed to take bottoms from tower #1 to tower
#2.
17. 30% failed to use any reflux on tower #2.
18. Of those that had correct feed to the tower #2, 60%
failed to select pressure and corresponding temperature
correctly on reflux drum to #2.
19. 80% failed to give proper temperature and pressure
for top of tower #2.
20. 42% failed to provide a reboiler of any type for tower
#2.
21. 70% failed to use correct transfer equipment for tower
#2 products where correct feed to tower was used.

There were many other mistakes, too numer-
ous to mention collectively, but it was extremely
revealing just how little our students have learned
to think. It was not a surprise to learn that many

Some of this weakness at our school may have
started when we dropped the teaching of
inorganic and organic technology.

would make mistakes on several of the above
items, but the percentage that made these type
mistakes and the grade point average (based on
quality point averages in engineering courses) of
some of the students that made mistakes was
alarming. Professors will likely be surprised to
learn their students will not do any better if they
give this or a similar examination. It is believed
other professors will have just as big a disappoint-
ment in the results as those of us that cooperated
on this test, especially if they will not drill them
on these specific type problems prior to giving the
test.
My analysis of the results reveals a very seri-
ous weakness on our part as professors in teach-
ing our students to think. It has uncovered a weak-
ness in our teaching procedures or curriculum that
I think is in need of correcting, if at all possible.
Just where and how to undertake to do this, in
the best possible manner, is the so-called "$64
question". Some of this weakness at our school

WINTER 1974

may have started when we dropped the teaching
of inorganic and organic technology. Any courses
where flowsheets of various processes were rather
thoroughly discussed emphasizing reasons for the
various pieces of equipment, operating conditions,
catalyst, etc., served to help the students apply
engineering principles.

PROCESS FLOWSHEET DISCUSSION

TWO OR THREE PROCESS flowsheets involv-
ing various types of equipment are discussed
in my plant design course. Then the students are
required to lay out a process flowsheet. Appar-
ently, they are able to find their particular process
flowsheets illustrated fairly completely in the lit-
erature, but they do not receive enough practice
in thinking out the reasons why all the specific
equipment is used. There are many items that the
students should have thoroughly fixed in their
minds before they undertake a course in plant
design. Some of these items are:
* Pumps are used to move liquids and compressors are
only used to move gases.
* It costs a great deal more to elevate the pressure to
some higher pressure by a compressor than it does a
like weight of liquid by a pump.
* One does not vaporize material and then use a com-
pressor to elevate it to some higher compression level if
it can be elevated to the higher compression level first
by a pump, then heated to the desired conditions to con-
vert it to a vapor.
* One does not heat something to a higher temperature
than the heating medium being used.
* Compounds having lower boiling points go out the top
of an ordinary fractionator and the higher boiling com-
pounds go out the bottom.
* All ordinary fractionating towers have a lower tempera-
ture and pressure at the top than at the bottom.
* All ordinary fractionating columns must have reflux and
reboilers.
These and many other statements that could be
listed should be fixed in the students' minds before
starting plant design.
I have tried to analyze why this weakness ex-
ists with our present day students. Just about all
graduates of 20 to 30 years ago were required to
take courses in organic and inorganic technology.
In those courses taught to me, process flowsheets
were discussed thoroughly in class and students
were required to give reasons why the type of
equipment used was needed; why specific operat-
ing conditions were best, based on kinetic and
thermodynamic relationships; the likely poisons
for catalyst, considering the chemical reactions
that were likely to occur, etc. These courses have

been dropped as required courses and in many
curricula are not even offered. At least, I think
those courses taught me to think and learn to
apply fundamental chemical engineering princi-
ples. This causes me to wonder if we have not
made a mistake in eliminating these courses. The
other possibility is to utilize flowsheets in teaching
some of the fundamental chemical engineering
principles in such courses as mass and energy
balances, unit operations, mass transfer phenom-
ena, thermodynamics, kinetics, and plant design.

NOT ENOUGH PRACTICAL APPLICATION

IT HAS BEEN OBSERVED that the students
are keen at memorizing fundamental principles,
laws, rules, and derivations of equations, but when
asked questions where these are to be used or
could be applied to think out an answer or a solu-
tion, the students seem to fail to recognize the
source of help. There appears to be too much em-
phasis placed on derivations of equations, theo-
rems, etc., and not enough practical application.
Perhaps the lack of industrial experience of fac-
ulty members or the tendency of faculty members
to teach undergraduates like they were taught
graduate courses, where derivations of equations
were stressed, may have something to do with the
weakness of students in the application of engi-
neering principles.
At any rate, this test has convinced me that
our ChE curricula have one serious weakness in
the fact that so many of our graduates cannot do
a better job of applying chemical engineering
principles. O

E. C. Oden is a graduate of the University of Alabama and Brook-
lyn Polytechnic (M.S. '38) and has done graduate work at Cornell and
the University of Michigan. He has many years experience in the
chemical and petroleum industries and is presently teaching plant de-
sign.

CHEMICAL ENGINEERING EDUCATION

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1973 4Awcad Leckti4e

THE THEORY OF DIFFUSION AND REACTION

A Chemical Engineering Symphony

RUTHERFORD ARIS
University of Minnesota
Minneapolis, Mn. 55455

ALTHOUGH CHEMICAL ENGINEERS have
been far from alone in their work towards a
comprehensive theory of diffusion and reaction,
their contributions have been so substantial and
significant that it is only stretching the truth a
little to claim the subject for our discipline. To
claim that it is a symphony, an articulated and
developed structure shot through with certain
themes, held together by the relationships of its
movements and breathing an inner life of its own
-that is a claim of another sort. Yet, at the risk
of being regarded as a shade fanciful or a mite
precious, I will persist in offering the analogy for
if, as Galileo held, "The book of nature is written
in the language of mathematics" and if, in mathe-
matics, structure is of the essence then we must
always be concerned for structure. Indeed some
have gone so far as to claim that a knowledge of
structure is the "only articulate or communicable
knowledge that we can attain". Be that as it may,
the emphasis on structure needs no justification
to a society devoted to engineering education. But
structures are not enjoyed entirely in isolation and
it is tempting to employ that bright gift of our
mediaeval brethren, the art of analogical think-
ing, to enliven this enjoyment. Nor am I alone in
this predilection for I have heard one of the great
men of our profession, R. B. Bird, subtitle his
seminar "A sonata on rheology and kinetic
theory". Like all analogies, its tempo and timbre
must be carefully controlled, but with this under-
stood the orchestra can be allowed its head at
least until we land in the ditch with a fine flourish
of mixed metaphors.

I would like to begin by delineating the main
outlines of the subject as I see it and to go on to
some comments on its history which may serve to
clothe the bare bones of abstraction with a few
sinews and a little flesh.

THE STRUCTURE OF THE SUBJECT
The theory of diffusion and reaction in perme-
able catalysts may be divided into four move-
ments. The first, an allegro in sonata form, states
and develops the partial differential equations
from which all must depend. It is followed by a
slow movement in sonata-rondo form, definitely
andante for it deals with the steady-state solution
of these equations and equally pedestrian, though
important, matters. The tempo picks up a little
(allegretto) in the third movement, a minuet and
trio concerned with the question of uniqueness and
its bearing on stability. This theme carries over to
the fourth movement, a set of variations on the
question of stability and transient behavior-presto
vivace.
The distinction between the first half of the
subject and the second is a clear one and the dif-
ficulties they present are those encountered by the
great lexicographer. For if the results on steady
state are, as Dr. Johnson said of the English
tongue, "Copious without order", the newer de-
velopments on uniqueness and stability are cer-
tainly energetick without rules". Indeed it will
be some years before a comprehensive account of
these developments can be given.

CHEMICAL ENGINEERING EDUCATION

. . if Galileo held, "The book of nature is written in the language of mathematics" and if, in
mathematics structure is of the essence, then we must always be concerned for structure.

The theory of diffusion and reaction in permeable catalysts may be
divided into four movements-allegro, andante, allegretto, and presto vivace.

"I r t

7 - ',co -

z ~-~~ p~.l~�

I1k _ 1

1o.,
"SPL. I

JV I , xtlo' e. v PI-1, 0 , o- ,

I Tnii8 oio t

THE TWO SUBJECTS OF the first movement
may be introduced without delay for they are
the partial differential equations governing the
concentrations and temperature in the catalytic
region f and the appropriate boundary conditions
to be applied on Dl. To take a case of fundamental
importance for the exposition, an irreversible re-
action whose rate R (u,v) depends on the concen-
tration, u, of a single reactant and on the temper-
ature, v, will give rise to the equations

-= 2u - 2R(u,v) (1)

1 = V2v + B22R(u,v) (2)
aT
where T is the time (made dimensionless by the
characteristic diffusion time), V- the Laplacian
operator in the dimensionless space variables of
the particle, P, the Prater temperature rise, _ ,
the Lewis number and 4 the Thiele modulus or
ratio of the diffusion time to the reaction time.
The concentration and temperature have been
made dimensionless by dividing them by the con-
centration and temperature far from Dn. Hence
the boundary conditions are
1 al 1 3v
S- u = 1and -+ v = 1 (3)
v an 1 In

"� )

WINTER 1974

/L and v being the Biot numbers for heat and mass
transfer to aD. The basic equations are thus seen
to be a pair of parabolic, quasi-linear partial dif-
ferential equations with Robin boundary condi-
tions.
The exposition continues by showing the de-
tails of the reduction of the equations to this form
and with the generalizations and specializations.
The generalizations would include the forms of the
equations when there are more chemical compon-
ents, more than one reaction or for the case of
volume change. The specializations include the
isothermal case (for which v is fixed) and the
Dirichlet problem (for which 1/ and v tend to in-
finity). The exposition of these two subjects con-
cludes with the definition of the characteristic
functional of the solution, the effectiveness factor,

= I R(u,v)dV (4)

In the development section the physico-chem-
ical basis of the equations may be examined.
They rest of course on the principles of the con-
servation of mass and energy, but the constitutive
relationships that go into these are based on the
laws of diffusion and of reaction and on certain
models and idealizations of the actual structures.
Thus the concept of an effective diffusivity in a
porous medium needs to be developed on the basis
of the best available understanding of the struc-
ture of these materials.
In the recapitulation the justification for using
a homogeneous model must be discussed. The
catalytic reaction actually occurs at discrete sites
on the walls of a network of pores and it is there
that the transformation of matter and exchange
of energy take place. The degree to which these
are minuscule events happening very close to-
gether and uniformly dispersed throughout the
particle is the degree to which an homogeneous
set of equations will be justified. The case of a zeo-
litic catalyst, where a small proportion of sieves
is sparsely distributed through an inert medium,
calls the homogeneous model in question. Here
also the circumstances in which the equations can
he reduced to a single equation and the forms
taken by the resulting nonlinearity may be con-
sidered.

The final transmogrification of the steady-state theme is to the question of
multiple reactions. For first order reaction systems there are immediate analogies
with the simplest theme of a single first-order reaction.

IF 1C _xlutrL oK4 t ciqatto5 J.- ct f -(auy

'. - -S<,, : , Lt~v uL. , ,,,,r,-

subject, the steady-state solution, appears in
four forms of increasing development and com-
plexity. The basic features are found in its first
exposition in the context of a first-order, iso-
thermal reaction (A1). Here the distinction be-
tween the Dirichlet and Robin problems, the ef-
fects of particle shape and the asymptotic be-
havior can be readily appreciated and these are
themes that recur. After a section (B') on varia-
tional methods, whose validity though rooted in
the linear situation yet reaches out to monotone
non-linearities, we come to isothermal kinetics not
of the first order (A'). This embraces the p"'
order reaction, Langmuir-Hinshelwood kinetics
and such added features as surface diffusion and
electrostatic effects. The possibility of unsym-
metrical solutions, which arises as soon as there is
more than one stable solution, and the utility of
singular perturbation analysis provide a bridging
section to A:, the discussion of the non-isothermal
case. Here the question of uniqueness really comes
to the fore and the problem of computing the ef-
fectiveness factor is an important one. It is there-
fore appropriate to consider the approximations
and applicable numerical methods (B2). These
have a certain affinity with variational methods
though this connection is not to be over-empha-
sised.
The final transmogrification of the steady-state
theme is to the question of multiple reactions. For
first order reaction systems there are immediate
analogies with the simplest theme of a single first-

order reaction. For in the one case we have

D u - ku (5)
dr2
with u u, at r = a and this leads to the solu-
tion u (r) = ucoshd (r 'a) /cosh4 and the effective-
ness factor 77 = (tanh ), where 2 = a'k D. In
the case of multiple reactions we have
2
d2u
D K u (6)
dr2
where D and K are matrices and u a vector of con-
centrations that is specified as u = u, at r = � a.
Let (1) be the matrix defined by ( = a-'D K and an
effectiveness matrix H be defined by setting HKu.
equal to the actual rate of reaction in the presence
of diffusion. Then it can be shown that
D-1H K = ()tanh(l (7)

in close analogy to (b21
reactant.

(tanh(f for the single

R .tsno ticcutt p u tidclu4Ce f I.

.t. Ev\p''e 0 LC't . rcs

1i0rnr on f rk e i' t ....ie. i'u''es

iif ito;'u v n.r t rtCA. '

T HE THIRD MOVEMENT takes us into the
question of uniqueness and the preliminary
considerations of stability. The general feature of
problems in diffusion and reaction is that for suf-
ficiently small and sufficiently large systems the
solution is unique. It is only for systems of inter-
mediate size that multiple solutions can exist and
then only if the kinetics are sufficiently nonlinear.
Thus we can discern three groups of parameters:
the kinetic group, such as the Prater temperature

CHEMICAL ENGINEERING EDUCATION

p/, the Arrhenius number y and the order of reac-
tion, p, as in the expression for a p"'-order irre-
versible reaction
R (u,v) = uPexpy (v-l) /v; (8)
the transfer group, namely the Biot numbers, It
and v, and the parameters of the internal dif-
fusion; finally there is the Thiele modulus which
measures the size of the system in terms of the
relative characteristic rates of reaction and dif-
fusion and thus links the chemical and physical
features of the problem. We can thus ask for suf-
ficient conditions on the parameters of one class
which will ensure uniqueness when the parameters
of another class lie in a given range. For example
if p and v are infinite (Dirichlet problem) we can
ask for conditions on p, p, y such that the solution
is unique for all values of b. Luss has shown that
the monotonicity of R (1-w, 1+pw) /w is sufficient
for this. Jackson has extended this to the Robin
problem by showing that the monotonicity of
R(1-w-w, l+3w+a/3w) /w (a = v/I) with re-
spect to both w and w is a sufficient condition.
Such conditions as these are "safe" but how prox-
imate they may be to the exact condition has to be
determined computationally; for example, Luss'
condition for a first order reaction in a slab is ex-
traordinarily close to the exact results.
Since uniqueness is to be expected for suffi-
ciently large and sufficiently small values of the
Thiele modulus (say, 4 > "4), < it),it is also of
interest to try and obtain estimates of these so-
called bifurcation values. In particular we would
like a lower bound for I,, and an upper for 4)" so
that the region of multiplicity would be effectively
delimited. Luss has obtained the former but the
results on the latter are still only partial.
In the third movement it is appropriate also to
raise the quasistatic questions of stability. Thus,
it is often possible to give sufficient conditions for
instability from an examination of the steady-
state equations or to use Liapounov methods of
the second kind which though involving the tran-
sient equations do not require anything approach-
ing a solution of them. Jackson has given a very
elegant geometrical interpretation to the analysis
of stability which shows that for the Dirichlet
problem only the maximal and minimal solutions
can be stable. Specifically, he divides the -q,o curve
up into segments at the points where dd/d4 be-
comes infinite. A segment such that (d '/d4)
-+ - sx at either or both of its ends must corre-
spond to unstable steady states.

(. Un iitt . co a vaost'

t' LI,,, i cY J "' .".t"1 ,,,Ls

+ C.i4 , I' l t'u
1 -1
L;. rpnLI-n. Co'(7C-C
>I ^X et's' f
l^ Dfl50> 'A.

THE FOURTH MOVEMENT is a set of varia-
tions on the themes of stability and transient
behavior. The key phrase is the introduction of the
Lewis number whose value has no influence on the
steady state as such but is critical in determining
its stability. In particular there is evidence from
many directions that a sufficiently small value of
the Lewis number, the ratio of the material and
the thermal diffusivities, will often render the
steady-state unstable even when it is unique. This
can give rise to limit cycles in which the concen-
tration and temperature at each point oscillate
and waves of concentration and temperature wax
and receed within the particle. Cyclic operation, as
a means of improving selectivity, has been delib-
erately cultivated in the work of Horn and Bailey
and a recent investigation of Cresswell and El-
nashie has shown that the influence of adsorption
capacity may have to be considered.
Because the exact treatment of the parabolic
equations is difficult various methods of approxi-
mation have been considered. These consist in
some process of lumping or replacing the para-
bolic equations by sets of ordinary differential
equations. This can be quite a crude analogy with
the stirred tank obtained from the first term of a
modal analysis or collocation method or a more
precise development in a series of equations cap-
able of giving as accurate a result as may be
wished. Even the simplest of approximations be-
trays the same general features but the danger of
an approximation of this sort is that its validity is
almost unpredictable and at best one can hope to
find qualitative and comparative results. The
equations governing reaction on the surface of a
catalytic wire are already in lumped form and this

WINTER 1974

. .a symphony or any work of art may be completed and stands for better or worse, a whole to be
praised and performed or disparaged and neglected. But the score of an area of natural philosophy cannot
be so ended, but must constantly be revised and rewritten for each performance.

allows them to be discussed rather fully. In par-
ticular it is found that even when conditions
around the wire are independent of position there
can be periodic solutions to the equation. How-
ever only the uniform state is stable.
It is quite otherwise in the case of other solu-
tions of the diffusion and reaction equations which
lack the symmetry of the problem. The class of
solutions discovered by Pismen, Kharkats, Marek,
Jackson, Horn and others contains unsymmetrical
members whose stability has been established with
great care by Aronson and Peletier. Jackson and
Patel have shown that the full diagram for the
effectiveness factor as a function of Thiele mod-
ulus should contains branches corresponding to
unsymmetrical solutions. Not only can unsym-
metrical solutions be stable, but the symmetrical
or uniform state may actually be unstable. Such is
the case in certain models of morphogenesis that
have developed from Turing's work and in a model

of chemotaxis considered by Keller and Segel. In
the work of Nicolis and his colleagues it further
appears that certain regions of a non-uniform
steady state may become unstable and limit cycle
behavior may be confined. The sophisticated use of
group theory by Scriven and Gmitro to find solu-
tions of varying degrees of symmetry has yet to
be published, but this is another variation that
adds colour and life to the finale.
Here the analogy certainly breaks down. For a
symphony or any work of art may be completed
and stands for better or worse, a whole, to be
praised and performed or disparaged and ne-
glected. But the score of an area of natural philos-
ophy cannot be so ended, but must constantly be
revised and rewritten for each performance. At
least they have in common that, whether it bring
relief or rapture, all such performances must be
brought to a close.

P1a4094m Notae

REFLECTIONS ON HISTORY AND DEVELOPMENT

PROPHETIC AS WAS Mikhailo Vasilyevich
Lomonosov's remark in 1745-"I saw not only
from other authors, but am convinced by my own
art, that chemical experiments combined with
physical show peculiar effects" [1]-it is straining
its context a little to apply it specifically to the
question of diffusion and reaction. Yet it has in-
terest as a dictum of the father of physical chem-
istry and an indication of the opinions far ahead
of his time. After his boisterous student days in
Marburg (1736-39 reading physics under Chris-
tian Wolf) and Freiburg (1739-40 reading metal-
lurgy under Henckel), Lomonosov arrived back
in St. Petersburg on July 8, 1741, just three days
after Euler left for Berlin. He had had a hectic
journey what with raising the money for it and
escaping temporary impressment in the Prussian
hussars and his early years at the Academy of
Sciences were so disturbed by his own turbulence
and that of his times that he does not seem to have

had time to write to the wife whom he had left
behind in Marburg. Indeed he had barely made his
peace with his colleagues in 1744 when, having
made contact with him on her own initiative, she
finally joined him in St. Petersburg. The chair of
chemistry at the Russian Academy of Sciences had
never adequately been filled for the first incumbent
had injured himself fatally by tumbling out of his
carriage in a drunken state when returning from
a symposium only five months after he had arrived
and for the next seventeen years it was held by a
botanist who spent ten of them exploring Siberia.
Lomonosov petitioned Elizabeth to be made pro-
fessor of chemistry and, after he had written a
satisfactory dissertation on metallurgy, an ukase
on his promotion was published on July 25, 1745.
With his promotion the petition for the building
of a chemical laboratory, which he had been re-
newing year by year since 1742, was finally
granted and it is from this proposal that Frank-
Kamenetskii takes the quotation.

CHEMICAL ENGINEERING EDUCATION

� L

But it was his insistence on the combination of
physical and chemical methods that gives him the
claim to be one of the founders of physical chem-
istry. In his "Elementa Chymiae Mathematicae"
(begun in 1741 but never completed) he conceives
chemistry as a science of clearly defined chemical
elements unified by mathematical methods and in-
corporated in a physical system based upon an
atomic theory. Ten years later in a "Speech on the
Uses of Chemistry" [2,3] he speaks of the relation-
ships between mathematics, physics, and chem-
istry
"Eyes are useless to the man who wishes to see the
interior of an object yet lacks a hand to open it. Hands are
useless to the man who has no eyes to observe the objects
once they have been disclosed. Chemistry may correctly be
called the hands, and Mathematics the eyes of Physics. But
as surely as each demands aid from the other, just as
surely, notwithstanding, they often divert human minds
into different paths. The Chemist, who sees in every ex-
periment different and frequently unexpected phenomena
and products and is thereby allured to gain a speedy ad-
vantage, laughs at the Mathematician as being involved
only in certain vain cogitations about points and lines. The
Mathematician, on the other hand, convinced of his proposi-
tions by exact proofs and evolving unknown properties of
quantities through incontestable and uninterrupted deduc-
tions, scorns the Chemist as occupied only with practice
and lost in many chaotic experiments; being himself ac-
customed to clean paper and shining geometric instru-
ments, he abhors the smoke and dust of Chemistry. And
thus up to this time these two sisters, closely associated
for the common good, have for the most part given birth
to sons of such different opinions. This is the reason why
the complete study of Chemistry has not yet been com-
bined with a profound knowledge of Mathematics."
If Lomonosov belongs to the prehistory of the
exact analysis of the problem of diffusion and re-
action, its early history and subsequent develop-
ment are bound up with some of the great names
of chemical engineering with those of DamkBhler
and Wicke in Germany, of Zeldowitsch and Frank-
Kamenetskii in Russian and of Thiele, Weisz and
Amundson in this country. Moreover we have
some useful historical accounts in the recollections
of Thiele [4] and the Murphree Award Address of
Weisz [5]. Indeed it was commonly thought that
the exact analysis flowered almost simultaneously
in Germany, Russia and the U.S.A. in the late
1930's in the work of DamkBhler, Zeldowitsch and
Thiele until a paper of Ferencz Jiittner was dis-
covered (as I understand it, by R. L. Gorring of
Mobil). This 1909 paper appears to have been al-
most totally overlooked for more than sixty years
and was certainly unknown to the three who in-
dependently arrived at some of its results thirty
years later. Jiittner (b. Feb. 28, 1878 Dr. phil.

1901, Breslau) was a natural philosopher who
published papers on thermodynamics, the theory
of matter and relativity besides the three on chem-
ical kinetics which we shall take note of. He is
listed in Poggendorf as "Lehrer, Gymnas Brieg
Schliesen, 1902", and was evidently a member of
the "Schlesischen Gesellschaft fur vaterlandische
Kultur" for he read one of these papers to its
Mathematical Section on the 4th of May, 1909.
In his paper on "Reaktionskinetik und Dif-
fusion" [6] Jiittner considers a general reaction
nA, nA + . . . n'A', + n'.,A' + . . . and

... it was commonly thought that the exact analysis
flowered almost simultaneously in Germany, Russia
and the U. S. A. in the late 1930's in the work of
Damkohler, Zaldowitsch and Thiele until a
paper of Ferencz Juttner was discovered.

assumes mass action kinetics, setting up the time
dependent equations for an arbitrary region and
different diffusion coefficients for each species. In
the stationary state and one space dimension he
recognizes that certain combinations of any two
concentrations will be at most linear functions of
position and in the symmetric case will be con-
stant. The equations can thus be reduced to a
single equation of the form
2
de g(x,c)
dx

where g is a polynomial of degree (n, + n, + . .)
or (n', +n', + . . .), whichever is the greater. In
the symmetrical case, when g is a function of con-
centration alone, Jtittner showed that the equation
could be solved by an implicit function given in
terms of an integral, while in the case of a re-
versible first order reaction he gives the explicit
solution in terms of hyperbolic functions. In the
general case he refers to the "new and important
researches of Painlev6 on algebraic differential
equations of the second order" that had appeared
in Acta Mathematica in 1902, but he again treats
the reversible first order reaction in detail giving
the solution under general boundary conditions.
For the second order reaction he gives a series
solution and remarks that the implicit solution for
irreversible nth order dissociation gives elliptic
functions for n = 2 and 3. In discussing the tran-
sient case Jiittner gives a formal expansion of
(Continued on page 36.)

WINTER 1974

ENGINEERING

ENVIRONMENTAL SYSTEMS
ENGINEERING
LINVIL G. RICH, Clemson University. McGraw-
Hill Series in Water Resources and Environ-
mental Engineering. 1973, 405 pages (tent.),
$16.50 (tent.)
In this quantitative introduction to the subject,
Professor Rich uses a systems approach, in which
the focus is on the system as a whole and how its
components interact. Although water environment
is considered in greatest detail, also included are
air pollution and its control, solid waste manage-
ment and radiological health. The mathematics of
systems analysis and computer solutions is used
extensively.

THERMODYNAMICS, Second Edition
JACK P. HOLMAN, Southern Methodist Univers-
ity. 1974, 608 pages (tent.), $14.50 (tent.). Solu-
tions Manual. Six audio-tutorial cassette tapes
with an accompanying student workbook, $50.00
(tent.)
All standard thermodynamics topics can be cov-
ered from either the classical or statistical view-
point or from any desired integration of the two
with this book. This revision includes a sixty per
cent expansion of classical thermodynamics and
applications, and many new examples and prob-
lems worked in both fps and SI units have been
added.

MOMENTUM, HEAT AND MASS
TRANSFER, Second Edition
C. 0. BENNETT, University of Connecticut,
Storrs and J. E. MYERS, University of Cali-
fornia, Santa Barbara. 1974, 604 pages (tent.),
$16.50 (tent.). Solutions Manual
Combining a rigorous approach to fundamentals
with an extended treatment of practical problems,
this revision treats principles of transport phe-
nomena as applied to simple geometries and then
extends the discussion to analyze practical areas
such as flow in pipes and equipment, filtration,
heat exchangers and evaporators, gas absorption,
liquid-liquid extraction and distillation.

THE INTERPRETATION AND USE OF
RATE DATA
STUART W. CHURCHILL, University of Penn-
sylvania. 1974, 512 pages (tent.), $17.50 (tent.)
Here is a completely new treatment of rate proc-
esses in which a generalized structure is used,
greatly simplifying and reducing the number of
concepts needed to study bulk transfer, mo-
mentum transfer, heat transfer and chemical re-
lations. Emphasis is on the relationship between
design and uncertainties in measurement, and
these concepts are reinforced with over 300 prob-
lems based on raw experimental data from the
literature.

SOLIDIFICATION PROCESSING
MERTON C. FLEMINGS, Massachusetts Insti-
tute of Technology. 1974, 580 pages (tent.),
$19.50 (tent.)
Here is the only significant book in the field in
ten years. Building on the foundations of heat
flow, mass transport and interface kinetics, the
author presents the fundamentals and relates
them to practice. Among the processes considered
are crystal growing, shape casting, ingot casting,
growth of composites and splat cooling.

INTRODUCTION TO METALLURGICAL
THERMODYNAMICS
DAVID R. GASKELL, University of Pennsyl-
vania. 1973, 550 pages, $19.50
Treating in depth the thermodynamics of high
temperature systems encountered in metallurgy,
this book demonstrates the thermodynamic
method through an extensive illustration pro-
gram, using as examples real systems which have
been carefully selected to illustrate the principles
involved. The text introduces basic laws and nec-
essary thermodynamic functions and makes appli-
cations that are numerous and thoughtful.

McGraw-Hill Book Company

CHEMICAL ENGINEERING EDUCATION

MEANS McGRAW-HILL

MASS TRANSFER
THOMAS K. SHERWOOD, ROBERT L. PIG-
FORD, CHARLES R. WILKE, all of the Uni-
versity of California at Berkeley. 1974, 512 pages
(tent.), $18.50 (tent.)
Compared with the 1952 version, Absorption and
Extraction, this volume is substantially more so-
phisticated, providing a much broader coverage
of mass transfer. Emphasis is on the practical
aspects and real problems that demand an under-
standing of theory. Yet theoretical derivations are
minimized by explicit citation of over 1100 con-
temporary references.

SCIENTIFIC STREAM POLLUTION
ANALYSIS
NELSON LEONARD NEMEROW, Syracuse
University. 1974, 380 pages (tent.), $16.50 (tent.)
A careful balance of the hydrological, chemical
and mathematical concepts involved in the evalu-
ation of stream quality is achieved in this com-
prehensive description of the analysis of water
pollution. Practice problems are presented to dem-
onstrate the difficulties surrounding stream anal-
ysis, and computation techniques for deoxygena-
tion and reaeration rates are described and ana-
lyzed, as are all factors affecting oxygen concen-
tration to give and overall oxygen sag curve in a
stream.

AIR POLLUTION
H. C. PERKINS, University of Arizona. 1974,
480 pages (tent.), $16.50 (tent.). Solutions Man-
ual
To date, this is the only truly engineering-oriented
text on the subject that draws on the student's
background in analyzing and solving problems in
air pollution. The treatment is sufficiently detailed
to enable chemical, mechanical and sanitary engi-
neering students to solve a variety of problems,
and many applications-type problems are included.

ENVIRONMENTAL PROTECTION
EMIL T. Chanlett, University of North Carolina
at Chapel Hill. 1973, 569 pages, $15.50
ENVIRONMENTAL PROTECTION is man-cen-
tered. This book describes the rationale for the
management and protection of our land, air, water
and energy resources, and examines the conse-
quences of mismanagement at three levels: 1)
effects on health, 2) effects on comfort, conveni-
ence, efficiency and esthetics and 3) effects on the
balance of ecosystems and of renewable resources.

CONSERVATION OF MASS AND ENERGY
JOHN C. WHITWELL and RICHARD K.
TONER, both of Princeton University. 1973, 512
pages, $14.95. Solutions Manual
Unique in chemical engineering literature is this
treatment of degrees of freedom for material and
energy balances. Either chemical or physical proc-
essing elements are handled in a unified manner.
The authors have included the first law of thermo-
dynamics, unsteady state mass and energy bal-
ances and all physical chemistry required. The
modular organization of the material offers the
instructor a wide choice for his particular syl-
labus.

EXPERIMENTAL METHODS FOR
ENGINEERS, Second Edition
JACK P. HOLMAN, Southern Methodist Uni-
versity. 1971, 448 pages, $14.50. Solutions Manual
A broad treatment of instrumentation and anal-
ysis of experimental data is offered in this re-
vision, which contains more information on ex-
periment planning and the importance of feed-
back during experiments, emphasizing the anal-
ysis of uncertainties in planning experiments and
instrumentation. A variety of numerical examples,
problems and methods are included.

Prices subject to change without notice.

1221 Avenue of the Americas, New York, N.Y. 10020

WINTER 1974

Nth

l laboratory

INDIRECT MEASUREMENT OF REACTION RATE

R. D. WILLIAMS
University of Arizona
Tucson, Arizona s

This paper describes an experiment which can
be used to study the kinetics of chemical reactions
which are accompanied by measurable heat ef-
fects. An indirect method of data collection takes
advantage of the fact that the rate of reaction is
proportional to the rate of energy release or ab-
sorption.
Laboratory experiments in chemical engineer-
ing curricula should be carefully selected accord-
ing to the laboratory objective. Experiments
which demonstrate several points are especially
effective in the curriculum squeeze of today.
At the University of Arizona the undergradu-
ate kinetics laboratory is used to give the student
practical experience in the more important points
covered theoretically in the lecture course the
semester before.
The first three experiments of the lab are con-
cerned with a demonstration of the differences in
behavior of batch, continuous stirred and tubular
reactors. The integral method of analysis is used
in conjunction with isothermal batch kinetic data
in order to determine the kinetics of the saponifi-
cation reaction between ethyl acetate and sodium
hydroxide. These kinetics are then used to predict
behavior of the two continuous reactor types and
these predictions are experimentally checked. The
wet chemical method of data collection in these
three experiments is tedious and by the end of the
third the student is convinced that all kinetic de-
terminations must be equally frustrating.
The fourth experiment was chosen in part for
its comparative experimental simplicity. But more
than this several important points from the theory
course are well illustrated. These are enumerated
below.
* An indirect data collection method is illustrated.
* An energy balance is required in addition to the material
balance.
* The data cannot be conveniently analyzed by the integral
method whereas the differential method can be used.
* Not only the kinetics, but also the stoichiometry and
heat of reaction may be very simply determined.

Dick Williams received his undergraduate degree at Texas Tech
University and his graduate degrees at Princeton University, all in
Chemical Engineering. He has been at the University of Arizona since
1968 where his research has been involved primarily with chemical
reaction engineering. Current research projects include design of a
system to reduce automobile pollutants while increasing fuel economy
and a study of hydrometallurgical leach recovery of minerals from
their ores with emphasis on characterization of the underlying mecha-
nisms involved.

This fourth experiment involves the deter-
mination, in an adiabatic-batch reactor, of the

kinetics of the exothermic reaction between hy-
drogen peroxide and sodium thiosulfate. Glasser
and Williams' have demonstrated a slightly more
general technique using the acetic anhydride hy-
drolysis reaction. The former reaction has the
pedagogical advantage of a non-obvious stoichio-
metry which can be experimentally determined.
Several possible reactions between hydrogen per-
oxide and sodium thiosulfate are listed in Table 1.

CHEMICAL ENGINEERING EDUCATION

Root and Schmitz' utilized this reaction in dem-
onstrating reactor instability in an adiabatic loop
reactor. Their analysis did not require a detailed
knowledge of the kinetics. Cohen and Spencer:
have calorimetrically studied this system to obtain
the kinetic details.

An indirect method of data collection takes advantage
of the fact that the rate of reaction is proportional
to the rate of energy release or absorption.

that the maximum occurs near a reactant ratio of
two implying that the major reaction occurring is
VI in Table 1. A check on this result can be made
by calculating the theoretical heat of reaction and
comparing this value with values obtained from
the experimental data using Equation 1. These re-
sults are given in Table 2.

HRH pC 'T
RA 0

FIuURE I: [/PICAL TEMPERATURE - TIME TRACE.

EXPERIMENTAL

The experimental apparatus consists of a 500
ml beaker, a magnetic stirrer, and a thermo-
couple-strip chart recorder arrangement. Volumes
of two molar solutions of each of the reactants are
mixed in the beaker and the temperature is re-
corded as the reaction progresses. An s-shaped
curve such as shown in Figure 1 is obtained. If
the total reaction mixture volume is held constant
while varying the relative amounts of each re-
actant, then the temperature rise will go through
a maximum when the reactants are mixed in their
stoichiometric ratio. A graph of AT versus initial
concentration ratio will exhibit this behavior. A
typical result is shown in Figure 2. It can be seen

TABLE 2: Comparison of Student and Literature Vlues

kcaI/ole Na S23 kcal /moe iters/iole-see

student
i terature
Sef. 3

7.33 X 1011
6.35 X 10

THEORETICAL

The kinetic data can be analyzed in light of
the theoretical temperature-time relationship. The
material and energy balances for an adiabatic,
constant volume batch reactor are given below.

dal
dt A

SdT
pC - (-H ) R
p dt R

(3)

(3)

These are subject to the initial conditions,

a(O) = ao; T(O) = To.

Equation 2 can be divided by Equation 3 in
order to eliminate the nonlinear rate term. Inte-
gration of this result gives a relationship between
reactant concentration and temperature.

WINTER 1974

A 11 KJ ,

7C
a=a (T-T)
S HR A

Assuming the reaction to be irreversible and
first order with respect to each reactant the ki-
netic rate expression becomes,

R=kab

.. the exothermic reaction between hydrogen
peroxide and sodium thiosulfate has the pedagogical
advantage of a non-obvious stoichiometry which
can be experimentally determined.

where

B
b = b + B ( a - a )
A

or when reactants are initially present in the
stoichiometric ratio,

b B
b =--a.
).

Assuming Arrhenius temperature dependence for
k, Equations 4, 5 and 7 can be inserted into Equa-
tion 3 to give a single nonlinear ordinary differ-
ential equation giving the temperature-time de-
pendence,

dT (T 2
dt Y (Tf - T)

e-E/R T
e g

3 , I I I I , I 1
3.0 3,1 3,2 3,3 ",4

This suggests that a plot of log (dT/dt 2) versus
(Tf- T)
1/T should give a straight line of slope -E/R, if
the assumptions made with regard to the rate ex-
pression are correct. The pre-exponential factor
can then be calculated from Equation 8. The
temperature derivative is easy to determine in
this experiment since a continuous temperature-
time trace is obtained. Typical student results are
plotted in Figure 3. As was the case in Figure 2
these data are from experiments run by several
different groups on different days. Values of E
and k,, from Figure 3 are given in Table 2. D

REFERENCES

1. Glasser, David and Williams, Don F., "The Study of
Liquid-Phase Kinetics Using Temperature as a Meas-
ured Variable," I&E.C. Fund., 10, 516 (1971).
2. Root, R. B. and Schmitz, R. A. "An Experimental
Study of Steady State Multiplicity in a Loop Reactor",
AIChE J., 15, 670 (1969).
:3. Cohen, W. C. and Spencer, J. L., "Determination of
Chemical Kinetics by Calorimetry," Chei. Engr. Prog.,
58, 40 (1962).

a,b
C,
E
AH,

k
lko
R

R,
t
T
AT

v
P

NOMENCLATURE
reactant concentrations, moles/liter
solution mean heat capacity, calories/gm-�K
activation energy, kcal/mole
heat of reaction for a given stoichiometry, kcal/
mole
reaction rate constant, liter/mole-sec
pre-exponential factor, liter/mole-sec
reaction rate for a given stoichiometry, mole/liter-
sec
gas constant, calories/ mole- K
time, sec
temperature, �K
temperature rise, �K

Greek Letters

a constant
stoichiometric coefficient
solution density, gm/liter

Subscripts
A,B denote different reactant species
O denotes an initial condition
f denotes a final value

CHEMICAL ENGINEERING EDUCATION

FIGURE j: ACTIATIJN ENER'

o

0

!T/ :
T- T2

Basic Principles

and Calculations in

Chemical Engineering

3rd Edition, 1974

David M. Himmelblau
University of Texas, Austin

NEW-the Third Edition of Basic Princi-
ples and Calculations in Chemical En-
gineering gives your students an aid to
solving a variety of practical problems in-
volving material and energy balances.
More than that, it guides your students into
forming generalized patterns of attack in
problem-solving which can be success-
fully used in connection with unfamiliar
types of problems.
The chapters have been organized into a
review of fundamental terms, an explana-
tion of how to make material and energy
balances, and a review of certain aspects
of applied physical chemistry. An Informa-
tion Flow Chart appears in each chapter
and shows how the topics discussed relate
to the objective of being able to success-
fully solve problems involving material and
energy balances.
In Basic Principles and Calculations in
Chemical Engineering, Professor Himmel-
blau strives to acquaint your students with a
sufficient number of fundamental concepts
so that they can continue their training in
chemical engineering, and start finding
solutions to new types of problems of their
own.

See why over 40 departments of
Chemical Engineering adopted this
book:
D Organization leads the student from
easy to more difficult material.
E Includes an abundance of examples
to represent every principle discussed.
D Provides a widevarietyof problemsthat
can be assigned without repitition.
D Emphasizes some of the more
meaningful problems in chemical engi-
neering today.
0 Provides answers to nearly 25% of the
problems.
Teaching and Learning aids:
D Completely worked-out example
problems illustrate the principles involved.
D A large number of illustrations are pro-
vided to amplify the text.
D Graphs and tables furnish sources of
data for the example and homework prob-
lems.
D ASolutionsManual isavailable which
contains detailed solutions to all of the
homework problems together with typical
examinations and course outlines.
January 1974, 544 pp., cloth $15.95

For further information please write:
Robert Jordan, Dept. CJ-740,
College Division,

rMeW classroom

4IM 2ndeur&a%9*da Cowue

INTERFACIAL PHENOMENA FOR ENGINEERS

A Bridge Between Engineering and Life Sciences

DINESH O. SHAH
University of Florida
Gainesville, Florida

D DURING RECENT YEARS it has become in-
creasingly evident that the principles and
techniques of chemistry and physics of surfaces
are of considerable importance in chemical engi-
neering. Theoretical and experimental research in
this area have appeared in the chemical engineer-
ing journals under the general title of "Interfacial
Phenomena." Therefore, it is not surprising that
many chemical engineering departments have in-
cluded in their curriculum courses on interfacial
phenomena or surface and colloid chemistry. In
the winter of 1972 I was asked to present three
lectures on the principles and techniques of sur-
face chemistry to undergraduate students in chem-
ical engineering as a part of the course on "Ma-
terials of Chemical Engineering." I presented an
introduction to surface tension, interfacial ten-
sion, miscibility of liquids, foams, emulsions and
wettability of surfaces. Surprisingly, about 15
undergraduate chemical engineering students sub-
mitted a petition to the department requesting
that an undergraduate course on interfacial phe-
nomena be offered. At the suggestion of the de-
partment, I formulated a course to be given be-
ginning the spring quarter of 1972.
My main objective in teaching this course was
not to make every student an expert in surface
and colloid science. Rather, the course would
offer them a better understanding and apprecia-
tion of the principles and applications of surface-
active molecules, the properties of surfactant solu-
tions at various interfaces, and also a number of
applications such as foams, emulsions, lubrication
and flotation of minerals. Among the textbooks
available, I suggested Physical Chemistry of Sur-

faces by A. W. Adamson. Interfacial Phenomena
by J. T. Davis and E. K. Rideal was suggested as
a reference book. However, it is important to men-
tion that these books were not appreciated by most
of the students. The fact that most of the material
presented to the class was derived from a number
of research papers, review articles, and other
specialized books, contributed to their poor ap-
preciation of these books. The course was de-
signed for 3 credit hours and was taught three
lectures per week. Instead of giving numerical
examples as homework problems, I decided to pro-
vide them a number of reprints related to the
topics being discussed in the class as required
reading material.

TOPIC OUTLINE
The following is a brief outline of the topics
followed during the quarter.
1. Introduction: surface-active molecules and
five major interfaces; i.e., gas liquid, liquid/liq-
uid solid liquid, solid/solid, solid/gas.
2. Properties of surfactant solutions: surface
tension, CMC, Gibb's adsorption isotherms, sur-
face excess concentration, solubilization, pH near
a charged surface (i.e., surface pH vs. bulk pH),
effect of salts, chain length, temperature and ad-
ditives on CMC; cylindrical and lamellar liquid-
crystalline structures of surfactants.
3. Spreading of a liquid on another liquid:
spreading coefficient, effect of surfactants on
spreading of oils, interfacial instability and inter-
facial tension, surface pressure, Marangoni effect.
4. Spreading of liquids on solids: work of co-
hesion and adhesion, contact angle and wettabil-
ity, critical surface tension of solids.
5. Insoluble Monolayers: surface pressure-area
curves, cross-sectional area of molecules, effect of
temperature on phase-transitions in monolayers,

CHEMICAL ENGINEERING EDUCATION

Dr. Shah received his undergraduate training at the University of
Bombay and his doctoral degree in biophysics from Columbia Univers-
ity in 1965. He spent a year at NASA Ames Research Laboratory in
California working on chemical evolution and the origin of life, and
surface chemical aspects of the origin of membranes. Later he moved
to the Biological Oceanography Division of Columbia University and
worked on dispersion of oil spills, retardation of evaporation and wave
damping by thin films of surface active agents and on surface chem-
ical aspects of sea water. Since 1970, he has been at the University
of Florida with a joint appointment in Anesthesiology, Biophysics and
Chemical Engineering Departments. Dr. Shah has published in the areas
of biological and model membranes, chemical evolution and the origin
of membranes, foams, microemulsions, boundary lubrication and sur-
face chemical aspects of vision, and anesthesia. He received the "Ex-
cellence in Teaching Award" of the University of Florida for 1972-73.

reactions in monolayers, surface potential, sur-
face radioactivity, surface absorption spectra
measurements, surface viscosity and two-dimen-
sional Newtonian and Non-Newtonian liquids,
equation of state for monolayers, electrical double
layer and Gouy potential, effect of pH and salts
on monolayers, surface pk vs. bulk pk for mono-
layers, mixed monolayers and molecular associa-
tions in 1:1, 1:2 and 1:3 molecular ratios. Mono-
layers of biological lipids and the correlations
with membrane phenomena.
6. Foams: stability of soap bubbles, rate of
drainage, surface viscosity and molecular pack-
ing, foam stabilizing and antifoaming agents,
foam fractionation and other applications.
7. Macro- and Microemulsions: oil-water-sur-
factant systems, effect of structure, concentration
and chain length of surfactant on emulsion prop-
erties, HLB values, spontaneous emulsification,
phase-inversion, emulsion rheology and stability,
various applications of emulsions.
8. Flotation of Minerals: collectors, brothers,
activators, and depressors, selective flotation, ab-
sorption of collectors on minerals, contact angle

and flotability, use of oppositely charged collec-
tors, ion-flotation.
9. Friction and Lubrication: Boundary and
hydrodynamic lubrication, coefficient of friction,
scuff load, percent metallic contact, wear rate,
biolubrication, synovial fluid, structure of lubri-
cant additives.
10. Gas/Solid Interface: Physical and chemical
adsorption, catalysis, various types of adsorption
isotherms, monolayer-multilayer adsorption and
capillary condensation, pore volume, hysteresis.
11. Artificial Organs: Nonthrombogenic sur-
faces, blood-clotting, Heparin, biomaterials, trans-
plants and implants, biological and model mem-
branes, surface chemical aspects of lungs and
cornea.

EXPLANATION BY DEMONSTRATION

On several occasions, I gave experimental dem-
onstrations to make concepts clear and interest-
ing. For example, two dimensional liquid and
solid monolayers of stearic acid, respectively, on
subsolutions of NaC1 and CaCL. were distin-
guished by sprinkling talc particles and blowing
air toward the particles. For monolayers in the
liquid state, the particles move freely in the sur-
face, whereas for solid monolayers, the particles
do not move at all. In another experiment on the
use of a wetting agent for wettability of surfaces,
I dipped a polished teflon bar into aqueous KMnO,
solution, and pulled it out. The teflon rod re-
mained white because water did not wet the
teflon. However, upon adding a few drops of soaps
or detergents, when the same process was re-
peated the teflon became pink when removed from
the KMnO, solution, suggesting that soap mole-
cules caused water to wet the teflon surface. Many
such demonstrations on foams and emulsions
made students appreciate the importance of sur-
face chemistry in many engineering applications.
There were two examinations, one mid-term
examination and a comprehensive final examina-
tion. Here again, instead of giving numerical ex-

The course would offer... a better
understanding and appreciation of the principles
and applications of surface-active molecules,
the properties of surfactant solutions at various
interfaces and a number of applications ...

WINTER 1974

S.. it was successful in giving a bird's eye view of a number of applications
of surface chemistry in chemical engineering . . . and . .. balancing
mathematically oriented courses, such as transport phenomena, process control,
and kinetics, with a descriptive and application oriented course.

amples to solve, I submitted extensive multiple
choice questions during both of these examina-
tions. Each of the questions tested their thorough
understanding of the principle involved rather
than any memorization of equations. The ques-
tions were phrased in such a way that the possi-
bility of guessing the answer was minimized. I
should mention that often students took as much
as two and one-half hours to answer 20 multiple
choice questions. A few of these questions are
mentioned as follows:
1. The contact angles of equimolar solutions
of hexanoic acid (C-,-COOH) and decanoic acid
(C,,-COOH) on a copper plate were found to be
respectively and . (0�,
700, 110")
2. An off-shore oil spill decreases the surface
tension of air sea interface to 40 dynes/cm. What
should be the spreading pressure (-) of a surface-
active agent to push the oil spill away from the
shore line?
3. The surface viscosity of monolayers of ste-
aric acid (CICOOH) cis, oleic acid (Cs-CH=CH
-C,-COOH) and elaidic acid (Cs-CH=CH-
C,-COOH) trans were measured at a surface
pressure 10 dynes/cm. The surface viscosities
were found to be respectively
, and
centipoises. (3.7 x 10-1, 4.1 x 10-4, 9.7 x 10-4)
4. For two sliding surfaces the coefficient of
friction was 0.02 and 0.07, respectively, at the
load of 1,000 gm and 2,500 gm. Is this hydrody-
namic or boundary lubrication?
5. The palmitic acid monolayers were studied
at 25'C, 35'C, and 45�C. The average area per
molecule at a surface pressure 10 dynes 'cm were
found to be respectively,
and A2 molecule. (28, 21, 35)
The numbers in parenthesis were not correct
values, but simply indicated the trend or ordering
of values. The first question is based on the effect
of chain length on adsorption of surfactant on
a solid surface. The second is based on the
Marangoni effect; i.e., the surface flow occurs

from a high surface pressure region to a low sur-
face pressure region. The third question is based
on the effect of cis or trans double bonds on the
area molecule or molecular packing and hence on
the surface viscosity of monolayers. The fourth
is based on the definition of hydrodynamic and
boundary lubrication from the variation of co-
efficient of friction with load. The fifth question
illustrates the effect of temperature on the aver-
age area per molecule in monolayers.

STUDENT AND TEACHER EVALUATION

A MONG THE 15 STUDENTS who took this
course, 12 made more than 85' points on
both comprehensive examinations. This was par-
ticularly satisfying because more than 60 ques-
tions were asked from the materials presented
throughout the course. The students were also
asked to prepare a term paper on a topic in the
general area of interfacial phenomena to be sub-
mitted at the end of the quarter. The process of
preparing a detailed term paper exposed the stu-
dents to most of the available sources of informa-
tion in the area of interfacial phenomena. The
quality of the term paper was taken into account
in giving the final grade for the course.
I would like to add a note regarding the evalu-
ation of this course by the students in the class.
Again, to my great surprise, this undergraduate
course on interfacial phenomena brought me the
Excellence in Teaching A'ward sponsored by the
Standard Oil of Indiana Foundation. The follow-
ing are a few comments made by students in the
teacher's evaluation forms about this course.
"Find a better textbook. . . It would be hard to
make improvement in such an excellent course...
I enjoyed it very much. Best course I ever had in
chemical engineering. . . Excellent course and
teacher; need better textbook... This is the most
interesting course I have ever taken. . . One of the
most interesting, well taught courses I have ever
had. Greatly increased my interest and knowl-
edge. . ."

CHEMICAL ENGINEERING EDUCATION

The course, because of its extreme breadth,
could not go into great depth in many of the topics
discussed. However, it was successful in giving a
bird's eye view of a number of applications of
surface chemistry in chemical engineering. This
course was successful in balancing a number of
mathematically oriented courses, such as trans-
port phenomena, process control, and kinetics,
with a descriptive and application-oriented course.
The course provided a brief introduction of de-
tergents, foams, emulsions, lubrications, and other
biomedical areas to chemical engineering students.
I also repeated this course in the spring of 1973

with very similar responses by the students who
took it. However, this time I used Surface Chem-
istry by L. I. Osipow (R. E. Krieger Publishing
Company, Huntington, New York) as a textbook,
which was better received by the students than
the previous two books.
I believe a course on interfacial phenomena
would be a very desirable part of the undergradu-
ate chemical engineering curriculum, and would
contribute greatly in exposing the students to the
real systems which chemical engineers are more
likely to encounter in their professional careers. D

Ilew &CC O eate...

CACHE COMPUTER PROBLEMS

CHEMICAL ENGINEERING EDUCATION, in
cooperation with the CACHE (Computer Aides
to Chemical Engineering Education) commit-
tee, is initiating the publication of proven com-
puter-based homework problems as a regular
feature of this journal. Problems should be
appropriate for use in an undergraduate or first
year graduate chemical engineering course.
Problems should be documented according to
the published "Standards for CACHE Compu-
ter Programs" (September 1971). That docu-
ment is available now through the CACHE
representative in your department or from the
CACHE Computer Problems Editor. Because
of space limitations, problems should normally
be limited to twelve pages total; either typed
double-space pages or actual computer listings.

Please submit 5 copies of all contributions to
Dr. Art Westerburg, C.C.P. Editor
Department of Chemical Engineering
University of Florida
Gainesville. Fla. 32611

WINTER 1974

- I �I � � I I � r

I I

THEORY OF DIFFUSION & REACTION
(Continued from page 25.)

The concept of the effectiveness factor does not
emerge from this work. The idea of a meaningful
fudge factor is peculiarly characteristic of the
engineer's need to wrap up the theory in an
effective and practical parameter, the physically
significant functional of an underlying function.

the solution for first order reversible reaction
and comments on a reduction to Fourier's equa-
tion when the reaction is irreversible. He con-
cludes with a correct formulation of the non-iso-
thermal problem in which the diffusion coefficients
are functions of temperature, remarking "Man
erkennt, wie ausserordentlich gross die Schwierig-
keiten fur eine theoretische Behandlung der
Gleichung sind". All in all it is a remarkable paper
coming in the early summer of the classical period
of kinetic studies and formulating, and where pos-
sible solving, equations that were not again taken
up until nearly thirty years later. It is interesting
to note that the concept of the effectiveness factor
does not emerge from this early work. The idea
of a meaningful fudge factor is peculiarly char-
acteristic of the engineer's need to wrap up the
theory in an effective and practical parameter, the
physically significant functional of an underlying
function.* When the biochemists examined the
question of diffusional hindrance with immobilized
enzymes their approach was not that of using a
multiplicative effectiveness factor but of modify-
ing the Michaelis constant for the reaction.
Jiittner's paper was followed by another in
which he enlarged on the topic of Painlev6's tran-
scendents [7] and a third on the general integrals
of "ordinary chemical kinetics" [8], which need
not concern us in the context of diffusion. Painlev6
had been concerned to find out how transcendental
functions were generated by differential equations
of the form
y" = R (y',y,x)
where R is rational in y', algebraic in y and ana-

*The concept of the effectiveness factor for these equa-
tions probably arose first for the problem of convection
from a thin fin. Indeed many of the solutions available for
this problem (see, e.g. [1001) can be reinterpreted in terms
of first order reaction and diffusion.

lytic in x [9]. In particular he found five canonical
forms, the first two of which,
y" 6y- + x, y" = 2y2 + xy + a
would be applicable to isothermal diffusion and
second or third order reaction in the slab.
Jiittner's paper is concerned with the conditions
under which the equations for a second order re-
action may be reduced to Painlev6's canonical
form, and the essence of his result is that the
quadratic terms in concentration and position
must form a perfect square. This is always the
case for the symmetrical solution but, in contrast
to most writers since his time, Jiittner was con-
cerned to have scope for general boundary condi-
tions and hence allowed for the possibility of un-
symmetrical solutions.
Thiele [4] notes that a German patent of 1899
has an implicit reference to the possibility of dif-
fusion limitation in catalysis and that there are
two experimental papers reporting the effect of
catalyst particle size [10,11]. In one of these Juli-
ard acknowledged that this result "s'explique par
le fait que chaque grain constitute un system
poreux pr6sentant une surface interne incompara-
blement plus grande que sa surface apparante"
but he was not able to assess this quantitatively.
Wicke and Brotz in 1949 [12] were the first to use
two sizes of catalyst and to compare their per-
formance in the light of the theory that had by
then been developed.

FOUR DIMENSIONLESS GROUPS

AT THE OUTSET OF his great series of papers
on the influence of flow, diffusion and heat
conduction on the yield of reactors [13,14,15,16,17]
Damk6hler recognized the importance of four di-
mensionless groups. The second of these is the
ratio of the chemical rate to the diffusion rate and,
though this is presented in the context of the
tubular reactor, it was obvious that this would
also be the key parameter in the study of the cata-
lyst pellet. Indeed in his comprehensive article for
the Eucken-Jacob handbook "Der Chemie-Ingen-
ieur", Damkdhler [181 expresses the condition for
there to be no diffusion limitation in the form
2 4v.W
transport time Z_ <.
p reaction time 2D
p dc.
P J
This ratio, in which p and d, are the length and
diameter of the pore, D, the diffusion coefficient
within it and vjW c, ratio of a mean reaction rate
to a mean concentration, is clearly of the same

CHEMICAL ENGINEERING EDUCATION

form as his parameter II for the tubular reactor
and the criterion is a valid one. However Dam-
k6hler does not appear to have published the solu-
tion to the full problem* which, in all cases except
that of first order reaction, would be needed to re-
late the means W and cj to observable concentra-
tions.
Zeldowitsch came to "the theory of reactions
on powders and porous substances", as he called
his 1939 paper, by way of studies on adsorption
and heterogeneous catalysis [19,20,21]. He recog-
nized that the porous catalyst would present an
intermediate region of internal diffusion limita-
tion between the conditions of small reaction rate
when transfer processes would be unimportant
and the conditions under which mass transfer to
the external surface would control. Without actu-
ally solving the differential equations he saw that
the depth of penetration would be proportional
to V\(D/kS), where D = diffusion coefficient,
k = rate constant por unit area, S = internal area
per unit volume, and hence the actual reaction rate
to V (DkS). He observed that an estimate of the
activation energy from data in this region would
give half the true value and that an n"t order dis-
sociation would appear to be of order (n +1)/2.
[22]
Thiele [23] considered a straight pore of length

At the outset of his great series of papers on the
influence of flow, diffusion and heat conduction
on the yield of reactors . . . Damkohler recognized
the importance of four dimensionless groups.

2ZP opening to a concentration c of the reactant at
either end. The concentration c (x) at a distance x
from the centre would then satisfy

D d2c- = kSc"
dx-
for the nt" order reaction in a slab or

D d (x2 d) kScn
2 dx dx
x
for the sphere. He obtained the solution for first

*The solutions are closely related to those given for a
chain reaction in slab, cylinder and sphere earlier in Dam-
kdhler's article (p. 375).

order reaction in slab and sphere, for second order
reaction in the slab and went on to consider the
effect of volume change with first order reaction.
The solutions and hence the mean reaction rates
were functions of the parameter ep VkS/D. This
parameter is proportional to the square root of
Damk6hler's X, and is the ratio of �p to Zel-
dowitsch's penetration depth. The name "Thiele
modulus" for this parameter has gained currency
and the attribution is not unjust since Dam-
k6hler's II was defined in the context of the tub-
ular reaction and the mention of X,, though prior
to Thiele's work, is a passing one. Thiele presented
the solution in the form of plots of the effective-
ness factor versus this modulus and it is this con-
cept of the effectiveness factor, or ratio of the
actual reaction rate to the rate that would obtain
if diffusion were infinitely rapid, that has proved
so useful. By definition the effectiveness factor has
the value 1 when the Thiele modulus is zero and
its asymptotic properties as the modulus becomes
large are of interest. It may be noted that Thiele
assumed that the concentration of the reactant at
the pore mouth would be known whereas Zel-
dowitsch, though not obtaining any solution of the
differential equation, recognized that this concen-
tration might be governed by external mass trans-
fer limitations.

DIFFUSION IN POROUS BODIES

AT THE SAME TIME as these developments
were taking place the whole question of dif-
fusion in porous bodies was being opened up by
the work of Wicke [24,25] and Wicke and Kallen-
bach [26], who developed the notion of an effective
diffusion coefficient, recognized that surface dif-
fusion could have an important role and did many
of the pioneer determinations. Mention should
also be made of the work of Wagner of Darmstadt
both for its general influence on the work in
Germany and for his papers [27,28], the last of
which discusses the question of multiplicity of
steady states. Damk6hler had also been concerned
with the temperature rise within a catalyst par-
ticle and showed that this could not exceed
(-AH) D,.c. 'vX, where AH is the heat of reaction,
D, the effective diffusivity, c, the surface concen-
tration of the reactant with stoichiometry coef-
ficient v and X, the effective thermal conductivity
of the pellet. His demonstration for a sphere, re-
peated later by Wheeler [29], was generalized for
any shape by Prater [30], who found that the max-

WINTER 1974

. "diffusion and chemical transformation" are interdisciplinary considerations. In fact until recently the
physiologists' contributions have been almost entirely overlooked by the engineer and vice-versa.

imum possible temperature rise for the dehydro-
genation of cyclohexane was some 53 C, consid-
erably in excess of the highest figure of 3�C
among Damkohler's examples.
Aside from these references to the internal
temperature the non-isothermal equations received
little attention until the late 50's, as Wheeler's
two reviews [31,29] and the incorporation of the
problem in its isothermal form into the pioneer
text of Hougen and Watson [32] show. Schilson,
working under Amundson's direction, showed how
to solve the equations both for single and complex
reactions, but the method of iteration that they
used did not lend itsel to calculating a large num-
ber of particular cases and they did not calculate
effectiveness factor curves, though they were the
first to report effectiveness factors greater than 1.
When their work was published [33] it appeared
only a short time before two papers giving effec-
tiveness factor curves, but using the positive ex-
ponential approximation to the Arrhenius temper-
ature dependence [34,35] and a perturbation solu-
tion by Tinkler and Pigford [36]. A year later the
comprehensive calculations of Weisz and Hicks
[37], which used the Arrhenius temperature de-
pendence of the rate constant, appeared.
The independent and almost simultaneous ef-
floresence of interest in a particular aspect of the
problem was to occur again in the mid-60's when
Bischoff [38], Petersen [39] and Aris [40] all called
attention to a normalization of the Thiele modulus
made possible by the implicit form of the solution
for the slab. Aris [41] had earlier (1957) given a
normalization with respect to shape and this al-
lowed the solutions for all problems with Dirichlet
boundary conditions to be presented as effective-
ness factor versus Thiele modulus curves with the
same asymptotes at both zero and infinity. The
same insensitivity to shape was discovered inde-
pendently by Roughton in a physiological context
[42] but both were ignorant of the fact that
Wheeler had stated a similar result without proof
as early as 1951 [31].
In the last decade the subject has broken wide
open and a rough count of the number of papers
published per year has jumped from an average of

3 in the 50's to 12 in the first half of the 60's to 35,
48, 59, 80, 70, 82, 60, 78 for the years 1965 to 1972.
Aside from filling in some of the gaps in the
steady- state picture the most stimulating activity
has been on the question of the uniqueness of the
steady state solution, its stability and the form of
the transient solution that may arise. The mono-
graph of Gavalas [431 was a pioneering effort in
this direction but many other names distinguished
in chemical engineering circles-Amundson [44],
Denn [45], Hlava6ek and Marek [46], Horn and
Bailey [471, Jackson [48,49], Lapidus [50], Levich
[51], Luss [52,53], McGreavy [54], Schmitz [55],
Varma [56], Villadsen [57], Wei [58], are to be
found. Mathematicians, such as Cohen and Keller
[59], Aronson and Peletier [60], Fujita [61],
Kastenberg [62], Sattinger [63,64] to mention but
a handful. Meanwhile results on the steady state
solution have continued to accumulate and have
been obtained and examined by Bischoff [65], Butt
[66], Carberry [67], Chu [68], Finlayson [69], Gunn
[70], McGreavy and Cresswell [71], Petersen [72],
Ray [73], Rony [74], Satterfield [75], Smith [76],
Stewart [77], and Ostergaard [78] and many
others. Nothing approaching a comprehensive
overview can be attempted here but it is hoped
that some sort of picture emerges from the ac-
count that I have endeavoured to give elsewhere
[79].
But this story has been told from a chemical
engineering viewpoint and, as Weisz has pointed
out [5], "diffusion and chemical transformation"
are interdisciplinary considerations. In fact until
recently the physiologists contributions have been
almost entirely overlooked by the engineer and
vice-versa. Yet as early as 1928 Hill and Roughton
were considering the absorbtion of oxygen into
tissue [80-82] and Roughton's 1932 paper contains
solutions of the diffusion reaction equations more
detailed than any the chemical engineers were to
derive for many years.

PATTERN AND RHYTHM
M ORE RECENTLY THE pioneering paper of
During [831 on morphogenesis has borne fruit

CHEMICAL ENGINEERING EDUCATION

in the effort to show how pattern and rhythm may
arise from the interaction of diffusion and reac-
tion as for example in Scriven's work with Othmer
[84,85] or with Gmitro [86]. Nicolis [87] has given
an excellent review of the work of the Brussels
school on dissipative structures and limit cycles
[88]. These indeed show some similarities of be-
haviour to the limit cycles found in non-isothermal
catalyst particles [89] hut depend for their ex-
istence on an autocatalytic step in an isothermal
reaction scheme. Allied to this is the current in-
terest in the Belousov-Zhabotinskii reaction [90-
93] and other forms of diffusion wave. The simpl-
est wavelike solution of the diffusion equation
arising in the one-dimensional propagation of an
isothermal autocatalytic reaction

c �2c
D + Kc(1 - c)
3x
arose as a problem in genetics [94] and was con-
sidered in 1937 by no lesser mathematicians than
Petrovsky and Kolmogoroff. The development of
this theory has been couched in terms of combus-
tion theory [95,96]. Another biological problem
that has had a significant input is the stability
theory of chemotaxis [97,98,99] in which it is
found that a uniform distribution of organisms is
unstable and that their aggregation may be ac-
counted for as a transient tending toward a stable
non-uniform steady-state.
This by no means exhausts the contributions
and interactions with biological problems, but
hopefully it will suffice to make us aware of the
need to pay attention to what our colleagues in
other branches of natural philosophy are con-
cerned with. D

REFERENCES

1. Quoted by D. A. Frank-Kamenetskii in Diffusion and
heat transfer in chemical kinetics. 2nd ed, revised
and enlarged. Plenum Press. New York. 1969.
2. Lomonosov, M. V. Collected Works. Published by the
Academy of Sciences St. Petersburg, 1891-1935.
3. Menshutkin, B. N. Russia's Lomonosov. Princeton
University Press. Princeton, N. J. 1952.
4. Thiele, E. W. Amer. Scientist. 55, 176 (1967).
5. Weisz, P. B. Science 179, 433 (1973).
6. Jiittner, F. Z. f. phys. Chem. 65, 595 (1909).
7. - . Z. f. Math. u. Phys. 58, 385 (1910).
8. --. Z. f. phys. Chem. 77, 375 (1911).
9. Painleve, P. Acta Mathematica 25, 1 (1902).
10. Juliard, A. Bull. Soc. Chim. Belges. 46, 549 (1938).
11. Larson, A. T. and Tour, R. S. Chem. Met. Eng. 26,
647 (1922).
12. Wicke, E. and Brotz, W. Chem. Ing. Tech. 21, 219

(1949).
13. Damkohler, G. Z. Elektrochem. 42. 846 (1936).
14. - . Ibid. 43, 1 (1937).
15. - . Ibid. 43, 8 (1937).
16. - . Ibid. 44, 240 (1938).
17. -- and Delcker, G. Ibid. 44, 193, 228 (1938).
18. Damkohler, G. in Der Chemieingenieur (Ed. A. Eucken
and M. Jacob). Bd. 3 Teil. 1. Leipzig (1937).
19. Zeldowitsch, Y. B. Acta Physicochim. URSS 1, 449
(1934).
20. . Ibid. 1, 1961 (1934).
21. . Ibid. 8, 527 (1938).
22. . Ibid. 10, 583 (1939).
23. Thiele, E. W. Ind. Eng. Chem. 31, 916 (1939).
24. Wicke, E. Kolloid Z. 86, 167, 296 (1939).
25. . Ibid. 93, 129 (1940).
26. -- and Kallenbach, R. Ibid. 97, 135 (1941).
27. Wagner, C. Z. Phys. Chem. A193, 1 (1943).
28. - . Die Chem. Technik. 18, 1, 28 (1945).
29. Wheeler, A. in Catalysis (Ed. P. H. Emmett) 2 Rein-
hold Pub. Co. New York. (1955).
30. Prater, C. D. Chem. Engng. Sci. 8, 284 (1958).
31. Wheeler, A. Adv. in Catalysis. 3, 249 (1951).
32. Hougen, O. A. and Watson, K. M. Chemical Process
Principles. John Wiley, New York (1947).
33. Amundson, N. R. and Schilson, R. E. Chem. Engng.
Sci. 13, 226, 237 (1961).
34. Carberry, J. J. AIChE. J. 7, 350 (1961).
35. Tinkler, J. D. and Metzner, A. B. Ind. Eng. Chem. 53,
663 (1961).
36. -- and Pigford, R. L. Chem. Engng. Sci. 15, 326
(1961).
37. Weisz, P. B. and Hicks, J. S. Chem. Engng. Sci. 17,
265 (1962).
38. Bischoff, K. B. AIChE. J. 11, 351 (1965).
39. Petersen, E. E. Chem. Engng. Sci. 20, 587 (1965).
40. Aris, R. Ind. Eng. Chem. Fundamentals. 4, 227 (1965).
41. - . Chem. Engng. Sci. 6, 262 (1957).
42. Roughton, F. J. W. Progr. Biophys. Mol. Biol. 9, 55
(1959).
43. Gavalas, G. R. Nonlinear differential equations of
chemically reacting systems. Springer Verlag. Hei-
delberg (1968).
44. Amundson, N. R. and Luss, D. Chem. Engng. Sci. 22,
253 (1967).
45. Denn, M. M. Chem. Eng. J. 4, 105 (1973).
46. Hlava6ek, V. and Marek, M. Coll. Czech. Chem. Comm.
33, 506
47. Horn, F. J. M. and Bailey, T. E. Ber. Bunsengesell-
schaft 73, 274 (1969).
48. Jackson, R. Chem. Engng. Sci. 28, 1355 (1973).
49. - , Horn, F. J. M., Martel, E. and Patell, C. Chem.
Eng. J. 1, 79 (1970).
50. Lapidus, L. and Berger, A. J. AIChE. J. 14, 558
(1968).
51. Levich, V. G., Kharkats, Y. I. and Pismen, L. M.
Doklady Chem. Tech. 170-1, 209 (1966).
52. Luss, D. Chem. Engng. Sci. 23, 1249 (1968).
53. -- and Lee, J. C. M. AIChE. J. 16, 620 (1970).
54. McGreavy, C. and Thornton, J. M. Chem. Eng. J. 1,
296 (1970).
55. Schmitz, R. A. and Winegardner, D. K. AIChE. J., 14,
301 (1968).

WINTER 1974

56. Amundson, N. R. and Varma, A. Chem. Engng. Sci.
27. 907 (1972).
57. Villadsen, J. and Michelsen, M. L. Chem. Engng. Sci.
27, 751 (1972).
58. Wei, J. Chem. Engng. Sci. 20, 729 (1965).
59. Cohen, D. S. and Keller, H. B. J. Math. Mech. 16, 1361
(1967).
60. Aronson, D. G. and Peletier, L. Arch. Rat. Mech.
Anal. 53, 000 (1974).
61. Fujita, H. Amer. Math. Monthly 76, 132 (1969).
62. Kastenberg, W. E. J. Math. Anal. Applies. 29, 29!)
(1970).
63. Sattinger, D. L. Ibid. 24, 241 (1968).
64. - . Indiana U. Math. J. 21, 979 (1972).
65. Bischoff, K. B. Chem. Engng. Sci. 22, 525 (1967).
66. Butt, J. B. Chem. Engng. Sci. 25, 801 (1970).
67. Carberry, J. J. Catalysis Reviews 3, 61 (1969).
68. Chu, C. and Chon, K. J. Cat. 17, 71 (1970).
69. Finlayson, B. A. The method of weighted residuals
and variational principles. Academic Press. New York
(1970).
70. Gunn, D. J. Chem. Engng. Sci. 22, 1439 (1967).
71. McGreavy, C. and Cresswell, D. L. Ibid. 24, 608
(1969).
72. Petersen, E. E. Ibid. 23, 94 (1968).
73. Ray, W. H. Ibid. 27, 489 (1972).
74. Rony, P. R. Ibid 23, 1021 (1968).
75. Satterfield, C. N. Mass transfer in heterogeneous
catalysis. M.I.T. Press. Cambridge, Mass. (1970).
76. Smith, J. M. and Suzuki, M. AIChE. J. 18, 326 (1972).
77. Stewart, W. E. and Villadsen, J., Chem. Engng. Sci.
22, 1483 (1967).
78. (Astergaard, K. Proc. Int. Cong. on Catalysis. Amster-
dam (1964).
79. Aris, R. The mathematical theory of diffusion and

reaction in permeable catalysts. Clarendon Press. Ox-
ford. 1974.
80. Roughton, F. J. W. Proc. Roy. Soc. Bill, 1 (1932).
81. - . Ibid. Bl40, 203 (1952).
82. Hill, A. V. Ibid. B104, 39 (1928).
83. Turning, A. M. Phil. Trans. Roy. Soc. B237, 37 (1952).
84. Scriven, L. E. and Othmer, H. G. Ind. Eng. Chem.
Fundamentals. 8, 302 (1969).
85. - . J. Theor. Biol. 32, 507 (1971).
86. Scriven, L. E. and Gmitro, J. I. in Intracellular trans-
port. (Ed. K. B. Warren) Academic Press. New York
(1966).
87. Nicolis, G. Adv. in Chem. Phys. 19, 209 (1971).
88. - and Herschkowitz-Kaufman, M. J. Chem. Phys.
56, 1890 (1972).
89. Hlava6ek, V. and Marek, M. Proc. IV Eur. Symp. on
Chem. Reac. Engng. Brussels Sept. 1968. Pergamon
Press. Oxford (1971).
90. Zhabotinskii, A. M. Biofizika 9, 306 (1964).
91. Franck, G. M. Oscillatory processes in biological and
chemical systems. (In Russian). Pub. House Nauka.
Moscow (1967).
92. Zhabotinskii, A. M., Zaikin, A. N., Korzukhin, M. D.
and Kreitser, G. P. Kim. i Kat 12, 584 (1971).
93. Scriven, L. E., DeSimone, J. A. and Beil, D. L. Science
179, 000 (1973).
94. Kolmogovoff, A., Petrovsky, I. and Piscounoff, N. Bull.
de l'Univ. d'Etat a Moscou. Al, 6 (1937).
95. Zelenyak, T. I. Diff. Eqns. 2, 98 (1966).
96. - . Ibid. 3, 19 (1967).
97. Segel, L. A. and Keller, E. F. Nature 227, 1363 (1970).
98. - . J. Theor. Biol. 26, 339 (1970).
99. - . J. Theor. Biol. 30, 225, 235 (1971).
100. Kern, D. Q. and Kraus, A. D., Extended Surface heat
transfer McGraw Hill, New York 1972.

THE PROJECT APPROACH TO CHEMICAL ENGINEERING-WPI PLAN
(Continued from page 15.)

* Engineering Studies on an Enzymatic Process for Con-
verting Cellulose to Sugars. This process was developed
by scientists in the U.S. Army Natick Laboratories. How-
ever, no engineering studies had been performed to obtain
data necessary for design purposes. Two groups of Chem-
ical Engineering students (one group of three sophomores
and one group of two seniors) worked on the project to
obtain some data which would be useful in the design of
a process to convert cellulosic wastes to useful food.
Students worked closely with the Natick Laboratory
scientists under the direct supervision of the WPI Center
Director. They performed experimental studies to obtain
rate data in a batch process. They also studied the effects
of mechanical stirring, particle size of the ground waste
and grinding time on the reactivity of the enzymatic re-
actions.
In addition to performing experimental work, students
also were required to have some specific background in
mathematics, biology and engineering for successful analy-
sis of their data. They obtained some of this background
from their course work, but had to learn a major portion
of the material on their own in order to satisfy their
specific needs.
While close supervision was maintained in the Center,

the students were provided with the opportunity to try out
some new ideas. For example, one group tried to use
ultrasonic equipment to treat the suspension of shredded
newspaper and to test its reactivity.
Both groups performed very well in their work. The
sophomore group wrote an excellent report detailing their
findings and their interpretation of the experimental re-
sults. The work performed by the senior group was re-
ported in the student paper session of the ACS meeting in
Boston, Mass.
* Determination of the Effects of Gymnema Sylvestre on
the Taste Receptors in Hamsters. This project, which is
entirely different from the usual chemical engineering
projects, involved one sophomore. She worked closely with
a scientist from the U.S. Army Laboratories. As this is a
highly specialized field outside that of chemical engineer-
ing, a major portion of the supervision was provided by
the Army personnel. However, the Center Director still
maintained his control of the project by regularly dis-
cussing her progress with her. The final evaluation of her
report was done by the Director in consultation with the
Army personnel.
Hamsters were used as test subjects in this case. The
student had to spend a large portion of her time under

CHEMICAL ENGINEERING EDUCATION

close supervision getting familiar with the testing pro-
cedures and the handling of the animals. These were done
in a closely supervised manner.
After two years' experience, we find the operation of
the Center very encouraging. Excellent cooperation has
been provided by Natick Laboratories personnel. They have
highly praised our students in terms of their working
habits as well as their intelligence. The experience was
viewed by the students as very valuable.
As the WPI Plan moves into full operation at
the upperclass level, project work is expected to
consume about half of the total time of the faculty
devoted to undergraduate education. The experi-
ences to date in involving chemical engineering
students in a wide variety of activities suggest
that the transition, though not simple, will be suc-
cessful. D

CHEMICAL ENGINEERING AT BERKELEY
(Continued from page 10)

Thermodynamics

Experimental and statistical thermodynamic analysis of
fluid mixtures. Liquid crystalline behavior and other phase
equilibria. Interfacial phenomena. Equations of state based
on molecular properties. Electrolyte dissociation and ac-
tivity-coefficient behavior. Adsorbed state of diatomic
molecules. (Bromley, Lyon, Newman, Pigford, Prausnitz,
Redlich).

Transport Phenomena
Fluid Mechanics. Laminar-flow systems. Rheology of poly-
meric systems. Flow of molten alloys. Mechanics of sus-
pended particles. Properties of liquid films. Wave propaga-
tion in dispersive media. Mixing and dispersion phenomena
in liquids. Drag reduction. (Donaghey, Goren, Newman,
Shen, Vermeulen, Wilke, Williams).
Heat Transfer. Nucleate boiling. Promotion of dropwise
condensation. Boiling enhancement by additives. Direct-
contact heat transfer between immiscible liquids. Thermal
conduction of solids. (Bromley, Donaghey, Goren, King,
Lyon, Wilke, Williams).
Mass-Transfer Fundamentals. Transport properties of con-
centrated electrolytes. Absorption with chemical reaction.
Atmospheric spread of pollutants. (Grens, Newman, Pig-
ford, Vermeulen).

Separations and Mass Transfer
Gas-liquid mass transfer and accompanying interfacial
effects. Computation methods for distillation, extraction,
and absorption. Separations of fine-particle systems. Ab-
sorption and ion exchange. Oscillatory processes. Foam
fractionation. Membrane separations. Separations by freez-
ing. (Goren, Grens, Hanson, King, Klein, Lynn, Merrill,
Pigford, Sherwood, Vermeulen, Wilke).

S book reviews

Chemical Engineering Thermodynamics: The
Study of Energy, Entropy and Equilibrium, R. E.
Balzhiser, M. R. Samuels, and J. D. Eliassen, 696
pp. Prentice-Hall, Inc., (1972).
Reviewed by T.S. Storvick. University of Missouri-Columbia

The significant flux of thermodynamics text-
books into the technical literature suggests that
there is a general dissatisfaction between authors
of these books and those who use them. This
book appears to have been conceived in this
atmosphere.
The evolution of thermodynamics textbooks
indicates that they must now contain the classical
material and some new elements:

* It must be written for readers from more than one
discipline.
* The particle theory matter must be used in the
logical development of the subject.
* The use of electronic computers must be demon-
strated.
* Thermodynamics of irreversible processes must be
introduced.

The authors have written for Mechanical and
Chemical Engineering students( the title is un-
fortunate in this sense), they have used combi-
natorial and probability arguments to introduce
the entropy function, provided computer codes
for several of the calculations in the worked ex-
amples and concluded with a short chapter in-
troducing irreversible thermodynamics.
To this reviewer, the relationship that exists
between the authors of thermodynamics textbooks
and their readers is similar to that of a chef and
the clientele of his restaurant. The basic ingredi-
ents are always the same but the menu, the di-
vision into courses, the spicing and flavoring, and
the service and atmosphere are all designed to
enhance the practical experience of eating. A
satisfactory relationship is established when there
is a match between cuisine and palate. It is the
same with textbooks.
Most undergraduate engineering students
should learn to use classical thermodynamics in
their first course on the subtect. This book is
written for that audience and the authors provide
over 90 worked examples and 225 exercises for
the student. Some of the exercises will require
considerable time to complete. The text is clearly
written, the illustrations are generally useful and

WINTER 1974

there appears to be very few troublesome typo-
graphical errors.
The order of presentation is conventional in
nearly all respects (except for the introduction of
of the entrophy function discussed below). The
thermodynamic functions are introduced in the
early chapters, the sections on work producing
cycles and fluid flow are expanded to accommodate
the needs of the mechanical engineering student.
The final 215 pages are devoted to physical and
chemical equilibrium of mixtures. A 20 page intro-
duction to the currently important electrochemical
processes is also included.
There are some features of the book that may
be related to matters of "taste" that this reviewer
feels should be discussed in more detail. The
mathematical structure of classical thermody-
namics is disarmingly simple to undergraduate
students who have completed much of their for-
mal work in mathematics. Their concurrent ex-
perience with dynamical mechanical systems
and the rate processes that are described by
more complex mathematical formalism adds to
this confusion. The authors never clearly state
what experiments establish the relationship of
internal energy, volume and composition to the
equilibrium state of a system. The mathematical
form of the internal energy function as it passes
through successive equilibrium states as work is
done by the system and heat is added to it is left
implicit. This may cause the student more trouble
as he seeks to find the relationships between
physical systems and the thermodynamic func-
tions.
It is an open question whether statistical ther-
modynamics should be taught to undergraduate
engineering students in their first thermody-
namics course. The authors use the mathematics
of permutations and combinations to compute the
number of distinguishable configurations of a
mascroscopic thermodynamic system. They then
compute the probability pi that a particular con-
figuration will be found and say, after Boltzmann,
that the entropy of that configuration is given by
Si = k in Pi.

The equilibrium state is then proclaimed to be
the one with the maximum probability, pi,..nx (and
therefore the maximum entrophy S,) consistent
with the constraining conditions that there be N
particles in volume V with total energy E. None
of the statistical thermodynamics formalism is
developed and therefore, all of the real compu-

national power of statistical thermodynamics is
lost. The Carnot cycle is used to establish the
relationship between reversible heat flow, the
thermodynamic temperature and the entrophy.
It is never clearly established that the total en-
trophy change for all spontaneous processes must
be positive and that this is the criteria for all the
equilibrium considerations used in later chapters.
This presentation does not appear to be a useful
way to introduce the entropy function and it can-
not be called an introduction to statistical ther-
modynamics.
One can ask, would it not have been better
to use the postulatory approach of Cullen?
(Thermodynamics, H. B. Cullen, John Wiley,
New York, 1960, p. 24-25). This approach es-
tablishes the central role of the state function in
the mathematical formalism of thermodynamics.
It then yields the processes ( work and heat flows,
mass flows, etc.) by differentiation of the state
functions. On page 52, the authors have listed
nearly all of the necessary equations to implement
this approach. It is still necessary to make the
identifications between the mathematical func-
tions and the physical systems that an engineer
must make. But, as the authors say, "The utility
of the entropy concept depends on relating it
to the changes with which we as engineers are
involved. Since our concerns are generally macro-
scopic in nature, it is necessary to associate en-
tropy with marcoscopic phenomena, such as heat
and work, so that it can be used in the analysis
of processes involving these energy flows and
interconversions" (page 129). Since the authors
follow the phenomenological approach everywhere
in their book except for the introduction of the
entropy function in Chapter 3, the postulatory
approach would be consistent with the presenta-
tion they have made. It is also true that the macro-
scopic descriptions of statistical thermodynamics
must be inferred from macroscopic experience
whether it is taught before or after a course in
applied macroscopic thermodynamics.
There are some specific comments about the
presentation that should also be made. The au-
thors have chosen to use the general energy bal-
ance for an open system to introduce the relation-
ships between heat and work and the other
terms in that balance. The discussion that fol-
lows does not establish the important and startling
mathematical fact that a conservative or state
function, or exact differential of the internal
energy written in terms of the physical parame-

CHEMICAL ENGINEERING EDUCATION

ters (for instance, temperature, volume, and com-
position) is always equal to the heat added to and
the work done by the system! Both the heat and
work terms are path dependent functions. Once
this has been established and is clearly under-
stood by the student, the addition of potential and
kinetic energy terms to obtain the general energy
balance should cause little difficulty because the
students have studied Newtonial mechanics.
The treatment of the entropy function pro-
ceeds by writing an entropy balance. It is in-
ferred, but never clearly shown or stated that the
entropy is a state function of the same thermo-
dynamic coordinates as the internal energy. The
authors use the "lost work" term to account for
irreversibilities in a process and therefore do
not state the powerful mathematical relationship
for all spontaneous processes.

f ] = dSTota 0
Subsystems T rev ota
The authors then write (page 161) ". .. the third
basic equation of thermodynamics (the energy
balance and the entropy balance are the other
two)

dU = ds - P dV
syst syst syst syst syst
This is not a third basic equation but rather the
combined first and second law equations.
The authors incorrectly state (page 362) that
c
n nidGi = 0
i=-i
is the Gibbs-Duhem equation rather than the
previous equation
C
SnidG = VdP - SdT.
i=l
The development of the procedures to compute
the fugacity coefficient (page 373) does not ex-
plicitly state that the integration must proceed on
an isotherm (although the original partial deriva-
tive that is integrated is clearly marked as taken
at constant temperature). Further ". . . to elim-
inate computational difficulties in the limit P*-O0,
we subtract the equation
P
In(P/P*) = 1 dP
from P*

/P) P*
P*

In f/P = -T dP."
RT P
P*
This is a mathematical problem and the inte-
grand in this final equation still appears to di-
verge at P->P*'-,O even with the reassuring
statement "we anticipate no further problems
arising in the limit P*--O because the right-hand
side remains bounded as P becomes small." This
statement could have been made explicit by sub-
stituting the compressibility factor z/p = V/RT
and using L'Hopital's rule to obtain

,i0. ( Z 1 (-
Lim

where B(T) is the second virial coefficient, a
well defined experimental quantity. This proce-
dure not only provides a satisfactory mathemati-
cal answer to the problem but provides an
analytical method for making the extrapolation.
It is clearly much easier to criticize a book
than to write one. The authors have presented
their method for presenting thermodynamics to
engineering students. They have found this treat-
ment to be successful and this success can only be
judged by allowing students to read the book.
Their tastes and appetites are nearly always dif-
ferent than those who grew up a decade or two
ago.

DEPARTMENT

CHAIRMEN

If you have not renewed your departmental sub-
scription to CEE for 1974, please write R. B. Ben-
nett, Business Manager, CEE, Department of
Chemical Enginering, University of Florida,
Gainesville, Florida 32611.

BULK SUBSCRIPTION RATES: $4/yr. each,
with a $25.00 minimum for six or fewer sub-
scriptions.

ASEE-CED & AIChE
MEMBERS
INDIVIDUAL SUBSCRIPTIONS are available at
$6/yr. (Regular rate $10/yr.)

WINTER 1974

WATERLOO PROGRAM FOR HIGH SCHOOLS

E. RHODES
University of Waterloo
Waterloo, Ontario

"W HAT'S THE DIFFERENCE between
SChemistry and Chemical Engineering?"
That's a question often asked by high school stu-
dents (and teachers and guidance counselors)
when they are seeking out a career with a chem-
istry bias. We have even been asked the question
by students who have already chosen to study
chemical engineering. The question is no doubt
symptomatic of the lack of communication be-
tween schools and chemical engineering depart-
ments which, to my mind, has arisen because
traditionally we could attract all the students we
wished to enroll and we were definitely blas6 about
recruiting. Times have changed however, and now
departments are worried about falling enrolments
and the solid decline in the overall number of stu-
dents wishing to study engineering in general and
chemical engineering in particular. We must com-
municate with the schools and somehow we must
get across to students and teachers the attractive-
ness of chemical engineering as a study discipline
and career opportunity. In return we need to be
educated in the changing patterns of high school
curricula so that we are flexible and agile enough
to adjust our courses to accommodate the needs
and abilities of the new Freshmen. How can we
open up this line of communication. No doubt
there are many ways tried by many departments
across North America and the world.
The Waterloo programme was inspired by my
sabbatical experience at the University of Queens-
land, Australia, where I was called upon to take
part in the Chemical Engineering High School
Day Programme. This kind of educational pro-
gramme is aimed at challenging small numbers
of interested students to seriously learn about
chemical engineering and consider the profession
as a career opportunity. In our High School Pro-
gramme we do not invite busload after busload of
uninterested students to the campus and deliver a
pep talk, a movie, and a donut in the hope of
catching a few. Instead, we send out a limited
number of invitations to those students who have

We must communicate with the schools and somehow
we must get across to students and teachers the
attractiveness of chemical engineering as a study
discipline and career opportunity.

a curiosity (be it mild or strong) about chemical
engineering.
On a typical High School Day we can entertain
about 33 students from outside the university. To
these we add 11 of our own volunteer first-year
undergraduates, several professors and some
graduate student demonstrators. Small groups
consisting of three high school students and one
undergraduate, tackle four experiments selected
from a total offering of eleven. Each experiment
takes about one hour to complete and the students
have to do the work themselves, although Profes-
sors are close at hand to introduce the basic prin-
ciples of the experiments and answer questions.
The experiments have been developed by the Pro-
fessors of the department and strongly reflect
their own interests, thus illustrating the breadth
of the Waterloo degree programme and the scope
of Chemical Engineering.

EXPERIMENTS TO CHALLENGE
HIGH SCHOOL STUDENTS
1. Expansion of the Kitchener waste treatment plant
(P.L. Silveston).
The object of the experiment is to illustrate
what goes into process design and how one sets
about it. The experiment gives the student a brief
introduction to pollution control, computers and
computer-aided design. In the explanation of the
experiment (we have a High School Programme
Manual) the concept of a process system is ex-
plained by reference to the present Kitchener
(Ontario) Sewage Treatment Plant. It is then
shown how the plant can be simulated by use of a
digital computer programme. At this stage the

CHEMICAL ENGINEERING EDUCATION

existing programme is handed over to the students
and they are requested to find out:
* If the present plant is capable of handling 95'
of the Biological Oxygen Demand and Sus-
pended Solids expected in 1985;
* What will be the effect of adding cylindrical
tanks in the settlers or rows of square tanks to
the aerators;
* What will be the cost to expand the city of
Kitchener Plant to meet the 95'/; target.

2. Enzyme Catalysis (J.M. Scharer)*.
Intended to illustrate the involvement of bio-
chemical applications of chemical engineering, the
student is asked to determine the Michaelis-
Menten constant for a particular enzyme reaction
and the maximum reaction rate for a given
enzyme concentration. The reaction studied is

k k
H20 + E > X - 2O +1/2 2 + E
k

in which E represents catalase, and X an en-
zyme-HO, complex. The catalase is synthesized
by use of bacteria such as E. coli, B. subtilis, S.
Faecalis and S. Aureus, while the evolution of
oxygen indicates the presence of the enzyme. Hav-
ing determined the two constants from the system
the students are asked:
* To explain why most aerobic organisms can
synthesize catalase;
* How a change in enzyme concentration would
affect the experimental results.

3. Analog Computation in Chemical Engineering (K.S.
Chang).
A short presentation is given to the students
in which the general purpose analog computer is
described as an orderly collection of amplifiers,
potentiometers, resistors, capacities etc. The patch
board is introduced and the students are asked to
patch up the circuit to be used for generating the
4 sin t and 4 cos t functions. The signals are dis-
played on an oscilloscope and an X-Y recorder.
Among other questions, the students are asked:
* Why the signals produced by the circuit are
4 sin t and 4 cos t.
* To develop a circuit diagram which would gen-
erate 4 sin(lOt) and 4 cos(lOt).

:Gorber, D.M. and Scharer, J., CEE 5 (2), 141 (1971).

4. An Advanced Analog Computation Problem (T.Z.
Fahidy).
Following on from experiment (3) the stu-
dents investigate the oscillatory behaviour of the
Van der Pol Equation. Having done this the stu-
dents then go on to:
o Sketch the shape of the limit cycle at various
potentiometer settings and describe the findings.
* Discuss the practical use (if any) of such an
electronic circuit.

5. Elastomers-A Fourth State of Matter? (B.M.E. Van
der Hoff).
After a general introduction to the concept of
viscoelasticity and the chemistry of rubber, the
students use an Instron tester to investigate the
properties of natural rubber and polyvinylchloride
softened by the addition of oil. For example an
elastic band is elongated in the machine and the
force acting on the band is measured against time
at constant elongation. The sample is then heated

We sent out a limited number of invitations
to those students who have a curiosity
about chemical engineering.

and the experiment repeated. Hysteresis is meas-
ured in the form of a force-elongation curve. Typ-
ical questions asked of the students are:
* What is the value of the initial modulus at small
elongation and the modulus just before break?
o Why is the area of the hysteresis loop larger for
the polyvinylchloride than for the natural rub-
her?
" Why does a sample not return to its original
length?

6. Experiments Demonstrating some Industrial Electro-
Chemical Processes (K. Enns).

The objects of this experiment are to demon-
strate a) the electrowinning of copper, b) electro-
etching and c) brass electroplating. It is explained
that all electrochemical processes found in extrac-
tive metallurgical, metals refining and finishing
industries involve cells containing anodes and
cathodes. The students find out by experimenta-
tion the amount of copper won per kilowatt hour
and calculate the energy cost per ton of copper.
Then by building a cell using graphite for the
anode and a partially covered copper sheet for the
cathode, electroetching is discovered, and the

WINTER 1974

amount of copper removed during the etching
process is calculated. Finally another cell using a
sheet steel cathode and a brass anode is built to
enable the plating of the steel. Cu-Zn-cyanide solu-
tion is used in this experiment. Typical of the
questions posed to the students at the end of this
session are:
* Why is brass plated from a Cu-Zn cyanide solu-
tion ?
* Why not plate brass from a much less poisonous
CuSO,-ZnSO, solution?

7. Waste Water Renovation by Ion Exchange and Ad-
sorption (K. Enns).
This experiment is designed to demonstrate
the demineralization of water by cation anion ex-
change and colour removal by adsorption. A
"waste water" sample is renovated firstly by ex-
changing all positively charged ions in the waste
by H+ using a cation exchanger. After testing for
metals by atomic absorption, the solution is
treated with an anion exchanger and then ac-
tivated charcoal. By now the original murky solu-
tion is quite clean. The students are asked typ-
ically:
* Is it economically feasible to use ion exchangers
to treat concentrated solutions?
* Can you suggest a reason why ion exchangers
generally prefer (are selective for) bivalent and
trivalent species over univalent species?

8. Determination of Lead in Gasoline by Polarographic
Analysis (K. Enns).
Here the students find out what is meant by
the polarographic method of analysis and deter-
mine the concentration of lead in a typical sample
of gasoline. The significance of the typical 'S'
shaped polarogram is explained and the students
firstly calibrate a machine by making up a known
sample containing lead nitrate, and secondly, in-
vestigate the unknown gasoline sample previously
extracted into an aqueous solution. Typical ques-
tions to round off the session are:
* In what form is lead usually present in gasoline?
* Why can't we carry out polarographic analysis
directly on the gasoline sample?

9. Determination of a Chemical Reaction Rate Constant
By Thermal Analysis (K. Enns).
By a simple thermal analysis method the re-
action rate constant of the catalyzed reaction be-
tween n-butanol and phenyl isocyanate is deter-

mined. The principles of heat of reaction and re-
action kinetics are explained, and the students
after being presented with an adiabatic reactor
(thermos flask), magnetic stirrer, thermometer
and automatic delivery syringe are put to work.
The students are asked typically:
* Is it reasonable to assume that the thermos
flask approximates an adiabatic reaction?
* Is the rate constant data obtained in this way
useful? Or is it just an academic exercise?

1C. Measurement of Liquid Flow (J. D. Ford).
It is explained that an important problem fre-
quently encountered by engineers is that of meas-
uring the rate of flow of a liquid. Whether it is
the flow of a river or the flow of water into a
kitchen sink, a few simple principles enable such
measurements to be accurately made. The students
are asked to investigate the use of an orifice for

One student presented the enzyme experiment
in the form of a series of cartoons of whale-like
bugs gobbling up molecules and burping up
the new ones all over the place.

measuring the flow from a large variable head
tank. The students discover the relationship be-
tween mean velocity in the orifice and head of
fluid and are finally asked the following:
* A one pound ball falls to the ground from a
height of 2 ft. At what velocity does it hit the
ground ?
o Considering the above question is related to our
graph of log (velocity) versus log (head), what
is the theoretical value of the exponent n in the
relationship (velocity) a (head)".

11. Flow Through Porous Media (F.A.L. Dullien).
In part one of the experiment the students are
set the task of measuring the permeability of a
porous material consisting of a packed bed of glass
beads or sand by establishing the relationship be-
tween pressure drop and flow rate across the
sample. In the second part of the experiment the
students observe the phenomenon of dispersion by
use of a dye tracer injected into the flow of a
packed bed. Typical questions are:

CHEMICAL ENGINEERING EDUCATION

* What is the permeability of a non-porous sub-
stance?
* What factors may influence dispersion in porous
media?

BULL SESSION
When each group has completed four experi-
ments it must prepare a two minute verbal report
on the final experiment. This report is presented
at the closing session of the day. Half an hour is
allotted for report preparation and the usual vis-
ual aid materials are provided for the assistance
of the students. The reports have been remarkable
for several reasons. For example, the students
have been seen to respond amazingly well to the
challenge and have quickly learned the principles
on which the experiments are based. Secondly, it
has been worth noting how interesting and often
amusing the students have made their two-minute
presentations. One student presented the enzyme
experiment in the form of a series of cartoons of
whale-like bugs gobbling up molecules and burp-
ing out new ones all over the place.
Each group having made one report, the whole
programme of eleven experiments is covered and
the final half hour is devoted to informal open dis-
cussion. It has been our experience that at this
stage, most of the barrier of shyness has been
broken down and everyone is anxious to get a
word in. Our own undergraduates make a big con-
tribution to the discussion. Marilyn was a very
glamorous first-year chemical engineer in 1971
and she came to all our High School Days in flam-
ing hot pants. When one High School threw out
the question "What was it really like to be a chem-
ical engineering student?", it was answered by
Marilyn with a very eye-catching gesture and one
word "Fabulous." Despite the fact that from then
on, the Professors thought Marilyn was our best
advertisement, she left us at the end of the year
for academic reasons, a very sad departure for one
and all.

EFFECTIVENESS OF THE PROGRAMME
So far the only method of measuring the ef-
fectiveness of the programme has been to ask the
students for their opinions at the end of the day
and to observe the reactions of both students and
professors in the laboratory and in the culminat-
ing group discussion.
Nearly all the students responding to a ques-
tionnarie say the programme is suitable for

One fellow suggested we insert a steak dinner
into the program and another felt the program
would be helpful for his school teachers.

Grades 12 and 13 High School Students but not
for Grade 11. Most of the experiments were
judged to be correct level of difficulty, although
most problems were caused by the analog com-
puter experiments and least difficulty was experi-
enced in the waste water treatment and fluid flow
experiments. Many students would have liked an
extra day to do all the experiments and most felt
they had learned a lot. Several students indicated
that the opportunity for discussion was a very im-
portant factor contributing to the success of the
programme. One fellow suggested we insert a
steak dinner into the programme and another felt
that it would be very beneficial for his school
teachers. This last comment prompted us to invite
the local School Teachers' Federation to include
an evening of working in our laboratories on their
Professional Development Programme. One such
evening has now been held with enormous suc-
cess. The format was the same for the teachers as
it was for the students and the closing discussion
provided a real opportunity for the exchange of
ideas on education.
It has been mentioned that first year under-
graduates were also used in the programme. Their
reaction has also been very positive and we are
considering offering the programme to all the
Freshmen during registration week. Its purpose
here will be to break down the barriers between
Faculty and students almost before they have time
to be erected, and to motivate the students by pro-
viding them with a broad view of the department
at the very beginning of their university career.
Does our programme answer the question
"What is the difference etc .... "At least it il-
lustrates the breadth of interest of chemical engi-
neering, which we believe is one of its most at-
tractive features. It also provides a forum where
all kinds of people by working together, find com-
municating questions, answers and ideas to be
very easy.

The High School Programme Manual can be obtained by
writing to Professor E. Rhodes, Chemical Engineering,
University of Waterloo, Waterloo, Ontario, Canada. Please
enclose a cheque for $2.00 to cover the printing and post-
age costs. The cheque should be made payable to Chemical
Engineering, University of Waterloo. ]

WINTER 1974

A JUNIOR COURSE IN

CHEMICAL ENGINEERING COMPUTATIONS

E. M. ROSEN
Monsanto Co.
St. Louis, Missouri -

N THE SPRING of 1973 the author was asked
to develop a three unit course in chemical en-
gineering computations based on the text "Ma-
terial and Energy Balance Computations" by E. J.
Henley and E. M. Rosen.1 This was to be the sec-
ond semester course in the two semester Elements
of Chemical Engineering sequence for third year
chemical engineering students at Washington
University, St. Louis. It was a listed prerequisite
for the senior Systems Analysis and Design
course.
Typically at this stage, students have had a
course in thermodynamics, and a course in the
use of mathematics and the methods of engineer-
ing in the analysis of chemical and physical proc-
esses. In addition, they have had a course in basic
chemical process principles including stoichio-
metry, ideal gas law and gas mixtures, vapor
pressure, solubilities and energy balances. Only
those interested (about 1 3 to 1 2 of the stu-
dents) had taken the optional one unit digital
computer programming course. In general, the
student had not used the computer as an integral
part of his previous course work. The traditional
unit operations courses covering such topics as
distillation, absorption and heat transfer were no
longer offered, though a two semester junior se-
quence in transport phenomena was a listed re-
quirement.
The basic approach to the material in the text
has been described previously.' Major emphasis
was given to the machine methods chapters in the
text, chapters 5, 8 and 9. Table 1 gives the general
outline of the course and the number of sessions
devoted to each topic. Each session was scheduled
for 75 minutes twice a week in the evening hours.
Almost one third of the course was devoted to
graphical methods in distillation and absorption.
This was done in part to fill the lack of exposure
to the unit operations. Outside reading:'- was used
in support of this portion of the course in addition
to the use of a secondary text."

Edward M. Rosen received his BS and MS from the Illinois Institute
of Technology and his PhD from the University of Illinois. Currently
he is a Science Fellow and Manager, Systems Technology at the
Monsanto Co. where he has been since 1959, except for a postdoctoral
academic leave at Stanford University in 1962-3. With E. J. Henley, he
is co-author of the text "Material and Energy Balance Computations".
(John Wiley, 1969)

CONDUCT OF THE COURSE

THE COURSE WAS A traditional lecture type
with homework (which was not graded) as-
signed from the text or specially designed and
handed out. In addition the class was divided into
teams of three persons each for the purpose of
doing the five computer problems that were as-
signed and which formed 20''4 of the course
grade. The reason for the teams was two-fold:
* Some members of the class did not know FdRTRAN
programming.
* It was desired to hold the computing bill down.
Eight one hour exams, of which only the highest
six were counted, (60%' of grade) were given,
plus a final (20% of grade). The comparatively
large number of exams was designed to prevent
members of the class from falling behind and to
provide them a means of gaining new insights
to the topic areas. The number of exams received
little class criticism though not grading the home-
work (though it was always discussed) appar-
ently gave the students little motivation for doing
it.

CHEMICAL ENGINEERING EDUCATION

THE COMPUTER PROBLEMS

T HOUGH THE COMPUTER problems were
intended to be a major portion of the course
they were weighted comparatively lightly since
knowledge of FORTRAN was not a course pre-
requisite. It was intended that every member of
each team would participate equally in the com-
puter problem analysis and that those members
knowledgeable in coding would teach the un-
knowledgeable ones. This, it was felt, closely

TABLE 1-COURSE OUTLINE

Session Numbers Topics
Part A. Chemical Process Calculations
1-2 Course Conduct

3
4-5

6-7

8-9

10
11-12

Part B. Distillation
13-14

15-16

17

18-19

Part C. Plant Simu
20
21
22-23

24

25
26

WINTER 1974

Review of General Energy and Ma-
terial Balance Equations
Matrices and Vectors
Independence, Orthogonalization and
Rank. Solution of Linear Equations
and Material Balances
The One Dimensional Nonlinear Equa-
tion and Flash Calculations
Chemical Reactions and Their Inde-
pendence. The Extent of Reaction.
Chemical Equilibrium
Energy Balances: Adiabatic Flash and
Adiabatic Flame Temperatures.

and Absorption
Binary Distillation-The McCabe-
Thiele Method.
Minimum Stages and Minimum Re-
flux. Analytical Shortcut Methods.
Multicomponent Methods-Tridiagonal
Equations
Absorption-Graphical and Analytical
Methods

nation
Streams and Building Blocks
The Split Fraction Concept
Partitioning and Tearing Equations.
The Convergence Block Concept
Direct Substitution and Wegstein's
Method
Information Feedback
Comprehensive Flow Sheet Calcula-
tions

The intent was for the student to formulate
the problem, code the main program but let the
subroutine do the tedious work of computation.

paralleled the environment found in industrial
organizations. Each member of the team was re-
quired to hand in a problem analysis though only
one computer output per team was required. How-
ever, this did not turn out satisfactorily, since the
knowledgeable FORTRAN students spent a dis-
proportionate amount of time coding and debug-
ging the computer problems while the others
spent comparatively little time.
At the start of the course source decks for
the four FORTRAN subroutines listed in the
rear of the text' were handed out to each team.
(This was necessary since only the WAT IV com-
piler which required all source coding could sup-
ply adequate turnaround). The four subroutines
supplied to each team were:

GSMT
GELG
ROOT
BSOLVE

Gram Schmidt Orthogonalization
Simultaneous Linear Equation Solver
One dimensional Root Finder
Simultaneous Nonlinear Equation Solver

The intent was for the student to formulate the
problem, code the main program but let the sub-
routine do the tedious routine work of computa-
tion. The five problems were either formulated by
the author or adapted from the recently released
CACHE committee volume of computer programs
on Stoichiometry." Table 2 lists the titles of the
problems for the course and the subroutines which
were to be used.

COURSE EVALUATION

A TOTAL OF ELEVEN students enrolled in
the course and were asked to fill out a ques-
tionnaire at the conclusion of the course. The
questionnaire asked the student to rate each of
the computer problems for instructive value and
interest. Other questions relating to the useful-
ness of the computer problems and course organ-
ization were then asked. Finally the student's re-
sponse to specific topics was queried. Table 3 lists
the raw responses of the class to the question-
naire. Overall the course elicited a broad range of

rather strong responses. Students with an ade-
quate computer background appeared to respond
favorably while those without the background
appeared to be much less satisfied. There appears
little question that a prerequisite for the course
should be coding proficiency in F(bRTRAN by all
participants.

Efforts were made continuously to
relate the numerical methods portion of
the course to direct application.

REFERENCES

TABLE 2-COMPUTER PROBLEMS

Problem

Description

1. A. Inconsistent and Incomplete
Material Balances'
B. Linear Material Balances'
2. Flash Vaporization
3. Simultaneous Gas Phase
Equilibrium Reactions
4. Theoretical Maximum Flame
Temperature'
5. Recycle Calculations Using
Split Fractions

Use of Subroutine

GSMT

GELG
ROOT
BS4LVE

ROOT

GELG

1. Taken from Reference (6), p. 85, 147.
2. Adapted from (6), p. 198.
3. Copies of the problems may be obtained from the
author on request.

The use of teams seems to be little justified.
Students complained that only one person on the
team did all the work and were not sufficiently
credited for their effort. There seemed little basic
difficulty with the level of the course material in
the text though some complaints were recorded
about its clarity in places.
Efforts were made continuously to relate the
numerical methods portion of the course to direct
applications though it should be noted that the
text separates these functions for ease of refer-
ence and development. This meant considerable
jumping around in the text and required care-
fully planned reading assignments.
Rather strong interest was displayed in the
unit operations section of the course as evidenced
by the desire for more time to be spent in this
area. No time was spent on heat transfer calcula-
tions and this would certainly be an area for
course expansion. Whether or not the course was
best separated into its three distinct parts or
could better be integrated into a single topic called
process simulation is unclear at this time. D

1. Henley, E. J. and Rosen, E. M. MATERIAL AND ENERGY
BALANCE COMPUTATIONS John Wiley (New York),
1969.
2. Rosen, E. M. and Henley, E. J. "The New Stoichio-
metry" Chem. Eng. Ed., Summer 1968.
3. Smith, B. D. DESIGN OF EQUILIBRIUM STAGE PROCESSES
McGraw Hill, 1963.
4. Van Winkle, M. DISTILLATION McGraw Hill, 1967.
5. Henley, E. J. and Staffin, H. K. STAGEWISE PROCESS
DESIGN John Wiley, 1963.
6. Henley, E. J., Editor, COMPUTER PROGRAMS FOR CHEM-
ICAL ENGINEERING EDUCATION-STOICIIIOMETRY Sept.
1972.

TABLE 3-RESPONSE TO QUESTIONNAIRE

Questions 1-5: Computer Problems
Material Equi- Max. Split
Balance Flash librium Temp. Fraction

Very
Instructive
Instructive
Adequately
Instructive
Not
Instructive
Very
Interesting
Interesting
Fairly
Interesting
Dull, Dull

1 3 2 1

8 5 6 5 3

2 3 2 1 4

5 6 1 3 4

3 2 4 6 3
1 1 1

6. The computer problems
Added substantially to the course. 4
Added to the course 4
Added marginally to the course 3
Detracted from the course
7. Supplying the subprograms
Was very useful and did not detract from the
problems 10
Was useful but made the problems less instructive -
Marginally useful 1
Was a poor idea

CHEMICAL ENGINEERING EDUCATION

I � � _I

III

8. The course was
Well organized
Fairly well organized
Adequately organized
Poorly organized
9. Topic

A. Phase equilibrium
B. Inconsistent
material balances
C. Chemical reactions
D. Distillation
E. Absorption
F. One dimensional
equation solving
G. Multi-dimensional
equation solving
H. Plant simulation
I. Matrices and
vectors
J. Energy balances
K. Independence and
orthogonalization

Should be
Ex- Re-
anded duced
3
2 1

About
Right
8
7

5
5
1

Dropped

1

4
6
4
2 7

5 1
1

6 1
5

CHEMICAL ENGINEERING 0

DIVISION ACTIVITIES

3M COMPANY INCREASES LECTURESHIP
AWARD GRANT
The 3M Company has increased its annual
grant in support of the Chemical Engineering Di-
vision Lectureship Award from $1500 to $2500.
The additional $100 will cover an honorium and
expenses to allow the awardee to present his lec-
ture and visit on the campus of three institutions
to be selected by the Chemical Engineering Di-
vision. The increased funding is effective begin-
ning with the 1974 award.
The suggestion for the new visitation program
was made by Prof. L. E. Scriven of the University
of Minnesota, a former award winner and trans-
mitted to 3M by Prof. Leonard Baker when he
served as Division Chairman. Announcement of
the increased support was made by W. W. Burton
of 3M to Dr. George Burnet of Iowa State Uni-
versity, who participated in the discussion with
3M and was instrumental in obtaining the orig-
inal grant from that company.

[JIUI

lyIlHIIllt^

Parsons is a Good Place to Work!

There is no limit to the opportunities offered
by Parsons-high salaries, good benefits, ad-
vancement, professional freedom-and a work
environment unequalled anywhere.
Parsons is expanding its operations. Our new
world headquarters will be completed in the
summer of 1974. This $20 million, 400,000
square-foot facility was designed specifically
for our business. It is located in a suburban
area near the Rose Bowl in Pasadena, Cali-
fornia, close to some of the country's famous
universities in case you want to further your
academic career-with Parsons' tuition aid plan.

Parsons is one of the leaders in the engineer-
ing design and construction of petroleum re-
fineries, metallurgical plants and chemical
plants. We have prepared a booklet describing
the advantages of working for Parsons-for
your copy of "Parsons is a Good Place to Work,"
write to Personnel Manager,

The Ralph M. Parsons Company
ENGINEERS/CONSTRUCTORS
617 West Seventh Street, Jl
Los Angeles, Ca. 90017

AN EQUAL OPPORTUNITY EMPLOYER

WINTER 1974

ACKNOWLEDGMENTS

INDUSTRIAL SPONSORS: The ollowina companies donated

a d jo4 dhe d"uppfoa o CHEMICAL ENGINEERING EDUCATION d$uing 1973:

C F BRAUN & CO

MONSANTO COMPANY

THE 3M COMPANY

DEPARTMENTAL SPONSORS:

h14e joUowain 129 depi.atmen.t

coat'&dlte at tie dapp(at o& CHEMICAL ENGINEERING EDUCATION in 1973

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TO OUR READERS:

If your department is not a contributor, please ask your

department chairman to write R. B. Bennett, Business Manager, CEE, Depart-
ment of Chemical Engineering, University of Florida, Gainesville, Fla. 32611.
Bulk subscription rates at $4/yr each with a $25.00 minimum for six or
fewer subscriptions. Individual subscriptions are available to ASEE-CED and
AIChE members at $6 yr.
CHEMICAL ENGINEERING EDUCATION

What goes up must come down.

- ,i-.

The tires of most jetliners lose traction
on a half inch of snow.
That means runways must be kept
free of snow and ice. Or airports must
close and the planes land somewhere
else.
Which causes a lot of inconvenience
for passengers. Strange hotels. Long
lines. Missed relatives. And dreary
hours waiting for better weather.
But this winter the story may be dif-
ferent. Because of Union Carbide's
Runway De-Icer.
We discovered a new combination of
liquid chemicals that penetrates a cov-
ering of snow and ice and unglues it
from the runway surface.

So it can easily be pushed away.
It can also be laid down before a
storm to act as an anti-icer.
Last winter it was successfully used
at over 20 busy metropolitan airports.
This year we expect that more airports
will be using UCAR Runway De-Icer.
So now instead of just talking about
the weather, people can do something
about it.

THE DISCOVERY COMPANY

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

ZEfffl

In the energy field, there aren't

any easy answers

which is one very good reason for
considering Atlantic Richfield for your career.

It's energy that has created and maintains the fabric
of today's civilization. That's basic.
But getting and using energy has also created some
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disruption, resources depletion-to name a few of
the obvious ones.
Now, new answers must be found to developing and
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maintain our energy-based standards of living.
We want the best brains we can find to help us arrive
at these answers. We want people sensitive to the
human and natural environment-and realistic enough
to know that preserving both must come from tough,
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If tackling such large-scale, significant problems is
one of your criteria in selecting a job, join us.We can
offer you a career rich in challenge, rich in meaningful
work, rich in personal reward.
We typically offer opportunities to engineers,
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See our representative on campus or your
Placement Director.

AtlanticRichfieldCompany 0
An equal opportunity employer, M/F.

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S- ... �
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-. "rU--:� - -- ~- "i~c~

	Front Cover
	Table of Contents
	James J. Carberry of Notre...
	University of California-Berke...
	The project approach to chemical...
	Test to measure the ability of...
	The theory of diffusion and reaction:...
	Indirect measurement of reaction...
	Interface phenomena for engine...
	Book reviews
	Waterloo program for high...
	A junior course in chemical engineering...
	Acknowledgement
	Back Cover

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