Chemical engineering education

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Winter 1993

Chemical Engineering Education

Volume 27

Number 1

Winter 1993

EDUCATOR
2 Darsh Wasan, of the Illinois Institute of Technology,
David Edwards, Dimitri Gidaspow, Mary Dawson

DEPARTMENT
8 FAMU/FSU, B.R. Locke, P. Arce, M. Peters

CURRICULUM
14 A Jungle Guide Through Accreditation,
E.L. Cussler, John W. Prados

LABORATORY
20 Liquid-Phase Axial Dispersion in a Packed Gas
Absorption Column,
Richard A. Davis, Joe H. Doyle, Orville C. Sandall

34 Solid Phase Extraction Columns: A Tool for Teaching
Biochromatography, Polly S. Robinson-Piergiovanni,
Laura J. Crane, David R. Nau

52 Basic Chemical Engineering Experiments, W.E. Jones

CLASSROOM
30 The Other Three Rs: Rehearsal, Recitation, and
ARgument, David F. Ollis

38 Collaborative Study Groups: A Learning Aid in Chemical
Engineering, Duncan M. Fraser

44 Fluid Structure for Sophomores, J. Richard Elliott, Jr.

CLASS AND HOME PROBLEMS
42 Solving Chemical Kinetics Problems by the Markov-Chain
Approach, Thomas Z. Fahidy

VIEWS AND OPINIONS
60 Advanced Engineering Calculators: Don't Overlook Them!
Conan J. Fee

RANDOM THOUGHTS
28 What Do They Know, Anyway?: 2. Making Evaluations
Effective, Richard M. Felder

26,32 BOOKREVIEWS
27 POSITIONSAVAILABLE
19 CONFERENCES

CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the
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ED UCTO

DARSH WASAN

of the

Illinois Institute of Technology

DAVID EDWARDS,* DIMITRI GIDASPOW, MARY DAWSON
Illinois Institute of Technology
Chicago, IL 60616

"In his lectures, he's a spellbinder, an honest-to-goodness
twentieth century Indian snake charmer,"
is how one former colleague describes Illinois Institute of Technology's
Darsh Wasan. Professor Octave Levenspiel, now at Oregon State
University, understands the students' enchantment. He says,
"Darsh is an exciting teacher because he is concerned with young
people-his students-and he is in love with his subject. Research
ideas bubble from him, and students flock to work with him. He
works them hard, with evening and weekend conferences, but they
love it. I'd say that close to half the students in the department did
their theses with him."

Wasan's love for teaching and his ability to inspire
his students were evident right from the start of his
academic career. He came to the Illinois Institute of
Technology in Chicago in 1964 after receiving his
PhD from the University of California, Berkeley, and
by the academic year 1966-67, all of his undergradu-
ate and graduate classes had nominated him for the
university's Excellence in Teaching Award, which he
received that spring. In 1967 he was also promoted to
associate professor and, in 1970 to full professor.
Through the years since then he has received
numerous awards for teaching, including (in 1972)
the American Society for Engineering Education's
Western Electric Fund Award for Excellence in In-
struction of Engineering Students.
Teaching and research seem so natural for Darsh,
it is hard to imagine that he did not set out to become
an educator, but at nineteen he thought he wanted
to be a physician. One of eight children in his family,
he had completed some pre-med courses and had
* Massachusetts Institute of Technology, Cambridge, MA 02139

even been accepted into a medical school in his
native Bombay. But then his oldest brother, Madan
(who was studying for his doctorate in mathema-
tical statistics in the United States), proposed what
proved to be an irresistable alternative for Darsh:
chemical engineering. Madan had discussed his
younger brother's math and chemistry talents with
the admissions counselors at the University of
Illinois Champaign/Urbana (UI), and they offered
to admit Darsh to their undergraduate chemical
engineering program.
Darsh turned out to have an aptitude and an
enthusiasm for chemical engineering. At the UI he
studied under Tom Hanratty, John Quinn, Jim
Westwater, Daniel Perlmutter, and Max Peters (de-
partment chairman at that time). He did a senior-
year project on fluid mixing under Quinn and during
the summers served as an assistant in the research
laboratories of Hanratty and Harold Johnstone. In-
trigued with turbulent diffusion after a project under
Hanratty, Darsh later chose this as his doctoral dis-
sertation topic at Berkeley.

Copyright ChE Division ofASEE 1993

Chemical Engineering Education

Harold Johnstone introduced him to colloids and
interfaces. Wasan worked with Johnstone on an aero-
sol science project related to acid rain during 1959-
60. The importance of interfacial and colloidal phe-
nomena in chemical engineering processes and op-
erations helped convince Wasan to focus his later
research efforts in this area.
In August of 1960, after completing his under-
graduate degree in chemical engineering, Wasan
moved to California to enter graduate school. At
Berkeley, he studied under Andy Acrivos, John
Prausnitz, C. Judson King, Charlie Tobias, Eugene
Petersen, Don Hanson, Charles Wilke, and Chang-
Lin Tien (now Chancellor at Berkeley). While in grad
school he began publishing, co-authoring two papers
in turbulent transport ("Law of the Wall") with Tien,
who was teaching mechanical engineering.
Wasan's doctoral thesis research under Wilke, in
the field of mass and momentum transfer in turbu-
lent flow, was the subject of the ASEE Chemical
Engineering Division 3M Lecture that Wilke deliv-
ered at the 1964 annual meeting. Exactly twenty-
seven years later, Wasan himself gave the 3M Award
Lecture-this time on "Interfacial Transport Pro-
cesses and Rheology: Structure and Dynamics of
Thin Liquid Films.*
In the summer of 1966, Wasan returned to Bombay
and married Usha Kapur, a lovely and gracious woman
with a degree in history and a flair for the culinary
arts. They began their married life in a faculty apart-

TABLE 1
PhD Students of Darsh Wasan
N. Aderangi W. Jones R. Ramakrishnan
R. Alexander J. Kaellis M. Ranade
B. Baker' R. Kao S. Randhava
R. Borwankar M. Krawczyk F. Rasouli'
J. Bouillard' C. Lee' J. Rosenfeld
C.W. Chi L. Ting3 J. Rudin
C.V. Chi2 Y. Liu' S. Shah
P. Chowdiah' Y. Lo' S. Sheth2
S. Chung L. Lobo Y. Shih'
N. Djabbarah A.K. Malhotra S. Zheng4
D. Edwards3 H. Maru S. Suneja
L. Gupta V. Menon F. Tavakoli2
R. Gupta' A. Mukherjee' C. Thomas
D. Huang J. Perl M. Vora
U. Jayaswal' A. Pintar W. Wnek'
With* D.Gidaspow 2 R. Peck H. Brenner 4R. Beissinger

* Published in Chem. Eng. Ed., 26, 104, (1992)
Winter 1993

Wasan's love for teaching and his
ability to inspire his students were evident right
from the start of his academic career... all of his
graduate and undergraduate classes (have)
nominated him for the university's
Excellence in Teaching Award...

ment on the IIT campus, but after a few years and two
sons (Ajay and Kern) they moved to a nearby suburb
where they raised their sons (both now in college) and
where they recently celebrated their twenty-fifth
wedding anniversary. Both Darsh and Usha became
naturalized citizens of the United States in 1974.
A Wasan tradition that his students and colleagues
especially relish is the annual Indian feast that Usha
prepares at the end of each summer. Darsh invites
his research group of ten to twenty master's and
doctoral students, as well as post-doctoral fellows
and his professional colleagues, to share the good
food, informal and genial conversation, and a spirited
game of volleyball. Such occasions are only one of the
ways Darsh encourages camaraderie among his stu-
dents, many of whom regard him not only as an
adviser but also as a friend and mentor.
In his twenty-eight years at IIT, Wasan has super-
vised about a hundred graduate students, including
forty-five doctoral dissertations. Table 1 lists the
names of his former PhD students and the profes-
sional colleagues with whom he shared some of them.
Observations from his former students range from
"He's always been more than just a professor to us; he
genuinely cares about us," to "He has always been a
very busy person-more so now that he has advanced
in the IIT administration; but even now he always
makes time for his students."
Many former students laud Wasan's ability to
train his students in communication-in effectively
presenting their ideas. Several remember Wasan's
insistence on good presentations and good project
proposal writing. "As an alumnus of his laboratory, I
consider that as important as the research training I
received under his tutelage," Raju Borwankar (a
former student) says.
AS A RESEARCHER
Asked to comment on Wasan as a researcher, one
of his close associates, Bill Krantz (University of
Colorado), cites Wasan's prolific contributions to
fundamental chemical engineering and credits him
with "an exceptional ability to apply his research to

practical engineering
problems."
Several industrial
colleagues character-
ize Darsh as a man
who has good intuition
and who exploits it to
the maximum. One _
commented, "He is the
master of the scheme
of things and decides to work on problems which he
thinks are relevant. He always directs his efforts to
real problems encountered by industry and does this
research in collaboration and consultation with the
related industrial scientific community."
One of the first academics to promote the concept
of joint industry/university research programs,
Darsh set up an Industrial Technical Advisory Com-
mittee in 1978 that has since been providing direc-
tion for his ongoing basic research program at IIT.
Wasan himself describes his research philosophy
simply as that of a true engineer. "I try to attack
problems that need to be solved rather than choosing
a problem that can be solved," he says.
Wasan's research activities span several separate
but interrelated fields, focusing particularly on the
importance of interfacial transport processes and
rheology. This research has resulted in over two
hundred and thirty publications, including seven
research monographs, twelve book chapters, a text-
book, and three U.S. patents.
Darsh has maintained extremely good ties with
industry and academic researchers in the U.S. and
with researchers in Eastern Europe (especially Bul-
garia), even in times when such collaborations were
rare. Recognition of his collaborative work includes
the Bulgarian Academy of Sciences' presentation of
the Asen Zlatarov National Award in chemical sci-
ences to Wasan and his collaborators for their re-
search publications in thin liquid films.
His research contributions can be clustered into
the following three areas:
Particle-Fluid Separation Darsh and his col-
leagues were the first to simultaneously consider
both hydrodynamic and molecular forces for the cap-
ture of small particles by fibrous and granular media,
and the role of colloid chemistry in modeling deep-bed
filtration, cross-flow electrofiltration, and lamella
electrosettling for separating suspended particles from
aqueous and non-aqueous media.
Synthetic liquid fuels derived from coal, shale, and
tar sands contain particles ofunreacted solids (ash-

Darsh and his colleague Dimitri
-*Gidaspow examine computer model
resultsforparticle dispersion.

f Darsh and research associate Alex
Nikolov examine microstructure
formation in colloidal dispersions

carbonaceous _
residue) which
impede down-
stream process- e, .i
ing. The complex
nature of colloid
chemistry in
non-aqueous
media makes re-
moval of these
particles diffi-
cult. With sup-
port from the Amoco Corporation, the Department of
Energy, and the National Science Foundation, Wasan
and his IIT colleague Dimitri Gidaspow invented two
practical devices based on electrokinetic phenomena
(a cross-flow electrofilter and a lamella electrosettler)
to separate colloidal particles from synthetic liquid
fuels derived from coal, shale, and tar sands. These
methods, significantly more energy-efficient than con-
ventional techniques, have applications in upgrading
other synthetic crudes, heavy residual oils, fluid cata-
lytic cracking slurry oil, hydraulic oil, and other
organic liquid slurries.
In 1986 the National Science Foundation awarded
Wasan and Gidaspow a Special Creativity Award
for their work on electrokinetic phenomena in
non-aqueous media. More recently, their research
group has been developing a dry electrostatic
process for separating a powder mixture into its
components based on their work functions, and they
have successfully applied their new method to
mineral beneficiation.
Interfacial Rheology and Thin Liquid Sur-
factant Films Many separation processes utilize
surfactants, i.e., substances which are interfacially
active. In 1988, Wasan edited the first book on surfac-
tants-Surfactants in Chemical/Process Engineer-
ing. His quest to develop new instruments for mea-
suring dynamic properties of fluid-fluid interfaces
containing surfactants and the dynamic behavior of
thin liquid films formed from surfactant solutions
put him at the frontier of dispersion science and
Chemical Engineering Education

Wasan's research was the first to identify the significant role of the coalescence phenomenon in the oil
bank formation and propagation rate processes in porous media and the stability of emulsions in
optimizing oil recovery in both conventional and enhanced oil recovery processes.

Wasan's present research team.

technology, contributing to advances in areas such as
emulsification/demulsification, foaming/anti-
foaming, wetting, surfactant liquid membranes, and
enhanced oil recovery.
Noting that the field of interfacial rheology (and its
application to emulsion stability, thin film drainage
and rupture, and enhanced oil recovery by surfac-
tant/polymer processes) has developed as a science
largely in the past twenty years, Bob Schechter (Uni-
versity of Texas) credits Wasan and his students for
a significant part of this recent progress. He cites the
Wasan team's development of precise, reproducible,
and meaningful methods for measuring interfacial
viscoelastic properties. "His work significantly im-
proved the deep channel surface viscometer, and his
group has published more comprehensive studies
than any other group," Schechter notes.
A commercial version of Wasan's interfacial shear
viscometer is now used worldwide as the primary
tool in emulsion and foam stability research. A
second instrument for measuring dynamic inter-
facial tension (an expanding drop tensiometer) is
under development.
After developing reliable measurement techniques,
Wasan published a series of papers clarifying the role
of surface viscosity and elasticity in stabilizing thin
liquid surfactant films. These studies, fundamental
to an appreciation of both foam and emulsion stabil-
ity, provided the theoretical groundwork whereby
Winter 1993

interfacial theological considerations can be included
in coalescence phenomena and interfacial mass trans-
fer processes. Consequently, industry now recog-
nizes the potential influence of interfacial rheo-
logical behavior in the design of many engineering
processes involving dynamic fluid-fluid interfaces in
dispersed multiphase systems, such as suspension
and emulsion polymerization processes. Wasan
summarizes this work in his recent textbook, Interfa-
cial Transport Processes and Rheology, written with
his former doctoral student, David Edwards, and
Professor Howard Brenner.
In 1986, Darsh and his colleagues discovered a
new mechanism for the film stability induced by the
formation of "ordered" surfactant micelle structures
inside the film over distances of the order of l00nm or
1000A0 and ushered in a new era of research on
understanding the nature of interactions within
supermolecular fluids such as concentrated suspen-
sions of Brownian particles, surfactant micellar solu-
tions, and microemulsions. They showed that the
phenomenon of multilayer structuring or stratifica-
tion (i.e., internal layering of micelles) in thinning
liquid films is much more universal than previously
thought. Stratification can also be observed in con-
centrated submicron particle suspensions such as
those of polystyrene latexes and silica hydrosols with
narrow size distribution and prevailing repulsive
forces. The formation of long-range ordered struc-
tures inside thin films has many implications of both
fundamental and practical significance-for example,
the dynamic process of stratification in submicron
thin liquid films can serve as an important tool for
probing the long-range structural or interaction forces
in concentrated particle suspensions and colloidal
dispersions. The rheology of dispersions containing
stratifying films is quite different.
In 1988, when NSF recognized Wasan's discovery
of "ordered microstructures in thin liquid films" of
concentrated colloidal dispersions with another Spe-
cial Creativity Award, he became the first engineer-
ing scientist to receive the award twice.
Enhanced Oil Recovery After the oil embargo
of 1973, Darsh was one of the first academics to
embark on a basic research program aimed at im-
proving oil recovery. He sought understanding of the
fundamental mechanisms by which the oil is dis-
placed in porous media for successful applications of

surfactants/alkali, and foam processes. This program,
initiated and funded under the auspices of NSF-
RANN (Research Applied to National Needs), has
also received financial support for the Department of
Energy and industrial sources.
Wasan's research was the first to identify the
significant role of the coalescence phenomenon in the
oil bank formation and propagation rate processes in
porous media and the stability of emulsions in opti-
mizing oil recovery in both conventional and en-
hanced oil recovery processes. This basic research
program was also the first to elucidate the effect of
the presence of oil on foam performance. Wasan
discovered the importance of "pseudoemulsion" film
(i.e., water film between the oil and gas), which had
not previously been recognized, in controlling the
foam stability. His pioneering use of differential in-
terference microscopy to investigate film stability,
contact angles, and wetting and spreading phenom-
ena, has now been adopted by industry.
In 1978, Wasan's research on "Improved Oil Re-
covery" was one of the three research programs fea-
tured in the Annual Report of the NSF to President
Jimmy Carter. This research was selected from 834
NSF grants in force at the time in the Engineering
Division of NSF.
In 1989, the Chicago Section of the American Insti-
tute of Chemical Engineers presented Darsh with the
Ernest W. Thiele Award for outstanding contribu-
tions through the practice of chemical engineering.
He was cited for his "innovative research in particu-
late separations, petroleum recovery, and interfacial
phenomena as well as his contributions as an inspir-
ing teacher and dynamic leader of IIT."

WASAN AS AN ADMINISTRATOR
Wasan's contributions to engineering education
not only include award-winning teaching and re-
search accomplishments, but also academic leader-
ship as IIT's chemical engineering department head
(1971-77, 1978-87), College of Engineering dean (act-
ing, 1977-78 and 1987-88), vice president for Re-
search and Technology at IIT and IIT Research Insti-
tute (1988-91). In 1991 President Lewis Collens tapped
Darsh for the post of provost, noting that "Darsh will
bring great energy, enthusiasm, and insight to the
process of creating a new IIT for the 21st Century."
A former colleague, Larry Tavlarides, credits Darsh
with a "strong and positive influence in the growth
and stature of the chemical engineering department
at IIT during the decade of the seventies and on a
cadre of faculty who grew professionally during that
period." He notes that "the group included those of

us who moved on: Jim Vrentas, Herb Weinstein,
Tom Fitzgerald, and me," and adds that, "Those
who remained are among the pillars of the current
department: Dimitri Gidaspow and Rob Selman.
It took an enormous amount of skill, sincerity, and
good will so that we could all grow in stature in a
harmonious way.
As a long-term department chairman, Wasan was
responsible for keeping both the graduate and under-
graduate curricula relevant for the changing needs of
society. He did this by establishing an Industrial
Advisory Council for the department and appointing
such distinguished chemical engineers and IIT alumni
as Jim Oldshue and John Sachs, who are both former
presidents of AIChE. He also established premier
laboratories in the department for undergraduate
teaching and graduate research.
As acting dean of IIT's Armour College of Engi-
neering, he recruited an engineering faculty recog-
nized for its excellence and developed cross-disciplin-
ary specialized minors (which generally consist of
five courses) to enhance students' professional
breadth and potential for advancement.
As vice president for research and technology,
Wasan was the motivating force behind the creation
of the National Center for Food Safety and Technol-
ogy, housed at IIT's Moffett Campus. This unique
center brings together academia, industry, and gov-
ernment to do research in new food processing and
packaging technologies, with the goal of increasing
consumer food safety. Established in 1989 with a gift
from CPC International, Inc., of a five-building, seven-
acre facility including an industrial-scale pilot plant,
the center was initially funded with a $3.7 million
cooperative agreement between IIT and the U.S.
Food and Drug Administration (FDA). That agree-
ment, recently renewed at $2 million per year, supple-
ments funding from fifty leading food-industry re-
lated member-companies. Today, research at the Cen-
ter is being conducted by forty scientists from the
FDA, faculty from both IIT and the Department of
Food Science at the University of Illinois at Urbana-
Champaign, scientists from IIT Research Institute,
and from the member companies.
As provost, Wasan quickly took a bold step, cross-
ing traditional boundaries between engineering and
science at IIT-he moved the departments of biology,
chemistry, computer science, mathematics, and phys-
ics out of the College of Liberal Arts and Science into
a new, combined College of Engineering and Science.
His goal in this realignment was to bring an interdis-
ciplinary focus to engineering and science education
at IIT. To that end, he encouraged the environmental
Chemical Engineering Education

engineering department to add an environmental
engineering baccalaureate program that builds on
the strengths of its graduate program, and initiated
several five-year, double-degree (BS and MS) inter-
disciplinary programs, including medical engineer-
ing, computer systems engineering, manufacturing
engineering, food safety and technology, and environ-
mental engineering.
He has also embarked on a university-wide cam-
paign to revamp undergraduate curricula to prepare
students for significant careers in the 21st Century.
Quality, creativity, ethics, and leadership will be
taught across the curriculum. He is working closely
with advisers from Motorola University to introduce
these four critical elements and strengthen the de-
velopment of students' communications skills through-
out the curricula. "We are in a sense redefining and
sharpening the tradition of a liberal arts education in
the context of an institution focused on technology
and the professions," says IIT President Collens.
Wasan is also developing a new undergraduate
internship program with industry. The goal of the
program is more than just hands-on experience. Edu-
cational objectives are to be set for each internship
period, and companies are being asked to identify
appropriate employees to serve as mentors to the
interns. Ultimately, the mentor will determine the
educational objectives in cooperation with the intern's
faculty adviser, and work with the faculty adviser in
evaluating the student's performance.

SERVICE TO THE PROFESSION
Wasan's zeal for chemical engineering education
and research extends to scientific communication in
general and to the institutions that facilitate it. He
has chaired the ASEE Publications Board of Chemi-
cal Engineering Education, the technical program of
the AIChE's 69th Annual Meeting, and the Interfa-
cial Phenomena and Transport Processes research
committees of the AIChE. In addition, he served on
the AIChE Education and Accreditation Committee
and Ad Hoc Visiting Committee of ABET and was
president of the Fine Particle Society. In 1986 he and
Bill Krantz organized an NSF Workshop on Interfa-
cial Phenomena in New and Emerging Technologies.
Wasan has chaired some forty research symposia
at various national and international meetings and,
over the years, has delivered more than one hundred
lectures and seminars in academia and industry. He
has served as: a member of the Engineering Advisory
Committee for the Chemical and Process Engineer-
ing Division at NSF; member of the advisory commit-
tees for the Department of Energy's Oak Ridge Na-
Winter 1993

tional Laboratory Chemical Technology Division and
National Institute for Petroleum and Energy Re-
search in Bartlesville, Oklahoma; member of the
review committee for the Argonne National Labora-
tory Energy System Division; member of the Execu-
tive Committee of the Governor's Science Advisory
Committee for the State of Illinois; consultant to the
United Nations Development Program in India. In
addition, he has served as a consultant to several
industries, including Exxon Research and Engineer-
ing Co., Stauffer Chemical Co., American Cyanamid,
ICI of America, and Nelson Industries.
In recognition of all his accomplishments, ASEE
gave him the 1991 Chemical Engineering Division
3M Lectureship Award. The official citation reads,
in part:
The 3M Lectureship Award is presented to Darsh T. Wasan.fbr
his outstanding contributions to the field of chemical engineer-
ing. As a teacher, he has been an inspiring and enthusiastic
instructor, helpful to students inside and outside the classroom.
As a researcher, he has been creative, innovative and has been
a pioneer in advancing the frontiers of knowledge on interfa-
cial phenomena and utilizing this knowledge to solve energy
and environmental problems. As an administrator, he has
contributed to the drive for excellence of his department, the
College of Engineering, and IIT as a whole. As a professional
engineer, he has contributed to the solutions of industrial
problems as a consultant to industry as well as promoted the
growth of knowledge by organizing current state-of-the-art
symposia at professional meetings and by identifying the future
directions of research.
In summarizing Wasan's contributions to educa-
tion, research, academic administration, the profes-
sion, and collaborative efforts, many of his friends
and colleagues are struck with the exceptional bal-
ance that he has maintained throughout his aca-
demic career. Cynthia Hirtzel, in presenting Wasan
with the Donald Gage Stevens Distinguished Lec-
tureship Award of Syracuse University in 1991, ex-
pressed what many of Darsh's friends feel when she
said, "When I think of Wasan, many adjectives-
mostly superlatives-come to mind. One quality which
will always be foremost in my mental picture of him
is his phenomenal energy. His energy for his work,
for education, for research, for his students and col-
leagues, is prodigious and almost intimidating to
those of us who would strive to emulate his examples.
It is truly a privilege and a joy to know him."

ACKNOWLEDGMENT
A number of Darsh's colleagues and former stu-
dents contributed significantly to the preparation of
this article, and their kind and generous contribu-
tions are very much appreciated. 0

SM department

FAMU/FSU

Central atrium (above) and laboratory wing (right) of the
FAMU/FSU College of Engineering

B.R. LOCKE, P. ARCE, M. PETERS
FAMU/FSU College of Engineering
Tallahassee, FL 32316-2175
he Chemical Engineering Department at the FAMU/
FSU College of Engineering is part of a unique
program that developed through collaboration
between Florida Agricultural and Mechanical University
(FAMU), a historically black university, and the
Florida State University (FSU), formerly the Florida
State College of Women.
FAMU was chartered in 1887 and has traditionally
focused on a strong undergraduate education in basic
studies, business, engineering technology, and agri-
culture. It currently enrolls about 9,000 students from a
wide geographical area.
The roots of FSU go back to 1851, although it was not
until 1947 that the State Legislature granted it university
status. Total current enrollment is about 28,000 and
includes students from most states in addition to 105
foreign countries. There are approximately 4,500 grad-
uate students at FSU.
Although the College of Engineering is young (it was
authorized by the 1982 Florida State Legislature), it has
experienced an extraordinary rate of growth. Student en-

rollment has increased by an average of fifteen
percent per year over the last three years. ABET-
accredited undergraduate degrees are offered in
all departments: chemical, civil, electrical, indus-
trial, and mechanical engineering. MS degrees
are offered in all of the disciplines except indus-
trial engineering, and PhD degrees are offered in
chemical and mechanical engineering. The col-
lege currently enrolls over 1800 undergraduate
students and 200 graduate students. It has ap-
proximately seventy full-time professors.
Engineering students can enroll at either
FAMU or FSU. They must, however, satisfy both
the general education requirements of the school
in which they are enrolled and the specific re-
quirements of the Engineering College. All engi-
neering classes are taken at a single engineering
complex, which is convenient to both campuses,
while courses in basic studies, sciences, and
mathematics are taken at the student's respective
university. The degree is granted by the College
of Engineering through the university where the
student is enrolled.

@ Copyright ChE Division ofASEE 1993

Chemical Engineering Education

Although nationally recognized as a major football powerhouse,
FSU has traditionally also had strong programs in liberal arts and
the basic sciences. With the appointment of a new university
president (Dr. Dale Lick, a mathematician), along with the devel-
opment of the National High Magnetic Field Laboratory and the
Supercomputer Computations Research Institute, the expansion
of the centers for Materials Research and Structural Biology, and
the high quality of the physics, chemistry, biology, geophysics, and
applied mathematics departments, FSU is poised to become one of
the nation's top research and educational institutions. It is cur-
rently ranked among the top colleges by college-bound high school
seniors as a desirable place to study.
The home of the internationally known "Marching 100," FAMU
is ranked high by college-bound minority students as an attractive
place for pursuing higher education. Through the active recruit-
ment efforts of its president (Dr. Frederick Humphries, a physical
chemist by training), FAMU currently attracts a large number of
highly qualified minority students who are eager to major in
chemical engineering. Several FAMU students presently hold full
"life gets better" scholarships, supported by industry, which pro-
vide full financial assistance for obtaining a bachelors degree as
well as providing summer internships.

THE CHE DEPARTMENT
Fifty-five bachelors degrees, five masters degrees, and two doc-
torate degrees have been granted by the Chemical Engineering
Department as of fall, 1992, and current enrollment includes
approximately 250 undergraduate and 15 graduate students.
Research and graduate-level activities began soon after the
department was founded, and the PhD program was fully ap-
proved by the Board of Regents in the fall of 1989. The department
has embarked on a new five-year strategic plan emphasizing
research and education in newly developing areas of chemical
engineering science and technology.
Undergraduate Program
The department is committed to providing a high quality and
modern" education in the basic principles and practices of the
chemical engineering profession. In addition to maintaining a
strong curriculum which incorporates the fundamentals of chemi-
cal engineering, the faculty believes that it is important to incorpo-
rate applications from the emerging areas of chemical engineering
into the core courses. These include biotechnology and biomedicine,
advanced materials (polymers, ceramics, and composites),
computer-assisted process and control engineering, and sur-
faces, interfaces, and microstructures. 131 Also, because of the rapid
changes and added complexities in the profession, greater empha-
sis is being placed on occupational health and safety practices in
laboratories, environmental protection, waste minimization, and
recycling. In addition, elective courses in bio[41 engineering, poly-
mers, chemical-environmental engineering, advanced materials
science and engineering, molecular engineering, and macromolecu-
lar transport"51 provide, in part, a more comprehensive study of the
emerging areas in chemical engineering.
Winter 1993

A familiar student gathering in the atrium.
As part of its growth plan, the de-
partment is currently adding modern
developments to the undergraduate cur-
riculum, including new developments in
molecular structure, state-of-the-art in-
strumentation and experimental tech-
niques, statistical methods and their ra-
tional application to process design (in-
cluding design of experiments), and qual-
ity control.
All qualified undergraduates are
strongly encouraged to participate in re-
search projects through both the Honors
Program and Directed Individual Stud-
ies. The Honors Program emphasizes re-
search with faculty for the highly tal-
ented and motivated student.
The nationally accredited student
AIChE chapter is an active group that
sponsors a number of plant trips to local
industries, arranges and schedules talks
by professional engineers, and pub-
lishes a newsletter, The Innovator, twice
a year that contains articles by both stu-
dents and faculty. In addition, the stu-
dent chapter is the focal point for infor-
mation on graduate school opportuni-
ties and also schedules talks from visit-
ing academicians on graduate research
and education in chemical engineering.
The department awarded approxi-
mately $15,000 of industrially supported
scholarships to the top undergraduate
students in the 1991-1992 school year.

Graduate Program
The department offers both a thesis and a non-
thesis option leading to the Master of Science degree.
The core curriculum required for both options in-
cludes advanced chemical engineering thermodynam-
ics, transport phenomena, reactor design, and math-
ematical analysis, in conjunction with proficiency in
computational skills such as numerical solution of
engineering problems.
PhD students have the option of selecting gradu-
ate courses from a variety of choices that includes,
among others, applied mathematics, advanced
transport phenomena, macromolecular transport,
statistical mechanics, polymer rheology, and compu-

PhD students have the option of selecting
graduate courses from a variety of choices that
includes... applied mathematics, advanced
transport phenomena, macromolecular
transport, statistical mechanics, polymer
rheology, and computational techniques.

national techniques. A wide range of other advanced
courses is available in the departments of chem-
istry, physics, biology, applied mathematics, and
mechanical engineering.
The department is strongly committed to build-
ing a solid graduate research program in both ap-
plied and fundamental areas. The faculty believes
that graduate programs must be diverse, interdisci-
plinary, and flexible in order to prepare chemical
engineers to handle the applications of a quickly
changing technology.

FACULTY RESEARCH INTERESTS
Faculty members are actively involved in several
areas, including polymer processing, biochemical en-
gineering, materials research, semiconductor pro-
cessing, macromolecular dynamics, reaction kinet-
ics, molecular transport phenomena, expert systems,
thermodynamics, and applied and computational
mathematics. Many of these efforts are conducted in
close cooperation with the Florida State University
Supercomputer Computations Research Institute
(SCRI), the Material Research and Technology Cen-
ter (MARTECH), and the departments of chemistry,
physics, biology and applied mathematics at FSU.
Currently the department has seven full-time faculty
members, one adjunct teaching professor, and four
affiliate professors.
Pedro Arce joined the department in 1990 after
completing his Masters and PhD at Purdue under
10

the direction of D. Ramkrishna. He also has several
years experience in teaching and research at the
Universidad Nacional del Litoral (Sante Fe, Argen-
tina). His research revolves around a variety of prob-
lems in material design synthesis and processing,
with a strong emphasis on the application of funda-
mental principles, advanced mathematical methods,
and physical theory closely coupled with computa-
tional techniques and experiments. The central theme
of his investigation is an understanding of basic
transport phenomena and physicochemical aspects
involved in, for example, crystal growth, ceramics
technology, polymeric gel media, and composite flu-
ids. In the modeling approach, Dr. Arce uses ad-
vanced mathematical techniques such as operator-
theoretic and group-theoretic methods, bifurcation
theory, and asymptotic techniques in conjunction
with the application of computer-aided functional
analysis. In regard to complex and composite fluids,
his objective is to study the nature of, and the role
played by, the interparticle forces in order to yield
models capable of predicting interfacial behavior,
suspension stability, and "ordering" under the ap-
plied field. Hydrodynamic theories, statistical me-
chanics treatment of the microstructure, fractal theo-
ries, and computer-aided analysis are the main tools
of this research. Dr. Arce also has an interest in
active-learning techniques. For example, his efforts
have led to the development of a technique called the
"colloquial approach."'61
Ravindran Chella joined the department in
1986 after doing postdoctoral work at the University
of Pittsburgh. He obtained his PhD from the Univer-
sity of Massachusetts under the supervision of Julio
M. Ottino. He also has a Master of Science Degree in
Chemical Engineering from Rutgers University. His
current research interests are primarily in the char-
acterization of composites and polymer processing.
He is also a member of MARTECH and much of his
research is in collaboration with colleagues in the
department of mechanical engineering. Moire inter-
ferometry is being used for the thermo-mechanical
characterization of polymer and metal matrix com-
posites. Boundary element methods are being used
for stress analysis and characterization of compos-
ites under thermo-mechanical loading. The compu-
tational work is coordinated with experimental
microstrain measurements, and numerical algo-
rithms are being formulated to take advantage of
the extensive facilities available at SCRI for
vectorized and parallel computing, including a Cray
Y-MP super-computer and a 64-K node Connection
Machine. This is important for simulations involv-
ing complex geometries and nonlinear material be-
Chemical Engineering Education

havior. In the area of polymer processing, laser-
speckle techniques are being developed to obtain
instantaneous velocity distributions over a plane in
prototype two- and three-dimensional polymer pro-
cessing flows relevant to extrusion and coextrusion.
Experimental results are used in the verification
and refinement of finite-element and boundary-inte-
gral models of the flow.
David Edelson, a graduate in physical chemis-
try from Yale University, joined the department af-
ter a number of years spent in research at AT&T
Bell Laboratories. His research interests are in the
areas of chemical kinetics and reactive flows, and in
the use of computation simulation and the develop-
ment of expert systems for the elucidation of mecha-
nism, identification of controlling processes, and pre-
diction of the behavior of reactive systems. Dr.
Edelson is also a faculty associate with SCRI, and
together with colleagues in computer science, has
been engaged in the prototype design of an expert
system for the simulation of reactive flows.
Bruce Locke was hired as an assistant profes-
sor in 1989. He completed his Masters at the Univer-
sity of Houston under the supervision of Neal
Amundson and earned his PhD at North Carolina
State University under the direction of Ruben
Carbonell. With strong backgrounds in both math-
ematical modeling methods and experimental devel-
opment, Dr. Locke's general research interests are
in combining experiments with fundamental prin-
ciples in order to understand and improve a wide
range of processes and phenomena. Combining four
years of experience at the Research Triangle Insti-
tute (in North Carolina) in the area of aerosol phys-
ics and fine particle studies with work on macromo-
lecular separation processes at North Carolina State,
he now focuses on research in particle and macromo-
lecular transport processes. Dr. Locke, in collabora-
tion with Dr. Arce and colleagues in the depart-
ments of physics, chemistry, and biology at FSU, is
seeking to improve the separation of large DNA mol-
ecules using pulsed field electrophoresis. He also
has an underlying and continuing interest in apply-
ing chemical and biochemical engineering funda-
mentals to solving environmental problems. As part
of this environmental interest, Drs. Locke and Arce
are analyzing the combined reaction and transport
processes occurring in pulse streamer coronas in
order to improve design and operation strategies for
air and water pollution treatment.
Srinivas Palanki joined the department in 1992
after completing his PhD at the University of Michi-
gan under the supervision of Costas Kravaris and
Winter 1993

FAMU/FSU enjoys a unique multicultural
atmosphere that is fostering development of a
first-class chemical engineering department. [The
new dean], Dr. C.J. Chen, ... is actively working
on important projects for the future.

Henry Wang. As a graduate student he also spent a
year at Merck and Co., Inc., working on optimization
and scale-up of antibiotic fermentations. His pri-
mary research interest is in optimization and con-
trol of batch reactors with applications to biological
processes. Since batch reactors do not have a process
steady state, there are no conventional "steady-state
set points" to which a conventional controller can be
tuned. The major objective is to minimize an objec-
tive function at the end of the batch cycle. Due to
batch-to-batch variations in complex processes such
as biological fermentations, an a priori calculated
operating scheme may lead to suboptimal perfor-
mance. Using "geometric tools," Dr. Palanki is devel-
oping feedback laws for end-point optimization of
batch reactors. This approach attenuates uncertain-
ties and disturbances to the batch process and is
independent of initial conditions. Coupled with state
and parameter estimation algorithms, this approach
provides the basis of an on-line adaptive optimiza-
tion scheme. Dr. Palanki also has a strong interest
in developing techniques for understanding and
tracking key intracellular events which control the
production of chemical of interest in batch fermenta-
tions and using these methods for optimal design
and scale-up of batch fermentations.
Michael H. Peters is chair of the department.
He received his Master's and PhD degrees from the
Ohio State University in 1979 and 1981, respec-
tively, and his BS from the University of Dayton in
1977. His research interests are in the areas of mac-
romolecular dynamics, molecular transport phenom-
ena, and moelcular engineering. He is also a Faculty
Associate with SCRI. His supercomputer computa-
tional research is being conducted in the general
area of molecular and macromolecular dynamics. In
the area of macromolecular dynamics, computer
simulations, using Brownian dynamics methods, of
coupled, internal translational and rotational mo-
tions of flexible macromolecules are being developed
and tested. The significance of this work lies in the
fact that internal macromolecular motions are often
critical to the behavior and functionality of macro-
molecules. Some notable examples include biological
macromolecules, such as DNA, t-RNA, and a variety
of proteins and biopolymers, where internal flexibil-
ity or, more properly, the span of macromolecular

configurational space, is critical the degree of func-
tionality of the macromolecule. Other supercomputer
computational research is being conducted in the
area of Natural Nonequilibrium Molecular Dynam-
ics (NNMD). In this study, the goal is to include the
boundary and initial conditions of the problem as
they "naturally" occur in the real physical system.
There are some extremely useful applications of this
method despite the seemingly gargantuan system
size. One application under development is the trans-
port and deposition of aerosol particles in the human
lung airways (e.g., bronchial and alveolar regions).
Dr. Peters is also involved in research education in
the field of molecular engineering and is currently
working on a text entitled An Introduction to Mo-
lecular Transport Phenomena.
Samuel Riccardi, with a PhD from Ohio State
University and over forty years of industrial experi-
ence at Olin Corporation, joined the department in
1988 as an adjunct professor. He devotes his time
primarily to running the unit operations laboratory.
He has also taught courses in design, thermodynam-
ics, and industrial waste treatment. He has many
interests in process and plant design, environmental
control, and loss prevention in the process industries
and has held positions in a wide range of areas
including research and development, process engi-
neering, pilot plant and manufacturing operations,
plant and facility design, environmental control, and
loss prevention.
After four years of academic experience at the
University of Wisconsin-Madison, John Telotte was
hired in 1985 as an assistant professor. He did his
graduate work at the University of Florida under
the direction of John O'Connell. His current research
interests involve measurement and correlation of
physical-property data and modeling of heteroge-
neous transport processes. The applications of these
interests have been in the areas of biochemical pro-
cessing, semiconductor processing, and indoor air
quality. Ongoing research has been involved with
both measurement and correlation of solubility data.
A laboratory for complete thermodynamic character-
ization of dilute solutions has been set up and a
solution theory has been developed that is generally
applicable to solutions of a solute dissolved in a
mixed solvent to analyze experimental data. Specific
projects have examined amino acid solubility in mixed
solvents and the effect of added salts on protein
solubility and gas solubility in fermentation media.
Initial work for semiconductor processing has fo-
cused on the measurement of diffusion coefficients of
metalorganics in hydrogen and on viscosity mea-

surements of these mixtures. This will be extended
to the development of correlations for transport prop-
erties. His work in indoor air quality is concerned
with the development of models for radon transport
through soil, modeling of the dynamics of radon dis-
tribution inside buildings, and the development of
construction techniques to minimize hazards due to
radon infiltration.
Most recently, Jorge Vifials has been appointed
as an affiliate faculty with the rank of Graduate
Research Professor. He is a research scientist at
SCRI. He has a Masters and a PhD from the Univer-
sity of Barcelona, Spain, and has worked several
years at Carnegie Mellon University under the di-
rection of Professors Mullins and Sekerka. His re-
search interests are centered around theoretical stud-
ies of non-equilibrium phenomena. Current areas of
research include theoretical and numerical studies
of kinetic processes during first-order phase transi-
tions, morphological instabilities and growth during
solidification, and pattern formation following fluid-
flow instabilities. Dr. Vifials' efforts on phase transi-
tions seek to understand and generalize scaling prop-
erties and to implement renormalization group tech-
niques to situations far from the equilibrium. His
research methods include the application of pertur-
bation theory, Monte Carlo simulation, and numeri-
cal solutions to diffusion or Langevin-type equations.
He is also interested in investigating the steady-
state stability and transient evolutions of problems
such as cellular morphologies, dendritic solidifica-
tion, and viscous fingering instabilities.
The department has three additional affiliate pro-
fessors. Within a framework emphasizing
nontraditional areas in chemical engineering and
multidisciplinary efforts, they work closely with other
faculty members in directing graduate and under-
graduate students and in developing new areas of
research. They are H. Garmestani (PhD, Cornell
University, 1989; Assistant Professor in the Depart-
ment of Mechanical Engineering), P. Gielisse (Ph.D.,
Ohio State, 1967; Professor of Materials Science in
the Department of Mechanical Engineering), and
H. Lim (Ph.D., Rochester, 1986; Research Scientist
for the SCRI).
FUTURE PERSPECTIVES
The faculty strongly believes that an interdiscipli-
nary environment will provide the flexibility and the
state-of-the-art knowledge required to develop suc-
cessful chemical engineers for the future. The faculty
also recognizes the crucial role played by research
and graduate education in the overall performance of
a successful program. Following studies to modernize
Chemical Engineering Education

Figure 1. Present and future research focus for the ChE
department at FAMU/FSU College of Engineering.

and to re-orient the chemical engineering programs
across the country,[131 the Department has formu-
lated a strategic plan to focus on the development of
research areas that will add to and supplement exist-
ing programs. These include developments in process
control, surface science and catalysis, advanced ma-
terials, and biotechnology.
Figure 1 shows the four main areas of research
mentioned above and the potential interactions that
the different facilities and projects should display.
One can see the important role played by the Na-
tional High Magnetic Field Laboratory and the
Supercomputer Computations Research Institute as
well as the other first-class programs available at
FSU and FAMU. It is the general philosophy of Dr.
Jack Crow, director of the magnetic laboratory, that
the university must integrate research at the lab
with current programs in order to prevent the lab
from becoming merely a user facility for outside re-
searchers and to make it a valuable tool for building
programs at the university. He has been successful
at attracting internationally known experts in the
areas of magnet design. J. Robert Schrieffer, 1972
Winter 1993

Nobel prize winner in physics and former director of
the Institute for Theoretical Physics at the Univer-
sity of California, Santa Barbara, joined the faculty
in 1992. Also, Hans Jorg Schneider-Muntau, consid-
ered the best magnet designer in the world, joined
the engineering faculty in 1992. Other well-known
scientists have also joined the laboratory and be-
come members of the faculty at FSU. They include
John Miller (formerly at the Lawrence Livermore
Laboratory), Dennis Markiencz (formerly at
Intermagnetics General), and Steve Van Scriver (for-
merly at the Applied Superconductivity Center at
Wisconsin). The lab will be located next to the engi-
neering building, and both the chemical engineering
and mechanical engineering departments have taken
similar philosophies towards developing their pro-
grams to complement and fully utilize the lab.
The important role of SCRI is also crucial for the
development of chemical engineering. FSU is one of
the few universities in the United States to have
both a state-of-the-art Cray Y-MP and a Connection
Machine. The DOE-supported facility is currently
used intensively by faculty in the chemical engineer-
ing department.
FAMU/FSU enjoys a unique multicultural atmo-
sphere that is fostering development of a first-class
chemical engineering department. The College of
Engineering has appointed a new dean, Dr. C. J.
Chen (ex-Iowa) who is actively working on impor-
tant projects for the future of our college. In addi-
tion, the dynamic attitudes of the people involved in
the various university research programs have cre-
ated a critical mass of enthusiastic investigators
who are driving the development of high-quality pro-
grams. With the current budgetary constraints fac-
ing most states (including Florida), few universities
presently enjoy such a progressive atmosphere.
REFERENCES
1. Amundson, N.R., Editor, Frontiers in Chemical Engineering,
Research Needs, and Opportunities, National Academy Press,
Washington, DC (1988)
2. NRC, Directions in Engineering Research; An Assessment of
Opportunities and Needs, National Academic Press, Wash-
ington, DC (1987)
3. Ramkrishna, D., et al., eds., "Chemical Engineering Educa-
tion Curricula for the Future," Proceedings of the India-US
Seminar Held at Indian Institute of Science, Bangalore,
India, Jan 1-4, Phoenix Company Limited, Bangalore (1988)
4. Locke, B.R., "An Introduction to Bio(Molecular) Engineer-
ing," Chem. Eng. Ed., 26, 194 (1992)
5. Peters, M., "An Introduction to Molecular Transport Phe-
nomena," Chem. Eng. Ed., 25(4), 210 (1991)
6. Arce, P., "The Colloquial Approach: An Active-Learning Tech-
nique," J. of Sci. Ed. and Tech., (preprint) (1992) 0

n curriculum
-- .--------------

A JUNGLE GUIDE

THROUGH ACCREDITATION

E.L. CUSSLER
University of Minnesota
Minneapolis, MN 55455
JOHN W. PRADOS
University of Tennessee
Knoxville, TN 37996-2200
e, the authors of this paper, are both in-
volved in engineering accreditation. Each
of us has taught undergraduate chemical
engineering for at least twenty-five years, and each of
us continues to do so. Each of us has visited chemical
engineering programs by request, to evaluate whether
the programs meet nationally mandated accredita-
tion criteria. One of us (JWP) is past president of the
organization that develops and applies these criteria,
and the other (ELC) headed the Educational Advi-
sory Board of the American Institute of Chemical
Engineers (AIChE).
Holding these positions has made us lightning
rods for criticisms of the accreditation process. No
one likes to be judged, and everyone gets angry about
negative judgments. We have learned that any con-
versation beginning "What the *#?! do you @*&!*
think you're doing now?" usually introduces a rea-
soned comment on accreditation. Since this comment

Edward L. Cussler received his BE (with honors)
from Yale in 1961 and his MS and PhD from the
University of Wisconsin, both in 1963. His research
centers on new separation processes, especially
those involving membranes. Some membranes
currently under study are based on mobile carri-
ers tethered within solid polymer membranes. He
is Vice President of AIChE

John W. Prados received his BS at the Univer-
sity of Mississippi and his MS and PhD at the
University of Tennessee. He has been at the
University of Tennessee for 39 years, beginning
as a graduate assistant in 1953, progressing
through a number of professorial and administra-
tive positions to his present position of Vice Presi-
dent Emeritus, University Professor, and Head of
the Chemical Engineering Department.
Copyright ChE Division ofASEE 1993

often seems personal, and since any second comment
often seems exactly the opposite of the first, we and
our colleagues in accreditation often end up echoing
Freud's comment on his patients: "My God, what do
they want?"
While individual comments are usually emotional,
we believe that many have merit. This merit, how-
ever, is often obscured by individuals who complain
only every six years when their own program is up for
review, or who use accreditation as a convenient
weapon to fend off worthwhile curriculum reforms at
home. Still, we believe that common concerns run
through these complaints and that the concerns are
often justified.
We will explore these concerns in this paper. Our
experience suggests organizing them under three
headings, each of which will be discussed in the
following paragraphs:
What should the accreditation criteria be?
How are the criteria applied?
How can accreditation be improved?

WHAT SHOULD THE
ACCREDITATION CRITERIA BE?
To explore this issue, the AIChE Educational Ad-
visory Board mailed 180 questionnaires to chemical
engineering professors chosen from the listing in
Chemical Engineering Faculties. We sent question-
naires to 60 department chairs and to a roughly equal
number of tenured and untenured professors. This
gave every department at least one chance to re-
spond, and large departments had more chances
than small ones. Such a selection is not scientific, and
untenured faculty have the annoying tendency to get
promoted and ruin the distribution! Still, we got 164
responses: 51 chairs, 87 tenured non-chairs, and 26
untenured non-chairs, for a total response of 91%.
About ten more sent in unmarked questionnaires
with notes such as "I hate questionnaires" or "My
Dean doesn't let me say anything."
Chemical Engineering Education

Overall Requirements The results of this sur-
vey, summarized in Table 1, seem to reflect an over-
whelming endorsement of the value of accreditation
and of the existing chemical engineering curriculum.
These endorsements were independent of position,
i.e., the responses of chairs, tenured faculty, and
untenured faculty were the same. In particular, Table
1 shows that at least 86% of all respondents support
the current requirements of one-half year of humani-
ties, one year of mathematics and basic science, and
one and one-half years of engineering.
Smaller majorities support the division of engi-
neering into one year of engineering science and one-
half year of engineering design. This split, which has
proved to be almost impossible to judge fairly, is
being reconsidered (as discussed in more detail
below). Parenthetically, we note that these compel-
ling endorsements of basic accreditation require-
ments are echoed by a parallel survey of engineering
deans conducted by a joint task force representing
ABET and the ASEE Engineering Deans' Council.
On these issues, at least, chemical engineering fac-
ulty and deans agree.
Specific courses The specific courses required
for a chemical engineering degree are also endorsed
by a large majority of faculty members. At least
89% support courses in basic mathematics, chemis-
try, and physics; 88% support a capstone course in

TABLE 1
What Should the Accreditation Criteria Be?
(Source: Poll of 200 chemical engineering faculty members conducted in the fall
of 1990 by the AIChE Educational Advisory Board.)
% Favoring
Curricular Requirement Requirement
Overall requirements should include at least:
0.5 year of humanities and social science 86%
1.0 year of mathematics and basic science 92%
1.5 years of engineering 87%
1.0 year of engineering science 70%
0.5 year of engineering design 62%
Basic courses should include at least:
Mathematics through differential equations 96%
General chemistry 93%
General physics 89%
One design course' 88%
Mass and energy balances 93%
Fluid mechanics 94%
Heat and mass transfer 94%
Separation processes 88%
Reaction engineering 93%
One process control course 83%
One engineering thermodynamics course 74%
0.5 year of advanced chemistry 63%
One materials course 54%
One biology course 22%

Winter 1993

This wide agreement on the larger number of
required courses means that most... faculty
support a very rigid curriculum.... we are
dismayed that so many of our colleagues
subscribe to so many requirements.

design and one in separations; and still higher
numbers endorse material on stoichiometry,
transport processes, and reaction engineering. On
these topics, all agree.
Not surprisingly, there is less agreement on what
are often described as "emerging frontiers for chemi-
cal engineering." Slightly more than half of the re-
spondents would require a materials course, and less
than a quarter would require a course in biology. In
more traditional areas, about three-quarters applaud
engineering thermodynamics (we suspect that this
lower percentage reflects uneasiness over possible
repetition between the currently required thermody-
namics courses). Sixty-three percent agree with the
required one-half year of "advanced chemistry," a
classification which can now include courses on mi-
croelectronics or advanced materials.
This wide agreement on the larger number of
required courses means that most chemical en-
gineering faculty support a very rigid curriculum.
Quite frankly, we are dismayed that so many of
our colleagues subscribe to so many requirements.
To us, the best requirements would reflect more
flexibility. Thus, we would not require specific
courses in process control, materials, engineering
thermodynamics, or biology for all departments, even
while we might support some of these require-
ments for our own departments. In this sense, we
urge all to think through the difference between
nationally mandated criteria and those which are
self-imposed at a single institution.

HOW ARE THESE CRITERIA APPLIED?
Armed with this strong consensus about what
should be required, we now turn to the organizations
responsible for engineering accreditation. For those
who have not been involved in accreditation recently,
we will briefly review the alphabet soup of acronyms
involved. The key group is ABET (Accreditation Board
for Engineering and Technology), a federation of some
thirty-odd engineering societies. ABET is recognized
by the USOE (United States Office of Education) and
COPA (Council for Postsecondary Accreditation) as
the only group authorized to accredit programs in
engineering, engineering technology, and some engi-
neering-related specialties within the United States
and its territories. ABET gets the moral support of
the engineering profession from its member societies,
15

including AIChE. It also collects dues from them.
ABET accredits engineering programs through the
EAC (Engineering Accreditation Commission), which
conducts visits and votes accreditation actions for all
engineering disciplines, as shown in Table 2. The
AIChE interface with the EAC is the E and A Com-
mittee (Education and Accreditation Committee), a
group of chemical engineers appointed by the AIChE
Council. The EAC organizes accreditation visits, but
the E and A Committee designates the chemical
engineering visitors and exerts considerable influ-
ence on whether, and for how long, a chemical engi-
neering program is accredited.
All of this can be confusing, especially since many
call the E and A Committee the "ENA" Committee
and don't understand that it's not the EAC. At one
time, the E and A Committee did vote a separate
accreditation on behalf of AIChE for each chemical
engineering program, and ABET agreed to accept
whichever action-EAC's or E and A's-was the more
severe. For the past several years, chemical engineer-
ing programs have not been subjected to this kind of
double jeopardy.
ABET evaluates programs againstgeneral criteria
that apply to all fields of engineering and program
criteria that apply only to a specific field. While both
kinds of criteria must be approved by the ABET
Board of Directors, the chemical engineering pro-
gram criteria are recommended by the AIChE E and
A Committee. This causes extra stress for chemical
engineering programs in two ways:
1. Chemical engineering is the only major engineering
discipline which depends heavily on chemistry. Thus
chemical engineering curricula are always overcrowded
by major infusions of chemistry in addition to the
traditional "engineering core" based in physics. The E
and A Committee has tried to ease the burden by
counting other advanced sciences (e.g., biology, materi-
als science, solid-state physics) as part of the advanced
chemistry requirement and by double-counting some
advanced chemistry as a part of the engineering sci-
ence requirement, but the extra stress remains.
2. A second source of irritation is the criticism by some
ABET teams about faculty not being registered as
Professional Engineers. Professional registration is
much more important to disciplines such as civil and
environmental engineering, whose graduates often
work in private practice, than to others such as chemi-
cal and electrical engineering where most graduates
work for large corporations. Edwin Layton, in his book
Revolt of the Engineers, argues that some engineering
societies are controlled by corporations who oppose
professional registration as a form of unionism. In any
case, registration is not required by the general crite-
ria and only appears in a few program criteria, e.g.,

those for civil and environmental engineering. No
chemical engineering program can be denied accredi-
tation or have its accreditation term reduced just be-
cause its faculty are not registered. Still, since state
registration board observers often accompany ABET
teams, the issue is often raised-followed by the usual
round of finger-pointing and ABET-bashing.
We provide a brief summary of chemical engineer-
ing accreditation requirements in Table 3. The Offi-
cial Word is given in Criteria for Accrediting Pro-
grams in Engineering in the United States, published

TABLE 2
Accredited Engineering Programs as of November 1991
By Program Area
(299 Schools)
Source: 1991 Annual Report, ABET Engineering Accreditation Commission

Bachelor's Masters
Level Level

Program Area

Aerospace* 57 4 61
Agricultural 46 0 46
Architectural 13 0 13
Bioengineering (incl. Biomedical) 20 0 20
Ceramic 12 0 12
Chemical 145 1 146
Civil, Construction* 212 1 213
Computer 69 2 71
Electrical, Electronic* 255 3 258
Engineering undesignatedd) 31 0 31
Engineering Management 2 1 3
Engineering Mechanics 9 0 9
Engineering Physics, Science 28 0 28
Environmental* 11 8 19
Forest 2 0 2
Geological, Geophysical 18 0 18
Industrial* 93 1 94
Manufacturing* 10 3 13
Materials 30 0 30
Mechanical* 234 2 236
Metallurgical 30 0 30
Mineral 3 0 3
Mining 18 0 18
Naval Architecture and Marine 12 0 12
Nuclear 25 1 26
Ocean 6 2 8
Petroleum 21 0 21
Plastics 1 0 1
Surveying 6 0 6
Systems 11 1 12
Welding 1 0 1
Other 6 0 6
Less dual titles counted twice (5) 0 (5)
Total Accredited Programs 1,432 30 1,462

* Five programs within these disciplines have dual titles (e.g.. Aerospace and
Mechanical) and are counted twice.

Chemical Engineering Education

each year by ABET, 345 East 47th Street, New York,
NY 10017-2397. The requirements are always chang-
ing, so any department facing accreditation needs a
current copy.
To seek chemical engineering accreditation, a uni-
versity contacts ABET, requesting evaluation and
completing a self-study questionnaire describing how
its program satisfies accreditation criteria. ABET,
through the EAC, organizes a visit by a team that
includes a chemical engineering visitor designated
by the E and A Committee. The visitor compares the
criteria with the university's program as described by
the self-study questionnaire; interviews the chemical
engineering faculty and students; and examines
course materials, including samples of student work.
The visitor then writes a report which is reviewed by
the team chairman, an EAC editor, the EAC chair-
man, and at least two members of the E and A
Committee before it is sent back to the school for
review and comment. The E and A Committee re-

TABLE 3
Brief Summary of
Chemical Engineering Accreditation Requirements
I. Faculty
A. Absolute minimum is three full-time equivalents devoted to th
graduate program; more are required for graduate program, ri
courses offered to non-chemical engineers, etc.
B. Appropriate professional education, experience, and growth
H. Curriculum
A. Quantitative:
1.0 year of mathematics (beyond trigonometry and through d
ential equations) and basic science (including chemistry and
1.0 year of engineering science
0.5 year of engineering design
0.5 year of humanities and social science
0.5 year of advanced chemistry (chemical engineering only)
B. Qualitative:
Appropriate laboratory experience
Appropriate computer experience
Knowledge of probability and statistics
Competency in written and oral communication
Understanding of ethical, social, economic, and safety issues
m. Students
A. Appropriate preparation for engineering study
B. Maintain information on performance of graduates
IV. Administration
A. Adequate support for and commitment to engineering program
V. Facilities
A. Adequate classrooms, offices, laboratories, library, computers
B. Functioning plan for laboratory maintenance and modernizatic
VI. Institutional Commitment
A. Adequate level of financial support for program

Winter 1993

views the visitor's report and the school's response
and makes an accreditation recommendation; this
recommendation is then presented to the EAC by one
of the AIChE representatives. The EAC then takes
the final accreditation action.
In spite of its Byzantine complexity, the system
works. It presumes rational behavior by all con-
cerned, and clearly, it relies especially heavily on the
individual visitors. Still, the current accreditation
system does have problems, and we discuss them in
the next section of this paper.

HOW CAN ACCREDITATION BE IMPROVED?
We recognize that there are many complaints about
accreditation, and that most people complain when
they are being critically judged. Because the com-
plaints are often vehement, we are reassured by the
fact that such a wide percentage of faculty support
both the general concept of accreditation and its
specific requirements, as detailed above. We believe
that the system for carrying out accredita-
tion is effective, although ponderous.
The system seems to work best for chemi-
cal engineering-over the last five years,
two-thirds of the chemical engineering pro-
grams visited received accreditation for the
e under- maximum term of six years, although some
search, were required to submit written reports af-
ter three years to describe correction of prob-
lems observed at the time of the original
visit. This percentage of programs receiving
six-year accreditation is higher than that for
iffer- any other major engineering discipline.
physics) At the same time, we know that there are
problems with the current system. We see
four of these as
the design requirement
the self-study questionnaire preparation
the visitors who evaluate programs
the need for educational innovation
Each problem merits consideration and is
discussed more fully in the following para-
graphs.
The Design Requirement Twenty
years ago, the accreditation criteria did not
include any quantitative statement on engi-
neering design. Beginning in 1972, accred-
ited programs were required to include at
least one-half year of "design, synthesis,
,n and systems," in addition to the existing
requirement of one year of engineering sci-
ence, and two years later the present re-
quirement of one-half year of engineering
17

design went into effect. These changes reflected a
real concern that engineering faculty were becoming
obsessed with mathematical analysis and were not
giving students experience with open-ended prob-
lems where economic and social judgments are im-
portant. We are sympathetic to this concern.
However, a reliable evaluation of the quantitative
split between engineering science and engineering
design has proved to be impossible in almost every
engineering discipline. One visitor commented that
design is like pornography-he couldn't define ei-
ther, but he knew it when he saw it!
Such a definition is not very helpful in maintain-
ing consistency with different visitors or in planning
curricular changes. Visitors have had great difficulty
in judging whether a unit operations course contains
20%, 30%, or 50% design. More than one chemical
engineering department has been told that its cur-
riculum had barely enough design, but was accept-
able-then six years later, a different visitor judged
the same curriculum deficient in design by 5-6 semes-
ter credits. The EAC and the E and A Committee
work very hard to try to make consistent judgments
in a given year, but have trouble remembering what
happened six years ago. It has been a mess.
As a result, the EAC has proposed combining the
present engineering science and engineering design
requirements into 1.5 years of "engineering topics."
These must include a "meaningful, major design ex-
perience" that is developed throughout the curricu-
lum and culminates in one or more capstone courses
that integrates earlier technical work with economic,
safety, and environmental constraints. For chemical
engineering, this means a strong senior process de-
sign experience and the generous use of open-ended
problems and projects in courses such as material
and energy balances, unit operations, and chemical
reaction engineering. The department must show
how it meets the design requirement in its self-study
questionnaire and its course materials exhibits. The
key question for the visitor will be how well the
curriculum develops student abilities to attack prob-
lems with more than one right answer, to communi-
cate, to work in teams, and to understand the non-
technical contributions to engineering decisions.
We are pleased with this overdue change. It will
not in any sense reduce the emphasis on design, but
it will focus attention on the quality and rational
development of the student's design experience and
move us away from the unproductive bean-counting
of the last eighteen years. However, the change is not
yet in place. It was approved on first reading by the
ABET Board of Directors in October of 1990, but will
18

not go into effect for at least two years (to allow public
comment), and so a society that wants to insist on a
quantitative design requirement can propose one for
its program criteria. The earliest date for final ap-
proval would be October of 1992, with the change
effective for visits in the fall of 1993.
Preparation of the Self-Study Questionnaire
* The accreditation procedure requires preparing a
self-study questionnaire which details factors such
as the economic health of the institution, the profes-
sional activities of faculty members, and the syllabi of
all required courses. The completed questionnaire, in
two volumes, can run to hundreds of pages. Prepara-
tion is a chore that can take as much as a year out of
some unfortunate person's life. While the question-
naire contains much useful information, many com-
plain that it is too long, too elaborate, too detailed,
and too much work.
We agree. But we are unsure of how to improve the
situation. Short biographies of all faculty provide
important details (such as industrial and consulting
experience) which go beyond existing sources like the
ACS Directory of Graduate Research. Course descrip-
tions and syllabi are also necessary, especially since
catalog descriptions are cryptic, dated, and often
unreliable. We agree that the best way to evaluate a
course is to look at excellent notes, exams, homework,
and sample student papers assembled by the profes-
sor in charge of the course. Unfortunately, we find
that an embarrassing number of professors do not
keep excellent notes, let alone exams.
Moreover, we believe that preparing the self-study
questionnaire is an effective challenge for engineer-
ing deans. They may be paragons of fairness and
virtue, but they are subject to major pressures that
involve hard choices. These choices are usually finan-
cial and, in our opinion, are often resolved to the
detriment of the chemical engineering program-
this may be because chemical engineering's chemical
basis is expensive and not completely understood.
Preparing the questionnaire forces every dean to
justify decisions to relatively impartial outside ob-
servers untarred by local politics. Still, we recognize
that preparing the questionnaire is onerous work,
and we welcome suggestions for making it easier.
The Accreditation Visitors The third problem
with the accreditation process is the visitors them-
selves, who do the on-site evaluation of how well an
engineering program satisfies the ABET criteria.
Such visits are not fun. They require deciphering
almost inevitably tangled, incomplete questionnaires
and incomprehensible student transcripts. Trying to
determine course content, credit-hour distributions,
Chemical Engineering Education

and what students are really required to do can be
difficult. Moreover, the accreditation team is under
such intense time pressure that the visitor cannot
even see professional colleagues and friends at the
school being visited.
Most visitors do a good job. The E and A Commit-
tee works hard to insure that the visitors (known as
"program evaluators" in the trade) are trained for
their task; each must attend a three-hour accredita-
tion workshop and then go on one accreditation visit
as an observer before serving as an evaluator. How-
ever, even with this help a few of them still apply too
rigorously the standards they think they remember
from their own education, perhaps thirty years ear-
lier ... or disregard the criteria and inject their own
educational theories into the evaluation. The E and A
Committee must learn of these biases quickly and
correct them in any summary report. Repeat offend-
ers are not assigned to new visits. In addition, any
school can object beforehand to an individual visitor
who may have a conflict of interest or is thought to be
biased. However, one school objected to 80 of 83
potential visitors, an action interpreted as an effort to
predetermine the outcome of the visit.
We are indebted to those currently serving as
visitors, and we are eager to encourage more who are
interested. We recognize that we can offer no rewards
but the feeling of service and the chance to work with
other professionals in doing ajob well. We admit that
serving as a visitor is an invitation to criticism; every
visitor who finds something lacking in a program
runs the risk of vilification. At the same time, we
always need good, new visitors-especially those
underrepresented in our current pool. These
underrepresented segments include women, minori-
ties, and those with significant industrial experience
(most of all, those with experience both in industry
and in teaching).
If you-you, there- were critical of your last ac-
creditation visitor, and yet (like most of us) believe
that accreditation has value, why not volunteer?
Educational Innovation Finally, we want to
stress that the accreditation criteria do allow exemp-
tions for educational innovation. We are dismayed
that few departments, if any, seek accreditation on
this basis. We can imagine many good reasons for
such failure. One reason may be a university-wide
core curriculum that restricts student choice; such
curricula can cripple chemical engineering programs.
Another, probably more significant, reason is the fear
that deviations from a "standard" chemical engineer-
ing curriculum taught in a "standard" manner will
jeopardize a program's accreditation.
Winter 1993

The chemical engineering program criteria require
coverage of certain subjects, but don't specify how
much time must be devoted to each of them. If you feel
that your curriculum could be improved by reducing
duplicate coverage in thermodynamics and increas-
ing student electives, why not give it a try? Why not
consider replacing traditional mathematics courses
with "just-in-time" modules? How about the possibil-
ity of eliminating certain required courses altogether
and replacing them with student projects? If you are
concerned with how these innovations affect your
accreditation, discuss your goals with the E and A
Committee as part of your planning.

EPILOGUE
In the final analysis, accreditation is a creature of
the engineering profession, heavily influenced by
engineering educators. Faculty members and deans
make up the majority of the E and A Committee, the
EAC, and the ABET Board of Directors. If accredita-
tion is a problem, you and we are a big part of that
problem-and you and we must be a big part of its
solution. O

p]M conferences

International Conference on
Natural Gas Hydrates
June 20-24, 1993
Lake Mohonk Mountain House; New Paltz, New York
Meeting purpose is to determine the state-of-the-art of natural gas
hydrate knowledge and to determine the areas in which future
work will be needed. A broad field of noted researchers will present
the latest findings and will be available to exchange views aimed at
bringing the current science and engineering of hydrate formation,
control, and utilization into focus. Conference Steering Commit-
tee: E. Dendy Sloan (Colorado School of Mines) and John Happel
(Columbia University). For further information, contact Confer-
ence Department, New York Academy of Sciences, 2 East 63rd
Street, New York, NY 10021 (212-838-0230) 0

Reaction Engineering and
Applied Catalysis
May 12-14, 1993
The University of Michigan; Ann Arbor, Michigan
Fee: $765
Chemical reactions occur in a variety of different systems and are
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mental engineering. The goal of this course is to provide a back-
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For complete information or to register, contact Engineering Con-
ferences, 300 Chrysler Center, North Campus, The University of
Michigan, Ann Arbor, MI 48109-2092 (313-764-8490) D

I laboratory

LIQUID-PHASE AXIAL DISPERSION

IN A

PACKED GAS ABSORPTION COLUMN

RICHARD A. DAVIS, JOE H. DOYLE,
ORVILLE C. SANDALL
University of California
Santa Barbara, CA 93106

he cost of electronic instrumentation has

come down recently as a result of newer tech-
nologies and lower computer prices. We have
taken advantage of this trend to create new and
dynamic experiments using existing steady-state ex-
periment apparatus. Our purpose was to enhance the
learning process by removing some of the data-collec-
tion tedium and thereby leaving more time for experi-
mental design and analysis.
One of our upgraded experiments is a packed-
column apparatus used for the absorption ofCO2 into
water. The column was instrumented with conduc-
tivity probes to indirectly measure inlet and exit
liquid-phase concentrations. Large amounts of real-
time data are readily acquired with the aid of a
computer. For example, accurate unsteady-state and
steady-state operations are easily observed. It is com-
mon to assume plug-flow conditions when analyzing
mass transfer in a packed column. This paper pre-
sents an experiment and analysis to examine the
validity of this assumption in the liquid phase.
In the first part of the experiment, the residence
time distribution (RTD) of the liquid phase is deter-
mined by measuring the exit response to an impulse
concentration perturbation on the liquid feed. The
second half of the experiment consists of determining
the overall liquid-phase mass transfer coefficient from
gas-absorption measurements in the packed column.
The results from the RTD experiments are used in a
dispersion model to account for deviations from plug
flow (e.g., back mixing in the liquid phase). Disper-
sion effects on mass transfer are evaluated by
comparing mass transfer coefficients calculated as-
suming plug flow with mass transfer coefficients
calculated from non-ideal flow conditions. This new
Copyright ChE Division ofASEE 1993

approach adds a degree of difficulty to the experi-
ment by removing the plug-flow constraint and pro-
vides a setting wherein students can make critical
judgements on a well-known solution.
THEORY
A model of dispersion in the liquid phase is devel-
oped for flow without interphase mass transfer
to obtain a dispersion coefficient. The results are
used in a second model which accounts for dis-
persion with interphase mass transfer in a packed
column. A model for the limiting case of plug flow is
also presented.
Dispersion Model
Levenspiel"' presents the dispersion model for de-
viations from plug flow in the axial direction as
C -_ E ,2C ac (u
at a2 (1)

Richard Davis received his BS degree in chemi-
cal engineering from Brigham Young University
and his PhD from the University of California,
Santa Barbara. He is a member of the chemical
engineering faculty at the University of Minne-
sota, Duluth. His research and teaching inter-
ests are in the areas of separation processes
and environmental remediation.

Joe Doyle holds a BS in chemistry from UCSB
4 and is a Development Engineer in its Chemical
and Nuclear Engineering Department. His inter-
Sests include analytical instrumentation, data-ac-
quisition systems, and exploration of the world's
largest aqueous sodium chloride reactor.

Orville Sandall is a professor in the Chemical
and Nuclear Engineering Department at UCSB.
He is a graduate of the University of Alberta
(BSc, MSc) and the University of California,
Berkeley (PhD). His teaching and research in-
terests are in the areas of mass transfer and
separation processes.

Chemical Engineering Education

where C = concentration
t = time
z = axial coordinate
u = superficial liquid velocity
E = dispersion coefficient which characterizes
convective back-mixing as well as diffusion
Usually, the dispersion coefficient is much larger
than the diffusion coefficient. Eq. (1) can be made
dimensionless as follows:
C _E ) 2C -C (2)
W0 \uh azz*2 z*
where the quantity
E/uh = the dispersion number (=1/Pe)
h = the length of the column.
The dimensionless variables are
= t (3)
where t is the mean residence time
S= h(4)
U

z*=
h

(5)

The concentration is normalized such that
C=

where

Q = C dt (6)
o
Thus we have

C dt = 1 (7)
0
Eq. (2) is examined for two regimes: small and large
extents of dispersion.
For an impulse perturbation of tracer on a fluid
with little dispersion, the shape of the tracer curve
does not change significantly from the point of injec-
tion to the measurement point. The C curve at the
measurement point is a Gaussian distribution.

TC- 1 exp ) (8)
2(1) 4 E )
The dispersion coefficient can be obtained by two
relatively simple methods. First, at the mean resi-
dence time, 6 = 1 and the C curve reaches a maxi-
mum. Eq. (8) may be solved for the dispersion num-
ber in terms of Cmax

E 1 1 (9)
ub i Je tC(9)
Wi4 nter 199Cma
Winter 1993

In a second method, the variance of the C curve can
be expressed in terms of the dispersion number

(2 2(X) (10)

The variance is defined as

2 t2 C dt 2 (11)
0
The solution for the dispersion number is found by
rearranging Eq. (10) to give
E 02
uh2 2 (12)

For small extents of dispersion, the experimental
procedure and analysis are straightforward because
the shape of the C curve is insensitive to the bound-
ary conditions imposed on the packed column.
A characteristic of large extents of dispersion is an
unsymmetrical response to an impulse perturbation
about the mean residence time. The C curve typically
has an extended tail. In this case, the boundary
conditions become important. The current experi-
mental setup in our laboratory is best described by
closed boundary conditions (i.e., the flow pattern
changes abruptly at the boundaries). In this case,
there is no analytical solution for the C curve. The
variance of the C curve is given as

2 )- 2 ( 2 1- exp[- )]} (13)
The dispersion number may be found by determin-
ing the variance as defined by Eq. (11) and then
solving the non-linear Eq. (13) for E/uh by Newton's
iterations. Good initial guesses for E/uh can be ob-
tained by using Eqs. (9) and (12) to solve for E/uh.
Levenspiel[21 offers the following estimates for the
extent of dispersion:
small: E/uh < 0.01 large: E/uh > 0.01
Tanks-In-Series
Levenspielrl] also presents the tanks-in-series (TIS)
model to account for deviations from plug flow condi-
tions. In this model, the liquid flows through a series
of n completely mixed stirred tanks. The C curve for
this model is

TC = (n-)! exp(-8n)
8(n 1)!

(14)

The number of tanks can be determined from the
value for Cmax
n(n-1)n-1n
Cmax -1) exp(1-n) for n > 5 (15)
A simpler technique uses the value of max
A simpler technique uses the value of Omax

n 1 (16)
1- lmax
The dispersion number is related to the number of
tanks as
E 1 (17)
uh 2n

Differential Model with Dispersion
King131 discusses a differential model which in-
cludes dispersion effects for a stripping column in
counter-current flow. A simplified version of this
model for absorption is developed here. The current
experimental apparatus limits the study of disper-
sion effects to the liquid phase. Thus, the experi-
ments are designed so that dispersion in the gas
phase is unimportant. This is accomplished by using
100% CO2 in the gas phase for absorption experi-
ments. Thus, the mole fraction of CO2 in the gas
phases remains constant for our experimental de-
sign. An idealized picture of the flow conditions in a
counter-current gas-liquid absorption column is shown
in Figure 1.
A shell balance around a differential element of
the column gives the transport equation for the liquid
phase as

LCL +EACL d +K aA(xe-x)=0 (18)
dz dz2 L

where L = volumetric liquid flow rate
KL = overall liquid phase mass transfer coefficient
a = effective interfacial area per unit volume
A = cross-sectional area of the column
CL = concentration of the liquid phase
x = mole fraction of the solute in the liquid stream
at position z
For the small mass transfer rates considered here, it
is assumed that G, L, CL, and KL are constant. The
subscript e indicates equilibrium conditions. If the
equilibrium relationship between the phases is lin-
ear (which is the case for our system of dilute CO2 in
water) then xe can be replaced by the equilibrium
relationship
y = mx (19)
The boundary conditions are discussed in Lo, et al.14]
At the liquid entrance, the net axial solute transport
away from the upper boundary is equated with the
solute feed into the boundary
LCLx, EAC = LCLX (20)

where the subscript f indicates feed conditions. Eq.
(20) can be written as

(x, -x) = A d
(xf ) I L dz

The same argument as above leads to a similar
condition at the liquid exit boundary

(x-x) =EA at z= (22)
L dz
The left- and right-hand sides of Eq. (22) are of
opposite sign. Thus, Eq. (22) is only valid for the case
where x = xo. This result is summarized as follows

dx
dz

at z= 0

The balance is made dimensionless as follows (not-
ing that, for the case considered here, xe is constant
since pure CO2 is absorbed)
dX + d2X NX 0 (24)
dw Pe dw2
where

X = xe x (25)
-z
w = (26)
h
Pe Lh uh (27)
EA E

N=KLahA (28)
LCL

The dimensionless boundary conditions are

dX_=0
dw

at w=0

Pe(Xf-X) = at w=l (30)
The Peclet number, defined in Eq. (27), is the inverse
of the dispersion number in Eq. (2). Note also that, as
Pe oo, the transport equation reduces to the plug-
flow equation.
Equation (24) is linear and homogeneous and can
be conveniently solved by the method of undeter-
mined coefficients. From inspection of Eq. (24), the

z=h

z=0

at z = h

GCGYh
T

LCxf
I$

dy )Cdx dx d2 x
d-z' LCL(x + d'~z AECL( d^z2
d2 Z
d~llz)I~ ;,),, -r

--T -
dz -- --> Ka (xe x)A dz
4$

-AECL d
Ldz

LIQUID PHASE

GAS PHASE

__________________________________ J

T 4
GCGyf LCLxO
Figure 1. Idealization of gas-liquid contacting in a
packed column.
Chemical Engineering Education

GCGy

LCLx

GC (Y

solution for X must be of the form
X = cie(dlw) + 2 e(d2w) (31)
where di are the roots of the characteristic equation

-Pe Pe2 + 4 PeN
d (32)
2
The integration constants, ci, are determined from
application of the boundary conditions. The result is

d2 Pe Xf (3
C= d2(Pe+dl)exp(dl)-dl(Pe+d2)exp(d2) (

dcPeXf (34)
C2 dl(Pe+d2)exp(d2)-d2(Pe+d) exp(d)

The experimental results are applied to this solu-
tion to predict the overall mass transfer coefficient
combined with the effective interfacial area per unit
volume, KLa. The effects of axial dispersion on the
overall mass transfer coefficient can be observed by
comparison with predictions from the solution to the
model for plug flow.

Plug Flow Model
In the case of plug flow, the second order term in
Eq. (24) is dropped. The resulting transport equation
can be integrated directly for dilute systems where
the driving force (xe x) is a linear function in x. The
solution is

N KahA (xo -x) (35)
LCL (xe x)1m

A = gas vent
B = tracer injection
syringe C
C = tracer injection tube B V
D = liquid distributor D
E = liquid inlet
conductivity probe F
F =computer '
G = electronic liquid flow
meter --------- --sj
H = gas mass flow meter
I = gas rotameter
J = C2 source
K = N2 source
L = liquid rotameter H
M = gas distributor M I
N = liquid exit T
conductivity probe N
O = exit liquid storage T K
Q = liquid feed reservoir
R = stripping column R
(not shown)
S = pyrometer
T = thermocouple
U = packed column
V = injection signal
switch

Figure 2. Packed-column apparatus used in tracer and
absorption experiments.
Winter 1993

where the log-mean driving force is defined as

(X. x)L (xe X)(
(x x)m ( x-x- f (36)
e (X) X)r

The subscripts 0 and f indicate the conditions at z = 0
and h, respectively. The details for the derivation of
Eq. (35) are found in Bennett and Myers.'51 The solu-
tion to the plug-flow model can also be obtained by
solving the general model for large values of Pe.
APPARATUS AND PROCEDURE
A diagram of the apparatus is shown in Figure 2.
The apparatus consists of two identical 4-inch inside
diameter glass columns packed with 4 feet of 1/2-inch
ceramic Intalox saddles. One column is used for gas-
absorption experiments and the other for stripping
operations. To conserve water, the columns are ar-
ranged so that water can circulate through both
columns simultaneously in the case of absorption
experiments. In the case of tracer experiments, water
is pumped from a 30-gallon plastic storage tank to the
top of the absorption column. The liquid feed is dis-
tributed evenly over the top of the packing and al-
lowed to flow through the packing. The exit stream is
collected in a separate 30-gallon holding tank. The
liquid flow rate is measured with a rotameter and
an electronic flow meter. The flow rate is controlled
by a valve that restricts liquid recirculation to the
pump. The lower limit on the liquid flow rate is
approximately two gallons per minute. Below this
limit we found that the packing did not completely
wet. The upper limit is set at approximately four
gallons per minute to avoid flooding. Custom conduc-
tivity probes by Microelectrodes are situated in the
liquid feed and exit streams just above and below
the packing to determine the inlet and exit liquid
concentrations. The conductivity probes are situated
so that a mixing-cup measurement is obtained at the
exit stream of the liquid phase. CO2 and N2 gas are
passed to the bottom of the packing through rotame-
ters and electronic mass flow meters. The gas flow
rates are controlled by needle valves. The tempera-
tures of the gas/liquid feed and exit streams are
measured with thermocouples. An IBM personal com-
puter is used to monitor the gas/liquid flow rates and
the liquid conductivities. The software Labtech Note-
book is used to collect and display the signals from
the column on the computer. The data are imported
directly to the spreadsheet program Lotus 123 for
manipulation and analysis.
The procedure for the gas absorption experiment
consists of setting the gas and liquid flow rates and
monitoring the liquid-phase conductivities until a
23

steady state is reached. The conductivity probes are
calibrated against aqueous CO2 solutions with known
concentrations by titration. Each student group car-
ries out its own calibration. The CO2 is fixed in
solution by adding excess NaOH, then precipitated
with BaC12. The excess NaOH is titrated with HC1.
Pure CO2 gas was used in the absorption column to
avoid gas-phase dispersion effects. The stripping col-
umn uses N2 gas.
In the case of tracer experiments, the conductivity
of the liquid is monitored to achieve a base line.
Approximately 1 ml of 5 M HC1 is injected through a
1/16-inch ID Teflon tube into the liquid feed just
before the liquid distributor at the top of the column.
The volume of the injection tube is approximately 1
ml. A rubber septum caps the end of the injection tube
in order to prevent tracer fluid from being forced back
out of the tube, and an electric switch is provided to
record the beginning and duration of the tracer injec-
tion period. It can be assumed that the initial pertur-
bation approaches an impulse or delta function if the
time period of the tracer injection is small relative to
the time span for the signal at the bottom of the
column. With the arrangement described here, we
found that it required approximately 0.25 seconds to
inject the tracer. This may be compared to mean
residence times greater than 20 seconds. The conduc-
tivity data of the liquid exit stream are collected until
the value of response returns to the base line. The
conductivity of HC1 was found to be a linear function
of concentration over the range of conditions for this
experiment. Therefore, it is unnecessary to calibrate
the conductivity probes for HC1 because the response
to the tracer is normalized for the total amount of
tracer injected.

ANALYSIS OF RESULTS
The analysis has two parts: calculation of the
dispersion coefficient, and calculation of the overall
liquid-phase mass transfer coefficient combined with
the effective interfacial area per unit volume. A com-
puter spreadsheet is used to convert the tracer-ex-
periment data to a usable form.
The RTDs from tracer experiments are used with
the dispersion model to obtain a dispersion number.
It must be assumed that the tracer injection is an
ideal impulse perturbation because the variance at
the top of the column cannot be obtained experimen-
tally from our arrangement. For either small or large
extents of dispersion, it is necessary to calculate the
variance of the RTD for the tracer at the liquid exit.
Initially, the baseline concentration signal is sub-
tracted from all the concentration data. The mean
residence time and variance are obtained from the

0
Figure 3. C curves from tracer experiments compared with the
small extent of dispersion model

0.5

0.0
0.0 0.5 1.0 1.5 2.0
0
Figure 4. Comparison of tanks-in-series and the small extent of
dispersion models for intermediate-to-large extent of dispersion.
3.0
o Dispersion
*Tanks-In-Series
o -- Eq 41
0
2.5

X 2.0

1.5
0

I ,,,.j,,,,I.,111.I ,,, I

1.5 2.0 2.5 3.0 3.5 4.0 4.5
L (gpm)
Figure 5 Experimental results for the dispersion number as a
function of L.
Chemical Engineering Education

I I I

discrete concentration vs time data according to the
following approximationsm1"
N
Q= CiAt (37)
i-i

C Ci (38)
Q
N
tu=- Xt. C At (39)

02 it CiAt- 2 (40)
i-i

where At is the time interval between sampling, and
N is the number of data pairs. Experimental C curves
are plotted in Figure 3 for three liquid flow rates.
Care must be taken when applying Eqs. (37) to (40) to
the experimental data. The final results may depend
on the choice of the last data point due to the scatter
in the measurements around the base line. When this
is difficult, Levenspiel21 suggests drawing a curve
through the data by hand and picking points at
uniform intervals from the curve.
The dispersion numbers were determined from
Eqs. (9), (12), or (13), depending on the extent of

TABLE 1
Comparison of KLa from Plug Flow and Dispersion Models
T = 24C; P = 1 atm; x = 0.00060;m G = 10 Lmin

K ( Ibmol
L Flow .)
Dispersion IPlug Flow

2.0 0.00012
3.0 0.00016
4.0 0.00017

I E/uh

0.027
0.022
0.016

243 2
340 3
414 4

34

0.00049
0.00049
0.00048

r ,,, I,, . ,,I,,,, I . . . ,, I,, ,
1.5 2.0 2.5 3.0 3.5
L (gal/min)
Figure 6. Comparison of KLa from plug flow and
models.
Winter 1993

dispersion. The criteria for determining the extent of
dispersion is based on the shape of the C curve. As
seen in Figure 3, there is little dispersion for liquid
flow rates of 3 and 4 gallons per minute. At 2 gallons
per minute, the shape of the C curve begins to deviate
from the symmetric Gaussian distribution of Eq. (8),
indicating a larger extent of dispersion. The TIS
model was found to fit the data better than the small
dispersion model at this low flow rate. Both models
are compared in Figure 4. A numerical solution ofEq.
(2) is necessary to obtain the dispersion model C
curve for large extents of dispersion. This is beyond
the scope of the present experiment.
In order to demonstrate the procedure, four tracer
experiments were performed at each of the three flow
rates above. The experimental results for the disper-
sion number from the dispersion and TIS models are
plotted in Figure 5. They indicate small-to-interme-
diate amounts of dispersion in the packed column.
For this limited range of operating conditions, the
results for the dispersion number from the dispersion
model can be correlated by a least-squares method to
Eq. (41)

E =0.038-0.0055L(gpm) (41)
uh
A similar correlation was found from the TIS re-
sults for the dispersion number. The dispersion num-
ber is a decreasing function of liquid flow rate. This
indicates that plug flow conditions are approached as
the liquid flow rate increases. This may be due to a
decrease of liquid stagnation in the packing at higher
flow rates.161

130 2.9 Dispersion numbers from Eq. (41) are used in the
105 2.2 differential model to predict KLa, assuming the tracer
measurements are valid under mass-transfer condi-
tions. This is probably a good assumption in this case
since a relatively small quantity of CO2 is absorbed.
The non-linear transport equation for the liquid phase,
A Eq. (31), is readily solved for KLa by application of
Newton's method with a computer. The solution
method requires guessing values for KLa until the
calculated exit conditions match the experimental
results for the liquid-phase exit concentration. The
experimental data and results are listed in Table 1
and the calculations for KLa are compared with the
plug-flow case in Figure 6. The largest deviation from
the plug-flow model was found to be approximately
4%. It is important to note that dispersion in the
liquid phase has a negative effect on gas absorption.
4.0 4.5 This is demonstrated here by the difference in magni-
tude of KLa for each case. KLa for the dispersion model
dispersion must be larger to achieve the same separation as the
plug-flow model.

Dispersion
So Plug Flow

I

%
Deviation

I ' ' i

DISCUSSION
The results from the analysis reveal that, for our
absorption column, dispersion effects are small over
the range of operating conditions reported. Thus, the
plug-flow assumption is valid in this case, and the
analysis of the mass transfer coefficient is simple.
Often, simplifying assumptions are presented with-
out justification. This new experiment provides stu-
dents with the opportunity to verify the assumptions
that are used to derive the well-known result for the
mass transfer coefficient in a packed column. In this
paper we chose to present the differential model as
the one most closely representing the physical char-
acteristics of the flow pattern through the packing.
The students are not limited, however, to this model
to explain deviations from plug flow. Levenspiel,1[j
Lo, et al., 1 and King'31 describe several models used
for this purpose. For small-to-intermediate extents of
dispersion, a tanks-in-series model with back flow is
commonly employed. Other models use recirculation,
back mixing, dead volumes, and combinations of these
in conjunction with the tanks-in-series model. These
models are much more cumbersome, and we found
the dispersion and the tanks-in-series models ad-
equate for our purposes.
The apparatus described here was designed at
UCSB and was constructed by an off-campus contrac-
tor at a cost of $12,000. The electronic instrumenta-
tion was an additional $6,000. The apparatus is used
in each of our required two-quarter sequence courses
in Chemical Engineering Laboratory. In the first-
quarter course, steady-state data are taken to deter-
mine mass transfer coefficients, and in the second
quarter the axial dispersion measurements described
here are carried out.
ACKNOWLEDGEMENT
The authors benefitted from many enlightening
discussions with Professor R.G. Rinker regarding the
modeling of dispersion. This work was sponsored by a
Teaching Assistant Instructional Grant funded by
the UCSB Instructional Improvement Program.
NOMENCLATURE
a = interfacial area per unit volume, ft1
A = cross-sectional area of empty column, ft2
c = integration constants, Eqs. (33) and (34)
C = concentration, lbmol-ft3
C = normalized concentration, s 1
d. = roots to characteristic equation, Eq. (32)
E = dispersion coefficient, ft2-s-1
G = volumetric gas flow rate, ft3-hr-
h = column height, ft
KL = liquid phase overall mass transfer coefficient,
lbmol.ft 2.s-
L = volumetric liquid flow rate, ft3hr1

m = equilibrium coefficient
N = dimensionless group, Eq. (28), or number of
data pairs
n = number of tanks in tanks-in-series model
P = pressure of the gas phase, atm
Pe = Peclet number, Eq. (27)
Q = total tracer response integrated over all time
t = time, s
u = linear velocity of the liquid, ft-hr-1
w = dimensionless length, z/h
X = x-x
x = mole fraction of solute in the liquid phase
y = mole fraction of solute in the gas phase
z = axial coordinate, ft
* Greek Symbols
a = standard deviation
0 = dimensionless time
T = mean residence time, s
* Subscripts
e = equilibrium condition
f = feed condition
h = top of column
G = gas phase
L = liquid phase
Im = log mean driving force, Eq. (36)
0 = bottom of column
REFERENCES
1. Levenspiel, O., Chemical Reaction Engineering, John Wiley &
Sons, New York, pp 253-304 (1972)
2. Levenspiel, O., The Chemical Reactor Omnibook, Oregon State
University Bookstores, Inc., Corvallis, OR, Ch. 64-66 (1979)
3. King, C.J., Separation Processes, McGraw-Hill, New York, pp
570-573 (1980)
4. Lo, T.C., M.H. Baird, and C. Hanson, eds., Handbook of
Solvent Extraction, John Wiley & Sons, New York, pp 201-203
(1983)
5. Bennett, C.O., and J.E. Myers, Momentum, Heat and Mass
Transfer, McGraw-Hill, New York, pp 541-545 (1982)
6. Van Swaaij, W.P.M., J.C. Charpentier, and J. Villermaux,
"Residence Time Distribution in the Liquid Phase of Trickle
Flow in Packed Columns," Chem. Eng. Sci., 24, 1083 (1969)
7. Henley, E.J., and J.D. Seader, Equilibrium-Stage Separation
Operations in Chemical Engineering, John Wiley & Sons, New
York, 124 (1981) 0

book review

SEPARATIONS IN CHEMICAL
ENGINEERING: EQUILIBRIUM
STAGED OPERATIONS
by Phillip C. Wankat; Prentice Hall Publishing Co., 113
Silvan Ave., Englewood Cliffs, NJ07632; 707pages, $47.50
(1988) (Formerly published by Elsevier Publishing Co.)
Reviewed by
Roseanne M. Ford
University of Virginia
Engineering analysis and design of the classical
separation methods of distillation, absorption, and
Chemical Engineering Education

liquid-liquid extraction are covered in depth by
Wankat's Separations in Chemical Engineering:Equi-
librium Staged Operations.
This text has some excellent pedagogical qualities.
It is easy to read, has clear detailed descriptions, and
follows a logical progression which gradually builds
on previous concepts. The development of problem-
solving skills is emphasized throughout the text us-
ing a systematic approach (a modification of the
strategy developed at McMaster University*) which
follows six steps: 1) define the problem; 2) explore or
think about it; 3) plan; 4) do it; 5) check; and 6)
generalize. To reinforce the utility of this method, the
example problems in the text are worked according to
this procedure. This text would be very suitable for
self-study. The level of sophistication is appropriate
for sophomores, but may not appeal to senior-level
students. A knowledge of calculus, material and en-
ergy balances, and phase equilibria is recommended.
Mass transfer concepts are introduced only in Chap-
ter 19 within the context of packed tower design.
Many problems are provided at the end of each
chapter, some of which involve writing computer
programs. They are divided into several categories:
Discussion Problems, Generation of Alternatives,
Derivations, Problems, More Complex Problems, Prob-
lems Requiring Other Resources, and Open-Ended
and Synthesis Problems (a solution manual is avail-
able). A practical discussion of equipment design
which includes correlations and heuristics is enhanced
by some well-chosen photographs. However, the book
lacks an Appendix containing the usual data tables
necessary to make it a useful reference for design.
The text is comprised of nineteen chapters, the
first fourteen of which are devoted to distillation.
Chapter 1 defined an equilibrium stage process and a
unit operation, and introduces the approach to prob-
lem solving. Vapor-liquid equilibria are reviewed in
Chapter 2, including the conventional xy, Txy, and
Hxy graphical representations followed by dew point
and bubble point calculations.
Rigorous calculations for flash distillation are pre-
sented in Chapter 3 for binary and multicomponent
systems necessary for sizing the flash drum. Column
distillation is initially introduced as a cascade of
flash vaporizations in Chapter 4. Photographs of
actual equipment convey a sense of the size and scale
of a distillation tower. Possible flow regimes within
the tower and their effect on the efficiency of separa-
tion are described. The concept of external material
and energy balances is also introduced in Chapter 4.
Internal, stage-to-stage calculations are presented

* Woods, et al., Eng. Ed., 66, 238 (1975)
Winter 1993

POSITIONS AVAILABLE
Use CEE's reasonable rates to advertise.
Minimum rate, 1/8 page, $100;
Each additional column inch or portion thereof, $40.

UNIVERSITY OF COLORADO AT BOULDER
Department of Chemical Engineering
Applications are sought for a tenure-track faculty position from
candidates with strong backgrounds and interests in biotechnology.
Duties include undergraduate and graduate teaching of chemical engi-
neering courses, establishing and conducting a funded biotechnology
research program, and service. The appointment may begin August
1993, or later
The Chemical Engineering Department at the University of Colo-
rado has 14 faculty, 60 graduate students, and 250 undergraduate
students. Department faculty and students in biotechnology cooperate in
research and training with the highly regarded Departments of Chemis-
try and Biochemistry and Molecular, Cellular and Developmental Biol-
ogy, and with a strong local biotechnology industry. Excellent facilities
are available.
Applicants should send a resume, descriptions of research and teach-
ing interests, and the names and addresses of three references to Profes-
sor Robert Davis, Department of Chemical Engineering, University of
Colorado, Boulder, CO 80309-0424. The Search Committee will con-
sider all applications received by February 23, 1993; later applications
will be considered until the position is filled.
The University of Colorado at Boulder has a strong institutional
commitment to the principle of diversity in all areas. In that spirit, we are
particularly interested in receiving applications from a broad spectrum
of people, including women, members of ethnic minorities, and disabled
individuals. 1

WAYNE STATE UNIVERSITY
Department of Chemical Engineering
The Department of Chemical Engineering invites applications for an
anticipated tenure track faculty position. Rank and salary commensurate
with credentials. Qualifications include PhD in Chemical Engineering,
a commitment to undergraduate and graduate teaching, and potential for
developing an externally funded research program that would lead to
national recognition. All research areas will be considered, but prefer-
ence will be given to candidates working in either environmental or
materials research. Substantial funding may be available for start-up.
Preferred starting date is September 1993. Please send resume, a state-
ment of teaching and research interest, and names of three references to
Prof. Ralph H. Kummler, Chair, Department of Chemical Engineering,
Wayne State University, Detroit, MI48202. WSU is an Equal Opportu-
nity Affirmative Action Employer and encourages qualified women and
minorities to apply. O

in Chapter 5, according to the Lewis method, which
assumes constant molal overflow. Chapter 6 covers
the McCabe-Thiele graphical analysis, including
many variations on the theme such as open steam,
partial condensers, total reboilers, side streams, and
intermediate reboilers and condensers. Limiting con-
ditions, efficiencies, subcooled reflux, and superheated
boil-up are also discussed.
Building upon this knowledge of binary systems,
multicomponent distillation is described in the next
Continued on page 59.

Random Thoughts...

WHAT DO THEY KNOW, ANYWAY

2. Making Evaluations Effective

RICHARD M. FIELDER
North Carolina State University
Raleigh, NC 27695
wo columns agoll I tried to persuade you that
contrary to conventional faculty lounge wis-
dom, student evaluations provide reliable in-
dicators of teaching quality: they correlate well with
retrospective evaluations submitted by alumni and
graduating seniors and tend to be higher for instruc-
tors whose students do best on common examina-
tions. The question is not whether the evaluations
mean anything-they clearly mean a lot-but how
they should be structured to do the most good.
Following are some ideas for constructing, admin-
istering, and interpreting evaluations, starting with
the simplest forms and proceeding to methods that
take more work to implement but are more likely to
improve teaching quality. For more suggestions and
summaries of research on teaching evaluation, see
Reference 2.

* Collect overall course-end ratings of in-
struction.
Rate the instruction you received in this course on
a scale from 1 to 5, with 5 being the highest
response.
Ratings of this sort are most effective when
the numbers on the response scale are clearly
defined. Definitions like "excellent," "above
average," "fair," etc., don't do it; these terms
are ambiguous and when they are used a
very broad performance range tends to be lumped
into "above average." You can get greater dis-
crimination with a variation of the following
instruction:
When responding, use as a basis of comparison
all of your previous high school and college teach-
ers. A response of 5 denotes one of the three or
four best you've ever had; 4 = top 25%; 3 = 40-
75%; 2 = bottom 40%; and 1 = one of the three or
four worst you have ever had.

Richard M. Felder is Hoechst Celanese Pro-
fessor of Chemical Engineering at North Caro-
lina State University. He received his BChE
from City College of CUNY and his PhD from
Princeton. He has presented courses on chemi-
cal engineering principles, reactor design, pro-
cess optimization, and effective teaching to vari-
ous American and foreign industries and insti-
tutions. He is coauthor of the text Elementary
Principles of Chemical Processes (Wiley, 1986).

An instructor whose average rating is close to 5
on this scale is clearly doing a superb job and
deserves nomination for an outstanding teacher
award, and serious problems obviously exist if
an instructor's rating is consistently close to 1.
Ratings close to 4 indicate commendable teach-
ing performance and ratings close to 2 suggest
the need for corrective measures.

* Collect ratings of individual aspects of
instruction.
To get the most out of a course-end evalua-
tion, supplement the overall rating with ratings
of specific aspects of teaching performance, such
as clearly stating expectations, providing fre-
quent examples, repeating difficult ideas, point-
ing out practical applications, answering ques-
tions thoroughly, preparing tests that reflect
course content and emphasis, etc. (General ques-
tions about the instructor's preparedness and
knowledge of the subject tend to be less useful.)
The responses help identify areas of weakness
and may provide ideas about how to improve
teaching in the next course.
To be sure that the evaluations reflect a true
cross-section of student opinion, administer and
collect them in a single class session rather than
counting on students to return them later. Re-
sults of evaluations for which the return rate is
less than a minimal percentage should be re-
Copyright ChE Division ofASEE 1993
Chemical Engineering Education

garded with deep suspicion: the recommended
minimum is 50% (classes of 100 or more), 66%
(50-100), 75% (20-50), and 80% (<20).[2 p.891

* Collect evaluations midway through a
course rather than waiting until the end.
If the goal is to correct teaching problems and
not just to identify them, find out what the
problems are while enough time remains to do
something about them. Ask open-ended ques-
tions on midcourse evaluations, leaving plenty
of space for the responses:
1. What do you like best about this course and/or
the instructor? (List up to three things.)
2. What do you like least about the course and/
or instructor? (List up to three things.)
3. If you were the instructor, what would you do
to improve the course?

* Collect evaluations from small groups
rather than from every student.
One problem with individual evaluations is
that many of the responses may reflect isolated
gripes rather than widely held opinions. An-
other is that students may be fearful of offering
negative criticism while a course is still in
progress, even if the evaluations are anony-
mous (as they should be). A good way to counter
both of these problems is to collect evaluations
from groups of four or five students rather than
from individuals. The students in a group should
spend 5-10 minutes discussing the three ques-
tions given above and then prepare a collective
evaluation that only includes points agreed upon
by several group members.

* Interview student representatives.
Designate certain students as representa-
tives of subgroups within the class. At one or
more times during the semester, meet (or ask a
colleague to meet) with the representatives to
share the concerns of their constituents and to
discuss possible measures to correct perceived
problems. This procedure tends to generate
constructive criticism at a level rarely attain-
ed through written evaluations and also
gives students a greater sense that their opin-
ions are valued.

* Use a variety of sources of feedback.
Collect retrospective teaching evaluations

from alumni and graduating seniors. Have fac-
ulty colleagues observe your teaching and pro-
vide feedback. Have one of your classes video-
taped and review the tape (brace yourself-you
may not be thrilled by everything you see).

* Work with an instructional consultant to
interpret student feedback and plan teach-
ing improvement strategies.
It is one thing to know that some students
consider you a poor lecturer or think your tests
are unfair and quite another to know what to do
about it. Many universities have instructional
consultants whose job is to help faculty mem-
bers improve their teaching. These people can
provide a variety of services, such as helping
design and administer evaluation question-
naires, interviewing classes or groups of
students about their perceptions of the in-
struction, observing and critiquing live or
videotaped lectures, and working with instruc-
tors to help interpret evaluations and plan
corrective strategies. If no one like this is avail-
able on your campus, ask a faculty colleague
with a reputation as an outstanding teacher to
work with you.

Can properly interpreted student feedback im-
prove teaching? The research suggests that it does. In
one study, instructors who received no feedback in
the first half of a course received average end-of-term
ratings in the 50th percentile of the population stud-
ied; instructors who received feedback scored in
the 58th percentile; and instructors who got both
feedback and instructional consultation scored
in the 74th percentile.3'1 While midcourse evalua-
tions are not guaranteed to improve course-end
ratings and the teaching they reflect by that much,
.they are bound to have positive effects. A university,
school, or department seeking to raise the level of its
teaching program (e.g., as part of a TQM initiative)
might well consider instituting midcourse evalua-
tions and providing instructional consultation as a
strong first step.
REFERENCES
1. Felder, R.M., "What Do They Know, Anyway?" Chem. Eng.
Ed., 26, 134 (1992)
2. Theall, M., and J. Franklin, Eds., Effective Practices for
Improving Teaching, New Directions for Teaching and Learn-
ing No. 48, San Francisco, Jossey-Bass (1991)
3. Cohen, P.A., "Effectiveness of Student-Rating Feedback for
Improving College Instruction: A Meta-Analysis of Find-
ings," Res. in Higher Ed., 13, 321 (1980) O

Winter 1993

[m classroom

THE OTHER THREE Rs

Rehearsal, Recitation, and ARument

DAVID F. OLLIS
North Carolina State University
Raleigh, NC 27695-7905

Public speaking for undergraduates is rarely
mentioned in engineering curriculum lists or
discussions, yet the importance of clear and
concise communication and presentation has prob-
ably never been greater. To address this need, some
departments offer a one-term, one-unit oral presen-
tation class to give students an opportunity for train-
ing in the presentation of technical papers. (A sum-
mary of our NCSU senior seminar course was re-
cently published by Richard Felder.111)
The variety of circumstances where public speak-
ing may be expected of our engineering graduates is
considerable, ranging from short to long technical
talks in conference or corporate meetings to partici-
pation on multipartisan panels in public meetings,
and, even possibly, to the twenty-second to one-minute
"sound bite" responses so common in televised or
video-recorded conversations and interviews. In or-
der to address this variety, as well as the controver-
sial character and debate style implicit in some of the
settings, the student must be challenged with a se-
ries of presentation opportunities, each in a distinctly
different format.
Assuming that such a variety of presentations
may provide both substance and spice, a one-semes-
ter senior course of one unit value has been given by
the author with modest success. This paper summa-
rizes the course content and its rationale and offers
some reflections of both the students and the profes-

David F. Ollis is Distinguished Professor of
Engineering at NCSU. He received his BS from
Caltech, his MS from Northwestern, and his
PhD from Stanford. He has worked at Texaco
Process Research Laboratories and has pre-
sented or co-presented courses on chemical
reactor design, biochemical engineering, and
bioseparations. He is a coauthor of Biochemi-
V cal Engineering Fundamentals (McGraw-Hill,
1986) and co-translator of Photochemical Tech-
nology (Wiley Interscience, 1991).

sor. Each class section has 6-8 students, with the
senior class divided among as many faculty as are
required. This group size works well for one-hour-
per-week meetings on each of the presentation for-
mats discussed below.
Student speakers customarily use overhead trans-
parencies, which are easily prepared and can be
enhanced by color at minimal cost and effort. Trans-
parencies also fit well into late planning and reor-
ganization of talks. The usual short litany of guide-
lines for overheads is given to the students at the
outset: write legibly in large print, use only key
words and phrases, use no more than one transpar-
ency every two minutes of allotted time, etc.
Audience attention and participation is achieved
through a simple but effective requirement: at the
end of the presentation, each audience member must
ask a question of the speaker. This question/response
mode is usually a bit artificial and stiff for the first
one or two speakers, but the students soon begin
posing substantive questions after each talk. The
logic behind the demand for questions is simple:
students learn more from a presentation when they
are obligatory participants rather than mere observ-
ers-and the speaker enjoys the pleasure (or agony)
of an attentive and responsive audience. After every
presentation, I never ask questions, but I do provide
each student with a written set of brief comments,
including such items as extent of audience engage-
ment, voice clarity, logic of organization, and quality
and content of transparencies.
The presentation formats required of each stu-
dent are
informal brief (any topic)
technical process description
controversial topic (technical and/or non-technical)
town meeting
recitation (poem)
The purpose and form of these topics are as fol-
low:

Copyright ChE Division ofASEE 1993

Chemical Engineering Education

Informal Brief (1 period of 6-8 speakers) The
student must present a five-minute talk, with or
without transparencies or model, etc., on any topic of
personal interest. The informal mode (no fixed pre-
sentation style) is a nice way to begin the semester
and to have the students learn a bit about each other.
It also provides the faculty member with a survey of
the student's speaking talents. Speaker interest is
normally high since the student can choose a topic for
which he or she has considerable involvement and
knowledge. Topics usually include "last summer's
job" and "my favorite hobby," occasionally spiced by a
presentation of "my favorite pet" (a ferret once as-
sisted!), a campaign statement (pro-choice or pro-
life), or a comment on biological evolution (all sides).
Technical Presentation (2 periods of 3-4 speak-
ers each) The student must summarize a technical
production process, including its historical develop-
ment, current process flow diagrams, product uses,
and prospects for the future. This is the only "straight-
arrow" presentation of the semester. Each student
chooses the process to be summarized and prepares
all transparencies. I insist that there must be conti-
nuity in both the visual and oral presentations: the
entire talk should appear logical to an audience mem-
ber who can only see or only hear.
Controversial Topic (2 weeks for reading and
preparation followed by two weeks for 3-4 presenta-
tions per allotted hour) In the old high school debate
classes of the 1950s (long since abandoned), contro-
versy and argument were center stage. A student
had to prepare for both sides of a given question,
since the point-of-view to be defended or attacked
was unknown until just prior to the debate session.
One motivation for this procedure was to test the
speaker's knowledge of the subject from all sides.
To prepare for our class presentations, an assort-
ment of books (dealing with controversial but often
technical topics) is offered to the students, who are
then asked to pick one, read it, and present a two-
part summary to the class. The first part of the
summary (approximately ten minutes) should out-
line the issue and the author's arguments and con-
clusions, following the author's version and words
as closely as possible. The second part (a brief three-
minute presentation) should be the student's cri-
tique of the author's approach, using the student's
own words. The idea is to make the student present,
clearly and distinctly, both the views of others and
his or her own. Some students, perhaps numbed by
the problem/solution/textbook approach which char-
acterizes so much of our curriculum, appear reluc-
tant to present a controversial subject in a public
Winter 1993

I am always uncertain of the students'
attitudes toward this assignment. The challenge
is clearly one of presenting the author's view in
only his or her own words-a situation
foreign to the analyst/engineer.
forum. This method presents an opportunity to re-
verse that feeling. Some of the books we have used
include Kennan's The Nuclear Delusion, Fallow's
National Defense, Djerassi's Politics of Contracep-
tion, Ray's Trashing the Planet, Petroski's To Engi-
neer is Human, Carson's Silent Spring, Meadow's
Limits to Growth, Wade's The Ultimate Experiment,
and Florman's Existential Pleasures of Engineering.
These books are well-written and take strong posi-
tions. Most students find clear areas of agreement or
disagreement with each author.
Town Meeting (1 week) "Resolved: that the State
of North Carolina (Wake County, or City of Raleigh,
as you prefer) will site, construct, and operate a
hazardous waste incinerator." The students divide
into three groups of two, representing industry, local
government, and concerned citizens. The stances of
these groups are naturally for, ambiguous about,
and against the proposition, respectively. I usually
choose a seventh, strong student to act as mediator.
To set the stage at the "meeting," one student
briefly introduces the RCRA and TSCA statutes
which motivate the development of such a resolu-
tion. Then one student in each group gives a parti-
san position summary (no questions; five minutes
each for three presentations). A subsequent fifteen-
minute pause allows each group to frame its
rebuttal (blank transparencies and marking pens
are provided). Following the presentation of re-
buttals (two-minute maximum), I (representing the
public at large) charge the mediator and the three
groups to negotiate in good faith; then I leave the
room for ten minutes.
Upon my return, the mediator presents any con-
sensus position that has been developed. This is
done most easily by indicating what each group will
"win" from the outcome and how each group's pri-
mary concern will be addressed by the others. The
challenge to the students is, "If you, as a collection of
technically educated students, cannot reach any plau-
sible and acceptable ground on this issue, how can
you expect society at large to do any better?" The
students usually see that seeking a win-win-win
result works and that such an outcome should leave
future relationships in far better shape than any do-
or-die proposition which is too rigidly promoted.
Recitation (1 week) The easiest manner to test
31

whether a student knows exactly what to say is to
hear a brief (approximately one minute) recitation of
a poem. This recitation also provides the ultimate
example of the claim that, with care and proper
editing, any story or report can be fully presented in
a very short period of time. It also helps the student
see that poetry is successful because of its brevity
and the ease with which the listener's mind con-
structs a full image from a few words. Who would
not agree with such a characterization for Blake's
Tiger, tiger, burning bright,
in the forest of the night.
The use of images already familiar to a technical
audience is also clearly a way to maximize impact
and minimize delivery time.
Even with Blake and another example or two to
lighten up the prospect of the following week's poem
presentations, I am always uncertain of the students'
attitudes toward this assignment. The challenge is
clearly one of presenting the author's view in only his
or her own words-a situation foreign to the analyst/
engineer. Not surprisingly, most students fail to re-
hearse sufficiently to present an unhesitant, logically
continual delivery. A bright spot is that nearly all
students have favorite poems. My first year's group
caught me off guard: half the class recited interesting
poems which they had written in high school (not
college) English!
Perhaps we should try the same approach with
graduate students. Would not our somnolent AIChE
and ACS meetings profit by an occasional poetic
rendering? As an example, a graduate student might
recite Fame's Penny-Trumpet (Lewis Carroll, 1869)
with a prelude that is still relevant for the 1990s:
"Affectionately dedicated to all 'original researchers'
who 'pant' for endowment." For a partisan view, we
could hardly do better than the closing stanzas:
Deck your dull talk with pilfered shreds
of learning from a nobler time,
And oil each other's little heads
With mutual Flattery's golden slime:
And when the topmost height ye gain,
And stand in Glory's ether clear,
And grasp the prize of all your pain -
So many hundred pounds a year -
Then let Fame's banner be unfurled!
Sing Paeans for a victory won!
Ye tapers, that would light the worlds,
And cast a shadow on the Sun -
Who still shall pour His ray sublime,
One crystal flood, from East to West,
When ye have burned your little time
And flickered feebly into rest!

Doubtless, the now-attentive audience would offer
other views.

FEEDBACK
"We learn by doing" seems to characterize most
student evaluations; while each general assignment
seemed plausible at the outset, the students usually
saw the presentation possibilities and purpose much
more clearly in retrospect.
What else to add? A semester of these round-
robin presentations has several times led to enough
group coherence that a student skit was suggested,
as was the inevitable roast of the professor. In defer-
ence to pending exams, these suggestions were tabled.
Clearly, I underestimated the theatrical interests
of the students. Their enthusiasm for additional
opportunities suggested that they may have come
to look forward to oral presentations. On the next
round, we will try the skit (memorize your own
words), after the poems.
REFERENCES
1. Felder, R. M., "A Course on Presenting Technical Talks,"
Chem. Eng. Ed., 22, 84 (1988) O

book review

PROCESS DYNAMICS & CONTROL
by Dale E. Seborg, Thomas F. Edgar, and Duncan A.
Mellichamp
John Wiley & Sons, New York (1989)
Reviewed by
Jeffrey C. Kantor
University of Notre Dame
Notre Dame, IN 46556
Process control has been continuously evolving
since its introduction in the chemical engineering
curriculum during the late 1950s and early 1960s.
Since then, each decade has been marked by a new
textbook with significant market share. The 1965
book by Coughanowr and Koppel was perhaps the
first of these. The market for this book was later split
by the appearance of Luyben's book in 1973 and then
largely supplanted in 1984 by Stephanopoulos.* The
recent textbook by Seborg, Edgar, and Mellichamp

* By citing these, I don't mean to diminish the significant contri-
butions of many others, including P. Buckley, N. Ceaglske, D.
Eckman, P. Harriott, E. Johnson, D. Perlmutter, W. H. Ray, and
T. Williams. These people and others wrote useful books that,
for whatever reason, did not achieve broad acceptance as under-
graduate course texts.
Chemical Engineering Education

being reviewed here is clearly a successor to this list.
A Synopsis This is a long and detailed book
consisting of seven parts totaling 717 pages. The
short first part describes motivations for process
control, introduces block diagrams as a conceptual
way to diagram the flow of information, and reviews
aspects of process modeling. While there is a good bit
of material here, one or two lectures should be enough
for students familiar with dynamical modeling from
their other coursework. The main point is that mod-
eling for control purposes is different than modeling
for process design or optimization. A different audi-
ence might spend more time reviewing this material
at a more detailed level.
Part 2 of the book focuses on the transient behav-
ior of linear system models. This is the part that
contains the traditional detailed treatment of Laplace
transforms, transfer functions, and the linearization
of process models given as differential equations.
This treatment does not reach for any high level of
mathematical rigor, but it does include a rather com-
plete discussion of how to execute the algebra for
computing transforms and expanding by partial frac-
tions. My students say that the discussion regarding
linearization about an operating point is very helpful.
Overall, these chapters are satisfactory from the
point of view of the usual treatment of Laplace trans-
forms. However, a course less mired in tradition
could deemphasize the detail to focus more on the
essential concepts of poles, zeros, and their qualita-
tive effects on transient behavior.
Part 3 turns attention to the ideas of linear feed-
back control. Chapters 8 and 9 spend some time
discussing practical issues of instrumentation and
PID implementation. Subsequent chapters provide a
conventional Laplace domain analysis of closed-loop
stability, including the Routh condition, root locus,
and some direct synthesis techniques. Relative to
other books, an important addition in this text is the
discussion of internal model control (IMC) in Chapter
12 and a comparison of IMC-inspired tuning rules
with more traditional techniques such as Zigler-
Nichols and Cohen-Coon. Chapter 13 is a nuts-and-
bolts chapter that covers much of what is needed to
tune and troubleshoot an existing control loop. This
part contains very applicable material, even though
the theoretical connections between time and fre-
quency domain analysis are not well elucidated.
Part 4 focuses on the frequency domain interpreta-
tion of the Laplace transform, with particular atten-
tion on the Bode plot, stability margins, and fre-
quency domain identification. In my experience, stu-
dents find this treatment repetitious of Part 3, and it
Winter 1993

is not clear to them what practical advantage is
gained. An instructor might wish to give an inte-
grated presentation of the topics of Parts 3 and 4.
In particular, I like to use the IMC framework as
a starting point for the quantitative analysis of
model uncertainty and its effects on closed-loop per-
formance. Moreover, some of the advanced control
techniques like time-delay compensation and predic-
tion are much better treated from the IMC view-
point. This approach, however, requires some supple-
mentary materials.
Advanced control techniques are covered in Part 5.
This includes a solid introductory treatment of
multi-loop methods for feedforward design, relative
gain array, and decoupling. Other important topics
are discussed in a cursory way, including adaptive
control, statistical quality control, and optimiza-
tion. Also mentioned are expert systems, batch pro-
cesses, and ladder logic. This is one of the few
texts to even attempt to include some of this
material, but at the level given, it would be dif-
ficult for instructors to build these topics into their
courses in a detailed form.
Part 6 is an extensive, self-contained 170-page
discussion of digital control techniques. On the posi-
tive side, a course emphasizing digital techniques
could use this material as an alternative to Part 3. In
a more balanced course, however, there is again a
problem of duplication and repetitiousness. For ex-
ample, some implementation details for PID control
are described here for the third time in the book.
Part 7 concludes the book with an overview of
developing control strategies for processing systems
with examples. This is an ambitious goal, and it is
certainly material that can bring a course to a solid
conclusion, but there are only 27 pages devoted to it.
The book contains a substantial number of end-of-
chapter problems. My students have found these well
designed for the most part. The wide selection of
problems makes it possible to give out different prob-
lem sets each year, which is one way to beat the
dormitory filing systems.
Commentary It is clear that this is an ambitious
book containing a large amount of information-
clearly too much to be covered in a single under-
graduate course. The Preface makes clear that this
was by design and suggests that the book be read in
a "modular" fashion. Segments on the frequency do-
main and digital control, for example, could be omit-
ted or included at the instructor's discretion.
My own feeling is that this sound practical goal
Continued on page 64.

laboratory

SOLID PHASE

EXTRACTION COLUMNS

A Tool for Teaching Biochromatography

POLLY S. ROBINSON-PIERGIOVANNI,
LAURA J. CRANE,* DAVID R. NAU*
Lafayette College
Easton, PA 18042
Biochromatography is difficult to teach to un-
dergraduate students because it requires
knowledge of molecular interactions not often
covered in a typical undergraduate curriculum. But
with up to sixty percent of the total protein manufac-
turing cost directly related to the purification pro-
cess, a basic knowledge ofbiochromatography and its
inherent efficiencies is an essential part of the bio-
chemical engineer's education. Class lectures on the
subject attempt to explain and diagram column dy-
namics, but hands-on experience will help the stu-
dents grasp the concepts and remember them far
longer. Thus, we have developed two laboratory ex-
periments for protein chromatography.
The experiments were designed to require mini-
mal and inexpensive equipment and to be performed
within a two-hour laboratory period. The students
were each given three 1 ml Bakerbond speTM col-
umns cationicc, anionic, and hydrophobic interac-
tion), a size-exclusion column, and an unknown
protein or mixture of proteins. Based on the
binding and elution properties of the proteins and
the known physicochemical properties of several pos-
sible protein candidates (pI and relative hydropho-
bicity), the students were asked to determine which
protein(s) were present. Colored proteins were cho-
sen as the unknowns so that no special detection
equipment was required.
THEORY
A mixture of proteins can be separated with the
use of chromatographic techniques based on the ten-
Address:
J.T. Baker Inc., 222 Red School Lane
Phillipsburg, NJ 08865

Polly Robinson-Plergiovanni is Metzgar Assistant Professor of Chemi-
cal Engineering at Lafayette College in Easton, Pennsylvania. She
received her BS in chemical engineering from Kansas State University
and her PhD from the University of Houston. Her research and teaching
interests include biochemical engineering, specifically scale-up of ani-
mal cell cultures, and dynamic process control.
Laura Crane, Director of Laboratory Products Research at J.T. Baker
Inc., received a BS in chemistry from Carnegie-Mellon University, a MA
in chemistry from Harvard University, and a PhD in biochemistry from
Rutgers University.
David Nau, Scientist at J.T. Baker Inc., in Research and Product
Development for chromatography products, received a BA in biology
from Gettysburg College, a BS in chemistry from Rutgers University,
and a PhD in biochemistry from Rutgers University.

dency of the various proteins to adsorb to the column
packing. In ion-exchange chromatography, adsorp-
tion of proteins depends on the proteins' isoelectric
point relative to the column pH. Proteins with a high
isoelectric point will bind tightly to a cation exchange
column in the presence of a low pH and a low salt
concentration. Proteins with a low isoelectric point
will bind tightly to an anion exchange column in the
presence of a high pH and a low salt concentration.
Hydrophobic interaction chromatography uses
a high salt concentration to induce an interaction
between hydrophobic regions of a protein and a
weakly hydrophobic column packing. In all three
cases, elution of the bound proteins can be achieved
using a salt gradient.
Another type of chromatography, size-exclusion
chromatography, separates molecules based on their
relative size. The column is filled with a packing with
a specific pore size distribution. Smaller molecules
enter the pores and linger inside them, while larger
molecules, which cannot fit into the pores, pass more
rapidly through the column.
Bakerbond spe Wide-Pore columns are small (12 x
65 mm) reusable polypropylene tubes (6 ml total

Copyright ChE Division ofASEE 1993
Chemical Engineering Education

In their laboratory reports, the students showed that they recognized that the Gaussian distribution
of the pore size for size-exclusion chromatography has an effect on the column resolution, and they
noted that protein shape could also have an effect. Several students took their observations one
step further and applied them to separation problems that might be encountered in industry.

volume) which contain 500 mg
(1.5 ml) of 40-mm silica-based TA
stationary phases. These inex- Matl
pensive columns are designed to .
be used for sample preparation
prior to conventional open col- Bovine serum albumin
umn chromatography or high- a-Chymotrypsin
performance liquid chromatogra- a-Chymotrypsinogen
phy (HPLC), and can also be used
Conalbumin
to determine the physicochemi- Con m
cal properties of a particular "tar- Cytochrome C
get" protein as well as its reten- Ferritin
tion behavior on various chro- P-Glucosidase
matographic matrices. The avail- Hemoglobin
able stationary-phase surface Lactoperoxidase
chemistries include Bakerbond Lysozyme
Wide-Pore BUTYL (-C4, reversed- Myoglobin
phase matrix), Bakerbond Wide- Ovalbumin
Pore CBX (-COO, weak-cation Ribonuclease A
exchanger), Bakerbond Wide-
Pore PEI (-NH3', weak-anion ex- Dyes
changer), Bakerbond Wide- Phenol red
Pore HI-Propyl (-C3, hydro- Erioglaucine blue
phobic-interaction matrix),
and SephadexTM G-25 (size- ColumnPackings
exclusion matrix). Solid phase Sephadex G-10 (<0.7
extraction columns are available S G (
Sephadex G-50 (1.5 to
from other manufacturers, but S G-
Sephadex G-75 (3 to 7
have not been tested with these
experiments. Sephadex G-100 (4 to 1
Scale-up of chromatography Higher values are more
columns for protein separation **Estimated
and purification is an important
issue for biochemical engineers designing a process.
The purest product is obtained with a minimum band
width for each protein. Various forces influence the
band width, or zone spreading, such as longitudinal
diffusion, eddy diffusion, and the lack of a local equi-
librium at the front and rear of the band. These forces
can be modeled by assuming the molecules move
through the column according to the random-walk
theory (the molecules move in a series of random
stops and starts). A Gaussian distribution of the
molecules is also assumed, with o = 1-n, where n is
the number of random-walk steps and 1 is the step
length. The resulting model[1'2' is
2
H= = +A+Csu+C (1)
Winter 1993

where
02
H=L

represents the plate
height, used to express
the net effect of zone
spreading

BLE 1
erial Data14'
relative
MW (kDa) pl hydrophobicity*

69.0 5.1 20.5
21.6 8.6 16.6
25.0 9.2 18.1
77.0 6.3 6.3
12.2 9.4 0.6
500.0 4.3 20.8
130.3 7.3 15.6
64.0 7.0 1.1**
85.0 9.5 19.5
13.9 11.0 8.5
17.5 7.1 0.8
43.5 4.7 6.5
13.5 8.7 1.6

0.35
0.78

kDa)
30 kDa)
0 kDa)
50 kDa)

hydrophobic

the average width

R= tRB tRA (2)
0.5 (tWA + t)WB
where
tRB, tA = retention times of components A
and B
twA, twB = width of peak A and peak B

In column chromatography, peaks become broader
proportional to the square root of the column length,
but their separation increases in direct proportion to
the column length.[3] Thus the resolution is propor-
tional to the square root of the column length. This
means that to double the separation between two
35

S = longitudinal diffusion

A = eddy diffusion
C u = resistance to mass
transfer at the
solute-stationary
phase interface
Cmu = resistance to radial
mass transfer caused
by particles of the
packing material

The magnitude of each of
these effects is determined by
the velocity of the sample (u)
in the column. If the velocity is
too high, the mass transfer re-
sistances predominate and
there is more band spreading.
If the velocity is too low, the
longitudinal diffusion in-
creases the band width. There-
fore, there is an optimal sample
velocity for each mixture of pro-
teins.
The resolution of two peaks,
R, is defined as the distance
between the peaks divided by

bands, a column four times as long is required.
These scale-up concepts, when explained in a class
lecture, are not always intuitively obvious to the
undergraduate student. Varying these factors in a
laboratory exercise, however, allows the students to
observe the effects of the column length and sample
velocity on the degree of separation.

EXPERIMENT PROCEDURE

Each student is given molecular weight, is
point, and relative hydrophobicity data on
of proteins, and size data on two dyes as wel
types of Sephadex that will be used (see r
They are also given the necessary buffers (Ti
Bakerbond spe columns (WP PEI, WP HI-Pr
WP CBX), and a column for size-exclusion
tography. The students are to process the ui
through the various columns and determi
identity. The samples can be pulled
through the spe columns using a
vacuum system or forced through the
spe columns using compressed air. In
order to use the laboratory time effi-
ciently (to make sure the students have
thought about chromatography con-
cepts before lab time) the homework
assignment shown in Table 3 is given
the week before the experiments.

Chromatography Lab 1
Each student is given a single un-
known protein (chosen from the list in
Table 4) and a mixture of two or three
of these proteins, each dissolved in buff-
ers at both pH 6 and pH 7.5. The
Bakerbond spe columns must first be
equilibrated to the correct pH by pass-
ing 5 to 10 ml of buffer through the
column before any protein samples are
added. When the column eluant is at
the correct pH, about 0.2 ml of protein

TABLE 2
Solutions

20 mM KHPO4 pH 6 and pH 7.5
1M Na2SO,
2M NaSO4
200 mM KH2PO4 pH 7
500 mM KH2PO4 pH 7

oelectric
a variety
1 as four
Table 1).
able 2), 3
)pyl, and
chroma-
iknowns
ne their

sample is added to the column. The students slowly
process the protein samples through each of the three
Bakerbond spe columns and visually observe whether
or not binding occurs. By comparing their observa-
tions with the table they completed in the homework
assignment, the protein(s) can be identified. Proteins
can be eluted from the column (and the column cleaned
before introducing the next sample) by running a salt
solution (200 or 500 mM) through the column.

Chromatography Lab 2
This laboratory exercise has two goals: (1) to
determine whether an unknown sample contains
ferritin, hemoglobin, cytochrome C and/or a dye, and
(2) to determine the effects of the column length and
sample velocity on the resolution of the mixture.
Each student is given an empty column, a mixture
of protein and/or dye, and small quantities of the

Chemical Engineering Education

TABLE 3
Homework Assignment

In order to prepare for next week's laboratory session, you must fill out the
table below. Use a "+" sign to indicate binding and a "-" sign to indicate
that the protein will flow through the column without binding. This will
help you determine which protein(s) you have in the laboratory assign-
ment. Also consider under what conditions the proteins would elute.

Column Conditions:
* CATION EXCHANGER: Equilibrate column with pH 6 buffer
* ANION EXCHANGER: Equilibrate column with pH 7.5 buffer
* HIC: Equilibrate column with 1 M salt solution (assume 6.1 relative hydrophobicity)
COLUMN TYPE
Cation Anion Sephadex-
Protein Exchange Exchange HIC G-10 G-50 G-75 G-100
Bovine serum albumin
a-Chymotrypsin
a-Chymotrypsinogen
Conalbumin
Cytochrome C
Ferritin
P-Glucosidase
Hemoglobin
Lactoperoxidase
Lysozyme
Myoglobin
Ovalbumin
Ribonuclease A
Phenol red
Erioglaucine blue
What mixtures of proteins could not be separated by any combination
of the columns and conditions above?

four types of Sephadex gels. Before starting the
experiment, the Sephadex beads must be swollen in
20 mM salt solution. The beads should be poured
carefully into the column, so that cracks and holes in
the packing are avoided. In addition, the column
should not be allowed to become dry during the
course of the experiment.
To accomplish the first goal, the sample is pro-
cessed through similar columns filled with different
sizes of Sephadex. The students choose which sizes to
use in order to determine what protein/dye combina-
tion is in their sample. For at least two different sizes
of beads, the students observe whether the com-
pounds pass quickly through the columns or stay
near the top of the column. From their observations
they can identity the unknowns in the mixture. To
observe scale-up effects, only one size of Sephadex is
used (one that separated the student's unknown into
two bands). Samples are processed under four condi-
tions: (1) short column (2 cm) and gravity flow; (2)
short column and vacuum-induced flow; (3) long col-
umn (8 cm) and gravity flow; and (4) long column and
vacuum-induced flow. The students can easily ob-
serve the effects of column length and sample velocity
on the degree of separation.
The results of this experiment can be quantified by
collecting samples of the eluant and measuring the
absorbance with a spectrophotometer. The students
can then produce a chromatogram and calculate the
resolution under the different conditions.

CONCLUSIONS
The students found the labs relatively
uncomplicated and possible to complete within the
two-hour laboratory period. The use of colored pro-
teins allowed them to actually observe the "binding"
rather than simply studying a chromatogram that
comes from a spectrophotometer. The students did
request that proteins of different colors be used in the
exercise (all of the proteins used are brown or red-
dish-brown) so that they could confirm their deduc-
tions based on color observation. By limiting the
proteins to one color, however, the students were
forced to determine the protein identity based on

TABLE 4
Proteins Used as Unknowns
Conalbumin 50 mg/ml
Cytochrome C 20 mg/ml
Hemoglobin 20 mg/ml
Ferritin 20 mg/ml
Winter 1993

adsorption properties, not on color. By the end of
the first laboratory exercise the students had a clearer
idea of how proteins could be separated based
on differing isoelectric points. Properties of size-
exclusion chromatography were understood after
the first half of the second experiment. Several stu-
dents commented on the unexpected property ex-
hibited by the smaller dye molecules which moved
more slowly than the larger protein molecules through
the size-exclusion column-a concept not easily
grasped in class lectures.
Consequences of scale-up, such as the effects of
velocity and column length on zone spreading (band
width) were similarly difficult to comprehend during
the lecture, but were very clear when observed first-
hand. In their laboratory reports, the students showed
that they recognized that the Gaussian distribution
of the pore size for size-exclusion chromatography
has an effect on the column resolution, and they
noted that protein shape could also have an effect.
Several students took their observations one step
further and applied them to separation problems
that might be encountered in industry, suggesting
changes that would have to be made.
It is important that the theoretical concepts be
explained in class before the students attempt the
laboratory exercises. Operational problems also be-
came clear while the students were performing the
experiments. For example, the importance of equili-
brating the column before introducing samples was
discovered by several students who found that none
of the proteins would bind to their column if it had not
been equilibrated. The problems that occur when the
column is allowed to become dry (cracks or holes in
the packing) were noted by several students perform-
ing size-exclusion chromatography.
The students rated the laboratory experiment
highly and as "very worthwhile." It allowed them to
perform and validate what they had learned in class.
They were able to use chromatography techniques
and to more clearly understand the interaction of
protein properties and column phases.

REFERENCES

1. Giddings, J.C., Dynamics of Chromatography: Part I. Prin-
ciples and Theory, Marcel Dekker, New York (1965)
2. Braithwaite, A., and F.J. Smith, Chromatographic Methods,
4th ed., Chapman and Hall, New York, 11-20 (1985)
3. Miller, James M., Chromatography: Concepts and Contrasts,
John Wiley & Sons, New York, 53-56 (1988)
4. Fausnaugh, J.L., L.A. Kennedy, and F.E. Regnier, "Compari-
son of Hydrophobic Interaction and Reversed Phase Chro-
matography of Proteins," J. Chromatograpy, 317, 141 (1984)
0

e, classroom

COLLABORATIVE STUDY GROUPS

A Learning Aid in Chemical Engineering

DUNCAN M. FRASER
University of Cape Town
Rondebosch, Cape, 7700 South Africa

Towards the end of the 1990 academic year, I
introduced a system of collaborative study groups
into a foundation course in chemical engineering-it
proved to be the most exciting thing I have done in my
twelve years as a teacher. Apart from the excitement
of seeing how well the system worked, it was also the
first innovative teaching technique I have found that
is actually less work for everyone concerned. The
course, "Chemical Process Analysis" (CPA), is taken
in the second year of study for a four-year degree in
chemical engineering. It lasts two semesters and
covers basic material and energy balances in addition
to computation and chemical process industries.[1
The pressures which drove me to do something
are evident in Figures 1 and 2. They show the in-
creasing size of our second-year class, as well as its
changing composition. The figures show students
classified according to racial background because
until lately the educational system in South Africa
has been divided along those lines. The categories
used in the figures are white, other (colored and
Indian), and African.
The inequalities of resources and teaching qual-
ifications have meant that non-white students
have been disadvantaged to a greater or lesser
degree relative to the white students. The result
of the educational disadvantage has been reflected
in the pass rates in the CPA course: from 1986 to
1990, 81% of the white students passed CPA, while
only 52% of the "other" students and 39% of the

Duncan McKenzie Fraser received his PhD
degree from the University of Cape Town in
1977. He worked in industry for a short time
before returning to teaching in 1979 as Senior
Lecturer in chemical engineering at the Univer-
sity of Cape Town. His research interests are in
the areas of modeling of chemical engineering
processes such as leaching and oligomerisation,
heat exchanger network synthesis, and engi-
neering education.
Copyright ChE Division ofASEE 1993

Figure 1. Second-year class size.

African students passed.
I have yet to fully exploit the potential of this
system, nor do I claim to understand all that is
involved; but here is what I did and why it seemed to
work so effectively.
BACKGROUND
Over the past few years I have been grappling with
how best to cope with the increasing proportion of
disadvantaged students in CPA and their poor suc-
cess in the course. My first attempt was to set up
special tutorials for students who were struggling,
but this was only marginally helpful, largely because
it added extra work for those who were already
having trouble. Our department then decided to com-
mit more tutors to the regular tutorials in the course
so that extra help could be given to those who needed
it. But even this had little effect in improving the
success rate of disadvantaged students.
The tutorial system we were using at this stage
was one in which the students were given a set of
problems to work on and hand in, with one afternoon
per week set aside when they could receive help on
the problems. Attendance at the help sessions was
voluntary, and one-half to two-thirds of the class
generally attended for at least part of the afternoon.
Students were encouraged to work on the problems
Chemical Engineering Education

Figure 2. Second-year class composition.

ahead of time so they could come to the tutorial
sessions for specific help in areas where they had
encountered trouble. Generally, less than half the
students took this approach; the rest came unpre-
pared and only began work on the problems at the
last possible moment. Typically, if two weeks were
given for a set of problems, most students waited
until the last week to begin work on it.
While struggling to solve this situation, in mid-
1990 Professor Andrew Sass of ASPECT (a special
academic support program for disadvantaged engi-
neering students) introduced me to the concept of
collaborative study groups. Landis in fact contends
that a system of structured collaborative (co-opera-
tive) study groups is one of the key features required
for a successful minority program.[2] I immediately
saw that this might be a solution to the problems I
was facing and trying to resolve.
The system which we eventually designed differs
from the workshop program developed by Treisman
at Berkeley (and since implemented by others) which
generally involves minority students doing additional
and more complex problems and where a high level of
preparation is expected of the students.[1251 My previ-
ous experiences prompted me to include the whole
class in the exercise, to enable all to benefit from it, as
has apparently been done elsewhere,"6 without add-
ing extra work on any of them.

STARTING OFF
I discussed the idea of collaborative study groups
with the class, and together we hammered out the
details of running the system. Many of the students
were opposed to the scheme-particularly the better
students, who were concerned about having to spend
more time on the course and were unwilling to "carry"
the weaker students.
Winter 1993

Second Year Class Composition
1986 1991
100
African
80
Other
6 0 White
40|

In the end we agreed that we would experiment,
largely for the sake of the students who were strug-
gling. I would compose the groups on the basis of
student preferences. I would assign simple problems
that could be worked beforehand and would give
problems for each session as the students arrived.
These last problems would have to be completed
during that session. Each student would have to
submit his/her own solutions to the problems to en-
sure that each had done the work, with or without
help from the group.

I introduced a system of collaborative study
groups into a foundation course-it proved to be
the most exciting thing I have done ... it was also
the first innovative teaching technique I have
found that is actually less work
for everyone concerned.

This first class had been together for the preceding
six months and had had previous experience in group
work through a design project earlier in the year.
Some of the groups consisted of students who all
wanted to work with each other, but others were
more difficult to compose. In the end I had to appoint
some groups comprising only the class "loners." Each
group generally had a spread of abilities among its
members, either towards the top, middle, or bottom of
the class (i.e., students chose to work with others of
similar abilities).
As the students tackled the assigned problems
that first afternoon, I soon sensed an excitement in
the class. Although I gave them a break at mid-
afternoon, many of them worked right through, and
at the end of the session one student even commented
that he had never realized he could work for a solid
three hours. Altogether, I ran four of these kind of
sessions with the 1990 class. Feedback was posi-
tive-even from those who were originally opposed to
the idea. All ofthe students found that they spent less
time than they would normally have spent on solving
problems, partly because through the group approach
to a problem they could discover and avoid silly
arithmetic mistakes.
While the group plan was introduced too late in the
year to have a significant effect on the students'
success, they felt that it was so beneficial to them that
they asked that it be repeated in their courses the
following year. The second time around, when it was
used for the whole year, there was a marked improve-
ment in the pass rate for the course (detailed at the
end of this paper).

1986 1987 1988 1989 1990 1991
Year

PROBLEMS
There are problems which need to be addressed.
The first is the constitution of the groups. The first
time I used the system I noticed that the larger
groups of five or six students worked better than the
smaller groups of four. This was in spite of the fact
that the larger groups often split into smaller groups
of two or three. The reason for this seems to be
that a critical mass is needed for a group to work
effectively. Another factor could have been that
most of the smaller groups were comprised of the
"loners" in the class. I thought that they would be
better off in a group together where they would not
be overwhelmed by the others, but that may have
been the wrong decision.
In 1991 I again observed that the smaller groups
did not work as effectively, even though in this case
they were not groups of loners. In fact, one of the
groups started off with six members and was reduced
when some of its members left the course. This sup-
ports my contention that a critical mass is necessary.
The larger the class is, the more difficult it is to
form the groups. I experienced this in 1991 with a
class of eighty instead of the sixty that made up the
1990 class. It is also more difficult to constitute
groups where the students feel comfortable when the
members of a class do not know each other initially.
Another factor that I felt had to be considered was
that weaker groups needed to be reinforced by includ-
ing some of the better students in them. In the 1991
class, most of the self-appointed groups had a larger
spread of abilities, and I was careful to group the
remaining students in like manner, avoiding groups
made up of only weaker students.
There has not been any problem in getting stu-
dents to work together in this manner. Only a
few students isolated themselves from their groups,
and there was no significant copying from others in
the groups. Some groups of disadvantaged stu-
dents did not readily interact with one another at
the beginning, but this was overcome by simply
encouraging them to work together (and exciting to
see how they changed).
Another problem was how to determine exactly
what an average student could reasonably achieve in
one afternoon, but this will become easier to deter-
mine as we gain more experience in running these
sessions. At times I have had to let the students
complete some problems at home; but this is not
necessarily a bad thing.
Some instructors may have difficulty finding a
suitable environment for accomodated a class such as
this one. It is essential that each group be able to sit
40

around a table to work, which is impossible in most
lecture theaters. I was fortunate in have a suitable
flat design room which could be used.
BENEFITS
The benefits of an approach such as this are nu-
merous. The first direct benefit for me was the imme-
diate reinforcement of lectures in the problems tack-
led, relative to our previous system. This could be
achieved in other ways without collaborative study
groups, but it was a by-product for us.
Another benefit is that staff time is used more
effectively-especially important in view of the in-
creasing academic pressures. Staff can concentrate
on the more serious problems which the students
cannot jointly resolve in their groups. The result is
that students with serious problems have more
direct access to the best help since the lecturer is not
tied up with trivial problems. Moreover, senior staff
can be available to a whole class at once. I have also
found that I need fewer tutors.
Student time is also used more effectively since
they are able to immediately solve their difficulties
in a group setting of collaboration rather than
struggling for long periods of time on their own.
Marking tutorials become more efficient in that the
solutions from each group are generally the same.
This means that the instructor can concentrate on
conceptual problems and can more readily identify
common difficulties.
The system encourages peer-group learning and
helps students to build helpful working relationships
with others in the class. This is particularly impor-
tant for students who by their circumstances or na-
ture have difficulty in forming relationships outside
of regular classes. It also breaks down the dichotomy
found in many minority students between their work
and their peer relationships, which Treisman found
was a key factor in their failure.re'7 I would rate this
as one of the most significant educational benefits
from the collaborative study group system. It is also
in accord with the emphasis placed by Landis on
collaborative study. 21
Another benefit is that students learn to communi-
cate with one another on a technical level, which is
very important for aspiring chemical engineers. This
was noted by Hudspeth in the academic excellence
workshops run at California State Polytechnic Uni-
versity,3'5'8s as well as being one of the reasons Landis
used to encourage students to work in such groups.
An additional advantage is that the problems from
previous years can be re-used since students work
the solutions on their own in class and do not copy the
Chemical Engineering Education

solutions. This is particularly helpful when there are
significant numbers of repeating students in the class
(as was the case in this course).
The second time I taught these sessions I realized
that most students were not solving the straightfor-
ward problems I gave them as preparation, which
meant that they were taking too long coping with the
more complex problems. I rectified this by assigning
a straightforward problem first off, and it had the
desired benefit of enabling them to handle the more
difficult problems that were assigned later.
With students working in groups there is also the
potential to pose problems which require interaction
and which cannot be solved alone. I have yet to
exploit this potential.

ESSENTIAL FEATURES
The following key elements can be identified as
essential features of the collaborative study group
system. I doubt whether the system would work if
any one of the features was missing.
* Students work in groups but produce their own solutions
to the problems.
The groups are chosen on the basis of student prefer-
ences, subject to the constraint that each student must be
part of a group.
The groups are large enough to allow for significant
interaction between the members, but not so large as to
be unwieldy (six members per group seems to be
optimum).
Attendance at group problem-solving sessions is
compulsory. (This is done by making it a requirement
for entry to the examination.)
The groups work together on the problems. (Students
who like to streak ahead are discouraged from doing so,
as are those who want to work entirely on their own.)
The groups work around a common table. (A group of
six working in a row does not allow for meaningful
interaction.)

Amount Learned From Tutorial Sessions
Chemical Process Analysis Evaluations
100-
SProblematical
Satisfactory
Seo Good
S--
S-

1986 1987 1988 1989 1990 1991
Year
Figure 3. Student evaluation of tutorial sessions.
Winter 1993

The problems assigned are not known by the students
beforehand (allowing the session to become a shared
experience, which generates much of the excitement).
Solutions to the problems must be handed in by the end
of the session. (This makes the students get on with the
job; there has been some flexibility as to how much
must be completed).
The system was adapted from similar systems used
elsewhere, in consultation with the students themselves.

OUTCOME
Figure 3 shows the response in course evaluations
to the question concerning the amount learned from
tutorial sessions. The effect of the few group sessions
run in 1990 can be clearly seen in the increase of
those responding positively, compared to previous
years, with a concomitant decrease in negative re-
sponses. There was further improvement in these
responses in 1991 (when the collaborative study group
system was used for the whole course), with 69%
responding favorably and only 5% indicating that
they had problems.
In 1991 the pass rate for the course improved as
follows: for the white students it increased by 15%;
for the disadvantaged students, 65%; and for the
class as a whole, by 28%.191 This is a clear indication of
the general educational benefit of collaborative study
groups, as well as the special benefit derived by
disadvantaged students.
Judging from the student reaction and by the
improved pass rates for the course, the system of
collaborative study groups was a success. One of the
secrets of its success was that the system structure
was jointly forged by the students and the instructor.
This meant that the next group of students also
accepted the system well in spite of not having been
involved in its formulation.
The challenge for me as instructor is to be creative
in how I use the system. But I am convinced that even
if I simply use the same problems that I have already
used, the students will still be much better off than
they were under the prior scheme. It took a good
amount of courage to implement the system the first
time, but that courage was amply rewarded. I strongly
encourage others to try something similar, even if
only a single period is available for this sort of exer-
cise instead of a whole afternoon. It can still have a
lasting impact on the way in which students learn.

REFERENCES
1. Fraser, D.M., "An Integrated Foundation Course in Chemical
Engineering," accepted for publication by Internat. J. ofEng.
Ed., October (1992)
2. Landis, R.B., "retnetion by 'Redesign': Achieving Excellence in
Continued on page 64.

rB. class and home problems

The object of this column is to enhance our readers' collection of interesting and novel problems in
chemical engineering. Problems of the type that can be used to motivate the student by presenting a
particular principle in class, or in a new light, or that can be assigned as a novel home problem, are
requested, as well as those that are more traditional in nature and which elucidate difficult concepts. Please
submit them to Professors James O. Wilkes and Mark A. Burns, Chemical Engineering Department, Univer-
sity of Michigan, Ann Arbor, MI 48109-2136.

SOLVING

CHEMICAL KINETICS PROBLEMS

BY THE MARKOV-CHAIN APPROACH

THOMAS Z. FAHIDY
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1

Imagine the following scene: you are correcting a
quiz given to students in your (say) second year
chemical kinetics course. You assigned the prob-
lem of a homogeneous mixture containing initially 1
mole of species A and 0.2 moles of species B. A <- B
reactions are by no means imaginary; the classical
gas-phase reaction between ortho-H2 and para-H2,[1
and the liquid-phase hydrolysis of lactone to
y-hydroxybutyric acid in strong hydrochloric acid so-
lutions121 are two real-life examples. In every minute,
75 mole % of A are converted to B, and 5% of B
converted to A. How many moles of A and B are
present in the mixture at one and two minutes after
the process has started, and what is the final (equilib-
rium) composition?
You are trudging your way through a motley
collection of answers based on more-or-less success-
ful attempts by your students to set up the conven-
tional differential rate equation and to integrate
them somehow. Your boredom threatens to reach
unprecedented depths-when suddenly you come
across the unexpected. One of your students almost
obtained the right answers ... without writing down
a single rate equation.
Congratulations! This student of yours apparently
recognized that the reaction process may be inter-
preted as a Markov chain in the theory of stochastic
processes. Composition is considered as a probability
(state) vector and the rate constants as transitional
@ Copyright ChE Division ofASEE 1993

Thomas Z. Fahidy received his BSc (1959)
and MSc (1961) from Queen's University and
his PhD (1965) from the University of Illinois
(Urbana-Champaign). He teaches courses in
applied mathematics to engineering students
and conducts research in electrochemical en-
gineering. His major research areas are
magnetoelectrolysis and the development of
novel electrochemical reactors. He is the au-
thor of numerous scientific articles.

probabilities; the final composition is given by a
straightforward application of the eigenvalue prob-
lem in linear algebra. For want of numerical careful-
ness, the answers are slightly off. Never mind-give
this student an A' for leaving behind the conven-
tional, the obvious, the unimaginative!
THE CHEMICAL REACTION AS A
MARKOV CHAIN
The key to this off-the-beaten-path approach is
that the amounts of species A and B present at the
(n+1)st time unit depend only on their amounts at the
nth time unit. Calling the amounts states, we can now
say that transition between two consecutive (adja-
cent) states is independent of transition between any
other states. We may think of the transition between
states as a probability matrix with its elements given
by the rate constants which, in turn, are interpreted
as transitional probabilities.
The Markov chain model of the reaction is
A(n + 1) = 0.25 A(n)+ 0.05 B(n) (la)
B(n + 1) = 0.75 A(n)+ 0.95 B(n) (Ib)
with A(0) =1 and B(0) = 0.2. The transition matrix
Chemical Engineering Education

(Markov matrix) is
(0.25 0.05
P= (2)
0.75 0.95)
and the state vector
CA(n)
Pn = p= P"Po (3)
.B(n))
yields the time-dependent concentrations. Numeri-
cally (in moles), the solution vectors after one minute
and two minutes are

B(1)) 0.75 0.95 0.2 )=0.94
and
A(2) 0.25 0.050.26 0.112
B(2)) 0.75 0.95) 0.94) (1.088)

The conventional, and more time-consuming, method
is to solve the differential rate equations
dA -0.75A+0.05B
dt
B = 0.75 A 0.05B
dt
which yield
A(t)= 0.075 + 0.925 exp(-0.8t)
B(t) = 1.125- 0.925 exp(-0.8 t)
The equilibrium concentrations are found via the
lim p = p* = const. property of the chain
n
which implies the relationship
Pp*=p* (4)
e.g., an eigenvalue problem with eigenvalue of unity.
In our case, Eq. (4) is
0.25 0.05 p ip I
0.75 0.95) p2 [P2
which yields an eigenvector

where k is an arbitrary real constant. Ifk is chosen as
the "normalizer" value
(A. +Bo) 1.2
(1+15) 16
the equilibrium values A* = 1.2/16 = 0.075 mol and B*
= (1.2)(15)/16 = 1.125 mol are found immediately.
The attractiveness of the Markov-chain approach
increases with the number of reacting components,
e.g., the dimensionality of the problem. Suppose that
three components A, B, C react in a mixture with
Winter 1993

differential rate equations
dA- = 0.3A+0.1B
dt
dB =0.2A-0.3B+0.1C
dt
dC = 0.1A+0.2B-0.1C
dt
with initial composition Ao = 1, Bo = 0.6, and Co = 0.3
mol. In the Markovian approach

(0.7 0.1 0.01 0.7 0.1 0.0' ( 1

Pn = 0.2 0.7 0.1 p 0.2 0.7 0.1 0.6 (5)
0.1 0.2 0.9, 0.1 0.2 0.9, 0.3
represents the state of the reaction mixture of each
time instant. The eigenvector associated with equi-
librium has the elements (1, 3, 7), and k = 2/11 is the
normalizer yielding the equilibrium concentrations
A* = 0.1818, B* = 0.5454, and C* = 1.2727 mol.
The handling of the equilibrium state does not re-
quire, of course, the solution of the differential rate
equations, but the manipulations of the algebraic
equation set obtained by equating the concentration
derivatives to zero are not simpler than the computa-
tion of the eigenvector.
The didactic value of the Markov-chain path of
solution lies not only in its simplicity and elegance,
but also 1) in demonstrating the power of probability
theory in handling a priori deterministic problems,
and 2) in applying fundamental tenets of linear alge-
bra to tangible physical problems of practical impor-
tance. Undergraduate students in engineering usu-
ally regard linear algebra as an esoteric nuisance (the
student in this story is a rare bird, indeed!); treating
chemical kinetics problems with appropriate tech-
niques of linear algebra proves the opposite.
The power of Markovian thinking is much wider
than what is presented here. Physics, biology, eco-
nomics, communications, and computer networks are
well-known areas of application. The interested reader
will find references 3-5 useful for further exploration.

REFERENCES
1. Wakao, N., P.W. Selwood, and J.M. Smith, "Low Tempera-
ture Ortho-Para Hydrogen Conversion-Kinetic Studies,"
AIChE J., 8, 478 (1962)
2. Long, F.A., W.F. McDevit, and F.B. Dunkle, "Salt Effects on
the Acid-Catalyzed Hydrolysis of y-butyrolactone. II. Kinet-
ics and Reaction Mechanism," J. Phys, and Colloid. Chem.,
55, 829 (1951)
3. Cox, D.R., and H.D. Miller, The Theory of Stochastic Pro-
cesses, Chapman and Hall, London (1965, 1970)
4. Rozanov, Y.A., Probability Theory: A Concise Course, Dover,
New York (1969)
5. Greenberg, M.D., Advanced Engineering Mathematics,
Prentice Hall, Englewood Cliffs, NJ (1988) J

a classroom

FLUID STRUCTURE FOR SOPHOMORES

J. RICHARD ELLIOTT, JR.
The University ofAkron
Akron, OH 44325-3906

Whenever new fields of technology are devel-
oped, they will involve atoms and molecules.
Those will have to be manipulated on a large
scale, and that will mean that chemical en-
gineering will be involved inevitably.
Isaac Asimov (1988)

he undergraduate course in chemical engi-

neering thermodynamics continues to present
teaching challenges despite its long-term pres-
ence in the curriculum. Students often complain that
it seems "too esoteric." But it is also a course that can
provide opportunities for giving students a strong
sense of "manipulating molecules" by illustrating
the development of engineering models which ad-
dress molecular scale interactions. Then students
might say that "it was especially good as an intro-
duction to engineering,"-and what a healthy shift
in perception that would be. The approach advo-
cated here is to integrate the esoteric principles with
the students' inherent intuition so they can see all
levels of the modeling process.
This general approach may seem obvious, but in-
troducing fluid structure as a means of reducing the
esoteric perception is probably not so obvious. There
always seems to be more subject matter than there is
time to cover it, and as a result there is a tendency to
reduce thermodynamics to its smallest kernel of
unique and general concepts (Maxwell's relations
and the Gibbs-Duhem equation, for instance). Focus-
ing so much on those concepts, however, would be too
esoteric-by themselves, these concepts do not help
students understand how liquefaction or distillation
works or why polymer blending rarely works. Clearly,
there must be some additional relations which dem-
onstrate the utility of the "pure thermodynamics."
We faculty recognize these as constitutive relations
like equations of state or Gibbs excess functions, and
when pressed for time it is tempting to present them
macroscopically, as empirical relations that should

basically be accepted on faith. In the discussion be-
low, an alternative strategy is presented which takes
advantage of common roots in the molecular perspec-
tive to rapidly generate the constitutive relations in a
way that highlights some great engineering models
and simultaneously leads to the kind of molecular
perspective that Asimov envisions.
The common root of constitutive relations is the
fluid structure. For solution models, we apply the
energy equation (Eq. 1). For the equation of state,
we apply the pressure equation (Eq. 2). But in all
cases we add up the local quantity (energy or force)
weighted by the local density. The local energy or
force field around an atom is clear to students from
introductory chemistry and physics. The various po-
tential models and the types of molecules they de-
scribe are reviewed during the first week of class. But
the "fluid structure," which describes the local den-
sity, sounds at first like an esoteric concept at its
worst. Building an appreciation of fluid structure is a
delicate undertaking, but once this appreciation is
established, a single framework can be repeatedly
applied for rapidly reducing to practical application.
Our approach is detailed below.
The concept of fluid structure does for energy
what the concept of particle distribution in boxes does
for entropy; it provides the connection to the molecu-
lar scale. For the treatment of particle distribution
in boxes we adapt the presentation of Balzhiser,
et al.,E11 at the same time that entropy is intro-
duced. Thus, the students are ready and waiting for a

J. Richard Elliott, Jr., is Associate Professor
of Chemical Engineering at the University of
Akron. He received his PhD from Pennsylvania
State University and his MS from Virginia Poly-
technic Institute. His background and interests
are primarily in phase equilibria and molecular
thermodynamics and related applications. In
the spring of 1992, he received the ASEE/Dow
Outstanding Young Faculty Award of the North
A *Central Section.
Copyright ChE Division ofASEE 1993
Chemical Engineering Education

molecular formulation of the complete problem and
are anxious for applications.
The presentation below emphasizes the develop-
ment of.the principles of thermodynamic modeling in
four stages. First, a brief introduction to how the fluid
structure influences the macroscopic properties is
given by the energy equation and the pressure equa-
tion. Second, the qualitative features of fluid struc-
ture are developed for several examples through
simple intuitive arguments. Third, the pressure equa-
tion is applied to develop the van der Waals equation
of state. And fourth, the energy equation for mixtures
is applied to show how mixing rules, the Scatchard-
Hildebrand theory, the Van Laar theory, and the
Flory-Huggins theory all result from simplifications
of the van der Waals equation of state. Local compo-
sition theory is then derived from alternative ap-
proximations of the fluid structure. In this way, each
constitutive relation is related back to intuitively
accessible concepts that all students can appreciate,
with the result that students can admire the depth of
ingenuity involved in engineering models instead of
being frustrated by arbitrary equations being pulled
from some place known only to a privileged few.

RELATING FLUID STRUCTURE TO
MACROSCOPIC PROPERTIES
To apply the relationships for relating changes in
properties to Cp, Cv, p, T, V, and their derivatives, we
need relationships between p, V, and T. These rela-
tionships are dictated by the equation of state. Con-
structing an equation of state requires considering
how the intermolecular forces are affecting the en-
ergy and pressure in a fluid. As the fluid becomes
dense, we know that the molecules will be closer
together on the average and this will give rise to a
potential energy contribution and to an increase in
the contribution of attractive forces. A common prac-
tical implication of this attractive energy is the heat
of vaporization of a boiling liquid.
But how can we make a quantitative connection
between molecular forces and macroscopic proper-
ties? The key is to consider the average number of
molecules at each distance from the center of an
average molecule. To get the internal energy, multi-
ply this average number of molecules by the amount
of intermolecular energy at that distance and inte-
grate over all distances. As for the pressure, the
complete statistical mechanical derivation is beyond
the scope of this introduction, but appreciation of the
relevant terms can be gained by highlighting the
similarity between the energy equation and the pres-
sure equation and the relation between the potential
Winter 1993

Students often complain that [thermodynamics]
is "too esoteric." But it is also a course that can
provide opportunities for giving students a
strong sense of "manipulating molecules"
by illustrating the development of models
which address molecular scale interactions.

and the force. These considerations give rise to the
energy equation and the pressure equation, and most
importantly, to the definition of this "average num-
ber of molecules." The average number of molecules
at a particular distance from an average molecule is
given by the "radial distribution function" ("g").
The Energy Equation

- Uid 2 kT ug 4r2 dr
0

The Pressure Equation

where
g _-
Z =
p -
k =
u -
N -
V -
uid

SP = 16- p r()g4 r2 dr
pkT 6kT 0 rO

radial distribution function (rdf)
compressibility factor
N/V is the number density
Boltzmann's constant
intermolecular potential function
number of atoms
total volume
internal energy of the ideal gas

AN INTUITIVE METHOD OF
INTRODUCING FLUID STRUCTURE
The fluid structure described by the rdf can be
initially introduced by considering two simple ex-
amples that can be solved exactly: the low density
hard sphere fluid and the body centered cubic crystal.
These provide the two limits of density, and the other
examples can be considered as variations. The other
examples are the high-density hard-sphere fluid, the
low-density square-well fluid, and the high-density
square-well fluid.
As a prelude to a general description of fluid struc-
ture, it may be helpful to review the structure of
crystal lattices like those in body centered cubic (bcc)
metals. Such lattices possess long-range order via
repetitive arrangements of the unit cell in three
dimensions. As an example, we can compare the
structure of a body-centered cubic crystal to that of a
face-centered cubic crystal. A specific arrangement of
45

atoms gives a single value for the density, and it
correlates with many of the macroscopic properties of
the material (e.g., strength, ductility). Having an idea
of such a specific structure for a solid provides the
basis for contrast to the structure of a fluid.
The structure arising from the distribution of at-
oms in bcc crystals is fairly easy to understand, but
how can we address the distribution of atoms in a
fluid? For a fluid, the positions of the atoms around a
central atom are less well-defined than in a crystal.
To get started on a generally applicable description of
fluid structure, think about the simplest fluid-an
ideal gas.
Consider a fluid of point particles surrounding a
central particle. What is the number of particles in a
neighborhood surrounding the central particle? Since
they are point particles, they do not influence one
another. This means that the number of neighbors is
proportional to the size of the neighborhood.

dN- NdV (3)
dN V
where dNv is the number of particles in the volume
element.
Recalling that p N / V,
dNv = pdV (4)
If we would like to know the number of particles
within some spherical neighborhood of our central
particle, then
dV = 4nr2dr (5)
where r is the radial distance from our central par-
ticle, and
Nc Ro
N = dNv = p4nr2dr (6)
0 0
where Ro defines the size of our spherical neighbor-
hood, and N, is the number of particles in the neigh-
borhood (also known as the coordination number).
Now consider the case of atoms which have a finite
size. In this case the number of particles within a
given neighborhood is strongly influenced by the size
of the neighborhood. If the range of the neighborhood
is less than two atomic radii, or one atomic diameter,
then the number of particles in the neighborhood is
zero (not counting the central particle). Outside the
range of one atomic diameter we do not know exactly
how the number of particles changes. We can express
these insights mathematically, however, by introduc-
ing a "weighting factor" which is a function of the
radial distance. The weighting factor takes on a value
of zero for ranges less than two atomic radii, and for
larger ranges we will consider its behavior undeter-
mined as yet.
46

Then we may write

Nc =p jg(r)4nr2 dr
0

0 r < a
g =
? r a

where g(r) is our "weighting factor" referred to as the
radial distribution function (rdf). This radial distri-
bution function provides the quantitative description
of what we refer to as "fluid structure."
As a first approximation, we might assume that
atoms outside the range of two atomic radii do not
influence each other. Then the number of particles in
a given volume element goes back to being propor-
tional to the size of the volume element, and the rdf
has a value of one for all r greater than one diameter.
The approximation that atoms outside the atomic
diameter do not influence each other is reasonable at
low density (see Figure 1).
Far from the low density limit, we approach close-
packing. The ultimate in close-packing is a crystal
lattice. It is necessary to clarify what is meant by the
rdfof a lattice, as opposed to its crystal structure. The
rdf of a bcc lattice can be deduced from knowledge of
N, vs. neighborhood size using some elementary ge-

Figure 1. The radial distribution function vs. radial
distance for a hard sphere fluid at low density.

Figure 2. The radial distribution function vs. radial
distance for a body centered cubic crystal.
Chemical Engineering Education

01
C 2 3
r/u

ometry and applying Eq. 7.
If we assume that the atoms in a crystal are
located in specific sites and that no atoms are out of
their sites, then g must be zero everywhere except at
a site. For a body centered cubic crystal, these sites
are at
r ={ 1. 15 a, 1.6 ,...}
For instance, the location of the second shell at 1.150
is given directly from the length of the side of the unit
cell. Since the atoms are assumed to be only at
specific distances, the rdf looks like a series of spikes
(see Figure 2).
The distribution of atoms in a substance is most
conveniently referred to as its "structure." The struc-
tures of the low density hard sphere and the bcc
crystal clarify what is meant by the rdf and how we
represent it. Next, we can develop some insight about
the high density hard sphere fluid. Its behavior is
something of a hybrid between the low density fluid
and the solid lattice. Similar to the low density case,
when atoms are too far away to influence each other,
the rdf approaches unity because the increase in
neighbors becomes proportional to the size of the

3

0 1 2 3
r/o

Figure 3. Radial distribution function vs. radial distance
for a hard sphere fluid at high density (No3/V = 0.60).

(a) (b)
Figure 4. The radial distribution function vs. radial distance for a square-well
fluid (kT/e = 3.0) (a) at low density, and (b) at high density (No3/V = 0.60).
Winter 1993

neighborhood. Near the atomic diameter, however,
the central atom influences its neighbors to position
themselves in "layers" in an effort to approach the
close packing of a lattice. Thus the value of the rdf is
large, very close to one atomic diameter. Because
liquids lack the long-range order of crystals, the
influence of the central atom on its neighbors is not as
well defined as in a crystal, and we get smeared peaks
and valleys instead of spikes (see Figure 3).
As a final case, consider the influence of attractive
forces on surrounding neighbors. The range within
the atomic diameter is still off-limits, and the value of
the rdf there is still zero. But what about the rdf at
low density for the range where the attractive poten-
tial is significant? We would expect some favoritism
for atoms inside the attractive range since that will
release energy, but overlap would still be off limits
and there would be no influence outside the range of
the potential at low density.
For the square-well potential, the changes with
radial distance are very distinct:

[0 r u(r)= -e < r < Ro
0 Ro

The impact of the attractive force then becomes clearly
recognizable (see Figure 4a). As for the rdf at high
density, we expect packing effects to dominate be-
cause attaining a high density is primarily affected
by efficient packing. At intermediate densities, the
rdf will be some hybrid of the high and low density
limits (Figure 4b).
Qualitative description of these sample fluid struc-
tures is about as far as intuition can carry us. A
mathematical formalization of these intuitive con-
cepts is presented in several texts[2'31 but the diffi-
culty of such a rigorous treat-
ment is beyond the scope of our
introductory presentation. For
our purposes, we would simply
like to understand that some-
thing called "fluid structure"
exists and that it is described
Sin detail by the "radial distri-
bution function."

VAN DER WAALS
EQUATION OF STATE
Having laid the foundation
for intuitively considering fluid
structure and its impact on mac-

i

g

2 3
r/u

?
T/(T

roscopic properties, the derivations of every theory
from equations of state to local composition theory
can follow in rapid sequence. These derivations can
serve to illustrate model development and simul-
taneously demonstrate the utility of the "pure
thermodynamics." One of the most successful and
useful equation of state has been the van der Waals
equation. Even the most popular engineering equa-
tions currently used are only minor variations on
the theme originated by van der Waals. The beauty
of his argument is that detailed knowledge of the
rdfis not necessary-only the kind of general knowl-
edge of its existence as described in the preceding
section. As pointed out by Abbott,"41 we can assume
that van der Waals started with the pressure equa-
tion and reasoned that the integral could be broken
into two parts:

P =1- pT r(d 4nr2 dr- p ( 4nr2 dr (9)
pkT 6kT ar 6kT @r
0o
Each integral can now be analyzed separately. Math-
ematically, analysis of the first integral is difficult
because g = 0 except at r = s, and the derivative of the
potential is zero except at r = s, where it becomes a
Dirac delta function. This leads to the result

P Fr 'g4nr2 dr= -3 p (10)
6 kT 'fr 3

We have already recognized that g(o) increases
with density, but we need a simple analytical func-
tion which can be used to provide a numerical repre-
sentation of this increase. One of the simplest func-
tions leads to

P r ) r bp (11)
6 kT rarg4r2 dr (1- bp)
0
where b = close-packed volume. This is the function
which van der Waals suggested. It should be noted
that Eq. 11 suggests that p -> near the close-
packed density and that this helps to understand
how engineering models of such divergences are
often developed.
As for the second integral, this basically repre-
sents the attractive force at each distance times the
number of particles at that distance integrated over
all distance. As an example, consider what happens
to this integral when u is given by the square-well
potential (with Ro = 1.5a). Then

P Fr(u -g4n r2dr= ( (F )g4Xu2dxx2 (12)
6kT J 1. 6kT J\ xo / (2

where x -- r/o. The integral on the right-hand side is
48

independent of the particular substance of interest
because the only way of distinguishing different sub-
stances in the square-well potential is by different
values of a and e. By factoring the a and 8 out of the
integral, we obtain a dimensionless integral which
can be applied universally to any substance multi-
plied by a dimensionless constant which accounts for
the substance dependent values of e and a. Van der
Waals did not have quantitative information avail-
able about g; therefore he made the approximation
that the value of this integral was some constant
independent of T and p for all substances. This may
seem somewhat crude since we know that g changes
significantly with respect to density, but the way that
g oscillates about unity leads to a weak density de-
pendence for the integral. When this universal con-
stant is factored in with o3 and e, a single substance-
dependent constant is obtained

a = C x( /3 )g4 x2 dx (13)
6 x ax )gx

The resulting equation of state is
= 1, bp ap 1 ap (14)
(1-bp) kT (1-bp) kT
When this equation is compared to currently popu-
lar equations, it is clear that the theoretical basis of
modern equations of state is not significantly differ-
ent from that developed by van der Waals. For ex-
ample, the Soave[51 equation is
Z=l+ bp ap (15)
(1- bp) kT (1+bp)

where a = a(T) is an empirically determined tem-
perature-dependent function.
The function used to correct for the density depen-
dence is 1/(1 + bp). The principal difference is the
modification of the temperature and density depen-
dence of the attractive term, but this modification is
based on experience and empiricism more than any
theoretical insight. The methods of these empirical
developments provide excellent examples of the in-
terplay between theory and application, and discus-
sion of these developments can provide keen insight
into the development of engineering models.
FROM FLUID STRUCTURE TO
SOLUTION THEORY
The development of solution theory closely paral-
lels the development of van der Waals' equation for
pure fluids. The final equations presented here are
familiar to the reader, but the ease of relation back to
the molecular perspective may be simpler than imag-
ined at first thought. We begin with the van der
Waals equation for pure fluids and consider how to
Chemical Engineering Education

adapt it to mixtures. Essentially, all that is necessary
is to define "a" and "b" for a mixture. Since "b"
provides a crude representation of the close-packed
volume, it is not unreasonable to crudely approxi-
mate it by a molar average. To determine the compo-
sition dependence of the "a" parameter, the energy
equation can provide guidance. For mixtures, the
energy equation is given by exactly the same method
of adding energies times interactions that was ap-
plied for pure fluids
U U'd U. P16)
"= 47xcx k g4r2 dr (16)
NkT 2=XxxJj- kTr8dr
The only term that may seem mysterious is the
factor of one-half in front. This factor arises because
we imagine summing all the interactions by going
from one atom to the next. But the j-i interaction is
really the same as the i-j interaction, so we would be
double counting if we did not divide by 2. Applying
classical thermodynamics to the van der Waals equa-
tion gives
U-Uid -ap -a (17)
NkT kT vkT
where v = 1/p is the more traditional manner of
representing the density term. Comparing Eq. (17) to
Eq. (16) shows that

a= EXii g ui g 4ir2dr (18)

when xi -> 1,

aii Suiiii 4nr2 dr (19)
Assuming gij is weakly dependent on composition,
we obtain
a- xixai, (20)
where the cross-term, aij, is traditionally approxi-
mated by
aij = Va (21)
Expressions for free energy and fugacity via the
equation of state can then be quickly developed by the
usual methods.
Turning our attention to Gibbs excess models for
liquids, we find that we already have all of the theo-
retical foundation laid for many of the models. All
that is required is some specific approximations and
simplifications for the specific application being con-
sidered. A brief outline of the derivation of regular
solution theory and Flory-Huggins theory from the
van der Waals equation follows.
The Gibbs excess energy of a van der Waals mix-
ture may be derived by considering the Gibbs depar-
ture functions of the overall mixture and the indi-
Winter 1993

vidual components in turn

-G d = (v-b) a .P+ -1 (22)
NkT kT vkT kT
and applying

GE=(G-Gid)- x,(G -Gid)- xi n(xi) (23

yields

GE n(v-b
NkT i (Vi -bi )

vkT xi )~kT l+ (v-Y xiv) (24)

A common approximation when developing solu-
tion theories for liquids is to assume that v = E xivii
While this is often inaccurate relative to volume
estimates for non-ideal solutions, it is accurate enough
for free energy estimates because the excess volume
makes a small contribution to the excess free energy.
This eliminates the last term in the above equation.
Following Flory,"61 we may assume that for liquids
v bi v (25)
which implies that the void fraction is roughly a
universal constant for all liquids (65% is generally
quite reasonable). Then,

v. b x (26)
vi -b, iD
where
x.v.
i xivi
This result is referred to as the Flory-Huggins
term. Noting that this term is independent of tem-
perature and applying classical thermodynamics to
the free energy shows that this term describes the
excess entropy of mixing and the remaining terms
describe the excess internal energy. Summarizing:

GE S UE
NkT = i XJ NkT (27)
Returning to the van der Waals theory, the inter-
nal energy may be written as

U- Ud -- Ei XIJa ij(
NkT kT xi(28)

For the pure fluid, taking the limit as xi -4 1, we
recover

U-Uid ) -a U Uid oln = i- (29)
For a binary mixture, subtracting the ideal solution
For a binary mixture, subtracting the ideal solution

result to get the excess energy gives

UE x1all + 22 (x2a +2xx212 a22 (30)
NkT vkT v2kT kT(xlv + x2v2)

Applying a 12= a1a22

UE xX2V222 V 2 Va2
NkT kT(xV + X2V2 V1 V2 V2

X1X2V1V2 1 2
xx2vv2 Va -2
kT(xv1 + X2V2 1 V2

UE (61 82)2
NkT kT 12 (XIV1+X2V22) (31)

where

V

Substituting

GE (, (81-52 2
NkT xi fnx kT 102 (x1V1 + X2V2) (32)

If we choose to neglect the Flory-Huggins term,
Scatchard-Hildebrand theory is obtained. The Van
Laar equation may easily be derived from the
Scatchard-Hildebrand form. If we choose to approxi-
mate (8 -82)2 by an adjustable parameter x, then
the full Flory-Huggins theory is obtained. If we retain
all of the above terms, then the theory of Blanks and
Prausnitz17' is obtained. The development of these
solution models can be interspersed with examples
of retrograde condensation, azeotrope formation,
distillation, and polymer mixing/blending to im-
press even the most skeptical application-oriented
student. And the conciseness of each theoretical de-
velopment makes the investment small enough to
maintain interest at every step.

LOCAL COMPOSITION THEORY
There is one last class of solution theories which
requires coverage even though the attention of the
student has been pressed close to its limit by this
stage in the course. Fortunately, the foundation for
development of this theory has been laid in the form
of the energy equation for mixtures and the deriva-
tion can quickly proceed as a slight modification of
the previously developed solution theories. While it is
difficult to motivate this further developmentapriori,
it is a necessity if students are to understand the
basis of the very popular and versatile UNIFAC
model."' The value of this investment can be rein-
forced by an application-oriented project which dem-
50

onstrates the power of the UNIFAC model.
The modification required to develop local compo-
sition theory is to realize that in developing the van
der Waals mixing rules, we made a key assumption
about the radial distribution function in a mixture.
Briefly, we assumed that gij was independent of com-
position. That assumption is accurate when the com-
ponents of the mixture are roughly the same size, but
it becomes more questionable when their diameter
ratio is greater than 1.5. Consider the differences in
packing that would occur when a few very large
spheres were surrounded by tiny ones vs. a few tiny
spheres dispersed among large ones.
To develop a more accurate representation of local
composition effects, we seek a description of the
excess internal energy which is at least "more
flexible" than that assumed by van der Waals. By
more flexible, we mean to recognize that predicting
complicated local composition effects may be more
difficult than predicting aij. The more flexible
expression we seek should be capable of at least
correlating the local composition effects even if pre-
dicting them seems too difficult.
We can relate the energetic of the mixture di-
rectly to the local compositions by recalling that the
intermolecular energy is a short-range function. The
square-well potential is especially useful for making
this point. These local compositions can then be mul-
tiplied by the energy associated with each type of
interaction to obtain the total energy from the energy
equation. We can define a local mole fraction by

Xi Ni / NcJ
Ni = number of i atoms around a j atom

Nc = iN

The local mole fraction can be related to the bulk mole
fraction by
3 Rij
V J 4n r2, dr1 (33)
= 0
where

r

R = "neighborhood" where intermolecular
energy is significant
Further, we can write
x.. Ncj N. fgij 4 drij x.
S_- A.ij (34)
xC Ncj Nj G0g 4x rdri xj
Chemical Engineering Education

Noting

x. A.. x.. x.
,i =j1= ii xJ x (35)
Xj Y x x Ai,
X.
> = xAi (36)

Therefore
xi A^
x -x (37)
k kCXk Akj
k
Substituting into the energy equation gives

UE 1 A (38)
NkT 2kT c Xk A38)

In our previous development of solution theories,
UE was assumed to be independent of temperature.
In local composition theory, it is more convenient to
assume some temperature dependence of Aij. In par-

ticular

gives

-.+j v j exp[(Fi T)
V, kT

GE C x
G-EkXTkTn(lxiAi) (40)
NkT kT T
where C is the temperature-independent integration
constant obtained from integrating the internal en-
ergy with respect to temperature. If we set C = 0, we
obtain the Wilson[19 equation. If we use the Flory-
Huggins theory to describe the integration constant,
we obtain essentially the UNIFAC expressions. Sev-
eral applications showing the predictive capability of
UNIFAC can then be exemplified to reinforce the
utility of having made this extension. This also pro-
vides another opportunity to illustrate the interplay
between theoretical development, empiricism, and
application that is so essential to engineering. Atten-
tion should be called to the number of adjustable
parameters inherent in the UNIFAC model and the
distinction between correlation and prediction. This
also provides the necessary background for consider-
ing Sandler's[10] award lectures without the necessity
of canonical partition functions.
CONCLUSION
All of this may seem like more theory than chemi-
cal engineering sophomores can absorb. Never-
theless, we have been incorporating this material
into our sophomore course for the past two years and
student evaluations show surprisingly few com-
plaints. In fact, our evaluations last year were the
highest obtained over the past six years. We feel that
Winter 1993

the key to this success is the immediate reduction
of each theory to practice. Our engineering students
are as pragmatic as any engineering students, but
presentation of the above theoretical developments
consumes only about seven lectures out of fifty-
nine. The remaining lectures are devoted almost
entirely to sample applications demonstrating the
utility of each theory.
But there may still be some doubt on the part of
thermodynamics instructors about whether this is all
worthwhile. To respond, we may consider Asimov's
quote given at the beginning of this paper. How close
are we chemical engineers to the "manipulation of
molecules on a large scale"? In reality, we teach
precious little about the connections between the
molecular scale and continuum scale. We occasion-
ally hear arguments that the molecular scale and the
statistical mechanics which connect it to larger scales
are the domain of chemistry, not engineering. But
our students do apply theories like UNIFAC. This
means that they currently apply the theories blindly,
like computer operators.
What we should be teaching our students is the
general engineering approach to understanding
a physical situation, modeling, empiricizing, and
reducing to practice. Through the concept of fluid
structure, we can achieve all this and maintain
constant focus on the fundamental sources of energy
and entropy.

REFERENCES
1. Balzhiser, R.E., M.R. Samuels, and J.D. Eliasen, Chemical
Engineering Thermodynamics: The Study of Energy, En-
tropy, and Equilibrium, Prentice-Hall, New York (1972)
2. McQuarrie, D.A., Statistical Mechanics, Harper and Row,
New York (1976)
3. Hansen, J.P., and I.R. McDonald, Theory of Simple Liquids,
2nd ed., Academic Press, New York (1986)
4. Abbott, M.M., "Thirteen Ways of Looking at the van der
Waals Equation," Chem. Eng. Prog., 85(2), 25 (1989)
5. Soave, G., "Equilibrium Constants from a Modified Redlich-
Kwong Equation of State," Chem. Eng. Sci., 27, 1197 (1972)
6. Flory, P.J., "Principles of Polymer Chemistry," Cornell Univ.
Press, Ithaca (1943)
7. Blanks, R.F., and J.M. Prausnitz, "Thermodynamics of Poly-
mer Solubility in Polar and Nonpolar Systems," Ind. Eng.
Chem. Funds, 3, 1 (1964)
8. Fredenslund, A., R.L. Jones, and J.M. Prausnitz, "Group
Contribution Estimation of Activity Coefficients in Nonideal
Liquid Mixtures," AIChE J., 21, 1086 (1975)
9. Wilson, G.M., "Vapor-Liquid Equilibrium: IX. A New Ex-
pression for the Excess Free Energy of Mixing," J.A.C.S., 86,
127 (1964)
10. Sandler, S.I., "From Molecular Theory to Thermodynamic
Models," Chem. Eng. Ed., 24(2), 80 (1990) 0

laboratory

BASIC CHEMICAL ENGINEERING

EXPERIMENTS

W. E. JONES
University of Nottingham
Nottingham, United Kingdom NG7 2RD
his article is concerned with laboratory work
undertaken in the early years of an under-
graduate chemical engineering course and is
based on the author's experiences at the University of
Nottingham. Our department teaches two under-
graduate courses in parallel: a six-semester BEng
and an eight-semester MEng. Each semester is of
fifteen weeks duration, and there are two semesters
per academic year. The first four semesters are com-
mon, and it is to this portion of the course that this
article is devoted.
The objectives of any student's experimental work
are:
to illustrate and reinforce chemical engineering theory
and principles
to provide hands-on experience with some commonly
used process equipment
to demonstrate experimental methodology and tech-
niques
Further time available for laboratory work is limited.
To meet the above objectives, a wide range of
experiments is required, and those used at
Nottingham in the first four semesters are summa-
rized in Table 1. The experiments must be tightly
defined and carefully arranged so that a two-student
team can perform the work in a three-hour session.
Groups of three to six experiments are associated
with appropriate modules, and in most cases stu-
dents will undertake one or two experiments from
this group as an integral part of the module.

Warren Jones holds BSc and PhD degrees in
Chemical Engineering from the University of
Nottingham and is a registered Chartered En-
gineer. He has a wide-ranging interest in both
front-end process and detailed plant design de-
veloped initially through nine years of experi-
ence with a major engineering and construc-
tion company. Teaching responsibilities include
several design courses, process economics,
and engineering thermodynamics.

Some of the experiments listed in Table 1 are
standard and are found in many undergraduate labo-
ratories. Others are "classic" chemical engineering
experiments, and yet others introduce unusual as-
pects to the laboratory. It is not the author's intention
to describe every experiment in the table, but rather
to take selected experiments and discuss
how some of the standard experiments can be made
more interesting
how some of the "classic" experiments can be per-
formed more effectively
how unusual aspects can be exploited in the labora-
tory

LABORATORY PHILOSOPHY
The experiments are all manually controlled. This
forces the students to "work the rig" and develop a
feel for the way a process plant behaves. They learn
that flow and pressure systems respond very quickly
and hence large quantities of data can be collected
very quickly, but that heat and mass transfer sys-
tems are much slower and may require considerable
time to reach steady state. Some process interactions
are found, e.g., many students are initially surprised
when steam pressure drops on increasing cold-side
flow through a heat exchanger.
Nottingham's laboratory has its own boiler, and
steam is distributed to most of the rigs that re-
quire heat input. This is in line with our policy
of trying to emulate industrial practice and is an
important element in mimicking the behavior of a
"real" process plant.
Many of the experiments are designed and built
with a significant glass and/or acrylic resin
perspexx) content so that students can see the pro-
cess operating. This is particularly important for
situations such as vapor-liquid contacting; boiling,
and two-phase flow. However, care is needed because
poor thermal conductivity (as compared to copper
or steel) can distort the heat transfer phenomena
being investigated.

Copyright ChE Division ofASEE 1993

Chemical Engineering Education

FLUID MECHANICS
Centrifugal Pump Operation Since centrifu-
gal pumps are widely used in process plants, it is
important for students to become familiar with their
performance characteristics. The simplest experiment,
commonly performed, is measurement ofhead-capac-
ity characteristics. (As an aside, it is worth consider-
ing how few student textbooks mention the head-
capacity curve, let along explain how it is used.)
However, several interesting variations on the basic
experiment are possible.
The first version measures head and shaft power
as a function of capacity at three speeds of rotation.
The speed variation is obtained by using a belt and
pulley drive from a fixed-speed electric motor. Belt
and pulley drives have significant friction effects,
and it is important to "back out" these losses when
determining the pump shaft power. To do this, the
pump must be capable of being disconnected and the
remainder of the system run with no load to deter-
mine a base power consumption. The shaft power is
then obtained as the difference between measured
power consumption of the motor in normal operation
and the base power consumption.
After measuring the head and shaft power, the
pump efficiency is easily calculated, and the students
are able to plot the three characteristic curves of the
pump: head, shaft power, and efficiency versus ca-
pacity, all with lines of constant speed. A further

TABLE 1

FLUID MECHANICS
Venturi tube*
Pipe flow friction*
Orifice discharge*
Velocity profiles in a pipe
Pressure drop in pipe fittings
Liquid distribution
Pump operation at varying speed
Pumps operated in parallel and series
Pump operated on various fluids
Air lift pump
MASS TRANSFER
Measurement of gas diffusivity
(stagnant film)
Measurement of gas diffusivity
(counter-diffusion)
Wetted wall column
Wetted disc column
ENGINEERING THERMODYNAMICS
Turbine isentropic efficiency
Fan polytropic efficiency
Refrigeration COP
PARTICLE MECHANICS
Packed and fluidized beds (air)
Packed and fluidized beds (water)
Particle elutriation

HEAT TRANSFER
Heat transfer coefficient in
Heat transfer coefficient ou
Double pipe heat exchange
Plate heat exchanger
Unsteady-state tank heatin1
Boiling heat transfer
Thermosyphon reboiler
Heat transfer in fluidized b
Unsteady-state heating of s
Temperature profiles in sol
UNIT OPERATIONS**
Packed column distillation
Oldershaw column distilla
Adiabatic humidification
Wet solids drying
Liquid-liquid extraction (m
CHEMICAL PROCESS PR
Boiler efficiency
Mass and heat balances on
combustion engine
Heat balance on batch proc
Heat balance on recycle pr
*Compulsory experiment
**Experiments take two three-hour s

feature of this experiment is that it may be used as
another illustration of dimensionless correlations.i1I
In particular, the collapse of the various head-versus-
capacity lines due to speed variation into one line on
dimensionless coordinates is very effective.
In some large pumping operations it is necessary
to run two or more pumps in parallel (e.g., cooling
water circulation), and this provides an idea for an-
other useful centrifugal pump experiment. Two pumps
are run individually, in series and in parallel. Stu-
dents measure the head-capacity characteristics for
each configuration and learn how individual pump
characteristics can be combined to predict the head-
capacity characteristics for series and parallel opera-
tion.[2] If the two pumps are dissimilar, then the
limitation imposed by the lowest shut-off head of the
pair again surprises students.
The third centrifugal pump experiment is simpler
and demonstrates the important characteristic that a
given pump will always throw up the same head at a
given capacity, even though it is pumping different
liquids, provided liquid viscosity is low. (This ex-
plains why water testing by a pump manufacturer is
often sufficient.) Hence, as the liquids pumped have
different densities, the pressure increase measured
across the pump changes. Measuring the head-capac-
ity characteristics of a pump on two different fluids
(i.e., water and kerosene) is a good way to demon-
strate this point.
Fluid Distribution One of the most
neglected areas of chemical engineering
is fluid distribution. The operation of
side tubes many real plant pieces can be impaired
itside tubes by mal-distribution, and the require-
r ments to obtain approximately uniform
g distribution are quite restrictive.3'41 An
experiment to illustrate the difficulties
studies one branch of a pipe distributor.
olids A variety of branches fabricated from 22-
ids mm ID pipe, each 1.0-m long, are avail-
able. Each branch has six uniformly
spaced discharge holes on the bottom,
tion and four (also uniformly spaced) pres-
sure tappings on the top. The branches
differ in discharge-hole sizes, which range
ixer-settler) from 5.6 mm to 10.3 mm. Each branch
INCIPLES may be connected in turn to a constant
head supply of water with the through-
erna put controlled by a throttling valve in
ess the supply line.
ocess When they first run the rig, most stu-
dents are caught unaware by the fact
sessions that the pressure increases along the

Winter 1993

branch and the increase is relatively more marked for
the larger-size discharge holes. This phenomena is
easily explained by application of Bernoulli's equa-
tion and is the cause of the mal-distribution problem.
The higher pressure at the closed end of the branch
causes a greater discharge rate there as compared to
the inlet.
Students determine the water discharge rate from
each hole and record the pressure profile along the
branch for a few throttle valve settings. The proce-
dure is then repeated for other branches, and this
collected data allows the students to infer the re-
quirements for good distribution in terms of water
inlet velocity to the branch and pressure drop across
the discharge holes. Friction loss along the branch is
not significant in this rig. The criterion used for good
distribution is that the maximum variation between
highest and lowest hole discharge rates for a given
throttle valve setting should be less than 10%.
Two-Phase Flow Two-phase flow occurs fre-
quently in process plants, and incorrect analysis or
neglect may result in poor plant performance or
hazardous situations.'5 It is often an area not covered
in undergraduate courses, and suitable student ex-
periments that can be performed in three hours are
rare. The easiest way to introduce a two-phase flow
element into the laboratory is with an air-lift pump.'61
The rig is based on a nominal 25-mm ID glass riser,
and liquid lifts of up to 3.33 m are used. Motive air
may be injected at submergences up to 5.5 m, and
students are asked to investigate the variation in
water throughput as the air flowrate is changed. The
water throughput passes through a sharp maximum
illustrating the gravity- and friction-dominated re-
gimes at low and high air flowrates, respectively.
HEAT TRANSFER
Effect of Velocity The fundamental experi-
ments in this group involve measurement of inside
and outside tube heat transfer coefficients. The sim-
plest and most effective way to perform both of these
measurements is to ensure that the resistance of the
coefficient to be measured is the dominant effect.
Hence, the inside-tube heat transfer coefficient is
measured for low-pressure air flowing through a
copper tube and heated by condensing steam in a
surrounding jacket. Likewise, the outside-tube heat
transfer coefficient is obtained by blowing low-pres-
sure air over the "shell side" of bundles comprising
copper tubes arranged on square and triangular
pitches; heating is again by condensing steam, but
this time it is contained in the tubes. The heat trans-
fer resistance provided by condensing steam and
copper tubing is negligible compared to the air-film

resistance, and the measured overall heat transfer
coefficient is a very good approximation to the air-
film coefficient. Both experiments will produce
straight line plots ofNusselt number versus Reynolds
number on log-log axes.
Our experience indicates that the best technique
for demonstrating the effect of velocity on a liquid
film heat transfer coefficient is construction of a
Wilson plot."' This approach is used because assum-
ing the measured overall heat transfer coefficient
approximates the individual film coefficient is not
sufficiently accurate when heating a liquid. The Wil-
son plot takes the condensing steam, copper wall, and
dirt resistances as constant, and hence the reciprocal
of the measured overall coefficient can be plotted as a
straight line against the reciprocal of (process water
flowrate)0.8 if we assume that the Dittus-Boelter equa-
tion models the water film coefficient inside a tube.
The experiment is performed in a steam-heated
double-pipe exchanger with condensing steam in the
annular space. Extrapolation of the straight line to
its intercept with reciprocal of the measured overall
coefficient axis gives an estimate of the sum of all the
other resistances to heat transfer. Using a typical
condensing steam film resistance (not very signifi-
cant) and calculating the resistance due to the copper
wall means the only unknown resistance, sum of the
dirt films, can be determined.
The advantage of performing the heat-transfer
experiments as described above is that it avoids
measuring the metal-wall temperature which can be
unreliable and consume considerable technician time
in dismantling the equipment to investigate suspect
readings.
Condensate Blanketing and Sub-Cooling *
The tank-heating experiment compares warming a
batch of liquid using a submerged coil in the tank
with a pumparound through an external heat ex-
changer. The heat transfer area of the coil and ex-
changer are equal so for the same steam operating
pressure it is interesting to observe that the tank
may be heated faster or slower than by the coil,
depending on the pumparound through the exchanger.
Applying the equations in Perry and Green"s8 it is
possible to determine the overall heat transfer coeffi-
cients for the unsteady-state heating process in each
case. However, the overall heat transfer coefficient
determined for the submerged coil tended to be
unreproducible and lower than expected.
As originally built, the submerged coil used 6-mm
diameter tubing with a large number of turns.
Excessive condensate "hang up" in the coil, obscuring
the heat transfer area, was suspected, and therefore
Chemical Engineering Education

the coil was replaced by a harp using vertical tubes
of 13-mm diameter tubing. The condensate now
drains freely and the measured overall heat coeffi-
cient is larger, in line with the anticipated value, and
reproducible.
An extreme example of obscuring the heat transfer
surface by condensate was encountered in the plate
heat exchanger unit. The very good heat transfer
performance of the plate heat exchanger means that
the steam is not only condensed but highly sub-cooled

Temperature

-o Sub-Cooling
Duty QS M

IT IT,

IT2

IT'
m Dut

Condensng
Duty Q

Ts = steam saturation temperature at operating pressure
Tc = steam condensate exit temperature
T1,T2 = process water inlet/outlet temperature
m = process water flowrate
Estimate of cross-over temperature

hwater(T) -hwater T (Tc
hsteam(Ts water M ) )
Condensing duty, Q, = m[hwr(T2) hw.,r(T')]
Sub-cooling duty, Qsc = m[hwate,(T') hwatr(Ti)]
Log-mean temperatures are given for the condensing and
sub-cooling regions by

AT T2 T' and A (T -T')- (T -T,)
AT=- and ATc = Ts-T'
e -Ts 2 n Tn

Define

(UA)
(UA)c -AT

sca
and (UA)sc =s

Weighted temperature difference
QC + Qse
(UA)c + (UA)s,,
Weighted overall heat transfer coefficient

U = Q + Qs (UA), +(UA)s8
ATwA A
Figure 1.
Winter 1993

to a temperature near that of the cold inlet process
water to be heated. The plate heat exchanger is
arranged for parallel flow, i.e., strictly counter-cur-
rent operation, but the heat transfer process deviates
substantially from the commonly analyzed example
in undergraduate courses. Figure 1 clearly illus-
trates the discontinuity in the enthalpy-versus-
temperature plot which is the source of the dif-
ficulty. Analysis of the experimental results is diffi-
cult because the heat transfer areas for condensing
and sub-cooling cannot be identified. The best ap-
proach is to determine (UA), and (UA)sc based on
an estimate of the process cross-over temperature, T',
as indicated in the figure. The performance of the
unit can then be expressed in terms of the weighted
temperature difference, ATw, and weighted heat
transfer coefficient, Uw.?9 This experiment is impor-
tant in illustrating to students that you simply do
not take the four terminal temperatures of a heat
exchanger to calculate a log mean temperature dif-
ference without considering the process actually
occurring in the unit.
Boiling Heat Transfer One area of heat trans-
fer where visual inspection is important is boiling.
We use a proprietary rig for demonstrating nucleate
and film boiling and for measuring heat flux varia-
tion with temperature difference. This works well,
but industrial reboilers exhibit much more complex
phenomena. The choice generally lies between verti-
cal and horizontal thermosyphons. If a vertical
thermosyphon (where boiling occurs in the tubes)
is selected for laboratory work, then a heavy duty
glass tube is required in order to see the boiling and
the thermal resistance of the wall dominates the
heat transfer. Hence, for the laboratory, boiling on
the outside of copper tubes in a horizontal
thermosyphon is a better choice. This construction
means that condensing steam is contained in the U-
tube bundle and flow boiling phenomena can be in-
spected through a glass shell.
The experiment most suitable for second-year
students is the measurement of overall heat trans-
fer coefficient variation with shell-side flow
through the unit. But a word of caution is required-
this type of unit (both laboratory- and commercial-
scale) commonly exhibits an instability at low
loads.!101 In fact, an excellent third-year laboratory
project is to determine the stability envelope for the
unit in terms of the two parameters, steam pressure
and shell-side flow.
Fluidized Bed Heat Transfer Heat transfer
from a hot surface to a fluidized bed is worth includ-
ing because the heat transfer coefficient passes
55

through a maximum as fluidizing air flow is varied.
The rig comprises a vertical copper tube (heated by
condensing steam) located at the center of a small
fluidized sand bed. Again, the measured overall heat
transfer coefficient will be a good approximation to
the film coefficient of interest. The heat transferred is
based on the gain in air temperature between the bed
inlet and outlet. In addition, a few thermocouples are
located in the bed to demonstrate the very effective
mixing which occurs and the resulting uniformity
through the bed. But do not place the lowest of the
bed thermocouples closer than about 25 mm to the
bed support because there is a very rapid tempera-
ture transition in this region.
Ideally, students should investigate the heat trans-
fer coefficient versus air-flow curve for various fluid-
ized solids. Unfortunately, the rig is slow to stabilize
at new conditions, and readings on only one fluidized
solid are possible in the period of three hours. Corre-
lations for heat transfer between hot surface and
fluidized bed tend to be problem specific and not very
accurate, so the experiment simply asks students for
a comparison of the measured maximum heat trans-
fer coefficient with that predicted by the equation of
Zabrodsky, Antonishin, and Parnas.['11
Heat Losses Finally, the quality of experimen-
tal results can be significantly affected by the way
measured data is processed. This is particularly true
of heat transfer experiments where the small scale
means the rigs have a relatively high surface-to-
volume ratio leading to high heat losses. This prob-
lem is compounded in some cases by the fact that rigs
are left at least partially unlagged for visual inspec-
tion of the process. Good engineering practice means
that students are encouraged to check the consis-
tency of their data by comparing heat gain by the
process stream with heat released from the steam
condensate collected. But students need to consider
which heat load to use in the calculation of heat
transfer coefficients. As a rule of thumb, if a condens-
ing steam is involved the heat losses will be large and
it is best to base the calculations solely on the process
heat gain. If two streams, both at modest tempera-
ture, are exchanging heat, then the average of heat
gain and heat lost is likely to be the best assumption.
MASS TRANSFER
The major problem with mass transfer (and for
that matter, unit operations) is that it involves com-
position measurement. Compared to temperature,
pressure, and flow measurements, composition mea-
surement is much more time consuming and offers a
greater potential for error. Thus it is worth expend-
ing some effort to devise experiments which either

automate the composition measurement or use mate-
rials for which a simple physical measurement can be
used to infer the composition.
Gas Diffusivities The measurement of gas
diffusivity in the context of a stagnant film by Stefan's
method is an excellent experiment as it avoids direct
composition measurement. In the case of counter-
diffusion, we use Gover's method1121 modified by intro-
duction of a tracer gas to simplify the GLC analy-
sis.'13' The use of a tracer gas means that all concen-
trations of diffusing component can be measured
relative to the tracer and thus avoids absolute con-
centration measurement, which is helpful.
Film Mass Transfer Coefficients The wetted-
wall column[14] for investigating gas-film mass trans-
fer coefficients has a reputation as a difficult experi-
ment to make work with respect to establishing and
maintaining a wetted wall. Most of the difficulty is
due to the initial liquid distribution. The technical
staff at Nottingham has devised a distributor which
allows a stable film to be easily established at the
start of a three-hour session and just as easily main-
tained throughout the period (see Figure 2). The only
maintenance needed is cleaning of the small-diam-
eter holes which can foul. The film produced normally
has a slight ripple (as one might expect at slightly
higher liquid loadings), but the data collected by
students is sufficiently good to demonstrate that the
Sherwood number is proportional to the (Reynolds
number)08s. The rig is run on water and air, and the
inlet and outlet gas compositions are easily measured
by a humidity probe utilizing electrical capacitance.
To investigate liquid-film mass transfer coefficients,
we use a wetted disc column""51 and strip dissolved
oxygen out of water using nitrogen.!6' The advantage
of this system is that oxygen compositions can be
easily measured by using a dissolved oxygen meter
and the quantity stripped is so small that the gas
phase may be treated as pure nitrogen.

Figure 2. Distributor for wetted-wall column
Chemical Engineering Education

UNIT OPERATIONS
Distillation The small scale distillation col-
umns are run on a methyl ethyl ketone-toluene mix-
ture which has the advantage that compositions are
easily inferred by refractive index measurement.1171
The columns are run at total reflux, and the liquid
from the condenser and bottom of contacting section
are sampled to determine separation performance.
Students investigate the effect of reboiler heat
input, i.e., effectively changes vapor-liquid traffic in
the column, on the separation achieved. To obtain
measurable changes in distillate composition it is
necessary to carefully select the composition of the
mixture initially charged to the reboiler. A mixture
comprising 90% toluene/10% methyl ethyl ketone is
about right and will give distillate compositions in
the range of 80-95% methyl ethyl ketone provided
excessive separation capability is not installed (see
below). Distillate compositions approaching 98%-plus
of methyl ethyl ketone should be avoided.
The main problem areas of distillation experi-
ments are heat losses and column end effects. Col-
umns of 50-mm diameter are the very minimum to
use. Despite being well insulated or vacuum jack-
eted, heat losses are significant, and the vapor-liquid
traffic changes through the column. Thus the separa-
tion performance variation with heat input mea-
sured is at best indicative. In the case of packed
columns, heat losses help accentuate the tendency for
liquid channeling along the wall. Using a column

Figure 3. Packing support-simplification of a
commercial injection plate.
Winter 1993

diameter of 50 mm means that a column diameter-
packing size ratio of 8 can be achieved, and this helps
counter channeling.
End effects are mass transfer occurring outside
the contacting section of the apparatus, e.g., mass
transfer between liquid leaving the bottom of the
contacting section and vapor rising from the reboiler.
These effects can be minimized by placing the liquid
sample points close to the top and bottom of the
contacting section.
There is an additional end effect which is easily
introduced into packed towers by using inappropri-
ate packing support. If the vapor and liquid are not
routed separately through the packing support, a
liquid pool forms above the support-and the vapor
must bubble through this pool. This arrangement
effectively adds the equivalent of one theoretical plate
to the height of packing, it distorts mass-transfer
performance, and it is potentially dangerous because
it induces premature flooding.
Figure 3 shows the preferred arrangement. It al-
lows the ascending vapor to enter the packed bed
through chimneys while the descending liquid drains
through holes in the support plate deck. The chim-
neys should occupy 15-20% of the cross-sectional
area, and the hats prevent liquid from draining down
the inside.
The unit operations experiments require two af-
ternoons (see Table 1). In the case of packed column
distillation, two separate packed heights are investi-
gated (one on each afternoon): 23 cm and 46 cm of 6-
mm ceramic Berl saddles. If excessive end effects are
avoided the students should be able to confirm that
roughly twice the number of transfer units are avail-
able in the longer bed compared to the short one. The
Oldershaw column distillation also takes two after-
noons and investigates columns containing 3 and 5
actual plates, but the experiment provides an inter-
esting detective challenge for the students.
The Oldershaw plates in the two columns are
identical: same diameter, same number of holes, and
same hole size. The three-plate column is correctly
assembled and exhibits a plate efficiency of approxi-
mately 70%. But the measured separation of the five-
plate column is not proportionately better, and stu-
dents are asked if they can see any factors leading to
the deterioration in performance.
The five-plate column is incorrectly assembled.
The plates are not level, so only part of the plate
bubbles and the downcomer is badly located-with
the result that much of the plate is short-circuited.
The experiment very effectively points out the need
for proper vapor and liquid contacting.
Mass and Heat Transfer in Packed Towers A
57

simple experiment illustrating the influence of gas
and liquid rates on gas phase transfer coefficients in
packed towers is based on adiabatic humidification 1"'
using the air-water system.
Water is circulated over the packed bed in a
pumparound system and it stabilizes at the adiabatic
saturation temperature. Obviously, there is no liq-
uid-phase mass or heat transfer resistance, so all the
resistance lies in the gas film and the problem of
interface condition has been eliminated. Compressed
air (hence, of very low humidity) is pressure-reduced
to just above atmospheric, and then heated to near
100C prior to counter-current contact with the circu-
lating water. Contacting is over a short depth of
relatively open packing: 125 mm of 30-mm metal
Intalox Saddles. As before, use of the air-water sys-
tem means composition measurements can easily be
made by using a humidity probe.
The driving force for heat transfer is the tempera-
ture difference between the air and circulating water
at any elevation. Likewise, the mass-transfer driving
force is the difference between the saturation humid-
ity at the water temperature and the actual humidity
of the air. If the packing depth is too great or the air
flow is too low, these driving forces will go to zero at
the top of the packing. It is therefore important to
limit the packing depth and use high air flows in
order to obtain measurable driving forces. Obtaining
suitable air flows without flooding requires use of a
relatively open packing, but packing wetting is then
never completely satisfactory. The experimental re-
sults are particularly sensitive, as one might expect,
to the condition of the humid outlet air.
The mass and heat transfer coefficients may be
correlated by equations of the form181
hDa = CDGmL and hGa = CGCL
where (hDa) and (hGa) are the volume-based mass and
heat transfer coefficients, G and L are the gas and
liquid loadings on the packing, and CD and GG are
constants. Hence, by collecting a grid of measure-
ments comprising four gas loadings by four liquid
loadings it is possible to plot on log-log axis (hGa) and
(hDa) versus G at constant L, or L at constant G. In
the time available, the values obtained for m, n, p,
and q are not particularly accurate (e.g., m and p
range 0.5 to 0.9, and n and q range -0.1 to 0.4), but the
experiment clearly illustrates the strong dependence
on G and weak dependence on L of gas-phase transfer
processes in packed towers. It is also useful to illus-
trate adiabatic saturation temperature and as prac-
tice in heat balancing over the tower.
Liquid-Liquid Extraction Work is currently
underway on a small mixer-settler experiment for
58

liquid-liquid extraction. Mass transfer is from kero-
sene to water, with kerosene drops dispersed in water
as the continuous phase. This makes it easy to recycle
kerosene. (The water contains a secondary haze and
should not be disposed of directly to a sewer.)
The equipment is largely fabricated from glass
because wall coalescing effects are minimized when
using water as the continuous phase. Further advan-
tages are visual inspection and easy maintenance.
The experiment has a number of unusual features.
One is that the component transferred is methyl red
indicator which changes color from yellow to red upon
transfer from the kerosene phase to water (actually
0.01-M sulphuric acid). The color intensity in either
phase can be related to concentration, and hence the
phases can be sampled and subjected to colorimetry
to determine the concentration of methyl red. Mixer
samples need to be taken through hydrophobic and
hydrophilic probes. Use of kerosene-water-methyl
red is based on previous experience with this system
in a pilot-plant scale liquid-liquid extraction unit.!191
The second unusual feature is that the apparatus
allows the choice of two types of settler. A vertical
settlerE20'211 is used on one afternoon, and a horizontal
unitE221 is used on the second. So in addition to having
the potential to investigate the effects of such vari-
ables as throughput and mixer speed on stage effi-
ciency, students can also study the effect of through-
put on coalescing band depth in the vertical settler
and coalescing wedge length in the horizontal unit.
A few words of warning on the use of methyl red
are necessary. The properties of kerosene can vary
slightly, and so the equilibrium line for distribution
of methyl red between the kerosene and water phases
has to be checked occasionally. Also, commercial
methyl red should be recrystallized to improve purity
before dissolving it in kerosene.
SUMMARY
This article has presented an overview of
Nottingham's approach to basic experimental work
in the laboratory. In addition to commonly performed
experimental work, a number of novel experiments
and unusual approaches have been adopted that both
emphasize the practices and highlight the problems
of industry. The author realizes that some of the
descriptions are brief and would be pleased to answer
any follow-up questions or hear of other academics'
experiences with similar experiments.
REFERENCES
1. Kay, J.M., and R.M. Nedderman, Fluid Mechanics and Trans-
fer Processes, 1st Ed., Cambridge, 273 (1985)
2. Karassik, I.J., W.C. Krutzsch, W.H. Fraser, and J.P. Messina
(Eds.), Pump Handbook, 1st Ed., McGraw-Hill, New York, 2-
170 (1976)
Chemical Engineering Education

3. Senecal, V.E., Ind. Eng. Chem., 49, 993 (1957)
4. Perry, R.H., and D. Green (Eds.), Perry's Chemical Engineers'
Handbook, 6th Ed., McGraw-Hill, New York, 5-48 (1984)
5. Tilton, J.N., and A.W. Etchells, The Chemical Engineer, No.
465, 3 (1989)
6. Perry, R.H., and C.H. Chilton, Chemical Engineers' Hand-
book, 5th Ed., McGraw-Hill, New York, 6-14 (1973)
7. Coulson, J.M., and J.F. Richardson, Chemical Engineering,
Vol. 1, 4th Ed., Pergamon, 410 (1990)
8. Perry, R.H., and D. Green, (Eds.), Perry's Chemical Engi-
neers' Handbook, 6th Ed. McGraw-Hill, New York, 10-38
(1984)
9. Ludwig, E.E., Applied Process Design for Chemical and Petro-
chemical Plants, Vol. 3, 2nd Ed., Gulf, 50 (1983)
10. Kister, H.Z., Distillation Operation, 1st edn., McGraw-Hill,
New York, 451 (1990)
11. Zabrodsky, S.S., N.V. Antonishin, and A.L. Parnas, Can. J.
Chem. Eng., 54, 52 (1976)
12. Gover, T.A., J. Chem Educ., 44, 409 (1967)
13. Paterson, W.R., Chem. Eng. Ed., 19, 124 (1985)
14. Gilliland, E.R., and T.K. Sherwood, Ind. Eng. Chem., 26, 516
(1934)
15. Stephens, E.J., and G.A. Morris, Chem. Eng. Prog., 47, 5, 232
(1951)
16. Sherwood, T.K., and F.A.L. Holloway, Trans. Am. Inst. Chem.
Eng., 36, 39 (1940)
17. Steinhauser, H.H., and R.R. White, Ind. Eng. Chem., 41, 2912
(1949)
18. Hensel, S.L., and R.E. Treybal, Chem. Eng. Prog., 48, No. 7,
362 (1952)
19. Hills, J.H., private communication
20. Ryon, A.D., F.L. Daley, and R.S. Lowrie, Chem. Eng. Prog.,
55, No. 10, 71 (1959)
21. Gondo, S., and K. Kusunoki, Hydrocarbon Processing, 48, No.
9, 209(1969)
22. Hanson, C., (Ed.) Recent Advances in Liquid-Liquid Extrac-
tion, Pergamon, 544 (1971) 0

REVIEW: Staged Operations
Continued from page 27.
three chapters. Chapter 7 details the tedious hand
calculations performed for the design of multicompo-
nent systems. This provides motivation for the devel-
opment of a computer code to implement the methods
of Lewis-Matheson and Thiele-Geddes in Chapter 8
and the shortcut methods derived by Fenske,
Underwood, and Gilliland in Chapter 9.
Complex distillation methods which handle
azeotropic, extractive, and two-pressure distillation
are covered in Chapter 10. Chapter 11 presents a
switch from continuous operation to methods associ-
ated with batch distillation using the Rayleigh equa-
tion. Chapter 12 contains information regarding
staged column design including column diameter,
efficiency, and tray size, while packed column design
is discussed in Chapter 13. Consideration of economic
trade-offs between various design options leads to a
more detailed discussion of economics in Chapter 14,
which addresses such topics as capital and operating
costs, energy conservation, and column sequencing.
The processes of absorption and stripping are ana-
Winter 1993

lyzed in Chapter 15, using the Kresmer equations as
well as the McCabe-Thiele method. Immiscible ex-
traction in Chapter 16 is also discussed in the context
of the McCabe-Thiele analysis. For extraction involv-
ing dilute mixtures, the Kresmer equations are shown
to be appropriate. Example calculations for cross-
flow operations are also included.
In Chapter 17, generalizations of the McCabe-
Thiele analysis are applied to washing, leaching,
supercritical fluid extraction, and three-phase sys-
tems. Table 17.1 effectively summarizes the relation-
ships between the various separation processes in
terms of McCabe-Thiele analysis.
Extraction for partially miscible systems with tri-
angular diagrams and the lever rule is analyzed in
Chapter 18, and Chapter 19 introduces mass transfer
concepts for design of packed beds, mass transfer
coefficients, sum of resistances, and tray efficiencies
leading to HTU-NTU analysis for absorbers and strip-
pers. Note that rate-limited processes, including ad-
sorption, chromatography, electrophoresis, and mem-
brane separations, are included in a sequel to this
text entitled Mass Transfer Limited Separations.
The predominant concept in this text is the McCabe-
Thiele analysis. Distillation, absorption, and extrac-
tion processes are treated in terms of McCabe-Thiele
diagrams. This approach emphasizes the analogies
between these separation processes, which is very
instructive from a pedagogical point of view. But it
consequently results in a very narrowly focused book.
The narrow focus is my major criticism of this text.
Our current curriculum combines a study of equilib-
rium-staged separation processes with fundamen-
tals of mass transfer and rate-controlled separation
processes within a single course during the second
semester of the third year. This text would only cover
about one-third of the material for the course and
therefore would require either additional texts or
other supplementary material for the remaining top-
ics. Since students are generally opposed to purchas-
ing more than one text for any given course, I see this
book filling the role of a supplementary text to comple-
ment a primary text that covers a broader range of
material. The other alternative would be to devote an
entire course to equilibrium-staged operations, for
which this book would be an excellent text. However,
with the chemical engineering curriculum already
overloaded, it is difficult to justify creation of a new
course for this single topic.
One additional minor criticism regards the ap-
pearance of the print. The type is not particularly
easy on the eye since the book has evidently been
produced in camera-ready form on a low-resolution
(by printing standards) printer. D

M views and opinions
-- .---------------

ADVANCED ENGINEERING CALCULATORS

Don't Overlook Them!

CONAN J. FEE
University of Waikato
Private Bag 3105
Hamilton, New Zealand

I recently attended a conference on engineering
education where one of the sessions concerned
the use of computers in the chemical engineering
curriculum, during which the speakers described the
use of process simulation software and spreadsheeting
techniques in their teaching programs. At the end of
the session I asked if they had ever given any consid-
eration to including an instructional component re-
garding the use of calculators. In short, the answer
was "no," and I got the impression that the matter
was regarded as trivial by the majority of educators
present. I also noted an inconsistency: the speakers
had proudly outlined a "keyboard familiarity" com-
ponent in their introductory computing program,
yet with regard to calculators they voiced the
opinion that "one should not have to teach the stu-
dents absolutely everything-some things they
should learn by themselves!"
I agree wholeheartedly with the latter belief. In-
deed, it is fundamental to the university teaching
concept that students must take the major responsi-
bility for their own learning. I also applaud the inclu-
sion of computing skills in the curriculum; the prolif-
eration of affordable and powerful personal comput-
ers over the past decade and the emergence of spread-
sheets as an engineering tool combine to make this
essential for the engineering graduate.
But I take issue with the commonly held belief that
calculators are only a trivial component of the myriad

@ Copyright ChE Dwivsion ofASEE 1993

of tools available to the professional engineer. How
many of today's engineering educators would be sur-
prised to learn that the calculator that I currently
hold in my hand is capable of storing more than one
megabyte of information, available as RAM, and ten
megabytes of numeric information using data com-
pression? By way of comparison, this magnitude of
memory has only recently become widely available
for personal computers.
The amount of available memory is only one aspect
of today's advanced calculators; the real power of
these tools lies in how the information is utilized, and
I submit that it is this aspect that should be treated
seriously in the engineering curriculum. In the fol-
lowing discussion I will lean heavily on my personal
experience with one advanced calculator; the Hewlett-
Packard HP48SX Scientific Expandable. It is not
intended to be an endorsement of this particular
product or brand-in my opinion other makes of
calculators will likely soon rival the HP48SX, if they
do not do so already.
COMPUTERS EMBRACED-
CALCULATORS IGNORED
Before elaborating on the calculator's capabilities,
I want to give my view of how today's attitudes
towards computers and calculators developed. I be-
lieve the main reasons for the different attitudes are
1) that, unlike the PC, the advanced calculator does
not occupy a position of usefulness in the general
populace, and 2) that these two tools were introduced
at opposite ends of the utility spectrum. The PC was
driven by commercial (industrial) implementation
and was viewed as a way of putting mainframe com-
puting power in the hands of a single user. Huge
efforts in software development and the advent of
user-friendly software interfaces, pioneered by Apple's
Macintosh, have made the personal computer an
invaluable tool. This was quickly recognized by the
educational sector and accordingly was incorporated
into the curricula. Teaching efforts were at first di-
rected toward the development of programming skills
but, arguably, the evolution of spreadsheets and other
Chemical Engineering Education

Conan J. Fee received his BE and PhD (1984,
1989) from the University of Canterbury, New
Zealand, and was a postdoctoral fellow at the
University of Waterloo during 1989-90. He cur-
rently holds a joint appointment as a lecturer at
the University of Waikato and as a biochemical
engineer at the Meat Industry Research Institute
of New Zealand. His research interests include
bioreactors, bioseparations, and hemodynamics.

user-friendly packages have made this aspect (for
chemical engineers at least) less important in recent
years. The personal computer has been embraced by
educators.
In contrast, the calculator (at least in its affordable
form) had its origin at the very lowest level of the
utility scale, and it has never enjoyed the commercial
development to the extent that the personal com-
puter has. Whereas personal computers can be used
across a whole range of disciplines, from musical
composition to nuclear physics, the advanced calcula-
tor requires some measure of mathematical sophisti-
cation of its user. This dramatically limits its market.
At first, the calculator offered only the four basic
mathematical functions, replacing the slide rule. It
was seen by the old guard as not only unnecessary
but also as an actual threat to the development of
"essential" basic mathematical skills. To a certain
extent those fears have been realized-we of the
latest generation of engineers are probably neither as
quick at "in-the-head" calculations nor as good at
estimating magnitudes as our predecessors were.
(The argument could be made that these skills are
not as necessary as they once were. Perhaps the
necessity of "in-the-head" calculational skills for an
engineering professional is itself a subject for de-
bate.)
The calculator evolved to incorporate trigonomet-
ric and hyperbolic functions and, eventually, also
elementary statistical functions. Programmable cal-
culators appeared, but they were limited by available
memory to low-level languages and a finite number of
steps. Although various software applications be-
came available, the initial programming capability
was basic and time-consuming. For the student, the
usefulness of programming came mainly from the
automation of short, but tedious, repetitious number-
crunching during laboratory classes.
Alphanumeric displays soon followed, and the stu-
dent was now presented with higher-level languages,
the ability to write user-friendly software, and the
capability of storing information. With the advent of
larger displays came the ability to quickly and easily
plot functions and experimental data. Today, built-in
functions allow an engineer to enter eight or ten data
points and perform a regression analysis on the spot,
within a few minutes, without programming.
The following anecdote highlights the inaccessibil-
ity of advanced calculators to the public at large (and
even to other professional groups), which contrasts
distinctly to the accessibility (and hence the popular-
ity) of personal computers. A consulting engineer was
giving expert court evidence for the defense and was
Winter 1993

asked by the prosecution to estimate the outcome of
an hypothetical situation. The engineer replied that
he could not give an immediate answer since he did
not have his calculator with him. Smelling blood, the
prosecuting attorney offered the use of his own calcu-
lator, which had the four basic mathematical func-
tions. The engineer reiterated his inability to give an
immediate answer without his own calculator, at

Rather than viewing this as just another
subject vyingfor attention .., perhaps it should
be looked at as a way of easing the teaching load,
alleviating the drag caused by those students
who are overloaded with mathematical
tasks of dubious educational value.

which the prosecutor, this time smelling victory, cried,
"And you call yourself an expert?" This naive attempt
to question the engineer's competence backfired when
it became evident that the calculation required a
more sophisticated calculator and that the prosecu-
tor obviously did not understand the point of his own
question. The lesson is clear: the calculator has evolved
from its basic form into a device that requires consid-
erable mathematical sophistication to simply com-
prehend its potential utility.
For this reason it is only the knowledgeable users
who have driven its evolution and incorporated it into
everyday use. At each stage of its advancement stu-
dents have recognized the potential advantages of
the calculator's latest implementation (some cynics
might say it is only a result of the student's general
tendency to find the easiest route through any course),
whereas educators have consistently lagged behind
and have blocked its use by banning them from
exams. In all cases, the bans have eventually been
relaxed, but the negative knee-jerk reaction to new
technology persists at each stage.
CAPABILITIES OF THE LATEST CALCULATORS
I agree with the conference speakers that up until
the above stage of development, students could learn
to use calculators to their full capacity by themselves.
After all, these devices merely offered quick number-
crunching. Once you knew where the "cosine" button
was, what more was there to learn? But the current
generation of calculators has surpassed mere num-
ber-crunching and in the process has outstripped the
student's ability to comprehend their potential uses,
let alone to readily assimilate the available functions.
My own calculator comes with an 852-page manual,
plus an additional 230 pages for one of the expansion
cards, not to mention the 290-page external

programmer's development manual.
To illustrate my points further, let me describe my
calculator. (Once again, I advise that the following is
not intended to be an endorsement of a particular
product, and it obviously doesn't even approach an
objective, critical analysis of functionality!)
I have owned an HP48SX for about eighteen months
now and still have not grasped its entire functional-
ity. (I had previously owned two earlier models of the
same make.) The calculator has a 131x64 pixel graph-
ics display (which acts as a window onto a much
larger display area), divided into seven lines for text.
It has forty function keys, each having four built-in
functions and up to six user-defined functions, giving
400 immediate-entry functions. In addition, there
are six "softkeys" which take on various functions
according to the particular mode the calculator is in.
For instance, in the "Statistics" mode, these six keys
have 35 functions (plus user-defined functions) dis-
played on-screen in hierarchical sets of up to six
functions at a time. In all, the calculator has 2100
built-in functions.
It has, built in, 32k of ROM and 32k of RAM, with
two expansion slots for plug-in 32k, 128k, or 512k
cards that can be operated as ROM or RAM. In
addition, the calculator uses kermit protocol to com-
municate with remote devices (e.g., a personal com-
puter) via an RS232 port and features an infra-red
communication port for transferring data to a printer
or to another calculator. The power of the above
features alone is considerable. I also have eight mega-
bytes of application software for the calculator, stored
on my PC, which I can download or upload at any
time.
Do you still think the calculator is a trivial
tool? Read on...
The calculator is capable of symbolic algebraic
manipulation, differential and integral calculus, so I
can enter a function in algebraic mode (without pro-
gramming) and isolate a variable, simplify the ex-
pression, differentiate any variable (and define oth-
ers as functions of one or more variables), and inte-
grate between limits. It can even handle differential
equations. With the calculator, I can perform vector
and matrix algebra and solve systems of linear equa-
tions. Application software offers Gaussian elimina-
tion, row reduction, and determination of eigenvec-
tors and eigenvalues. Think of the advantage, for the
student learning process control, offered by a calcula-
tor that can perform Laplace transformations, solve
partial fractions, and produce Bode plots. This one
can do all of that.
62

The calculator has 147 built-in units which can be
combined in any consistent way and allows user-
defined units to be stored. It not only converts be-
tween units, but also allows the user to attach units
to any value and perform mathematical manipula-
tions, keeping track of unit consistency. For example,
I can add 10 ft/s to 10 mph and get 25 ft/s. (10 ft/s + 10
psi rightly gives an error.)
One of the most powerful features is the built-in
equation-solver. With this I can enter an equation
algebraically (no programming necessary), and the
calculator automatically gives an on-screen menu of
all variables involved and allows me to enter known
variables (with or without units) and solves for the
unknown. I can then change any values and re-solve.
This provides a "what-if' platform with obvious value
in design problems. Another available application is
the multiple-equation-solver. It links equations to-
gether and solves for any unknowns. For example, in
the plug-in Equations Library Card, one application
has eight linked equations for fluid flow. They are

(D2) (Ap 2kL
p^ v +gAy+V2 2f +-=L (1)
P 4 )avg- +gay+vg2f()+-))= w (1)
Ap=p2-pl (2)
Ay=y2-yl (3)
M = pQ (4)
Q= A Vvg (5)

A = D2 (6)
4

Re =D (7)

n (8)
P

Figure 1. Equations Library Card display of
fluid-flow system
Chemical Engineering Education

A
p2
Vavg

A
p
Vavg

(Nomenclature is standard and not worth including
for the purposes of this discussion.)
The press of a softkey displays each of these equa-
tions in turn, and another softkey displays an on-
screen picture of the system as shown in Figure 1.
Another softkey yields a description of the variables
and even the default units (the user may choose SI or
English):

Ap pressure change, kPa
p 1 initial pressure, kPa
p2 final pressure, kPa
Ay height change, m
etc.

By plugging the known values into the given menu
of all variables, the multiple-equation-solver can then
be asked to search through all eight equations and
solve for any unknown variables, repeating the pro-
cess until all possible solutions for unknowns have
been obtained from the given information. For identi-
fication purposes, calculated values are tagged differ-
ently from specified values.
The Equations Library Card has 128k ROM and
includes 315 common equations, organized under
fifteen categories (Columns and Beams, Fluids, Elec-
tricity, Solid Geometry, etc.). Also included are a
financial calculation package with time-value-of-
money, a set of engineering utilities (Re, friction
factor, etc.), and a collection of 39 commonly used
physical constants (gas constant, Boltzmann's con-
stant, etc.). Finally, it includes a periodic table of the
elements which contains all the chemical data that
appear in a standard periodic table of the elements.
The primary user-interface is the familiar grid of
elements and the user can select any element and
obtain a catalogue of 23 properties (melting point,
conductivity, etc.), each of which may be plotted
against atomic number. A molecular weight calcula-
tor allows typing in of formulae and quick calculation
of atomic weights.

Still a trivial and readily assimilable tool?
I have made no mention of the calculator's abilities
regarding complex numbers, binary arithmetic, or
user-defined functions, and have barely touched on
algebra, calculus, statistics, arrays, interactive plot-
ting, etc. Finally, a high-level language is available to
the user and an even more comprehensive instruc-
tion set (plus machine code) is available on the
freeware set of PC development tools for creating and
downloading application software for the calculator.
Winter 1993

THE PRESENT AND THE FUTURE
The point of the above description is to show that
calculators have now advanced far beyond the com-
plexity and capacity at which computers were wel-
comed into the engineering curriculum. The abilities
of today's advanced calculators go far beyond the
immediate capabilities of most (particularly the
less-advanced) undergraduates, yet their education
could be enhanced considerably by incorporating in-
struction on the use of the latest tools into the cur-
riculum. It is not sufficient to allow students to floun-
der about, applying tools beyond their level of com-
prehension and obtaining competence only (if at all)
in piecemeal fashion.
For those readers whose first instinct is to identify
and ban the most advanced calculators, I urge you to
think again. Recent history shows that such bans do
not last and instead a redesign of the things we are
testing is required. Indeed, if the advanced calcula-
tors are such a threat during exams, then their value
as tools is self-evident! But many educators tend to
ignore them during the student learning process and
attempt to abolish them during the student evalua-
tion process. This is a surprising oversight for sup-
posedly liberal institutions of higher education. Are
we doing justice to the teaching process if we ignore
these tools at the very time that an emerging profes-
sional requires the most guidance?
Our students use, and will continue to use, in-
creasingly sophisticated calculators on their own
throughout their university years and certainly be-
yond them. The knowledge-base of students has
steadily risen from year to year (the derivation of
Schrodinger's equation is standard first- or second-
year chemistry and superconductors are now old-
hat). We must allow more and more sophisticated
tasks to be delegated to number-crunching tools in
order to make room for the new knowledge. Should
our students really be spending their time struggling
through eigenvector and eigenvalue calculations when
they could instead be studying the relevant applica-
tion in more depth? (This is not to say, however, that
students needn't thoroughly understand the concepts
of eigenvectors and eigenvalues.)
Are those of us in the educational sector of the
engineering profession ignoring an opportunity to
contribute to the direction of the calculators' contin-
ued development? After all, they will continue to
develop, with us or without us. With the substantial
increases in solid-state memory capacity which are
certain to come, perhaps we will see the advanced
calculator being aimed at specific disciplines. That is,
instead of being aimed merely at business or engi-

63

neering professionals in general, as they are at
present, we may see calculators aimed specifically at
chemical engineers. Such a series of calculators might
consist of a common hardware core, with large-capac-
ity plug-in modules of extremely specific information
and operations which customize the calculator for
particular professions.
My own view is that the computing component of
the engineering curriculum should include serious
treatment of advanced calculators and that their
use in all aspects of engineering education (includ-
ing student performance evaluations) should be
encouraged. I do not suggest offering a course spe-
cifically on calculator usage for two main reasons.
First, how could one justify the selection of one brand
over another, or indeed the selection of calculators
per se over, for instance, spreadsheets as a topic
worthy of instruction? Second, the utility of such
material would rely heavily on existing technology
which quickly becomes outdated, leaving the gradu-
ate no further ahead.
Rather than viewing this as just another subject
vying for attention in an already overcrowded cur-
riculum, perhaps it should be looked at as a way of
legitimately easing the teaching load, alleviating the
drag caused by those students who are currently
overloaded with mathematical tasks of dubious edu-
cational value. In particular, using advanced calcula-
tors could give the instructor an opportunity to place
greater emphasis on "what if'-type problems from
which the students can quickly grasp the effect of
varying the parameter values on the outcome of a
solution without significantly increasing the time
required for completing the assignment.
Certainly, the future of calculators is aimed
at more comprehensive and sophisticated utility for
the engineering professional. We should take them
seriously. C

Cooperative Study Groups
Continued from page 41
Minority Education" National Action Council for Minorities in
Engineering, New York (1991)
3. Watkins, B.T., "Many Campuses Now Challenging Minority
Students to Excel in Math and Science," The Chronicle of
Higher Education, June (1989)
4. Triesman, P.U., "A Model Academic Support System," Chap-
ter 8 in Handbook on Improving the Retention and Graduation
of Minorities in Engineering," edited by R.B. Landis, National
Action Council for Minorities in Engineering, New York (1985)
5. Shelton, M.T., and M.C. Hudspeth, "Cooperative Learning in
Engineering Through Academic Excellence Workshops at Cali-
fornia State Polytechnic University, Pomona," 1989 Frontiers
in Engineering Education Conference Proceedings, American
Society for Engineering Education, Washington, DC

6. Hudspeth, M.C., "Developing an Academic Community
Through Academic Excellence Workshops," 1990 ASEE Con-
ference Proceedings, American Society for Engineering
Education, Washington, DC
7. Watkins, B.T., Berkeley Mathematician Strives 'to Help People
Get Moving, The Chronicle of Higher Education, June (1989)
8. Hudspeth, M.C., M.T. Shelton, and R. Ruiz, "The Impact of
Cooperative Learning in Engineering at California State Poly-
technic University, Pomona," 1989 Frontiers in Engineering
Education Conference Proceedings, American Society for En-
gineering Education, Washington, DC
9. Fraser, D.M., "A Model for Consistently Assessing the Effect of
Improved Teaching on Student Success," submitted for publi-
cation (1992) 0

Review: Process Dynamics
Continued from page 33.
has costs and benefits. The most evident cost is that
a sequential reading gives a repetitious treatment of
some topics. Material regarding PID implementation
is found in at least three different parts of the book.
Stability is treated in different parts with distinctly
different approaches. Counting the degrees of free-
dom in a process is discussed in both the first and last
parts of the book. A more subtle penalty is that this
already large book doesn't have room for more detail
on some important topics. Anti-reset windup, for
example, is mentioned in passing. Thus, an instruc-
tor has to carefully plan an approach to the book and
what parts to emphasize or omit. Students also have
to be patient with the discursive nature of the book.
Of course, the positive side of modularity is that
the book can be adapted to a variety of uses. This is a
strong feature, given that process control courses are
often by academics who are not experts in the field.
This is enhanced by the large set of well-chosen, end-
of-chapter problems.
References to widely available tools for computer-
aided control analysis are given in a separate appen-
dix. Unfortunately, these are not incorporated into
the text or problems. Matlab and its associated
toolboxes have been widely adopted in many univer-
sities. A low-cost student edition of Matlab is now
available which would be a good supplementary text
for a course based on this book.
Process control is a rapidly growing subject driven
by advances in computing technology, needs for im-
proved process automation, and new theory. This
text gives a contemporary overview in an accessible,
teachable format. I suspect that the ideal turn-of-the-
century course will deemphasize complex variables
in favor of statistics, optimization, and model predic-
tive control. But in the meantime, this book is a
worthy competitor for market dominance among ex-
isting process control textbooks. 0
Chemical Engineering Education

AUTHOR GUIDELINES

This guide is offered to aid authors in preparing manuscripts for Chemical Engineering Education
(CEE), a quarterly journal published by the Chemical Engineering Division of the American Society
for Engineering Education (ASEE).
CEE publishes papers in the broad field of chemical engineering education. Papers generally
describe a course, a laboratory, a ChE department, a ChE educator, a ChE curriculum, research
program, machine computation, special instructional programs, or give views and opinions on
various topics of interest to the profession.

Specific suggestions on preparing papers *

TITLE Use specific and informative titles. They should be as brief as possible, consistent with the
need for defining the subject area covered by the paper.

AUTHORSHIP Be consistent in authorship designation. Use first name, second initial, and
surname. Give complete mailing address of place where work was conducted. If current address is
different, include it in a footnote on title page.

TEXT We request that manuscripts not exceed twelve double-spaced typewritten pages in
length. Longer manuscripts may be returned to the authors) for revision/shortening before being
reviewed. Assume your reader is not a novice in the field. Include only as much history as is needed
to provide background for the particular material covered in your paper. Sectionalize the article and
insert brief appropriate headings.

TABLES Avoid tables and graphs which involve duplication or superfluous data. If you can use a
graph, do not include a table. If the reader needs the table, omit the graph. Substitute a few typical
results for lengthy tables when practical. Avoid computer printouts.

NOMENCLATURE Follow nomenclature style of Chemical Abstracts; avoid trivial names. If
trade names are used, define at point of first use. Trade names should carry an initial capital only,
with no accompanying footnote. Use consistent units of measurement and give dimensions for all
terms. Write all equations and formulas clearly, and number important equations consecutively.

ACKNOWLEDGMENT Include in acknowledgment only such credits as are essential.

LITERATURE CITED References should be numbered and listed on a separate sheet in the
order occurring in the text.

COPY REQUIREMENTS Send two legible copies of the typed (double-spaced) manuscript on
standard letter-size paper. Submit original drawings (or clear prints) of graphs and diagrams on
separate sheets of paper, and include clear glossy prints of any photographs that will be used. Choose
graph papers with blue cross-sectional lines; other colors interfere with good reproduction. Label
ordinates and abscissas of graphs along the axes and outside the graph proper. Figure captions and
legends will be set in type and need not be lettered on the drawings. Number all illustrations
consecutively. Supply all captions and legends typed on a separate page. State in cover letter if
drawings or photographs are to be returned. Authors should also include brief biographical sketches
and recent photographs with the manuscript.

ACKNOWLEDGMENT

DEPARTMENTAL SPONSORS

The following 152 departments contribute to the support of CEE with bulk subscriptions.

If your department is not a contributor, write to
CHEMICAL ENGINEERING EDUCATION,
c/o Chemical Engineering Department University of Florida Gainesville, FL 32611-2022
for information on bulk subscriptions

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I

	Front Cover
	Table of Contents
	Darsh Wasan, of the Illinois Institute...
	FAMU/FSU
	A jungle guide through accredi...
	Conferences
	Liquid-phase axial dispersion in...
	Book reviews
	Positions available
	What do they know, anyway?: 2....
	The other three Rs: Rehearsal,...
	Book reviews
	Solid phase extraction columns
	Collaborative study groups: A learning...
	Solving chemical kinetics problems...
	Fluid structure for sophomores
	Basic chemical engineering...
	Advanced engineering calculations:...
	Back Cover

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