Front Cover
 Table of Contents
 Department of chemical engineering...
 R. A. of Minnesota
 Stirred pots
 Fluid mechanics can be fun
 Book reviews and letters
 An entrance region mass transfer...
 What is chemical stoichiometry...
 ChE news
 Models for turbulent transport...
 Renewed emphasis on technical communication...
 A 15-month MS chemical engineering...
 ASEE news
 Back Cover

Chemical engineering education
http://cee.che.ufl.edu/ ( Journal Site )
Full Citation
Permanent Link: http://ufdc.ufl.edu/AA00000383/00061
 Material Information
Title: Chemical engineering education
Alternate Title: CEE
Abbreviated Title: Chem. eng. educ.
Physical Description: v. : ill. ; 22-28 cm.
Language: English
Creator: American Society for Engineering Education -- Chemical Engineering Division
Publisher: Chemical Engineering Division, American Society for Engineering Education
Place of Publication: Storrs, Conn
Publication Date: Winter 1979
Frequency: quarterly[1962-]
annual[ former 1960-1961]
Subjects / Keywords: Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )
Genre: serial   ( sobekcm )
periodical   ( marcgt )
Citation/Reference: Chemical abstracts
Additional Physical Form: Also issued online.
Dates or Sequential Designation: 1960-June 1964 ; v. 1, no. 1 (Oct. 1965)-
Numbering Peculiarities: Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
General Note: Title from cover.
General Note: Place of publication varies: Rochester, N.Y., 1965-1967; Gainesville, Fla., 1968-
 Record Information
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 01151209
lccn - 70013732
issn - 0009-2479
Classification: lcc - TP165 .C18
ddc - 660/.2/071
System ID: AA00000383:00061

Table of Contents
    Front Cover
        Front Cover 1
        Front Cover 2
    Table of Contents
        Page 1
    Department of chemical engineering at N. C. State
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
    R. A. of Minnesota
        Page 8
        Page 9
        Page 10
        Page 11
    Stirred pots
        Page 12
        Page 13
    Fluid mechanics can be fun
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
    Book reviews and letters
        Page 19
    An entrance region mass transfer experiment
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
    What is chemical stoichiometry?
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
    ChE news
        Page 32
        Page 33
    Models for turbulent transport processes
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
    Renewed emphasis on technical communication at Texas Tech
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
    A 15-month MS chemical engineering degree for BS students
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
    ASEE news
        Page 52
    Back Cover
        Back Cover 1
        Back Cover 2
Full Text

c hm ia *o e gin ee g ed ucatio


� <_W,

'^St, {

Chemicals? Pharmaceuticals? Consumer products?
Most people probably do.
But we're more than that.
A lot more.
We're a company who cares about the future.
And we're doing something to shape it. That includes
exploring new energy sources, and in the meantime
making the most of the energy we have. For example,
the same steam we use for manufacturing is also
used to produce electrical power.
Our energy conservation efforts in '77 in the U.S.
alone are equal to 10 million barrels of oil or 60
billion cubic feet of gas.
We care about clean air and clean water, too.
That's why we try to pioneer new products that are
n6n-allutinl, n n-haardoug, and bdegradale.
And after we sell our products, we continue to

care about them as long as they're in use. We call
this concern, "product stewardship." And it goes
with everything we sell.
We also care about helping to feed an ever-
growing population and discovering new cures for
disease. It's been that way as long as we've been
doing business.
So, if you know any students who feel a responsi-
bility to preserve and protect life the way we do, and
who have degrees in engineering, science, manufac-
turing or marketing, please refer them to Dow.
We'd like to tell them about the broad variety of
career opportunities we offer.
And how we give people a chance to show what
they can do.
Write directly to: Recruiting and College Rela-
1iOS, F, O B0 1710 , Midland, Michigan 48640.
Dow is an equal opportunity employer-male/female.
*Trademark of The Dow Chemical Company

Department of Chemical Engineering
University of Florida
Gainesville, Florida 32611

Editor: Ray Fahien
Associate Editor: Mack Tyner

Business Manager: R. B. Bennett
Editorial & Business Assistant:
Carole C. Yocum (904) 392-0861

Publications Board and Regional
Advertising Representatives:
Klaus D. Timmerhaus
University of Colorado
Homer F. Johnson
University of Tennessee
Vincent W. Uhl
University of Virginia
CENTRAL: Leslie E. Lahti
University of Toledo
Camden A. Coberly
University of Wisconsin
Darsh T. Wasan
Illinois Institute of Technology
WEST: R. W. Tock
Texas Tech University
William H. Corcoran
California Institute of Technology
William B. Krantz
University of Colorado
EAST: Thomas W. Weber
State University of New York
Lee C. Eagleton
Pennsylvania State University
NORTH: J. J. Martin
University of Michigan
Edward B. Stuart
University of Pittsburgh
NORTHEAST: Angelo J. Perna
New Jersey Institute of Technology
NORTHWEST: Charles Sleicher
University of Washington
Charles E. Wicks
Oregon State University
D. R. Coughanowr
Drexel University
Stuart W. Churchill
University of Pennsylvania
James H. Hand
N.S.F., Washington, D.C.

Chemical Engineering Education

2 Department of Chemical Engineering
N.C. State, Richard M. Felder

8 R.A. of Minnesota

14 Fluid Mechanics Can Be Fun,
Robert F. Blanks
26 What is Chemical Stoichiometry?
William R. Smith and Ronald W. Missen

20 An Entrance Region Mass Transfer Experi-
ment, G. R. Youngquist

34 Models for Turbulent Transport Processes,
James C. Hill

46 A 15-Month MS Chemical Engineering De-
gree For BS Students, Richard Hanks and
John L. Oscarson

40 Renewed Emphasis on Technical Communi-
cation at Texas Tech, Richard Wm. Tock and
Charles Brewer
12 Positions Available
12 Stirred Pots
19 Letters
32, 52 ChE News
39 Book Review
52 ASEE News
19, 52 Books Received

CHEMICAL ENGINEERING EDUCATION is published quarterly by the Chemical
Engineering Division, American Society for Engineering Education. The publication
is edited at the Chemical Engineering Department, University of Florida. Second-class
postage is paid at Gainesville, Florida, and at DeLeon Springs, Florida. Correspondence
regarding editorial matter, circulation and changes of address should be addressed
to the Editor at Gainesville, Florida 32611. Advertising rates and information are
available from the advertising representatives. Plates and other advertising material
may be sent directly to the printer: E. O. Painter Printing Co., P. O. Box 877,
DeLeon Springs, Florida 32028. Subscription rate U.S., Canada, and Mexico is $15 per
year, $10 per year mailed to members of AIChE and of the ChE Division of ASEE.
Bulk subscription rates to ChE faculty on request Write for prices on individual
back copies. Copyright � 1979 Chemical Engineering Division of American Society
for Engineering Education, Ray Fahien, Editor. The statements and opinions
expressed in this periodical are those of the writers and not necessarily those of the
ChE Division of the ASEE which body assumes no responsibility for them. Defective
copies replaced if notified within 120 days.
The International Organization for Standardization has assigned the code US ISSN
0009-2479 for the identification of this periodical.


department .


North Carolina State University
Raleigh, North Carolina 27650

partment at N. C. State in perspective, it helps
to know something about the region in which we
are located.
You can find grits, greens, and southern hos-
pitality in and around Raleigh; you may also find
the New York Philharmonic, Beverly Sills, the
Royal Shakespeare Company, the Marx Brothers,
and the Rolling Stones. Raleigh is the capital and
the cultural center of North Carolina. It lies at one
apex of the Research Triangle, a region bounded
by lines connecting North Carolina State Univer-
sity at Raleigh, the University of North Carolina
at Chapel Hill, and Duke University at Durham.
Within the Triangle-about 12 miles from Raleigh
-is the Research Triangle Park, a 5,500 acre
campus for industrial and government research
laboratories, including the National Environ-
mental Research Center of the U. S. Environ-
mental Protection Agency, and the new National
Center for the Humanities. More Ph.D.'s per
capital live in the Triangle area than anywhere
else in the country.
While Raleigh itself is a relatively small, at-
tractive, and uncongested city, the close proximity
of the major universities and research institutions
in the Triangle affords a range of activities
normally found only in major population centers.
The leading performers in the world regularly
appear in series and individual concerts of or-
chestral and chamber music, dance, drama and
musical comedy, jazz and rock. Classic film series
and first-rate college athletics-particularly the
heated rivalries of Atlantic Coast Conference foot-
ball and basketball-also provide much entertain-
ment to area residents.
Moreover, since Raleigh is situated near the
geographical center of North Carolina, all of the
recreational and scenic attractions of the state are
within easy driving distance. The Blue Ridge and

The Bell Tower, traditionally the symbol of North
Carolina State University.

Great Smoky Mountains offer some of the most
spectacular scenery in the eastern United States,
and North Carolina's shoreline contains many of
the most unspoiled and uncrowded beaches along
the Atlantic coast.

founded as a land-grant college in 1887, and
currently has an enrollment of about 15,000 under-
graduates and 2,500 graduate students. The School
of Engineering is one of the ten largest in the
United States. The technical resources on campus,
including a million-volume library, and the ease
of interaction with the other Triangle universities
provide a stimulating environment for study and
The Department of Chemical Engineering-
the only ChE department in North Carolina-
occupies 40,000 square feet in Riddick Engineer-
ing Laboratories, located in the center of the main



campus. The current department enrollment is
roughly 375 undergraduates and 50 graduate stu-
dents, the latter working for M.S., M.Ch.E. (non-
thesis), and Ph.D. degrees. The undergraduate
enrollment represents a nearly three-fold increase
in three years, and has imposed considerable stress
on classroom and staff resources; nevertheless, all
departmental courses are still routinely taught by
faculty members.
The most prominent of the department's re-
search facilities is a $2.4 million computer-con-
trolled fluidized-bed coal gasification and acid gas
removal pilot plant-as far as we know, the only
facility of its kind in the world-located in a three-
story high bay area in Riddick Laboratories. The
facility was constructed by Acurex Corporation
under contract to the EPA, and was brought on-
stream in the summer of 1978. During construc-
tion of the plant, an associated instrumental lab-
oratory for exhaustive analysis of gas, solid, and
liquid feed and effluent streams was assembled,
and a dedicated microcomputer was installed for
data logging and processing.
Other department facilities include well-
equipped laboratories for research in polymer sci-
ence and engineering, membrane transport proc-
esses, crystallization and other separation proc-
esses, phase equilibrium thermodynamics, and
infrared imaging thermography. A 10-MW Pul-
star nuclear reactor located in a neighboring build-
ing serves as a source of short-lived radioisotopes
for tracer studies, and a Co-60 gamma source is
available for studies of radiation polymerization.
The Department has its own fully-staffed machine
and electronics shops, and faculty members and
graduate students have ready access to such spe-
cialized equipment as electron transmission and
scanning microscopes maintained by the Univer-
sity's Engineering Research Services Division.


T HE ORIGINS OF ChE at N. C. State are some-
what fuzzy. To the best of anyone's knowledge,
the Department was founded sometime in the
period 1923-25 by E. E. Randolph, a professor of
chemistry, who served as Department Head until

The most prominent of the
department's research facilities is a $2.4
million computer-controlled fluidized-bed coal
gasification and acid gas removal pilot plant-as far as
we know, the only facility of its kind in the world ...

1945. In 1935 the Consolidated University of
North Carolina was formed, and all engineering
degree programs in the State, including a ChE
program at Chapel Hill, were moved to Raleigh.
In 1941, J. Frank Seely, an alumnus of the
University, joined the faculty after a two-year
internship with Texaco. Frank is still here, oc-
cupying the positions of principal undergraduate
advisor and principal source of wisdom and com-

Illllll i Br '
Dr. H. Kubota, a postdoctoral research associate
from Gunma University, Japan, performs research on
gas transport in high polymers.

mon sense to both students and faculty members.
In November 1945, Edward M. Schoenborn took
on the department leadership after ten years at
the University of Delaware, three of them in fruit-
ful collaboration with Allan Colburn. Kenneth O.
Beatty jr. joined the faculty in the fall of 1946.
after several years at Dow Chemical, four years
at the University of Rhode Island, and nearly
three years at the University of Michigan, where
he earned his Ph.D. under Donald Katz.
At about this time, a curriculum moderniza-
tion was undertaken, and emphasis shifted from
courses in topics like water demineralization and
gas engineering to such innovative areas as unit
operations, thermodynamics, and reaction kinetics.
Following an inspection by B. F. Dodge in 1948,
the program was fully accredited, and authoriza-
tion to award the Ph.D. was granted in 1949.
A number of faculty members no longer in
the department came during the 1950's, including
F. P. Pike (now retired from the University of
South Carolina), Don Arnold (Kerr McGee),
F. M. Richardson (N. C. State Department of
Engineering Research), Bob McAllister (Dean at
Lamar University), Russ Hazelton (University of
Louisville), John McGee (Department Head at


The noon bridge game in the AIChE student chapter
lounge is a department fixture.

Tennessee Tech), and Tom Godbold (Vanderbilt).
It was also in the 1950's that James Ferrell, the
current Department Head, earned the department's
first Ph.D. under the direction of Professors
Beatty and Richardson. Jim left the campus for a
tour of duty in industry and returned in 1961,
shortly before Donald Martin (from N. C. State),
David Marsland (from Cornell) and Edward
Stahel (from Ohio State) also joined the growing
In 1965 the legendary Warren McCabe came to
N. C. State after retiring as Dean of the Faculty
at Brooklyn Polytechnic Institute. "Mac" re-
mained active in research until his second retire-
ment in 1975, and his periodic visits continue to be
a source of pleasure to us.
A series of changes took place in the late
1960's, beginning in 1966, when Ed Schoenborn
stepped down as Department Head and was suc-
ceeded by Jim Ferrell. In 1967 the University was
awarded an NSF Science Development Grant,
which served as the basis for recruiting the emi-
nent polymer chemist Vivian Stannett, who re-
ceived his doctorate at Brooklyn Polytechnic In-
stitute. Shortly thereafter, Harold Hopfenberg
came from MIT by way of Vietnam.
Later arrivals, their schools, and the years they
came include Richard Felder (Princeton, 1969),
Ronald Rousseau (LSU, 1969), James Helt (Iowa
State, 1976), William Koros (University of Texas,
Austin, 1977) and Peter Fedkiw (University of
California, Berkeley, 1979). The faculty is
rounded out by the presence of two joint ap-
pointees: Robin Gardner (Penn State, 1967), who
spends most of his time in the Nuclear Engineer-
ing Department, and Michael Overcash (Minne-
sota, 1972), who resides in the Department of

Biological and Agricultural Engineering, and by
Henry Smith, who graduated from this Depart-
ment in 1938, received his Ph.D. from the Uni-
versity of Cincinnati, and came back in 1965 to
assume the position of Associate Dean for Re-
search and Graduate Programs. In 1975-76 Stan-
nett became Dean of the Graduate School and
Martin was appointed Head of the Department of
Computer Science, positions they still occupy, al-
though Stannett also actively continues his de-
partmental research activities.
In 1976, the department inaugurated a rotat-
ing visiting professorship. We were fortunate to
obtain as the initial occupant of this position,
Professor Peter Danckwerts, Shell Professor of
ChE and long-time Head of the ChE Department
at Cambridge University, who was with us for the
1976-77 academic year. We have subsequently en-
joyed visits from Dr. John Petropoulos of the
Demokritos Nuclear Research Center, Athens,
Greece, in the Spring of 1978, and Professor Giulio
Sarti of the University of Naples, in the Fall of


A UNIQUE FEATURE of the department is
the frequency of intra-department collabora-
tion, with the collaborators shifting from one
project to another.
Beatty and Ferrell have long-standing interests
in heat transfer and fluid dynamics. Ferrell has
contributed a number of papers on the heat pipe
and heat transfer in molten salts, and Ferrell and
Stahel wrote the annual IEC heat transfer review
for several years. Beatty's interests are currently
focused on the use of infrared imaging thermog-
raphy as a research tool in heat transfer, fluid
flow, and biomedical engineering.
Ferrell, Felder and Rousseau are the principal
and co-investigators on an EPA-sponsored study
of coal gasification and acid gas cleanup, research
centered on but not confined to the previously
mentioned pilot plant facility. Their studies in-
clude research on the thermodynamics and kinetics
of individual plant operations, evaluation of al-
ternative acid gas removal processes, and develop-
ment of methods and systems for sampling and

A unique feature of
the department is the frequency of
intra-department collaboration, with the collaborators
shifting from one project to another.


Several years ago a young assistant professor
searching for a way to tell freshmen what
ChE is all about thought of outlining the production
of alcohol from corn-a process reputedly important to
the economy of certain regions of North Carolina.

analysis, monitoring and control, data acquisition,
and data base management.
Ferrell and Rousseau are carrying out funda-
mental studies of adsorption phenomena, and have
worked on the development of adsorbant materials
for use in protective overgarments. Felder, Ferrell
and Koros are studying the use of polymeric inter-
faces for in situ monitoring of stack emissions;
Felder and Ferrell recently received a patent for
the development of a probe that permits contin-
uous unattended monitoring in dirty or corrosive
stack environments for long periods of time.
Felder and Rousseau have written a stoichiometry
text, Elementary Principles of Chemical Proc-
esses, published by Wiley in 1978.
Rousseau collaborated with McCabe in re-
search on nucleation and growth phenomena in
crystallization operations, and he has continued in
this field since McCabe's retirement. A recent out-
come of this research is a process to use selective
nucleation to separate solutes from doubly satu-
rated solutions. Rousseau and Schoenborn studied
vapor-liquid equilibria in systems containing non-
volatile salts; Rousseau has extended this work to
formulate predictive models, and currently is also
investigating phase equilibria of acid gas absorp-
tion systems.
A monumental body of work in the field of
polymers and membrane transport processes has
emerged from the efforts of Stannett, Hopfenberg,
Stahel, and Koros, working individually and in
various combinations. Stannett is an author or
coauthor of over 200 papers on most aspects of
polymerization, including applications in fiber and
wood and paper science. Hopfenberg and Koros
conduct research on the transport of gases and
liquids in polymers. Hopfenberg has investigated
membrane separation processes, including ultra-
filtration and reverse osmosis, and is currently
working on the development of selective ion sep-
aration processes, membrane barriers for the con-
trolled release of drugs, and liquid membrane
technology. Stannett and Stahel carry out research
on radiation-initiated polymerization, including
pilot plant studies.
Stahel and Felder have both worked in the

field of photochemical kinetics. Stahel is currently
performing research on atmospheric pollutant
production, and, jointly with members of the
NCSU Plant Pathology Department, on the design
of chemical reactors for use in the study of pol-
lutant uptake rates and pollution effects on plant
Marsland's interests center on engineering
economics, particularly as applied to pollution
abatement and control, and on computer solutions
of the partial differential equations of transport
phenomena. Gardner studies industrial radio-
isotope applications, and he has used radiotracers
to perform fundamental research into particulate
size reduction operations.
Among the newer members of the faculty, Helt
is interested in nucleation phenomena in crystalli-
zation, lubricating oil rerefining processes, and
ChE applications of nuclear fuel cycles; Koros is
conducting research on the sorption and transport
of gases in glassy polymers, with applications to
residual monomer removal and the design of gas
separation processes; and Fedkiw's principal in-
terests are in the field of electro-chemical engi-
neering, including electrorefining and selective ion
A number of awards and honors have accrued

Professor Ferrell, graduate student Victor Agreda,
and laboratory technician Larry Hamel analyze a coal
sample using an atomic absorption spectrophotometer.

to the faculty. Stannett received the first Silver
Medal Award of the Paper Synthetics Division of
TAPPI, the Education Service Award from the
Plastics Institute of America, the Gold Medal and
International Award of the Society of Plastics
Engineering, and from the American Chemical
Society, the prestigious Borden Medal of the


Plastics and Coatings Division and the Anselm
Payen Medal of the Cellulose, Wood and Fiber
Division. Hopfenberg won the first Alcoa Founda-
tion Engineering Research Achievement Award
given at North Carolina State University. Hopfen-
berg, Felder, and Rousseau have each won the
Sigma Xi Faculty Research Achievement Award,
and Hopfenberg and Felder have won Outstand-
ing Teacher Awards and have been elected to the
NCSU Academy of Outstanding Teachers.
Beatty has served as chairman of the AIChE
Heat Transfer and Energy Conversion Divisions
and the National Heat Transfer Conference Co-
ordinating Committee, and with E. R. G. Eckert,
organized the seven nation Assembly for Inter-
national Heat Transfer Conferences. Ferrell has
also served as chairman of the AIChE Heat Trans-
fer Division, and Rousseau as chairman of the
AIChE Forest Products Division.


A BROAD RANGE OF interests characterizes
the non-professional activities of the faculty.
An unusually high proportion of guitarists can be
found: Ferrell and Felder play classical guitar,
Hopfenberg is an ex-rhythm guitarist in a rock
combo, and Gardner plays folk guitar, specializing
in off-color ballads about various marine animals.
Ferrell also makes exceptionally fine guitars, not
to mention a white wine that must be tasted to be
Hopfenberg is a formidable gourmet chef,
whose forte is quick-stir Chinese cookery but who
also tosses off Northern Indian, Northern Italian,
and Southern Yonkers specialties with flair and
zest. Rousseau, who comes from Baton Rouge and
believes he is currently living in the North, is an
ex-jock who likes Cajun music, whatever sport it
is that Johnny Bench plays, Thomas Wolfe novels,
and a type of cooking which he swears is authentic
Creole from the heart of the Bayou, but which
anyone who knows anything immediately recog-
nizes as imitation Lower East Side Delicatessen.
Gardner is the other department jock-mostly
tennis, with a little lunchtime basketball for va-
Seely is one of the few native North Carolin-
ians to be found in Riddick Labs. His principal ac-
tivities include golf and wandering around the
United States. Several years ago a young assistant
professor searching for a way to tell freshmen
what ChE is all about thought of outlining the
production of alcohol from corn-a process re-

putedly important to the economy of certain
regions of North Carolina. The process was not
described in Shreve or any of the other standard
references. The young man thought of asking
Frank Seely if he knew anything about it... and
was rewarded with a recitation of feed composi-
tions, catalytic agents, optimal operating condi-
tions, and residence times to four significant fig-
ures. The young professor asked Frank how he
knew all that, and the subject was abruptly
Stannett is a chronic globetrotter, and the
leading department raconteur. Schoenborn is an-
other habitual world traveller, and is also a clas-
sical pianist. Overcash likes politics and junkets
to the Far East. Beatty has devoted much time and
energy to devising aids to the blind, including de-
vices for typing and computer transcription of
Braille, and multilevel polymer maps. Stahel is an
avid sailboater and antique collector; he also oc-
casionally designs palatial manors, which he then
lives in.
Marsland is one of the prime movers and
shakers of barbershop quartet singing in Raleigh
and environs. Martin is active in local community
affairs, and is also a Commander in the Navy Re-
serve; he looks magnificent when he wears his
dress whites to class, and his happiness would be
complete if only people would stop asking him to
hail them a taxi when he stands in front of a hotel.
Helt and Fedkiw are hikers and campers.
Koros is also a hiker, and an enthusiastic paddle-
boater. He makes superb coffee but he has the
strangest ideas of what barbecue is supposed to
taste like, and in other ways tries to project a
Texas macho image; if he ever succeeds in in-
timidating his small dog into staying out of the
living room he may convince the rest of us that it's
legitimate. Felder is a devotee of Gilbert and
Sullivan and Ursula LeGuin, and is a card-carry-
ing hedonist. He has no known faults or eccen-
Most of the faculty consider themselves out-
standing pool and poker players. They prove them-
selves wrong every year at the annual Christmas
party in Frank Seely's basement. Marsland, Fer-
rell, Felder, Gardner, Hopfenberg, Beatty, and
Stahel are passable bridge players, who have on
occasion dropped by the department lounge to give
the graduate student regulars a lesson or two. The
uniqueness and individuality of the faculty is at-
tested to by the fact that as of this writing, to the
author's best knowledge, not one of them jogs! O





Thin air. To the people at Union
Carbide, the air around us pro-
vides a limitless resource for
products and systems to benefit
everyone. For Union Carbide,
finding new ways to stretch our
precious natural resources,
through imagination and re-
sponsible technology, is the most
important thing we do.

At the Linde Division of Union
Carbide, highly sophisticated
systems liquefy air and distill it
into pure oxygen, nitrogen
and rare gases like argon,
neon and xenon.
To transport these
gases, we developed a
super-insulated tank truck
that can carry them from
coast to coast in liquid
form. For hydrogen,
- that means at a
temperature of
- minus 4200 E

An equal opportunity employer

Ever wonder how those "fast-
food" hamburgers get to you
tasting so fresh and juicy?
Liquid nitrogen freezes them
so fast that their molecular
structure remains intact. It
happens at 3200 below zero -
easy with Union Carbide's
liquid nitrogen, impossible for
any kind of home freezer.

When the U.S. steel industry
developed more efficient
steelmaking processes, using
oxygen, Union Carbide came
up with ways to supply the
vast amounts needed: on-site
oxygen plants and pipeline

More than 150 towns and cities use Union Carbide's
UNOX"wastewater treatment system. Pure oxygen
helps billions of microorganisms consume waste
/ quickly and cheaply. Sludge left over from
' UNOX, as well as plain old garbage, can then
be converted into usable fuel gas by our
. :pollution-free PUROX�system. So we're
making cleaner water and providing
needed fuel... right out of thin air.

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


of Minnesota

Prepared by his
Minnesota Colleagues
University of Minnesota
Minneapolis, Minn. 55455

JUST ABOUT EVERYONE with an interest in
the subject, both in and out of Who's Who,
knows that Aris Rutherford is a mythical char-
acter; created as a well-deserved admonishment
to a pompous bureaucracy by a gentleman and
scholar named Rutherford Aris. The more serious
matter to anyone who takes on the task of de-
scribing him is to recite the facts and still convince
the reader that Rutherford Aris is not himself
In the 23 years since he first came to Minne-
sota, Aris has compiled a record of scholarship
which has few equals in chemical engineering.
Nine texts and monographs, several book chapters,
and over 150 journal articles attest to the quantity
of the record; the spate of awards he has received,
the special lectureships to which he has been ap-
pointed, and his membership in the National
Academy of Engineering attest to its quality. But
impressive as this record is, it tells only a small
part of the story of a man who has been variously
described by his colleagues in and out of ChE as
". . .a saintly genius in the secular domain of
scholarship and seminal research . . .," ". . . the
most scholarly chemical engineer I know ...," "...
one of the last remaining polyhistors .. .," "... one
of the few university professors today who master
the nearly lost art of speaking correct English..."
and ". . my one colleague in chemical engineering
who shares an interest in Real Tennis... ."*
Fulsome praise? His colleagues at Minnesota,
where he has recently been made a Regents' Pro-

*The authors of each of these documented quotes will
remain anonymous, but several can be guessed. It is a game
Gus Aris would enjoy. Four out of five correct answers
rates an A and the Exxon Suite Award.

fessor-one of 15 among the faculty of some 3000
-would not think so. For in the institution at
which he has spent his entire teaching career, Gus
Aris is something of a Renaissance man. It will
undoubtedly come as no surprise that he offers
courses in Chemical Reactor Analysis and in
Mathematical Methods; elegant, axiomatic rendi-
tions of the principles which have attained a
central role in ChE today. But he has also fre-
quently offered courses and lectures on Medieval
Manuscripts and The History of Latin Handwrit-
ing and is working on a monograph on medieval
paleography. He is involved in collaborative re-

... he... earned an external degree
(B.Sc. in mathematics) from London after two
years of spare-time study at the ripe old age of 19.

search with a colleague in History on developing
mathematical techniques for dating documents of
the period from 900-1150 A.D. and he has played
a role in the evolution of courses in Science and the
Humanities. In fact, these kinds of contributions
have become so regular that this fall the Univer-
sity formalized the arrangement by making him a
de facto University Professor, freed half-time
from his ChE responsibilities to follow his inclina-
tions in these other fields. Thus, for the very un-
mythical Aris, there is now a new beginning-
which, naturally, stimulates recollections of his
first beginning.

mouth, on the south coast of England, in Sep-
tember of 1929, a fact that 20 some odd years in
the upper midwest, marriage, baseball, basketball,
and football have absolutely failed to overcome in
any way.


According to authoritative family sources,
young Rutherford, the second of four children,
first exhibited his interest in abstract quantitation
by taking charge of the family shopping list. With
that to build on, he went on to Canford, an Eng-
lish public school, and earned an external degree
(B.Sc. in Mathematics) from London after two
years of spare-time study at the ripe old age of 19.
He had already joined Imperial Chemical Indus-
tries as a "technical officer" and was working in
Edinburgh with C. H. Bosanquet, one of Britain's
early engineering scientists, when Neal Amund-
son, on sabbatical, arrived on the scene in 1955.
In the classic paradigm of the graduate student
recruiting we all know so well today, he convinced
Rutherford to come back with him to Minnesota,
where Amundson was then beginning a building
Rutherford accepted, came to the United
States, became "Gus" Aris and spent a year. Not
a bad one, at that. He wrote what has become a
classic paper on Taylor dispersion, which was pub-
lished in the Proceedings of the Royal Society. He
also published the first of what would be many
collaborative efforts with Amundson on reactor
stability. Most importantly, he met and subse-
quently married Claire Holman, a Minneapolis
native, with whom he has shared his life since.
With those ties established, he returned to Britain
for a year, earned another external degree from
London-this time a Ph.D. in Mathematics and
Chemical Engineering-and crossed the Atlantic
once again in 1958 to accept an Assistant Profes-

As an Englishman,
Aris does not claim a
deep knowledge of baseball,
but he knows where to begin.

sorship at Minnesota. Since 1963, the title has been
Professor and, from the Fall of 1978 onward,
Regents' Professor.

has, of course, focused on the effective appli-
cation of mathematics to the description, under-
standing, and control of reacting systems. In the
early years the applications were primarily in re-
action engineering-control, stability, optimization.
But that changed as he and his collaborators began
to look at a number of other areas. They laid a
strong, analytical foundation for multicomponent
chromatography, and Gus began to work on bio-
logical problems of several kinds: microbial popu-
lation dynamics; enzyme kinetics; membrane
transport; chemotaxis. Today, he is as active in
biological applications as in any other single area.
One of the reasons that Aris has been able to
work effectively in a number of fields is the ease
with which he is able to enter into collaborations
with colleagues. No doubt the longest and closest
collaboration was with "The Chief," Neal Amund-

Aris' ability to write is
remarkable. Many of us have watched him
sit at lunch and, in the calligraphic hand which
is something of his trademark, pen the draft of a
paper which, with few changes, will be
sent off as a finished work.


L. " .

Aris with Arvind Varma, one of his many Ph.D.
students who have gone on to productive academic

son, with whom Gus has coauthored almost two
dozen articles and a monograph. But he has also
worked at one time or another with four or five
other colleagues at Minnesota and as many or
more elsewhere.
Aris' ability to write is remarkable. Many of
us have watched him sit at lunch and, in the calli-
graphic hand which is something of his trademark,
pen the draft of a paper which, with few changes,
will be sent off as a finished work. It is tempting
to explain this ability as arising from the capacity
of a mathematician for ordered thinking, but
those who know him are more likely to agree that
it is his love of and constant immersion in words
and language that accounts for it.
This facility with words not only produces
papers; it produces an array of rhymes and limer-
icks, aphorisms and patter songs for every oc-
casion. His specialty is the reworking of well

known (or not so well-known) poems and arias to
fit more appropriately the topic or occasion at
hand. When Skip Scriven was feted as Lacey Lec-
turer at Cal Tech last year, the Cal Tech men's
chorus treated him to a rendition of "Now I am the
lecturer of Cal's Lacee .. ." with suitable apologies
to W. S. Gilbert and credit to R. Aris. When a
lunchtime conversation on coal liquefaction turned
to the use of the word liquefaction in a 17th cen-
tury poem by Robert Herrick, the poem was up-
dated by Gus....
Whenas in silks my Julia goes,
Then, then methinks how sweetly flows
That liquefaction of her clothes.
Next, when I cast mine eyes and see
That brave vibration each way free,
Oh how that glittering taketh me!
Robert Herrick

Whereas in gases fled its moles,
Now, now methinks research controls
The liquefaction of my coals.
I'll do it first by Fischer-T,
Take lots of points, then wait and see
Oh how that sells with D. O. E.!
Rutherford Aris
And recently, when he was asked to attend a
quasi-social meeting with some state legislators,
quite aside from what the meeting may have pro-
duced for the University, the following plaint was
found afterwards:
It was just as I feared it w'd be
When I went to the lawmakers' tea,
Their rumblings abdominal
Were simply phenomenal
And they slashed both the budget and me.

A RIS' INFLUENCE AT and on Minnesota has
been broad and deep. Some elements of that
influence are in the areas in which one would
expect them: new course development, graduate
student thesis advising (indeed, he has directed

He played a significant role
in the development of programs in Religious
Studies and in the History of Science at Minnesota,
both large issues to him, and well worth the price
of the many hours spent on small ones whose
greatest value is as subject matter
for quatrains and limericks.


He is as comfortable with English literature and poetry as he is
with reactor analysis ... He is a religious man, deeply so and privately. But
even that he finds a way to share with his friends at many levels-
historical, philosophical, moral.

Strath Spey, Scotland, Apr. 10, 1930; s. Archibald Mac-
Pherson and Ephygeneia (Aristeides) R.; diploma Strath
Spey and Glenlivet Inst. Distillation Engring., 1948;
B.Tech., Billingham Coll. Engring. and Tech., 1952, D.Eng.,
1955. Came to U.S., 1956, naturalized, 1961. Chief design
engr., tester Strath Spey Distillation Co., Ltd., 1955-56;
chem. engrin. cons., Chgo., 1956-60; vis. prof. distillation
practice Tech. Inst. of the Aegean, Corinth, 1960-64; prof.
chem. engring. U. Minn., Mpls., 1964-. Mem. County
Commn. for Local Industry, Speyside Area, 1955-56. Trus-
tee, Scottish-Greek Friendship Found., Edinburgh, 1960-64.
Served with Argyll and Sutherland Regt., 1948-50. Mem.
Burns Soc. Mpls., Distillation Club Edinburgh. Presbyn.
Clubs: Hellenophilic (Mpls.); Woods (Gleneagles, Scot-
land). Author: Sampling Techniques, 1957; American Foot-
ball-A Guide for Interested Scots, 1960; Distillation Pro-
cedures, 1963. Office: U Minn Sch Chemistry Minneapolis
MN 55455

The infamous Aris Rutherford as advertised in
Who's Who, 38th Edition, 1974-5.

the Ph.D. theses of 25 students thus far, several
of whom, like Mort Denn of Delaware, George
Gavalas of Cal Tech, and Harmon Ray of Wiscon-
sin have already become influential in their own
right). But, beyond that, Aris has interwoven his
own sense of eclecticism into the fabric of the de-
partment. For example, in the early 50's he initi-
ated a tradition in which, once every three years,
the graduate seminar program for an entire quar-
ter is devoted to topics outside of the normal pur-
view of ChE. Lecture topics have ranged from
Scandanavian literature to Brazilian folk culture;
from anthropology to stage movements with many
stops between. Every Ph.D. student has the op-
portunity to be involved with at least one such
series. While several people have helped in these, it
is primarily Aris who organizes them, introduces
them, and ultimately oversees their publication in
volumes with such titles as: The Scope of Scholar-
ship; Varieties of Academic Experience; and
Catastrophes and Other Important Matters.
When Amundson decided to step aside from
the headship in 1974 after 25 years, Aris was the
unanimous choice of the departmental faculty to
take over. It was not the kind of a position that a
man like Aris would relish, but it was clear that

he was the right person to lead the department
through a difficult transition in a time of economic
contraction. He did just that for four years, with
his good sense and his scholarly sense, his patience
and his wit. The evidence is, that upon stepping
aside from the post in 1978, all four remained
Gus has also been one of the most active faculty
members in the University in faculty governance,
a tribute to his sense of charity (agape, he would
explain). Foraying into the Byzantine intracacies
of University committees, using a cultivated in-
nocence as shield and weapon ("... But, Mr. Presi-
dent, since the NCAA is such a problem, is this not
a splendid opportunity simply to leave it, to aban-
don intercollegiate football and basketball. Surely
we'd be better off for it and could concentrate on
more important things . . ."), he has consulted,
advised, adjudicated, and resolved his way through
untold issues, large and small. He played a signif-
icant role in the development of programs in Re-
ligious Studies and in the History of Science at
Minnesota, both large issues to him, and well
worth the price of the many hours spent on small
ones whose greatest value is as subject matter for
quatrains and limericks.

AND WHAT IS ARIS LIKE outside of the con-
text of the University? Very much the same.
A man of books-books of every sort. He is as
comfortable with English literature and poetry as
he is with reactor analysis. He will show you his
volumes of etchings and line drawings of Euro-
pean birds. He will leaf through a fine edition of
T. S. Eliot with you. He is a man of languages-
classical ones, particularly Greek and Latin, but
with more than a passing interest in Norwegian
and Danish. He is a religious man, deeply so and
privately. But even that he finds a way to share
with his friends at many levels-historical, philo-
sophical, moral.
Then there is the Aris wit. Dry, you might say,
and perfectly suited to the art of dealing with de-
humanizing bureaucracies, overinflated egos, and
the other social ills to which we are too often ex-


posed. Aris' particular English background recog-
nizes class, but does not confuse it with worth nor
stand in awe of it. Perhaps that explains some ele-
ments of the Who's Who story*, which, for those
who don't know it, began with a letter from those
good people to one Aris Rutherford inviting him to
submit a biography. As one used to such errors, he
wrote back kindly, explaining that he was not Aris
Rutherford, but Aris (comma) Rutherford, and
under that latter name, he was already a
biographee in their prestigious publication. In re-
sponse, he was informed by some automatic type-
writer that individuals could not buy their way
into Who's Who. Thus challenged, Aris Ruther-
ford, the Scottish inversion of our English col-
league, was born and given a history.
And is Aris still an Englishman? Well, there is
this trouble he has understanding American foot-
ball- (time outs? cheerleaders? platoons ?-What-
ever for ?)-and these peculiar misspellings (be-
haviour, colour).
Finally, how, you ask, did he come to be called
Gus? That has to do with India and bath water-
well, not exactly bath water . .. Really, it's a long
story. You'd better ask him when you next see
him. O
*Editors note: See CEE, Vol. IX, No. 3, page 119, for
feature article pertaining to this.

Stirred pots

(Contributed by Peter Harriott, Cornell University)
Sir Osbourne Reynolds was a man of yore
Who liked to play with symbols that you might think a bore
But he figured out a problem and acquired some fame
And now the Reynolds number bears his name
Take a d times a v and a rho by mu
Put them all together with a little bit of glue
Then you've got a number that will see you through
And tell you what the fluid's going to do
Does the syrup in the pipe flow as smooth as can be
Or is it all mixed up like in a cup of tea
Enter all the numbers and press the little key
Laminar or turbulent, the answer will be
Now lots of other numbers may come to mind
Prandtl, Schmidt, and Grashof, and more of that kind
But when you've got a sticky problem and are getting in a
The old Reynolds' number is the first one to find
It's really very simple, so the profs all say
But the gol-darn dimensions keep getting in the way
The old English system has had its day
So better switch over to SI today

Use CEE's reasonable rates to advertise. Minimum rate
1/ page $50; each additional column inch $20.

The Department of Chemical Engineering seeks appli-
cants for a tenure-track position. Ph.D. in Ch.E. required.
Industrial experience desirable. Candidates should have an
interest and talent for teaching and research, with the
ability to develop a self-supporting research program. An
appointment effective January 1, 1979 is possible. Interested
candidates should submit resumes and references to: Raffi
M. Turian, Chairperson, Chemical Engineering Department,
Box 4679, Texas Tech University, Lubbock, Texas 79409.
Texas Tech University is an equal opportunity/affirmative
action employer.

Faculty position available in Nuclear Engineering at the
Assistant/Associate Professor level. Current research in-
terests of the Department include, radwaste, health phys-
ics, nuclear fuel cycle analysis, reactor physics, reactor
thermal-hydraulics and two-phase flow, reactor reliability
and safety, radiation damage in solids, fusion technology,
technology assessment, environmental measurements, neu-
tron cross sections, and mass spectrometric methods of
analysis. Applicants should have interest and experience
in one or more of the above areas of technology. An
earned Ph.D. with a chemical/nuclear engineering back-
ground is most suitable. Submit resume to: Professor John
C. Corelli, Department of Nuclear Engineering, Rensselaer
Polytechnic Institute, Troy, New York 12181. An equal
opportunity/affirmative action employer.

Shin Taiso Building, 10-7, Dogenzaka 2-Chome,
Shibuya-Ku, Tokyo 150 Japan
Telephone: 463-5396/5364/5346
Cable Address: Interedservices

Anyone with a bachelor's degree in chemical engineer-
ing or related engineering fields wishing to teach full-time
for one or two years in Japan should write to International
Education Services at the above address.
The position involves teaching Japanese businessmen
and engineers the basic vocabulary in various fields.
No Japanese-language is required for classroom instruc-
tion. Teaching experience is not required. An orientation is
given in Tokyo.
Information on salary, transportation and housing can
be obtained by providing International Education Services
with a detailed resume and a letter indicating an interest
in the position.
Personal interviews will be held in your area in the
middle of March.
Selected applications would be expected to arrive in
Tokyo from May through August, 1979.


At Celanese,

we won't force you into a mold.

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

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

An equal opportunity employer m/f



Michigan State University
East Lansing, Michigan 48824

IN MY FIRST FEW YEARS of teaching engi-
neering at the university level, I used the tradi-
tional lecture method. Homework assignments
were collected and routinely graded. Course grades
were assigned based upon a composite score of
homework grades, grades on hour examinations,
and a final examination grade. A class grade dis-
tribution was obtained from a statistical t-score
analysis. Student response to this approach was
generally favorable but not exciting. Several
events combined to motivate me to examine al-
ternative teaching methods.
An article in the student newspaper caught my
attention and plagued my conscious thoughts. In
effect, the article showed photographs of sleeping
or bored students in several classrooms and posed
the question, "Are these people enjoying this edu-
cational experience?". I began looking in class-
rooms and at my own classes with this question in
my mind. For the most part, I concluded that the
answer was "probably not."
At this point, I engaged in a continuing series
of lengthy discussions with a woman, who is now
my wife, Judy, about alternatives offered by the
field of humanistic education. Judy and I attended
several personal growth workshops led by Dr. Sid
Simon and a values clarification workshop led by
Dr. Howard Glasser-Kirschenbaum. I began read-
ing a great deal in this area, including a book by
Robert C. Hawley and Isabel L. Hawley [1]. The
title of the Hawleys' book is Human Values in the
Classroom. I began to try some of the strategies
and methods I was learning in my classroom. In
the fall of 1976, the experience and response in
my junior class of fluid mechanics was so reward-
ing that I decided to share it with others by writ-

*Presented at the November, 1977 AIChE Meeting, New
York Session, "Caring in the Classroom".

**Present address: Amoco Chemicals Corp., Napierville,
Ill. 60540.

Robert F. Blanks: I have had approximately equal periods of ex-
perience in chemical engineering education and in industry. After ob-
taining my PhD in ChE at the University of California, Berkeley, I
joined Union Carbide's Plastics Process R&D section in Bound Brook,
New Jersey. After seven years there, having moved up the ranks with
one foot on each side of the dual technical-administrative ladder, and
on the verge of moving into the administrative line, an old latent
urge motivated me to leave Union Carbide and join the ChE Department
at Michigan State University. I taught there for nine years and was
promoted to the position of Professor in 1978. During my academic
tenure, I consulted with Dow, Corning Glass, and Amoco Chemicals.
Although I enjoyed my classroom teaching experience, my consulting
work was more rewarding. Driven by salary differential, large classes,
and turned off by the grantsmanship game, I returned to industry
where I am now employed as a Senior Research Engineer by Amoco
Chemicals R&D in Naperville, Illinois.

ing this paper for a session at the fall, 1977,
AIChE meeting. The session title is "Caring in the


B ASED UPON THE experiences motivating me
to consider alternatives to the lecture method,
I offer the following hypotheses or rationale for
the methodology used in the course about to be
discussed. Much of this thinking comes from the
Hawleys' book [1], for which I am gratefully in-
It is difficult for a teacher to educate students
by talking at them, or by lecturing, in the manner
of a preacher or a wise parent. Students often
learn most by experiencing, by problem solving,
by creating and observing the need for knowledge



and then by seeking out the knowledge from sev-
eral available sources, e.g., peers, teaching as-
sistants, books, the professor. Role playing the
part of an industrial engineer on an assignment,
laboratory demonstrations, intriguing problems,
and analogies can combine to make the process of
learning effective and enjoyable to the student.
An authoritarian, judgemental attitude on the
part of the teacher can stifle creative thinking by
the students. Empathetic listening by the teacher,
in the classroom or on a one-to-one basis in recita-
tions and during office hours, may create a rapport
between teacher and students and among students,
which often increases academic achievement. This
community building can become an important
aspect of planning a class. Positive reinforcement
and positive feedback-from students to teacher,
from teacher to students, and among students-
tends to check boredom, to provide self-confidence,
and to generate enthusiasm on all sides.
In planning for the teaching of any given
course, it would be well for the instructor to con-
sider elements related to the process of learning
as well as those concerned with the chronological
sequence of content. Areas such as community
building, achievement motivation, providing for
student-teacher and student-student communica-
tion, and the physical set-up of the classroom may
be important concerns. Often the rigid physical
arrangement of rows of desks facing a lecture
stand is a limitation to open student-teacher inter-
action in a sharing sense. One of the teacher's first
tasks is to communicate to the students the goals of
the class as the teacher sees them. It is often help-
ful at this point to attempt to involve the students
in setting goals for the class.
One concept which is often difficult for me to
remember is that a group of students in a class do
not function collectively in the sense of their grasp
of material or response to particular teaching
methods. On the contrary, a class is composed of a
number of individuals with varying abilities, with
unique sets of external demands upon them, who
respond separately to different methods of teach-
ing such as the lecture, group work, independent
study, problem solving situations, etc. Therefore,
if a variety of learning situations can be created in
a classroom, or outside of the classroom, each stu-
dent may seek the method in which he or she is
most comfortable and most likely to learn.
A teacher may possess a great deal of knowl-
edge in a field and it is often most efficient to pass
this knowledge on to a class by means of lecturing.

However, in addition, it is important for the
teacher to help the student learn how to approach
problems, to develop solutions and assess the ac-
curacy of results, to become creative thinkers, and
to seek alternate sources of information. A teacher
might better view himself or herself as a facilita-
tor of learning rather than as a dispenser of in-
In the traditional lecture system, many stu-
dents attempt to place the responsibility for their
learning on the teacher. This responsibility be-
longs to the student. Self-motivation is one key to
high achievement. This is a more obtainable goal
when the students have played a role in establish-
ing course objectives, have a variety of alternative
learning processes available, have a good rapport
with the teacher and with each other, and have
even helped to establish criteria for measuring
achievement. It seems very desirable to attempt to
create a situation where students and teachers
alike work together to help everyone achieve to
the maximum of their abilities rather than an
adversary situation where students attempt to
outwit the teacher, or to beat each other at the
grading game. The negative aspects of grading are
discussed in the Hawleys' book [1] and elsewhere
[2, 3]. I will not attempt to thoroughly discuss this
controversial subject here. It appears to me that
there is a real conflict between the negative aspects
of grading, the need for honest evaluation of
achievement, and the desire for company re-
cruiters to have the students of engineering rank

IN THE FALL OF 1976, I attempted to incor-
porate some features of the humanistic educa-
tion approach into teaching fluid mechanics and

Role playing the part of
an ... engineer on an assignment,
laboratory demonstrations, intriguing problems,
and analogies can combine to make the process
of learning effective and enjoyable...

heat transfer to a group of 87 junior ChE students
at Michigan State University. The course was
divided into two sections of 48 and 39 students,
respectively. Each section met for five hours per
week, 3 one-hour periods and 1 two-hour period.
Two senior ChE students and one graduate stu-
dent met with me and the class in the classroom.


Class Outline
Text: Bennett and Myers, "Momentum, Heat, and Mass
Transfer," 2nd edition, McGraw-Hill Book Co.
Fluid Behavior
Overall Mass and Energy Balances
Overall Momentum Balance
Flow Measurement
Boundary Layer and Turbulent Flow
Dimensional Analysis and
Design Equations for Fluid Flow
Heat Transfer by Conduction
Convective Heat Transfer Coefficients
Heat Transfer with Laminar Flow
Heat Transfer with Turbulent Flow
Design Eq. for Convective Heat Transfer

The course was divided into 9 topic areas with
assigned problems and a one-hour examination
for each area. There was a two-hour final exami-
nation at the end of the term.
The course outline is shown in Table 1. Each
week began with a one-hour lecture introducing
the important concepts for the week. The follow-
ing three class hours for the week were devoted to
problem solving sessions. Students worked to-
gether on the assigned problems in groups of two
or three, or some students chose to work indi-
vidually. As the Hawleys pointed out, practice in
collaborative information processing can be a
valuable part of the learning experience. In indus-
trial and governmental research and engineering,
teams of people develop information for use by
management in decision making. Problems which
sometimes seem overwhelming to an individual
may be comprehensible to a group. Students work-
ing in group problem solving sessions obtain train-
ing in shared information processing and can be-
come aware of a need for interdependence in
achieving their own goals. They may develop a
sense of what to expect from different types of
people and learn something about the difference
between unwisely trusting incompetent sources
and being unwisely suspicious of helpful, com-
petent sources [4]. They also spent some time at
home with the assignment.
The student assistants and I circulated
throughout the classroom during the problem
solving sessions and talked to the individual stu-
dent groups as the need arose. Occasionally, I

would give a short "mini-lecture" on common
problem areas. The hour examination at the end
of the week was structured in such a way that
mastery of the concepts required to solve the as-
signed problems usually meant that a student
could do quite well on the examination. The stu-
dent's solutions to the assigned problems were not
picked-up or graded, yet almost all of the students
attended the problem solving sessions and at-
tempted to work the problems. Some students at-
tended the sessions in both sections. Some students
asked for, and were given, additional problems for
exercise. For two of the nine weeks, the student's
problem solutions were accepted in lieu of the hour
exam although an examination was also available
for those that chose that alternative.
A movie on turbulence and several demonstra-
tions in the fluid mechanics laboratory helped the
students visualize the application of theory. The
orientation of the course was problem solving and
students were helped to role-play engineering as-
signments. For example, copies of the final ex-
amination questions, some from the Bennett and
Myers textbook [5] are shown in the Appendix.

Feedforward Form

1. How would you like to see this class run and what would
you like your part to be in helping it to function in this
2. What do you expect from the class leader?
3. What do you expect from yourself?
4. What special concerns, issues, or questions would you
like to have considered as part of an input to this
5. Open comment:

By the end of the term, I had become ac-
quainted with all of the students on a first-name
basis. This was facilitated by holding a large
number of office hours and on some weeks specif-
ically requesting that the students stop in during
some portion of the office hours. I feel that an open
and caring atmosphere developed within the class.
On the first day of the class, the students com-
pleted a feedforward form telling about their ex-
pectations for the course, the professor, and them-
selves in the course. The form is shown in Table 2.
Frequent feedback forms were used as the course
progressed and helped to promote the openness.
Complete responses to the feedback forms were


It is difficult... to educate students by
talking at them, or by lecturing, in the manner of a preacher
or a wise parent. Students often learn most by experiencing, by problem solving,
by creating and observing the need for knowledge.

distributed to the students the period after they
were handed in. Examples of two feedback forms
are shown in Table 3 with student responses in-
The use of feedforward forms helps the stu-
dents to feel that they have a role to play in setting
the goals for the course. Students pause to think
seriously about their expectations and goals for
themselves. The feedback form helps to show a
willingness to change direction and that the
teacher is concerned with students feelings. Stu-
dents also communicate their feelings to each
other. The usefulness of feedback is discussed by
the Hawleys [6]. Students may feel rather power-
less over their lack of opportunity to influence the
course of their educational experience. Feedback
forms provide a way for the teacher to address
this need. Positive feedback from the class may
motivate the teacher to try even harder to give the
students a valuable and meaningful experience in
the classroom. Problem areas may be uncovered
which can be corrected before they become serious.
Responses by the students regarding the class
were overwhelmingly positive. Performance by the
students on examinations was better than any
previous time when I taught this subject. Most of
the students commented that they felt they had
really learned something in this course and a few
of their comments are listed in Table 3. I felt that
this was the best and most enjoyable course that I
have ever taught.

LARGE CLASSES MAY BE taught sensitively
with a significant amount of professor-student
interpersonal relationship developing. The lecture
mode of teaching may be successfully minimized
in a difficult and demanding technical course.
Group and individual problem solving sessions,
with professor and teaching assistant involvement,
are effective methods for learning. Frequent ex-
aminations are an effective motivation to learning
and tend to ease the pressure of exam taking.
Student feedforward and feedback forms give
the students a good feeling of being involved in a
course and give the professor a good feeling about
his/her teaching experience. An open, caring at-

Feedback Forms and Responses
Responses in italics
On a scale of 1 to 7 with 7 being high

The class rated
The lecture rated
The recitation rated
Teaching assistants rated
The professor rated

7 6 5
19 41 20
19 35 27
27 28 21
15 25 24
33 42 9

On a continuum scale from strongly disagree to strongly
agree please respond to the following:

CHE 305 requires too much time
outside of class hours
Having 9 tests per term is better
than having 4 tests per term
I feel like I'm learning some fluid

Majority Opinions


strongly agree

strongly agree

And I'd also like to say:
* I like the approach-noncompetitiveness.
* I think the way the class is being conducted is great.
* I enjoy the course and understand the material much
more than I would under standard classroom pro-
* I like it when the professor remains flexible through-
out the term.
* Best class I have ever had.

titude on the part of the professor promotes a like
response from students and a significant amount
of 1:1 professor-student contact outside of the
classroom. Students may be effectively motivated
to learn subject material without collecting and
grading homework. An open, humanistic approach
to teaching engineering can result in improved
student learning, self-confidence, and self-appreci-
ation. O

I would like to validate all of the people who have
helped me through some significant personal growth stages
in my life and who have helped me to become aware of the
concept of caring in the classroom. In particular, I want to
validate my wife, Judy, Sid Simon, Carrie Owens, and Carol
Weiskopf. I thank the Hawleys for such a lucid presentation
of valuable ideas in their book. I also appreciate the work
of the teaching assistants in the class; Mike Goodnight,
Barb Dittmann, and Terry Haske. Our department secre-
tary, Ann Brown, typed all of the feedback responses


weekly without complaining and that was a significant task.
Last, but not least, I appreciate the great class of students
enrolled in CHE 305 last fall.


1. Hawley, Robert C., and Isabel L. Hawley, Human
Values in the Classroom, Hart Publishing Co., New
York (1975).
2. Kirschenbaum, Howard, Sidney B. Simon, and Rodney
W. Napier, Wad-ja-Get? The Grading Game in Amer-
ican Education, Hart Publishing Co., New York
3. Glasser, William, Schools Without Failure, Harper and
Row, New York (1969).
4. Reference 1, page 136.
5. Bennett, C. 0., and J. E. Myers, Momentum, Heat and
Mass Transfer, McGraw-Hill, New York (1974).
6. Reference 1, pages 94 and 95.

Final Examination Questions

1. Water is retained in a mountain lake whose surface is
280 ft above the inlet to the turbines in a powerhouse.
Surveyors have laid out the best line location for the
piping system to bring water from the lake down to the
power house. The route is 3100 feet long.
You are the engineer working for the community's
power generating company. What is the minimum
standard diameter of pipe which may be used in the line
so that the natural flow will be 1000 gallons per minute
and the pressure at the turbine inlet will be 100 psig?
Assume turbulent flow.
After obtaining a solution, justify the neglect of any
terms in the equation required to obtain the solution
and justify any assumptions made about the type of

2. You are an engineer in the process development section
of a polymer manufacturing company. Specify the
horsepower required and the pressure which a pump
must develop for the following application. Pump 5000
lb/hr of a high viscosity, Newtonian, fluid 75 feet
through a 2-inch diameter transfer line. The material is
being transferred from one chemical reactor at 900 mm
Hg absolute pressure to another reactor at 450 mm Hg
absolute pressure. The material has a viscosity of 50,000
cps and a specific gravity of 0.95. Place the pump at the
exit of the first reactor. Assume that the efficiency of the
pump is 75%.

3. You are the design engineer in a petroleum refinery. Oil
is being cooled in the inner pipe of a double-pipe heat
exchanger. The oil flows at a rate of 27,500 lbs/hr and is
cooled from 1000F to 89�F. The inside tube is a 3/4"
16BWG steel tube. The oil is cooled by water flowing
counter-currently at a flow rate of 8000 lbs/hr. The
water enters the exchanger at 68�F. The outer tube is
3" sch 40 iron pipe. Calculate the required heat ex-
changer length. Oil properties are:

T�F 75 80 85 90 95 100
p(cps) 3.9 3.7 3.5 3.3 3.1 2.9

Cp = 0.474 Btu/lb�F
K = .0789 Btu/ft2hr OF/ft
p = 51.5 lb/ft3

4. You are a production supervisor in a food processing
plant. Orange juice is being concentrated by evaporation
of moisture from a film of juice flowing down the inside
wall of a large pyrex tube. The tube is heated on the
outside by steam at 2200F. The orange juice flavor is
easily affected by overheating; therefore, no portion of
the juice can have a temperature exceeding 1600F for
even a short period of time. Find the limiting bulk ve-
locity for the case where the bulk mixing-cup, tempera-
ture of the orange juice is 140�F, and the maximum
O. J. temperature is 1600F.
DATA: Convective coefficient for steam: h = 1000 Btu/hr
Convective coefficient for the orange juice: h =
150 u 1/2 where ub is bulk velocity of the film
in ft/sec and h is units of Btu/hr ft20F (i.e.,
conversion factors are built into the 150)
Thermal conductivity of pyrex = 0.5 Btu/hr
Pyrex wall thickness 1/4 inch

1. You are a design engineer in a petrochemical plant.
Calculate the horsepower required and the pressure
which a pump must develop for the following applica-
tion. It is necessary to pump benzene at 70�F from a
storage tank at atmospheric pressure to a pressure
vessel at 50 psig through the piping arrangement de-
scribed below. The flow rate is to be 320 gallons per
minute. Assume the pump to be used has an efficiency
of 80 percent.
Piping System: Ordinary entrance, 10 feet of horizontal
4" sch 40 pipe, pump, open gate valve, 80 feet of 3" sch
40 pipe plus 2 elbow and an open check valve, into the
pressure vessel. The level in the pressure vessel is 20
feet above the level in the storage tank. Assume that the
benzene enters the pressure vessel below the level of
liquid in the vessel.
Assume benzene density is 54 lbs/ft3.

2. You are a project engineer for a pipe-line company. A
20-mile-long pipeline delivers petroleum at a rate of
5000 barrels per day. The resulting pressure drop is 500
psi. If a parallel line of the same size is laid along the
last 11 miles of the line, what will be the new capacity
of this network? Flow in both cases is laminar and the
overall pressure drop remains 500 psi.

3. You are a process development engineer for a synthetic
plastics company. A process requires the development of
a heat transfer device. A fluid is to be heated in a double-
pipe heat exchanger. The fluid is flowing inside a 1-inch
sch 40 steel pipe with a velocity of 1 ft/sec. The fluid is
to be heated in the pipe from 100�F to 160�F. The an-
nular space between the pipes contains steam condensing
at 2000F. The heat-transfer coefficient for condensing
steam is 2000 Btu/hr ft2oF. The fluid has the following


average physical properties:
density - 56 lbs/ft3
specific heat - 0.47 Btu/lb�F
thermal conductivity - 0.07 Btu/hr ft�F
viscosity - 4.0 cps
Find the length of pipe required for the exchanger.
4. You are a tired and puzzled student in ChE 305 (the real
you?). The professor puts the following crazy question
on the final exam. (Don't panic this is a relatively easy
problem, just read carefully.)
The circulation of blood in the finger maintains a tem-
perature of 98.60F at a short distance, say 1/8 inch,
below the surface of the skin. The nerve endings, which
are temperature indicators, are 1/16 inch below the
surface of the skin, your distress is considered to be
noticeable when the nerve endings attain a temperature
of 1100F. Using these criteria, find the maximum tem-
perature of water in which you could hold your finger.
Assume the system is adequately modeled as a flat plate.
Thermal conductivity of
flesh and blood - 0.35 Btu/hr ft�F
Convective coefficient for
finger dipped in water - 100 Btu/hr ft20F
1 ft3 contains 7.48 gallons
1 H.P. = 550 ft-lb,/sec
1 bbl = 42 gallons

r~ii^ books received

"Advances in Cryogenic Engineering" Vol 3. Edited by
K. D. Timmerhaus, Plenum Press, New York. pp 747, 1978.
This is the proceedings of the 1977 Cryogenic Engineer-
ing Conference held at the University of Colorado,
Boulder, CO. Papers include superconductivity applica-
tions, heat transfer, mass transfer, cryogenic techniques
and applications, and LNG design and properties.
"Applied Cost Engineering" by F. D. Clark and A. B.
Lorenzoni. Marcel Dekker, Inc., New York. pp 297, 1978.
This is the first in a series of reference books and text-
books on cost engineering. It is concerned with cost
estimation and cost control and does not discuss engi-
neering economics, the third area of cost engineering.
The authors include few specific data but give the
reader basic philosophy and ideas for developing his own
data, estimating method or cost control system.
"A Programmed Review of Engineering Fundamentals" by
A. J. Baldwin and K. M. Hess. Van Nostrand Reinhold,
New York. pp 287, 1978. $18.95
This programmed text is for anyone preparing for the
National Engineering Fundamentals Examination. The
text includes review material in mathematics and sci-
ence and engineering fundamentals.
Continued on page 52



Dear Sir:
In the Fall issue of CEE Professors Carbonell and
Whitaker identified the origin of the method of volume
averaging as a pair of independent papers by Slattery
(1967) and Whitaker (1967). That citation unfortunately
overlooked the work of Anderson and Jackson (1967) who
also derived the spatial averaging theorem independently
and used the result to analyze motion in a fluidized bed.
Anderson, T. B. and R. Jackson, "A Fluid Mechanical
Description of Fluidized Beds", I.E.C. Fund 6, 527
Slattery, J. C., "Flow of Viscoelastic Fluids Through
Porous Media", AIChE 13, 1066 (1967)
Whitaker, S., "Diffusion and Dispersion in Porous
Media," AIChE Journal 13, 420 (1967)
Stephen Whitaker
Visiting Professor
University of Houston

Please publish the following announcement:
"National Conference on Case Studies in Engineering
Education" sponsored by the ASEE Engineering Case
Committee, March 28-30, 1979, Columbia, South Caro-
lina. Topics: Preparation, writing, and use of case
studies; application of cases to instruction in specific
engineering disciplines; case use in legal, political,
ethical, and economic aspects of engineering. Papers
dealing with these topics will be published in a Proceed-
ings which will be available at the conference. For in-
formation, contact the Office of Continuing Engineering
Education, University of South Carolina, Columbia,
South Carolina 29208; telephone 803-777-6693
Tim A. Jur
Conference Chairman

Dear Sirs:
The Irish Branch of the Institution of Chemical Engi-
neers is organizing an International Conference on Solids
Separation Processes to be held in Dublin in April 1980 in
association with the Annual General Meeting of the In-
The Conference Organizing Committee is inviting
papers for the conference and would be pleased if you could
give some prominence to the "Call for Papers" in your
Abstracts should be sent, as soon as possible, but not
later than April 1, 1979, to
Dr. John J. Kelly, Chairman, Tech. Com.
Intern. Conf. on Solid's Sep. Processes
Tramway House, Dartry Road
Dublin 6, Ireland
D. J. Menzies
Conference Secretary


~11-�1--~ _ .





Clarkson College of Technology
Potsdam, New York 13676

P ART OF CLARKSON'S undergraduate labora-
tory course is devoted to experiments which re-
inforce concepts introduced in earlier lecture
courses. This paper describes an experiment de-
signed to reveal the consequences of the develop-
ment of a concentration boundary layer. The rate
of a mass transfer limited electrochemical reaction
is measured and used to obtain the dependence of
average Sherwood number on Reynolds number
and entrance length. The experimental results may
be compared directly to theory for laminar flows
and to existing correlations for turbulent flows.
When a fluid enters a section of conduit where
mass is exchanged between the fluid and the con-
duit wall, the concentration profile in the fluid
undergoes rapid change. An initially flat profile
changes to one exhibiting a large concentration
gradient at the wall. The shape of the concentra-
tion profile in the fluid leaving a mass transfer
section will depend on the length of the section
until, for sufficiently long sections, the profile be-
comes fully developed. As a consequence of the de-
velopment of the profile, the local mass transfer
coefficient decreases from a large value at the lead-
ing edge of the mass transfer section to a min-
imum downstream. Correspondingly, the average
mass transfer coefficient decreases with increasing
length for the mass transfer section. Dependence

This experiment is simple to
carry out in the laboratory, and a large amount
of good data can be obtained in a
relatively short period of time.

Gordon Youngquist received his BS from the University of Minne-
sota and his MS and PhD from the University of Illinois. Since 1962 he
has been at Clarkson College of Technology where his teaching and
research interests are in reactor analysis, crystallization and porous

of the mass transfer coefficient on system prop-
erties and conditions is normally described as

ShAg. = f(Re,Sc, -- )


ShA. = kAvg. de. e de c
ShAv e V=
D v '



kAg. = average mass transfer coefficient
D = diffusivity
v = kinematic viscosity
de = equivalent diameter
= average velocity
L = mass transfer length
For laminar flow between flat plates, Leveque


analysis (Newman, 1968; Newman, 1973) gives

ShA,. = 1.85 ReScd (1)

For turbulent flow in circular tubes, Van Shaw,
etal. (1963) give

d) 1/

ShAvg. = 0.276 Re-8Sc1/3 (

Electrode reactions have often been used for
experimental determination of forced convection
mass transfer rates in solution (Lin, et al. 1951;
Van Shaw et al., 1963; Eisenberg, et al., 1955).
Some of the various reactions used are:
1.) Reduction of ferricyanide ion
Fe(CN)6-3 + e Fe(CN),-4
2.) Reduction of quinone
CeH402 + 2H+ + 2e-> C6H, (OH),
3.) Reduction of oxygen
02 + 4e + 2HO -- 40H-1
4.) Oxidation of ferrocyanide ion
Fe(CN) 6--- Fe(CN) -3 + e
Such reactions involve two steps: mass transfer
of reactants from the bulk solution to the surface
of the electrode and reaction at the electrode. At
low cell potentials, the reaction rate is reaction
limited. As the cell potential is increased, the rate
increases to the point where it is mass transfer
limited, the concentration of reactant at the elec-
trode surface is essentially zero, and the limiting
cell current is attained. Under these conditions,
the mass transfer rate is given by

1,AC -iL (3)
kAvg.ACoo (3)

A = electrode area
Coo = bulk reactant ion concentration
i, = limiting cell current
F = Faraday's constant
n = number of electrons per ion
reacted at the electrode

This paper describes an
experiment designed to reveal
the consequences of the development of a
concentration boundary layer. The rate of a
mass transfer limited electrochemical reaction is
measured and used to obtain the dependence
of average Sherwood number on
Reynolds number and entrance length.

FIGURE 1. Schematic Diagram of Apparatus

By measuring the limiting current and know-
ing the bulk reactant concentration and the elec-
trode area, the average mass transfer coefficient
may be calculated.

sodium hydroxide solution on a nickel cathode
is used to measure mass transfer rates in our ex-
Fe(CN)6-3 + e-- Fe(CN)6-4
The apparatus, shown schematically in Figure 1,
consists of a rectangular duct through which
Fe (CN) -3/Fe(CN) -4/NaOH solution is circu-
lated. Current is passed between the test electrodes
using a 6 volt storage battery as the D.C. source.
A ten-turn potentiometer is provided for cell
voltage control. Current and voltage in the test
section are measured with a digital multimeter.
Rotameters are provided for flow measurement.
PVC pipe was used for connecting lines and valves
and pump body were of stainless steel.
The test cell, mounted horizontally, is made of
Plexiglas with a duct 0.635 cm x 2.86 cm in cross-
section and approximately 125 cm in length. Six
cathodes (0.635, 1.27, 1.91, 2.54, 3.81 and 5.08 cm
x 2.86 cm) are provided. Oxidation of ferrocy-
anide ion takes place at a large anode (30 x 2.86
cm) placed opposite to the cathodes. The electro-
lyte solution contains equimolar amounts of potas-
sium ferricyanide and ferrocyanide (about 0.015
molar). Approximately 2 M. NaOH is used as an
indifferent electrolyte to eliminate ionic migration
To determine the limiting current, and hence
the mass transfer coefficient, steady flow at a de-


0 .2 .4 .6 .8 10 ;.2 1.4 1.6
FIGURE 2. Data for Determination of Limiting Current
sired rate through the test section is established.
Then, the cell current is measured as a function
of applied cell voltage for a given cathode. The
procedure is repeated for each cathode and over
the maximum flow rate range possible.
Additional details concerning the apparatus
and procedures are appended.


FIGURE 2 SHOWS cell current vs cell voltage
data acquired for determination of limiting
current for several electrodes at constant flow
rate. Some care must be taken to clean and ac-
tivate the electrodes properly and to avoid dis-
solved oxygen (see Appendix) or the limiting
current will not be well defined. It is apparent that
the limiting current is attained for each of the
electrodes in the cell voltage range 0.4-1.0 volts.
Similar behavior is observed at various flow rates.
Once this cell voltage range has been determined,
limiting current data may be obtained quickly for
the various electrodes and flow rates without
changing the cell voltage. The rapid increase of
the current at high voltages is caused by a second
electrode reaction which results in hydrogen evolu-
tion. Naturally, the data of interest are in a cell

FIGURE 3. Dependence of Average Sherwood Number
on Reynolds Number

voltage range below the point where this reaction
becomes of importance.
From the limiting current, the average mass
transfer coefficient may be calculated by rear-
rangement of Equation 3 according to

Avg. nFACoo

These data then may be compared to the predic-
tions of Equations 1 and 2. For calculation of the
Sherwood number, the diffusivity of ferricyanide
ion is necessary. Van Shaw, et al. (1963) give a
value of 5.2 x 10-6 cm2/sec. Alternatively, the dif-

The experimental results here
provide clear confirmation of several
qualitative cause-effect relationships commonly
used in introducing boundary layer theory.

fusivity might

be estimated from the Nernst

D -


Xi = equivalent conductance at
infinite dilution
Zi = ion valence
For calculation of the Reynolds number and
Schmidt number, the kinematic viscosity also is
needed and is easily determined by experiment.
Figure 3 depicts laboratory data for the de-
pendence of average Sherwood number on Reyn-
olds number for several electrode lengths. Trans-
port properties used for calculation are
D = 5.2 x 10-6 cm2/sec (Van Shaw, et al.,
v = 8.1 x 10-3 cm2/sec (determined experi-
mentally @ 31�C)
Figure 4 shows data for the dependence of av-
erage 'Sherwood number on entrance length. The
transition from laminar flow appears clearly as a
change in slope on the Reynolds number plot at
Re = 2400, and the Sherwood number decreases
with length as anticipated. The lines through the
data on each figure represent the predictions of
Equations 1 and 2. The agreement between experi-
ment and prediction is very good. The good agree-
ment with Equation 2 is somewhat surprising
since the corresponding experimental data were


- -' -0

-O o ,.--o e
o --o

.-- O0 ------- EQUATION 1
- ---- EQUATION 2

I I I I I l l

I I I I -

- D"-RE=1055
0- - -0 o-RE = 346
- --RE=84.6
9- 0- -
- O-
-------EQUATION 1

0.1 10
FIGURE 4. Dependence of Average Sherwood Number
on Entrance Length

all in the transition region. The average deviation
is 4.9% for the laminar flow data (72 data points)
and 5.9% for the turbulent flow data (48 data
The data also were correlated using a least
squares technique. Using the functional form of
Equations 1 and 2,

( d
ShAvg. = aScbRee ( (4)

where a, b, c, and d are unknown constants.
ln(ShAvg.) = ln(a) + b ln(Sc) +cln(Re)

+ d n ( .) (5)

Since it was not feasible to vary the Schmidt num-
ber experimentally, Equation 5 is of the form
y = A + cx, + dx2

y = In(ShAvg.)
A=ln(a) +bln(Sc)
x, = In (Re)

x2= In ( )

Good agreement of
experimental data with the predictions
of theory and/or existing correlations is often
satisfying to the students, although most
tend to need considerable guidance
in examining the data.

Using least squares, best values of A, c, and d
were determined from the data, separately for the
laminar and turbulent flow ranges. The results

ShAvg. = 20.1Re0o336 ( - )L 1

for laminar flow

/ \ 0.291
ShAvg. = 1.94 Re-628 e ) for turbulent flow
which compare favorably with Equations 1 and 2.
Using these correlations, the average deviations


FIGURE 5. Comparison of Experimental Data with
Correlation (Laminar Flow)

are 3.5% and 3.6% for laminar and turbulent
flow, respectively. The results of the correlation
are shown in Figures 5 and 6.


T HIS EXPERIMENT IS simple to carry out in
the laboratory, and a large amount of good
quality data can be obtained in a relatively short
period of time. (The data shown in this paper were
obtained in about three hours.) Students tend to
find the data acquisition somewhat boring, since
this largely consists of reading the rotameter and
multimeter while making occasional valve and
potentiometer adjustments. The real challenge lies
in developing some understanding of the physics
implicit in the data and in doing the data correla-
For many students, the notions of boundary







I ]1 I I I

200 800

FIGURE 6. Comparison of Experimental Data with
Correlation (Turbulent Flow)

layer development are difficult to grasp. The ex-
perimental results here provide clear confirmation
of several qualitative cause-effect relationships
commonly used in introducing boundary layer
theory. Good agreement of experimental data with
the predictions of theory and/or existing correla-
tions is often satisfying to the students, although
most tend to need considerable guidance in exam-
ining the data. Exposure to an electrochemical re-
action is educationally useful. Moreover, the tran-
sition from reaction control to mass transfer con-
trol observed in determining the limiting current
reinforces the importance of mass transfer to
many chemically reacting systems.
The equipment has been relatively maintenance
free, although some difficulty was experienced
initially in finding a suitable technique for bond-
ing the nickel electrodes to the Plexiglas duct.
Prolonged exposure to the NaOH solution being




circulated tends to weaken the adhesive bond of
many cements. Flushing the duct with water after
each use minimizes this effect. Care must be taken
to keep the electrodes clean and properly activated
(see Appendix) or the limiting current will be
ill-defined. This may require occasional disas-
sembly of the duct. Bubbling nitrogen into the feed
storage tank for several hours prior to the start of
the experiment serves to remove dissolved oxygen,
another cause of an ill-defined limiting current.
The electrolyte solution is stable, provided direct
exposure to ultraviolet light which catalyzes de-
composition reactions of the cyanides is avoided.
Use of an opaque feed tank and plumbing and
flushing the Plexiglas duct and rotameters after
use solves the problem. Fresh electrolyte solution
is normally prepared but once per semester. Con-


----- .-M , V .... -
1 T
~-�---- ' "



�--YT |

FIGURE 8. Schematic of Control and Measuring Circuit

centrations are checked periodically using iodom-
etric analysis for ferricyanide and permanganate
titration for ferrocyanide (Kolthoff and Sandell,
1952). Ordinarily these concentrations do not
change significantly over the course of a semester.


T HE ASSISTANCE OF Professor Der-Tau
Chin who suggested the experiment and Mr.
Peter Clark who did the data correlation is grate-
fully acknowledged.

Eisenberg, M., C. W. Tobias, and C. R. Wilke, Chem. Eng.
Progr. Symp. Ser. No. 16, Vol. 51, 1 (1955).
Kolthoff, I. M. and B. E. Sandell, Textbook of Quantitative
Inorganic Analysis, 3rd Ed., MacMillan Co., N.Y. (1952).
Lin, C. S., E. B. Denton, H. S. Gaskill, and G. L. Putnam,
Ind. Eng. Chem. 43, 2136 (1951).
Newman, J., Ind. Eng. Chem. 60, No. 4, 12 (April 1968).
Newman, J., Electrochemical Systems, Prentice-Hall, New
York (1973), p. 316.
Van Shaw, P., L. P. Reiss, and T. J. Hanratty, AIChE J. 9,
362 (1963).


FIGURE 7. Detail of Test Cell Construction

Test Cell Assembly: The test cell was made
from two pieces of 1/2 inch Plexiglas sheet ap-
proximately 10 x 125 cm (4 x 48 inches) as de-
tailed in Figure 7. A slot 0.635 cm deep x 2.86 cm
wide (1/4 x 1 1/8 inches) was milled in one piece
to form the flow duct. 22 gage nickel sheet was
used for the electrodes which covered the width of
the duct. Each piece of Plexiglas was additionally
milled to accommodate the thickness of the elec-
trodes (secured using "Krazy Glue") so that a
smooth flow channel was obtained. Electrical con-
necting pins were made by silver soldering a small
brass machine screw to the back side of each elec-
trode. The access hole through the Plexiglas for
each pin was backfilled using Epoxy Cement. The
halves of the cell were bolted together using Para-
film sheet as a gasket.
Some considerable care must be taken in at-
taching the cell electrodes. Many glues do not
provide a strong adhesive bond between the nickel
electrodes and the Plexiglas which is also resistant
to attack by NaOH. Flushing the cell with water
after use extends the useful life of the bond.

After attaching the electrodes and before bolt-
ing the cell together, the electrodes should be
cleaned and activated. The electrode surfaces
should be polished with fine emery cloth, followed
by washing with detergent. To activate the elec-
trodes, the test section is placed in approximately
2 M NaOH solution. A cell formed using a strip of
nickel as the anode and each electrode in turn as
the cathode is connected to a 6 volt D.C. source for
4 to 5 minutes. Caution should be used, as hydro-
gen evolution is considerable. Finally, the test
section is rinsed with distilled water and the cell
Control and Measuring Circuit: A schematic of
the control and measuring circuit is given in
Figure 8. The cell voltage and current were de-
termined using a digital voltmeter which could be
switched alternately to measure the voltage drop
across the cell and across a standard resistor
placed in series with the cell. The cathodes were
wired in parallel with an isolating switch for each.
A 6 volt storage battery was used as the power
source, and cell voltage was controlled using a 100
ohm, 10-turn potentiometer. O


Chemical Engineering

Texts... from

Charles D. Holland
and Rayford G. Anthony
-both of Texas A & M University
Written for the beginning student of chemical reaction
engineering and chemical kinetics, this new, concise
text makes wide use of actual chemical reactions, rather
than synthetic ones. Initiates all topics with first princi-
ples, and provides complete, rigorous and easy-to-
follow derivations.
Features include procedures for the analysis of kinetic
data taken in isothermal reactors-the thermodynamics
needed in the analysis and design of chemical reactors-
design procedures for adiabatic isothermal and noniso-
thermal reactors with single and multiple reactions -
1979 450 pp. (est.) Cloth $21.95

Prices subject to change without notice.
For further information, or to order or reserve
examination copies, please write: Robert Jordan,
Dept. J-440, Prentice-Hall, Inc., Englewood Cliffs,
NJ 07632.



Donald W. Sundstrom and
Herbert E. Klei-both of University
of Connecticut, Storrs
Examines the important physical, chemical and biologi-
cal processes that are used in treating domestic and
industrial wastewaters. Design equations are developed
from principles of thermodynamics, reaction kinetics,
fluid flow and mass transfer. Although a quantitative
approach is emphasized, sufficient descriptive material
is presented to introduce the nature and technology of
the operations.
Provides balanced coverage of the major operations
used in treating wastewater. Presents many of the newer
and advanced treatment techniques, such as pure
oxygen in biological reactors, rotating biological
contractors, membrane separation processes, chemical
coagulation and adsorption.
1979 400 pp. (est.) Cloth $21.95

LO classroom


Dalhousie University, Halifax, N.S.
University of Toronto
Toronto, Ontario, M5S 1A4

has arisen in recent years [1-21], which, based
on earlier work [22-29], has focused on the utility
of the description of the stoichiometry of closed,
chemical systems in terms of linear algebra. This
utility, however, does not seem to be appreciated as
widely as it should be.* This may be partly because
the treatments mostly involve stoichiometry as it
impinges on other fields, such as kinetics and
thermodynamics, with possibly some resulting con-
fusion over terminology and the nature of the
basic questions being resolved by stoichiometry
Here we focus on chemical stoichiometry, per
se, in a treatment free from kinetic or thermody-
namic considerations, in order to focus on these
basic questions and their answers. Specifically we
provide a means for determining the following:
* the number of stoichiometric degrees of freedom, which
is the same as the number of independent chemical
* the number of components
* a permissible set of chemical equations, and
* a permissible set of components,
for a closed system undergoing chemical reaction,
which includes allowance for mass transfer be-
tween phases. The treatment allows for the pres-
ence of inert species and charged species.
It is first necessary to justify the questions and
provide unambiguous terminology. The method is
then presented and illustrated with several ex-

as the constraints placed on the composition

*For example, the Chemical Engineers' Handbook [30]
has short sections on matrices [30a] and on solutions of linear
equations [30b], but the applications mentioned for the
former do not include chemical stoichiometry.

of a closed, chemical system by the necessity of
conserving the amount of each elemental or atomic
species in any physicochemical change in state oc-
curring within the system. These constraints take
the form of conservation equations. The difference
between the number of variables (e.g., relative
mole numbers of species in a basis amount of sys-
tem) used to describe the composition and the
number of such conservation equations may be
called the number of stoichiometric degrees of
freedom, denoted by F,. This is then the number of
pieces of information or relations among the vari-
ables required to determine completely any com-
positional state from a given one. These pieces of
information or relations may come from analytical
determinations or from kinetic rate laws or from
equilibrium constraints, but, apart from the num-

William R. Smith received his university degrees from Toronto
(B.A.Sc., M.A.Sc.) in ChE and from Waterloo (M.Sc., Ph.D.) in applied
mathematics. His main research interests are in statistical mechanics,
thermodynamics, and biomathematics. He has published 41 papers in
these areas. He is an associate professor of Mathematics at Dalhousie
University and holds a joint appointment in the Department of Physio-
logy and Biophysics. (L)
Ronald W. Missen is a Professor in the Department of ChE and
Applied Chemistry at the University of Toronto, where he has been
since 1956, and Vice-Provost (Professional Faculties) in the University.
He received B.Sc and M.Sc. degrees in ChE from Queen's University,
Kingston, Ontario, in 1950 and 1951, respectively, and a Ph.D. in phys-
ical chemistry from the University of Cambridge, Cambridge, England,
in 1956. From 1951 to 1953 he was with Polysar Corporation in
Sarnia, Ontario. He spent the year 1967/68 on sabbatical leave at the
University of California, Berkeley. His research and teaching interests
are mainly in thermodynamics and in chemical reactor behaviour. (R)


ber required, they are outside the scope of
stoichiometry. The determination of F. depends
only on the basic concept of conservation of atomic
species, and is independent of other concepts and
descriptive features, including temperature, pres-
sure, uniformity of a phase, whether or not a sys-
tem is at equilibrium, and the nature and mecha-
nism of reactions actually taking place.
The stoichiometric description of a chemical
system may be in terms of algebraic atom-balance
equations, or, more familiarly, in terms of chem-
ical equations. Chemical stoichiometry also en-
ables us to determine the number (R) of such
chemical equations and to write a permissible set
of them in terms of the reacting species involved.
It is important to see the connection between the
atom-balance equations and the chemical equa-
tions, and this is treated below.
Whether or not chemical equations are used, it
is convenient to divide the reacting species into
two groups: components and non-components (the
latter are sometimes [21] referred to as key com-
ponents) . In terms of chemical equations, the com-
ponents may be viewed as the "building blocks"
for formation of the non-components, one equation
being required for each non-component. The min-
imum number of such building blocks that must be
available in order that any compositional state of
the system can be realized is the number of com-
ponents C. Chemical stoichiometry enables us to
determine C and a permissible set of components
from the species making up the system.


We define the following terms:
Chemical species: a chemical entity distinguishable from
other such entities by (1) its molecular formula; or
failing that, by (2) its molecular structure (e.g., to
distinguish isomeric forms with the same molecular
formula); or failing that, by (3) the phase in which it
occurs (e.g., H20 (1) is a species distinct from H20(g));
the number of species is N
Chemical substance: a chemical entity distinguishable by
(1) or (2) above, but not by (3); thus H20 (1) and
H20 (g) are the same substance, water
Chemical system: a collection of chemical species and ele-
ments denoted by an ordered set of species and an
ordered set of the elements contained therein as follows:
[(A1, A2, . . ., Ai, . . ., AN), (El, Ez, . . ., E , . . ., EM)],
where Ai is the molecular formula, together with struc-
tural and phase designations, if necessary, of species i,
and Ek is element k; the list of elements includes (1)
each isotope involved in isotopic exchange, (2) the
protonic charge, p, if ionic species are involved, and (3)
a designation, such as X1, X,, . . ., for each inert sub-
stance in the species list, an inert substance being one

We may define chemical stoichiometry
as the constraints placed upon the composition
of a closed, chemical system by the necessity of
conserving the amount of each elemental or atomic
species in any physicochemical change in
state occurring within the system.

that is not involved in the system in the sense of phys-
icochemical change; the number of elements is M
Formula vector [25], ai: the vector of subscripts to the ele-
ments in the molecular formula of a species; e.g., for
C6H,NO2, a = (6, 5, 1, 2)T; in what follows, all vectors
are column vectors and superscript T denotes the trans-
pose of a vector
Formula-vector matrix, A: the M x N matrix in which col-
umn i is ai; A = (al, a, ..., ai ..., aN); A is also
the coefficient matrix in the element-balance equations
a akin, = bk; k = 1, 2, . .., M (see equ. (1), below),
where aki is the subscript to the kth element in the
molecular formula of species i
Species-abundance vector, n: the vector of non-negative
real numbers representing the numbers of moles of the
species in a basis amount of the chemical system; n =
(n., n2 ..... ni . . ., nN)T; ni 0
Element-abundance vector, b: the vector of non-negative
real numbers representing the numbers of moles of
elements in a basis amount of the chemical system;
the element-balance equations may be written as An =
b; b is often specified by the relative amounts of "re-
actants" for the system
Closed chemical system: one for which all possible n satisfy
the element-balance equations for some given b
Species-abundance-change vector, 8n = n(2) - n (1): the
changes in mole numbers between two states of the
closed chemical system; it must satisfy ASn = 0
Feasibility or infeasibility of a closed chemical system re-
fers to whether or not a given b is compatible with the
species list; e.g., for the system [(H20, H2, 0,), (H, 0);
b = (bH, bo)T], b = (3, 2)T is feasible, but b = (3, O)T
is infeasible; a necessary condition for feasibility is that
the rank of the augmented matrix (A, b), obtained
from the system of linear equations An = b, be equal
to the rank of A; this is not a sufficient condition be-
cause the algebraic theorem on which it is based allows
for the possibility of solutions involving negative values
for some or all of the ni; a sufficient condition for in-
feasibility is that the ranks be unequal; we assume in
what follows that all systems are feasible


In a closed system, the conservation of atomic
species can be expressed in a set of atom-balance
equations, one for each element:
Sakini = bk;k = 1,2,...M. (1)


In vector-matrix notation, this is
An = b. (la)
These equations may alternately be written so
as to express the change from one compositional
state to another. Thus in a closed system,

SakiSn l=0;k=1, 2,..., M,

A8n = 0.


The maximum number of linearly independent
atom-balance equations, which is the same as the
maximum number of linearly independent rows
(or columns) in the matrix A, is given by the rank
of A [31].
Before giving the general description, we use
an example to illustrate these relations and the
connection between them and chemical equations,
and also the ideas of components, non-components,
and stoichiometric degrees of freedom. Consider
first then a closed, reacting system made up of the
given species CH4, S2, CS2 and H2S. Formally, this
is represented as
[(CH,, S2, CS2, HS), (C, H, S)], (A)
where the first set is that of the species, arbitrarily
ordered as indicated, and the second set is that of
the elements, also arbitrarily ordered.
The atom-balance equations (1) are, for the
species and the elements in the order chosen, and
with subscripts 1, 2, 3 and 4 referring to CH4, S2,
CS, and H2S, respectively.
1 n, + 0 n + 1 n + 0 n = b,
4 n, + 0 n + 0 n, + 2 n, = b,,
and 0 n, + 2 n, + 2 n, + 1 n, = bs.
For a given b, we have three equations in four un-
knowns. We expect to be able to solve for any three
n's in terms of the fourth; that is, we have one
degree of freedom. Suppose we have one particular
solution of these equations (e.g., one corresponding
to an initial state), n* = (*, n*, n2* n*, n4*)T. For
a change from this state to any other state, with
composition n, on rewriting the above equations in
terms of n*, and subtracting one set from the
other, we have

18n, + 08n2 + 18n, + 08n, = 0,
48n, + 0S + 08n, + 28n5 = 0, (B)
and 08n, + 28n2 + 28ns + 18n5 = 0,

where an, = n, - n1*, etc.
The first of these, for example, states that the

amount of carbon in the closed system is fixed (8nc
= 0), regardless of how much chemical change
occurs. The second and third refer similarly to
hydrogen and sulfur, respectively.
The matrix A for this system is

1 0 1 0
A= 4 0 0 2 , (C)
0 2 2 1

where the columns are the formula vectors for the
species in the order given in specification (A).
Equations (B) can be rearranged to solve for
any three 6n's in terms of the fourth, e.g., 8n,, 8n2
and Sna in terms of 8n,. To accomplish this we re-
duce A to unit matrix form [31a] by elementary
row operations [31b]. The "unit matrix form" is
represented by [31a]

A*=[ Ic Z
0 0 ' (3)
where Ic is a (C x C) unit matrix, and Z is a (C x
(N - C)) matrix whose elements may be nonzero.
The number C is the rank of A and of A*. The pro-
cedure in general is similar to that used in the
solution of linear algebraic equations by Gauss-
Jordon reduction [31c]. In this particular case, we
obtain eventually a matrix A* given by

0 1
0 1 �
1 - I

Here the unit matrix is (3 x 3) and the rank of A
is then 3.
Equation (D) implies that equations (B) can
be written

8an + San4 = 0,
6n2 + n, = 0, (E)
and Sn, - �Sn4 = 0.

In other words the mole-number changes for re-
action involving these species can all be related by
stoichiometry to one mole-number change, such as
that for H2S, as indicated.
Alternatively we may write Equations (E) as

The stoichiometric description
of a chemical system may be in terms
of algebraic atom-balance equations, or, more
familiarly, in terms of chemical equations.


A* = 0
1 0

8n4 an 8n2 _ n
+1 -1/ -1 +1/2
Setting these quantities equal to a parameter 5,
and substituting for an1, etc. in equations (B), we
1(-1/2) + 0(-1) +1(1/2) + 0(1) = 0,
4(-1/2)e + 0(-1)e + 0(1/2)e + 2(1)( = 0,
0(-1/2) + 2(-1) + 2(1/2) + 1(1) = 0,
1 0 1
or -i 4 e-1 0 e+j 0 e+
0 2 2

0 0
1 2 = . (F)
1 0
And replacing each vector in (F) by the cor-
responding molecular formula, we have
- CH4 -lS2 + CS2 + 1 H2S = 0,
or i CH, + 1 S2 - CS2 = 1 H2S, (G)
or, as we would usually write,
CH, + 2 2S = CS2 + 2 HS. (H)
We thus see that a chemical equation is a short-
hand way of writing equation (F). Note that the
coefficients of the species on the left side of equa-
tion (G) are contained in the last column of matrix
A* in equation (D). Equation (G) is written as
though these species are the (three) components
or building blocks for the formation of one mole
of the non-component H2S. The components are
thus the species represented by the columns in the
unit matrix of A*, the non-component is the spe-
cies represented by the remaining column apart
from the unit matrix, and the coefficients in equa-
tion (G) are given in the order (down the last
column) in which the components are represented
in the first three columns.
(The technique described in this example lead-
ing to equations (D) and (G) can also be used to
balance an oxidation-reduction equation in inor-
ganic-analytical chemistry, as an alternative to
methods such as the half-reaction method using
oxidation numbers [32], and analogous ion-electron
and valence-electron methods [33], which require
additional concepts.)
A slightly more involved system results if we
add H, to our species list contained in (A). We
now have five 8n's in the three equations cor-
responding to (B). An additional column is added

to matrix A, which becomes

1 0 1 0 0
A = 4 0 0 2 2 (I)
0 2 2 1 0
By means of elementary row operations, this can
be reduced to

1 0 0 � �
A* = 0 1 0 1 (J)
0 0 1 -� -
Again the rank of the matrix is 3, which is the
number of components C. The same set of com-
ponents can be used, CH,, S2 and CS2. The differ-
ence is that there are now two columns apart from
the unit matrix, which implies two independent
mole number changes, or stoichiometric degrees of
freedom (F, = 2), or chemical equations (R = 2).
The matrix form (J) provides a solution for each
of 8n,, 8n2 and 8n, in terms of 8n4 and 8n5. Alterna-
tively, it provides the stoichiometric coefficients
for the two equations in which one mole of each of
the two non-components is "formed" in turn from
the three components. Thus from column 4 of (J)
for H2S, as before, we obtain

j CH, + 1S2 - I CS2 = H2S,
or CH, + 2S2 = CS, + 2H2S,
and from column 5 for H2, we obtain similarly
j CH, + S2 - CS2 = H2,
or CH4 + S2 = CS2+ 2H2.


Equations (K') and (L') can be said to represent
the stoichiometry of this (five-species) reaction
system. However, they are not unique; any linear
combination of them can be used to replace either
one. They carry no necessary implications about
the mechanism of reactions) occurring, or about
reactantss" or "products".
In these two examples no column interchanges
were required to obtain the unit matrix form (3).
This is because in each case the arbitrary ordering
of species was such that the first three (CH4, 82,
CS2) formed a permissible set of components, sat-
isfying the necessary condition that each element
be contained in at least one molecular formula. If
this is not the case, it will be automatically taken
care of by the requirement of column inter-
change (s) to arrive at the unit matrix form (3).
For example, in the second case, if the species were
arbitrarily ordered as H,, S2, H2S, CS2, CH4, the


first three would not form a permissible set of
components, since the element C is missing. The
procedure provided here would, however, reorder
the species automatically by column interchange to
provide a permissible set in the unit matrix.

Equations (1) or (la) are a set of M linear
algebraic equations in N unknowns n for given b.
The general solution of this set of equations may
be written

n = n* + I v jj, (4)
where n* is any particular solution of equations
(1); vj, j = 1, 2, .. ., R, are a set of linearly inde-
pendent solutions of the corresponding homog-
eneous equations (2); and ej are a set of arbitrary
real numbers. The number R is given by
R = N-Rank (A), (5)
and is the maximum number of linearly inde-
pendent solutions of equations (2).
The chemical significance of equation (4) is
that any compositional state of the system n, can
be written in terms of any particular state n* and
a linear combination of a set of R linearly inde-
pendent vectors vj obeying equations (2) or (2a).
Equation (4) leads naturally to the concept of
chemical equations. To show this, we first use the
fact that the vectors vj in equation (4) are solu-
tions of equations (2a) and write
Av = 0 ;j = 1,2,...,R. (6)
A convenient way of writing all R such equations
at once is by defining a matrix N whose columns
are the vectors vj ; that is,
N = (vi, v2, ..., ). (7)
This enables us to write equations (6) as the single
AN = 0. (6a)
The additional vector and matrix quantities in
equations (6) and (6a) are defined in general as
Stoichiometric coefficient vector, v: any non-
zero vector of N real numbers satisfying the
equation A v = 0; and
Complete stoichiometric coefficient matrix, N:
a matrix whose R columns are stoichiometric
vectors with the additional specification that
R = N - Rank (A), equation (5).
An alternative way of writing equations (6)
explicitly involving the columns of A is

Y aj vi - = 0 ;j f= 1, 2, ..., R,


where vi, is the stoichiometric coefficient of the ith
species in equation j. A set of chemical equations
results from equations (6b) when we replace the
formula vectors ai by their species names, Ai:

SAiv, = 0 ;j = 1, 2,..., R.

Equations (K') and (L') above together are an
illustrative set of equations (8) for the system
made up of reacting species CH4, S2, CS2, H2S and
H2. Thus such equations are a chemical shorthand
way of writing the vector equations (6b). By def-
inition a
Complete set of stoichiometric equations is the
set of equations (8), where the vij form a
complete stoichiometric coefficient matrix N, as
defined above.
In passing, we point out that the parameters ej
in equations (4), and the corresponding e's in the
examples above, are the "extent of reaction"
parameters introduced by De Donder [34].
If we define

C = Rank (A), (9)
the significance of C is as follows: we can solve
equations (1) for C n,'s given R ni's, provided the
formula vectors of those C ni's are linearly inde-
pendent. This is equivalent to partitioning the spe-
cies involved into two groups, components (num-
bering C) and non-components (numbering R), as
discussed above, where the components may be re-
garded as chemical "building blocks" for forming
the non-components in chemical equations, one
equation being required for each non-component.
This leads to the definition of a
Component: one of a set of C species of the
chemical system, the number of which is the
least number required to make up any composi-
tional state of the system; the formula vectors
of these species must have the property that
Rank (a1, a2,..., ac) = C, where C = Rank (A).

The procedure simultaneously determines rank
(A) and a complete set of chemical equations. A
Fortran computer program implementing it is
available from the authors, and we describe the
"hand-calculation" procedure below.
The steps are as follows:
1. Write the formula-vector matrix, A, for the given sys-


(3) (1) (2) (6) (4) (5)

We wish to emphasize that
the stoichiometric description of a
chemical system can be obtained solely from
a list of the species and elements involved. It does
not require, initially, a set
of chemical equations.

tem, with each column identified at the top by the chem-
ical species represented.
2. Form a unit matrix as large as possible in the upper-left
portion of A by elementary row operations, and column
interchange if necessary; if columns are interchanged,
the designation of the species (at the top) must be inter-
changed also. The final result is a matrix A*.
3. At the end of these steps, the following are established:
* the rank of the matrix A, which is C, the number
of components, is the same as the number of l's on
the principal diagonal of A*;
* a set of components is given by the C species above
the columns of the unit matrix;
* the maximum number of linearly independent
stoichiometric equations is given by R = N - C;
* the stoichiometric coefficients of a permissible set
of these equations are obtained from the columns
of the part of the matrix A* to the right of the
unit matrix; each column relates to the formation
from the components of one mole of the species
whose designation heads that column, and the
entries in the column refer to the stoichiometric
coefficients of the components in the order of the
component columns in the unit matrix.
The following illustrations demonstrate the pro-
cedure, and also show how inert species and
charged species are treated.
Illustration 1. For the system
[(CO , H.O, H,, CH4, CO, N2), (H, C, 0, XN2)],
determine F,, C and R, and a permissible set of
chemical equations. Note that N2 is inert.
Solution: Following the steps outlined above,
we have
1. (1) (2) (3) (4) (5) (6)


2 2 4 0 0
0 0 1 1 0
1 0 0 1 0
0 0 0 0 1
0 00 0 1

Here the numbers at the tops of the columns
correspond to the species in the order given,
and the rows are in the order of the elements
2. The matrix A can be put in the following form
by means of elementary row operations and
column interchanges:


A* 0�

0 0 0 4
1 0 0 1
0 1 0 -2
0 0 1 0


3. (i) rank (A) = 4 = C;
(ii) a set of components is H2, C02, H20, and
the inert N2;
(iii) R = N-rank (A) = 6-4 = 2 = F,
(iv) the set of two equations indicated by the
entries in the last two columns is
4H1 + 1CO2 - 2H2O = CH4,
and 1H2 + 1CO2- 1HO2 = CO,
or, as we would usually write them,
4H, + CO2 = 2HO + CH4,
and H2 + CO = HO +CO.
Illustration 2. For the system [35],
[(Fe(C04)+, Fe (C20) 2-, Fe(C204) 3-,
Fe3", S042-, HSO-, H+, HC204-, H2C204,
C204-), (Fe, C, O, S, H, p)],
determine F., C, and R, and a permissible set of
chemical equations.
Solution: Following the steps outlined above,
we have
1. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
1 1 1 1 0 0 0 0 0 0
2 4 6 0 0 0 0 2 2 2
4 8 12 0 4 4 0 4 4 4
A 0 0 0 0 1 1 0 0 0 0

0 0 0 0 0 1 1 1 2 0
1 -1 -3 3 -2 -1 1 -1 0 -2
2. The matrix A can be put in the following

(1) (2) (5) (6) (3) (4) (7) (8) (9) (10)
S1 0 0 0 -1 2 0 -1 -1 -1

0 1 0 0 2 -1 0 1 1
0 0 1 0 0 0 -1 -1 -2
0 0 0 1 0 0 1 1 2
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0

3. (i) rank (A) =4= C;
(ii) a set of components is Fe(C204)+(1),
Fe(C20)2-(2), SO.2-(5) and HS04-(6);
(iii) R = N - rank (A) = 10- 4 = 6 = F,
(iv) the set of six equations indicated is


A* =

2Fe(C20)-) = Fe(C204) + Fe(C204)3-
2Fe(C20)+ = Fe(C20) 2- + Fe3
HSO,- = S042- + H+
Fe(C204)2- + HSO,- = Fe(CO2) +
S042- + HC04-
Fe(C,04),- + 2HSO- = Fe(C20O)+ +
2S042- + H2C204
Fe(C204)2- = Fe(C20) + C202-
In conclusion, we wish to emphasize that the
stoichiometric description of a chemical system
can be obtained solely from a list of the species
and elements involved. It does not require initially
a set of chemical equations, no matter how gen-
erated. However, if a set of chemical equations is
used initially, the set can similarly be tested to
determine the maximum number of independent
equations [3a]. We do not recommend this ap-
proach for a stoichiometric point of view, but
rather recommend the approach, as described here,
that begins with the list of species and generates
a permissible set of equations. EO

Financial assistance has been received from the Nat-
ional Research Council (Ottawa).

1. Schay, G., and Peth6, A., Acta. Chim. Hung., 32, 59
2. Aris, R., and Mah, R. H. S., Ind. Eng. Chem. Funda-
mentals, 2, 90 (1963).
3. Aris, R., Elementary Chemical Reactor Analysis,
Prentice-Hall, Englewood Cliffs, N.J., 1969, Ch. 2; (a)
cf. pp. 11-15.
4. Peth6, A., Wiss. Z. Tech. Hochsch. Chem. Leuna-
Merseburg, 6, 13 (1964).
5. Lielmezs, J., Chem. Eng. Sci., 20, 363 (1965).
6. Petho, A., Chem. Eng. Sci., 20, 791 (1965).
7. Aris, R., Arch. Rational Mech. Anal., 19, 81-99 (1965);
ibid., 27, 356 (1968).
8. Amundson, N. R., Mathematical Methods in Chemical
Engineering, Prentice-Hall, Englewood Cliffs, N.J.,
1966, pp. 50-54.
9. Bowen, R. M., Arch. Rational Mech. Anal., 29, 114
10. Gavalas, G. R., Nonlinear Differential Equations of
Chemically Reacting Systems, Springer-Verlag, New
York, 1968, pp. 1-3.
11. Henley, E. J., and Rosen, E. M., Material and Energy
Balance Computations, Wiley, New York, 1969, pp.
12. Aris, R., Am. Scientist, 58, 419 (1970).
13. Balzhiser, R. E., Samuels, M. R., and Eliassen, J. D.,
Chemical Engineering Thermodynamics, Prentice-Hall,
Englewood Cliffs, N.J., 1972, pp. 506-509.
14. Bauder, A., and Giinthard, Hs. H., Helv. Chim. Acta.,
55, 2263 (1972).
15. Calzaferri, Von G., and Dubler, Th., Ber. Bunsen-
Gessellschaft fiur physik. Chem., 76, 1143 (1972).

16. Whitwell, J. C., and Dart, S. R., AIChE Journal, 19,
1114 (1973).
17. Bjirnbom, P. H., AIChE Journal, 20, 1026 (1974).
18. Schubert, E., AIChE Journal, 20 1232 (1974).
19. Bjornbom, P. H., Ind. Eng. Chem. Fundamentals, 14,
102 (1975).
20. Schneider, D. R., and Reklaitis, G. V., Chem. Eng. Sci.,
30,243 (1975).
21. Schubert, E., and Hofmann, H., Int. Chem. Eng., 16,
132 (1976); Chem-Ing-Tech., 47, 191 (1975).
22. Gibbs, J. W., The Scientific Papers of J. Willard Gibbs,
Vol. I., Thermodynamics, Dover, New York, 1961, pp.
63-100, 138-144.
23. Jouguet, E., J. de 1'Ecole Polytech. (Paris), IIe snrie,
21me cahier, 61-194 (1921).
24. Defay, R., Bull. Acad. Roy. Belg., 17, 940 (1931).
25. Brinkley, S. R., J. Chem. Phys., 14, 563 (1946).
26. Prigogine, I., and Defay, R., J. Chem. Phys., 15, 614
27. Peneloux, M. A., C.R. Acad. Sci. (Paris), 288, 1727
28. Christiansen, J. A., Advances in Catalysis, pp. 311-316,
Vol. 5, 1953.
29. Denbigh, K. G., The Principles of Chemical Equilib-
rium, 3rd ed., Cambridge, 1971, pp. 169-172, 187-194.
30. Perry, R. H., and Chilton, C. H., (Editors), Chemical
Engineers' Handbook, 5th ed., McGraw-Hill, New
York, 1973; (a) pp. 2-11 to 2-13; (b) pp. 2-50 to 2-52.
31. Noble, Ben, Applied Linear Algebra, Prentice-Hall,
Englewood Cliffs, N.J., 1969, p. 128; (31a), pp. 131-
132; (31b), p. 78; (31c), pp. 65-66.
32. Mahan, B. H., University Chemistry, 3rd ed., Addison-
Wesley, Reading, Mass., 1975, pp. 257-265.
33. Engelder, C. J., Calculations of Qualitative Analysis,
2nd Ed., Wiley, New York, 1942, pp. 122-127.
34. De Donder, Th., and Van Rysselberghe, P., L'Affinit6,
Gauthier-Villars, Paris, 1936, p. 2.
35. Swinnerton, J. W., and Miller, W. W., J. Chem. Educ.,
36,485 (1959).


Robert H. Perry, former professor of chemical engi-
neering at the University of Rochester, died Thurs., Nov.
9, in Crawley (Sussex) England. He was 54 years old.
Perry was a member of the University of Rochester faculty
from 1964 to 1968, and served for a year as acting chair-
man of the ChE department and as associate dean of the
College of Engineering and Applied Science from 1965 to
1968. Highly regarded as a teacher, researcher, adminis-
trator, and engineer, Perry was editor-in-chief of the
fourth and fifth editions of the "Chemical Engineers' Hand-
book." During his career he served as chairman of the ChE
department at the University of Oklahoma, program di-
rector for science faculties with the National Science
Foundation, and research engineer for several corporations.
In 1961 he assisted UNESCO in establishing a new tech-
nical university in Ankara, Turkey. A chemistry graduate
of Dartmouth, Perry held B.S. and Ph.D. degrees in ChE
from the University of Delaware and an M.S. in ChE from


Adopted By Leading Universities.
And Colleges Throughout The World

Edited by J.M. COULSON, University of Newcastle upon Tyne
and J.F. RICHARDSON, University College of Swansea
This classic series of textbooks, widely acclaimed for its authoritative and outstanding presen-
tations, consists of five complementary volumes all available now in SI units.

VOLUME 1: 3rd Edition
Fluid Flow, Heat Transfer and Mass Transfer
By J.M. Coulson and J.F. Richardson, with the
editorial assistance of J.R. Backhurst and J.H.
"... the selection of topics and their coverage are
excellent... " _

0 08 021015 5 soft
0 08 020614 X har

Professor Frank A. Anderson,
The University of Mississippi
cover $15.00
clover $35.00

VOLUME 2: 3rd Edition
Unit Operations
By J.M. Coulson and J.F. Richardson, with the
editorial assistance of J.R. Backhurst and J.H.
Thoroughly revised and updated, this new edition
includes new sections on fluidized bed combustion
and liquid-liquid extraction. American Units are
retained wherever appropriate.
824pp. 1978
0 08 022919 0 softcover $25.00
0 08 018090 6 hardcover $50.00

Special Topics
Edited by J.F. Richardson and D.G. Peacock
640pp. 1971
0 08 016438 2 hardcover $15.50

VOLUME 4: Solutions to the Problems in
Volume 1
By J.R. Backhurst and J.H. Harker
Written concurrently with the latest edition of
Volume 1.
208pp. 1977
0 08 020918 1 softcover $10.50
0 08 020926 2 hardcover $20.00

A new volume in the series
VOLUME 5: Solutions to the Problems in
Volume 2
By J.R. Backhurst and J.H. Harker
Written concurrently with the latest edition of
Volume 2.
220pp. (approx.) Winter/1979
0 08 022952 2 softcover $12.50 (approx.)
0 08 022951 4 hardcover $25.00 (approx.)

I Write to Department CEE on your department letterhead giving appropriate course title,
class size, and term offered, to receive an examination copy of any volume of Coulson and
Richardson's CHEMICAL ENGINEERING, as well as full details on our SPECIAL OFFER
to faculty who adopt Volume 1 and/or Volume 2.

Now Available At Reduced Prices!
By Stephen Whitaker, University of California, Davis
".. contains in each chapter a worked-out design prob-
lem, several practical examples, and a number of home-
work problems. " Physics Today
573pp. 1977 0 08 017866 9 hardcover $35 .00

By Stephen Whitaker, University of California, Davis
"... the design problems.... are appealing and should
stimulate student interest." Applied Mechanics
387pp. 1976 0 08 018959 8 softcover $15.00

Send For Your Free Sample Copy Of This Journal!
Executive Editor: P.V. Dankwerts
University of Cambridge, England Publis
Discusses applications of chemistry, physics and mathe- Annu.
matics to chemical engineering. Topics range from Two-y
general principles to particular industrial processes. For in

shed monthly
al library rate (1979):
rear library rate (79/80):
dividuals whose library subscribes:

Maxwell House, Fairview Park, Elmsford, N.Y. 10523, U.S.A.
Headington Hill Hall, Oxford OX3 OBW, England
Suite 104, 150 Consumers Road, Willowdale, Ontario M2J 1P9, Canada
Book prices slightly higher in Canada. Prices subject to change without notice.


M0 lecture


Iowa State University
Ames, Iowa 50011

developed quite rapidly over the last twenty or
thirty years but are, unfortunately, so abstract,
unwieldy, and unreliable that chemical engineers
seldom make any use of them. When one needs to
design a mixing nozzle for a pipeline reactor or to
estimate the ground level concentration of hydro-
carbon emissions from a process unit, one is not
inclined to read a discourse on the ergodic nature
of d-dimensional turbulence. (For good reviews
of statistical turbulence theory, intended for the
semi-specialist, consult References 1-3.) Even the
first of the modern statistical theories, the direct
interaction approximation [4] or DIA, is so diffi-
cult and expensive to use that very few calcula-
tions have been made with it. Instead we use ideas
only slightly more advanced than those proposed
by St. Venant and Boussinesq over a century ago.
Single point closures, on the other hand, show
more promise and do not require orders of magni-
tude more computing power than do laminar flow
problems. Furthermore, they can be formulated to
have some quantitative contact with the actual
dynamical equations [5, 6]. Most of the advances in
the technique of single point closures (or single
point models) are being made by mechanical and
aerospace engineers; very few ChEs seem to be
involved in the activity. It is the purpose of this
paper to introduce more of us (especially educa-
tors) to the subject and to suggest some areas of
needed research. Many reviews of various aspects
of the subject are available [7-15, for example],
and so only a brief outline is presented here. For
background any of the standard texts on turbu-
lence should be consulted [16-18].

*This paper, submitted after much prodding from the
Editor, is based on the 10-minute talk, "Problems With
Current Models of Turbulent Transport," which was pre-
sented at the New York AIChE Meeting (1977) as part of
a panel discussion on research needs in turbulent transport
and mixing.

Jim Hill is Associate Professor of ChE at Iowa State, which he
joined in 1971. He has a B.S. degree from Stanford University and a
Ph.D. degree from the University of Washington, was a NASA post-doc
at Goddard Space Flight Center, has worked for Shell Development
Company, and spent last year at the National Center for Atmospheric
Research in Boulder, Colorado. His research interests are fluid mechan-
ics, turbulence, and air pollution control of aerosols. Most recently,
between volleyball tournaments and handball matches, he has been
involved with direct numerical simulation of the turbulent mixing of
passive scalars, with and without chemical reaction.


A MODEL OF TURBULENT transport is sim-
ply a mathematical representation of the
process, and there are many kinds available. Cer-
tain models are more appropriate than others,
depending on the type of problem and the property
being transported. For example, many dispersion
(i.e., making diffuse) and mixing (i.e., making
uniform) processes that occur in wall turbulence,
free shear layers, and wakes appear to involve
gradient transport, and so this feature should be
preserved in those models.
The information desired from the problem also
affects choice-or perhaps availability-of a
model. For example, if knowledge of rate and ex-
tent of transport is required, then mean single
point information may suffice; but if spatial struc-
ture of the transported property is needed, at least
two-point closures are needed.
Other considerations that influence the avail-


ability or appropriateness of certain kinds of
models include the presence of interfaces (i.e.,
single phase or multiphase system ?), complicated
geometry, transient behavior, and whether or not
chemical reactions, variable fluid properties, and
non-Newtonian flow behavior can be treated. The
dynamical models described below are limited to
single phase flows.


available types of turbulent transport models
appears in Table 1. By far the most common
models are the empirical type that involve experi-
mentally determined parameters such as j-factors,
heat transfer coefficients, and the like. These mod-
els may incorporate sound physical ideas, such as
the weak Reynolds number dependence of large
eddy processes.
Mechanistic models, the second category, mod-
ify the true physics by assuming that certain
mathematically more tractable mechanisms domi-
nate the transport process. Examples include mix-
ing length models (which may also be imbedded in
dynamical models), surface renewal theory,
coalescence-dispersion models, Reynolds and Mar-
tinelli analogies, etc.
Dynamical models, the third category, are
based to a considerable extent on the true dynam-
ical equations describing the process, e.g., the
Navier-Stokes equations or the convective mass
transport equation. There is danger that the ap-
proximations invoked to permit solution may dis-
tort the physics more than direct use of a mech-
anistic analog, but dynamical models have the
promise of being formulated for very general ap-
plications. The models may be semi-empirical, i.e.,
Types of Models of Turbulent Transport
1. Empirical Models ..._-- . Transport coefficients
2. Mechanistic Analogs ..__ "Exact" solution of plausible
3. Dynamical Models -___ __. "Approximate" solution of
averaged equations of change
4. Other

Desiderata for Turbulence Models
(A Disjoint Set of Needs)
1. Adequate representation of the physics
2. Ability to solve realistic problems
3. Ease of computation

contain phenomenological coefficients, or may be
more or less rigorously derived using some sta-
tistical hypotheses.
Everything else is in the fourth category, in-
cluding integral methods that require parameter
estimation (by the techniques of either of the first
two categories) and also large eddy simulations in
which the large scale flow structure is solved nu-
merically but with a 'sub-grid' model that accounts
for the dynamics of the small scales [13].
The ideal model-if it were to exist-would
satisfy the criteria listed in Table 2. Let us now
briefly look at dynamical models to see how good
they are in this regard.


TABLE 3 DISPLAYS A sample of the available
kinds of dynamical models, mostly for mo-
mentum transport, the preponderance of which
are unsuited for practical application and are still
subjects of research. The classifications should not
be taken too seriously. The name 'single-point'
refers to dynamical equations that apply to single
spatial points, whereas 'two-point' theories involve
correlations or spectra. The order of the model is
the order of the equation in which the closure or
modeling is made; for example, second order
closures involve dynamical equations that are sec-
ond order in the dynamical variables.

1. Single Point Models
To illustrate single point closures, consider the
Reynolds equation obtained by averaging the
Navier-Stokes equations:

+ U + UW (1)
Dt au /a p axi
DU1/axi = 0 (2)


When one needs to design a mixing nozzle for a pipeline reactor or
to estimate the ground level concentration of hydrocarbon emissions from a process
unit, one is not inclined to read a discourse on the ergodic nature of d-dimension turbulence.

Dynamical Models of Turbulent Transport

Eddy-coefficient (vT,DT)
Mixing length

(Deissler, Loeffier, etc.)



Second Order One and Two-Equation Transport Spectral Theory and Cascade 3-point
Models [e.g., k-e models] Models Green's
Launder, Spalding, Kolmogorov, (Kolmogorov, Heisenberg, Functions
Lumley, Harlow, Saffman, Batchelor, Corrsin, Leith, (Weinstock)
Kovasznay, Wolfshtein, etc.) [including Corrsin
Jones & Launder, Harsha, etc.) isotropic mixer]
Stress Equation Transport Models Statistical Theory
[e.g., k-e-uv] (Kraichnan [DIA, LHDI,
(Rotta, Donaldson, Harlow, TFM], Orszag, Herring,
HanjaliC & Launder, Wolfshtein etc.)
et al., Launder-Reece-Rodi, etc.)

Third and Higher Order Transport Models Higher Order Statistical Higher Order
Higher Order [u-, etc.] (Chou, Davidov) Theory [including distribution Statistical Theory
functions] [including functionals
(Hopf, etc.)]

Ui = Ui+ui and - +U i -
Dt at xi "
Equation (1) may be closed at the first order with
an eddy viscosity model,

uiuj = -v, U + U )+ 2 kji (3)

where k is the turbulent kinetic energy k = 1/ uiui
and vT is the eddy viscosity, which may be repre-
sented as leddy Veddy. Some forms for v, are

12 jaU/aDx2
VT = c k1/21
c k2/e

(Prandtl 1925)
Prandtl 1945
Kolmogorov 1942)



where the turbulent dissipation rate, E = v(aui/
Dxj) 2, may be evaluated as E = c3k3/2/ 1, and where
1 is a prescribed turbulent length scale. This first
order model, Eq. (1)-(3), is inadequate for com-
plex flows.
Second order transport models introduce aux-
iliary dynamical equations for such quantities as
k, 1, and uiuj. The prescription for one- and two-
equation models is to a) express vT by Eq. (4b) or
(4c), b) develop a transport equation for k or e
based on the Navier-Stokes equations, and c) pre-
scribe 1 or develop a transport equation for kmln.
The best known example of the two equation model
is that of Jones and Launder [19],

Dk/Dt = V- - Vk -uiujaUi/xj -e (5)

The stress equation models,
for example, correctly predict negative
eddy viscosity effects, secondary flow in
noncircular ducts, and are accurate
for thin shear flows.

De/Dt = V- (V
( 0-

V ) -c4 e

UiujaUi/axj - - (6)

in which the car's (turbulent "Prandtl" numbers)
and the c's must be obtained from experiment, and


First Order

I a I I �

The name 'single-point'
refers to dynamical equations that
apply to single spatial points, whereas 'two point'
theories involve correlations or spectra.

(4c) is used for vy.
Stress-equation models, such as the Launder-
Reece-Rodi or LRR model [20], were introduced by
Rotta in 1951 and are now considered superior to
the two-equation models. (See also the recent
promising work of Jeandel et al [21].) Instead of
(33, a dynamical transport equation for uiuj is
formulated using the Navier-Stokes equations, to
obtain (symbolically)
D- 2
Dt uiui = Pij + Dij - 3 Ei + 0i (7)


stress generation + diffusional transport
plus dissipation plus pressure-strain redis-

In (7) the stress generation term Pij (from mean
gradients and body force) is treated exactly, "dif-
fusional" transport Dij (the divergence of triple
products) is modeled by gradient diffusion, the
dissipation term assumes isotropy of the small
scales, and the pressure-strain redistribution term
(which involves unmeasurable pressure-velocity
correlations) is nothing but trouble. ijb varies
from one modeler to the next; usually a form is
used based on almost-isotropic turbulence, even
for thin shear layers. In flows where stress genera-
tion and dissipation are not in good local balance,
oij causes problems. So does the present form of
Eq. (6).

m 0
C0 0
0 1 2
FIGURE 1. Sketch of typical predicted (solid lines) and
measured (circles) mean concentration and
concentration fluctuation intensity profiles
for a round jet (after Spalding [10]). The
subscript m denotes center-line value, r and
x are radial and axial coordinates.

Similar developments have been made for
scalar fields, i.e., heat and mass transfer [12]. The
appropriate 'scalar flux' equations needed are

D + ( (uic) = DV2C + R (8)
Dt + x,
Dt uic = somewhat similar to (7). (9)

As in (7), the pressure-concentration gradient
correlation causes difficulty. Scalar transport mod-
1.0 - 1.0
0.8 0.8
0.6- \ 0.
S0.4- 0.4
0.2- 0.2
0.0 0.0 I I I
0.0 0.2 0.4 0.0 0.2 0.4
r/x r/x
FIGURE 2. Sketch of axial (left) and circumferential
(right) velocity profiles predicted by Reyn-
olds stress closures [23] for swirling jet in
stagnant surroundings at x/D = 6. The
circles represent experimental data, the
dashed lines are for the standard form of
pressure-strain correlation ( (LRR model),
and solid lines have circumferential com-
ponents of 0 reduced by 60%.

els have recently been generalized to higher order
by Deardorff [22].
The single point models-especially the stress
equation and concentration flux models-have had
many successes. The stress equation models, for
example, correctly predict negative eddy viscosity
effects, secondary flow in noncircular ducts, and
are accurate for thin shear layers. An illustration
of successful application of a second order closure
to the concentration distribution in a jet is shown
in Fig. 1. On the other hand, weak shear (far
wake), rapid decay (round jet), swirl flows,
buoyancy effects, and recirculation lengths are
poorly treated if one insists that the empirical con-
stants (the c's and o-'s) be universal, i.e., be evalu-
ated with other types of flows. In the swirl jet, for
example, spreading rate and even the sign of the
Reynolds stress are in error, leading to the poor
agreement shown in Fig. 2. Computational re-
quirements for all of these models are quite mod-
est, in comparison with multipoint statistical


FIGURE 3. Wind tunnel with heated grid used by Wis-
kind [24] to generate a nearly homogeneous
turbulent flow with uniform mean tempera-
ture gradient.

theories, the main concern being core-limitation
for 3-D calculations.

2. Two-Point Models
Two-point models, especially those based on
statistical theories, are relatively undeveloped for
engineering problems. The present author, for
example, has applied the direct interaction ap-
proximation to heat transfer in a grid flow (Fig.
3) ; the results for variation of eddy diffusivity E.

A w


with Prandtl number (Fig. 4) for this simple
problem would cost tens of $1000 today in com-
puter time alone (the programming itself is quite
formidable), so it is not surprising that statistical
theory is not used much.


THE SINGLE POINT transport models de-
scribed above satisfy the criteria in Table 2
better than most other models for single phase
flows. Some areas of research that would improve
their usefulness are listed in Table 4. Some areas
are virtually untouched because ChEs have not yet
been involved much.
Modeling the essentially unmeasurable pres-
sure correlations for 0ij in Eq. (7) is a major prob-
lem, but large eddy simulations may be helpful to
examine the term. Chemical reactions have been
largely neglected [11]; current closures for non-
linear chemistry are inadequate, especially for

Suggested Research Areas
Pressure correlations Time-depeni
Chemical reactions Multiphase
Two-point models Non-Newtoi
Eddy structure Variable-pr
Error nronaraation Complicated

dent problems
nian fluids
operty effects
i. realistic flows

u00 -.- .
complex reactions, and the newer models have not
/ (1) been tested against liquid phase (high Schmidt
//2 number) experiments. Two-point models, neces-
/ (2) sary for description of spatial structure, are too
/ complicated for shear flows; furthermore, many
10 / basic problems in spectral theory are still unre-
solved, including diffusive subranges, small scale
dynamics, etc. New ideas about eddy structure,
especially near the wall and in free shear layers,
have not been incorporated in the transport mod-
els. The problem of error propagation and sensitiv-
ity to boundary and initial conditions has not been
. I I I I addressed. Time-dependent problems should be ex-
10-3 10-2 10-1 1 10 102 103 amined, as there appear to be problems with re-
Pr laxation effects [23]. Application of the models to
RE 4. Estimates of Prandtl number dependence of very complicated, realistic flows is sparse. More
thermal eddy diffusivity EH based on un- fundamental theory is needed for multiphase flows,
published direct interaction approximation non-Newtonian fluids, and variable property ef-
(DIA) calculations by the author. Curve (1) fects.
assumes a Gaussian shape of the longi- Although the above list is long, it is formulated
tudinal two-point two-time velocity correla- in response to the fine successes that single
tion function; curve (2) assumes exponential point models have had. If we can manage to get
shape. The dashed lines are theoretical these models to work accurately and reliably for
low-Pr asymptotes and the one data point us, perhaps we will have more time to read about
(air) was taken by Wiskind. d-dimensional turbulence. O



Preparation for the New York panel discussion-and
hence this paper-was made when the author was a Senior
Postdoctoral Fellow in the Advanced Study Program at the
National Center for Atmospheric Research, while on Faculty
Improvement Leave from Iowa State University. The author
gratefully acknowledges these two programs and the Engi-
neering Research Institute at Iowa State. NCAR is sup-
ported by the National Science Foundation.


1. Rose, H. A. and P. L. Sulem, J. Phys. (Paris) 39:441
2. Kraichnan, R. H., in S. A. Rice et al., eds., Statistical
Mechanics: New Concepts, New Problems, New Appli-
cations, Univ. Chicago Press (1972), p. 201.
3. Orszag, S. A., in R. Balian and J. L. Peube, eds., Fluid
Dynamics, 1973 Les Houches Summer School of Theo-
retical Physics, Gordon & Breach, New York (1977),
p. 235.
4. Kraichnan, R. H., J. Fluid Mech. 5:497 (1959); Phys.
Fluids 7:1048 (1964).
5. Leslie, D. C., Developments in the Theory of Turbu-
lence, Oxford University Press (1973), ch. 14 and 15.
6. Herring, J. R., in Proceedings of Langley Working
Conference on Free Turbulent Shear Flows (NASA-
SP-321, Langley Research Center, 1973), p. 41.
7. Launder, B. E., and D. B. Spalding, Lectures in Mathe-
matical Models of Turbulence, Academic Press, New
York (1972), and Comp. Meth. Appl. Mech. & Eng.
3:269 (1974).
8. Donaldson, C. duP., AIAA J. 10:4 (1972).
9. Mellor, G. L. and H. J. Herring, AIAA J. 11:590
10. Spalding, D. B., in S.N.B. Murthy, ed., Turbulent
Mixing in Nonreactive and Reactive Flows (Proceed-
ings of a Project SQUID Workshop, Purdue Univer-
sity, 1974), Plenum Press, New York (1975), p. 85.
11. Patterson, G. K., in R. S. Brodkey, ed., Turbulence in
Mixing Operations, Academic Press, New York (1975),
Ch. 5.
12. Launder, B. E., in P. Bradshaw, ed., Turbulence
(Topics in Appl. Phys., Vol. 12), Springer-Verlag,
Berlin (1976), p. 231.
13. Reynolds, W. C., Ann. Rev. Fluid Mech. 8:183 (1976),
also W. C. Reynolds and T. Cebeci, in Bradshaw [12],
p. 193.
14. Harsha, P. T. in W. Frost & T. H. Moulden, eds.,
Handbook of Turbulence, Vol. 1: Fundamentals and
Applications, Plenum Press, New York (1977), p. 187.
15. Lewellen, W. S., in Frost & Moulden [14], p. 237.
16. Tennekes, H. and J. L. Lumley, A First Course in
Turbulence, MIT Press, Cambridge (1972).
17. Hinze, J. O., Turbulence, 2nd Edition, McGraw-Hill,
New York (1975).
18. Monin, A. S. and A. M. Yaglom, Statistical Fluid
Mechanics: Mechanics of Turbulence, ed. J. L. Lumley,
MIT Press, Cambridge, Volume 1 (1971) and Volume
2 (1975).
19. Jones, W. P. and B. E. Launder, Int. J. Heat Mass
Transfer 5:301 (1972).

20. Launder, B. E., G. J. Reece, and W. Rodi, J. Fluid
Mech. 68:537 (1975).
21. Jeandel, D., J. F. Brison, and J. Mathieu, Phys. Fluids
21:169 (1978).
22. Deardorff, J. W., Phys. Fluids 21:525 (1978).
23. Launder, B. E. and A. Morse, in F. Durst et al., eds.,
Symposium on Turbulent Shear Flows, Pennsylvania
State University (1977), p. 4.21.
24. Wiskind, H. K., J. Geophys. Res. 67:3033 (1962).

Book reviews


By Stuart W. Churchill
McGraw-Hill, New York, 1974.
Reviewed by Robert L. Kabel,
Pennsylvania State University

"The Interpretation and Use of Rate Data"
does not fit in well with conventional chemical
engineering curricula. However, the book is so
unique and important that a way must be found
to convey its message to students and practicing
engineers. By the way, is the distinction between
a rate of change and a process rate fuzzy in your
Churchill has treated the rate processes in-
volved in heat transfer, momentum transfer, com-
ponent (mass) transfer, bulk transfer, and chemi-
cal reactions according to a rather general "Rate
Concept." In all of these areas the treatment is at
the level of sophomore and junior chemical engi-
neering courses. Attention is focused on principles
and procedures rather than on process complica-
tions by considering primarily one-dimensional
processes which can be described in terms of alge-
braic or separable differential equations. About
one-third of the book is devoted to chemical re-
actions, but all topics are intermingled in such a
way that the generalizations and methods are
emphasized instead of the specific applications.
This reviewer used all of the material on chemical
reactions in a review portion of an advanced
kinetics course and he read the remaining material
Following the introductory material, the early
emphasis is on real data and data handling. There
is then a shift to data correlation and finally to
process analysis. This order of presentation is the
reverse of that almost always encountered by
Continued on page 44




Texas Tech University
Lubbock, Texas 79409

ASK A PRACTICING chemical engineer the
following question:
"Do you consider writing ability to be essential to
the performance of your job?"
Ninety-five percent of those responding will prob-
ably answer in the affirmative. At least that was
the response obtained from 135 graduates of ChE
from Texas Tech University who were polled
about the importance of technical communication.
This appears to be a typical attitude representa-
tive of all engineering professions. For example,
articles on how to write better reports appear
routinely in professional journals [1, 2, 3]. And,
if the information is to be transferred to the pub-
lic domain, professional societies provide ample
information for the author on procedures for pre-
senting papers at professional society meetings or
in professional journals. Admittedly these instruc-
tions deal more with "form" rather than "style",
but the desire for clarity is still universal.
It is somewhat surprising, therefore, to learn
that there is a growing concern among educators
about the inability of students (and ultimately
engineers) to communicate [4, 5, 6, 7, 8]. At the
university level there has, of course, been a reduc-
tion of formal instruction on communication skills
in engineering degree programs over the last two
decades. Surveys by the AIChE reveal that the
average semester hours of credit required in com-
munications courses in ChE curricula has dropped
50 percent, from eight hours in 1957 to four hours
in 1976 [9]. Whether or not this de-emphasis has
contributed to the overall decline in the communi-
cations skills of engineering graduates is still open
to conjecture. However, because of an apparent
low level of performance in rhetoric by senior

.. the Technical and Professional
Writing Program of the English Department
was asked to prepare and administer a course
in technical writing.

students, the ChE Department at Texas Tech de-
cided to re-emphasize technical communication
At the beginning of the 1974-75 academic year
the department initiated a program which it hoped
would enhance the technical-writing skills of grad-
uates. To accomplish this, the Technical and Pro-
fessional Writing Program of the English Depart-
ment was asked to prepare and administer a
course in technical writing. This instruction was
to be supportive of the normal report writing re-
quired in the senior level unit-operations course
sequence. The final format which evolved required
each student to receive one hour of instruction per
week on the basics of technical communication.
The students were then asked to write their unit-
operations reports based on a variety of criteria.
For example, they were asked to submit their re-
ports in either (1) letter form, (2) as a memo-
randum or (3) as a fully documented formal re-
port. In addition, they were asked to write for a
variety of readers such as (1) a nontechnical ad-
ministrator, (2) nonscientific personnel, or (3) a
fellow engineer. A total of eight to ten reports
were prepared by each student throughout the
two-semester course sequence. In order to evaluate
a student's performance, a member of the engi-
neering faculty graded the reports on their tech-
nical content while report-design elements (lan-
guage, style, and format) were evaluated by the
faculty representative from the English Depart-
ment. The final course grade, therefore, became
an evaluation of the student's ability to master the
technical aspects of the unit-operations course as
well as his effectiveness in communicating this
technical information.


operations course did not change appreciably
following the adoption of the new program. In
general it followed a traditional format in which
the students were divided into working teams of
three to four members. The groups were then as-
signed four experiments to be carried out during
the semester. These included the standard heat
and mass transfer studies, those experiments


which gave a combination of heat and mass trans-
fer, a kinetics experiment, and a system to eluci-
date mixing operations. A list of the experiments
performed is shown in Table 1.
In general, the difficulty of the experiments
varied from rather simple repetitive measure-
ments to the development of complicated abstract
concepts. Hence the students were subjected to
varying degrees of difficulty in the type of tech-
nical information they were asked to communicate.
Communications content of the course is based
on the coursework-design used in Technical and
Professional Writing Program courses. Texas
Tech offers a major in technical writing and edit-
ing based on many new concepts in writer training
developed and tested over the past five years. In
the unit operations laboratory the central concept
used has been an "engineered approach" to writ-
In the "engineered approach", writing solely to
convey information is not stressed. Instead, the
objectives to be achieved (design criteria), audi-
ence characteristics (materials), and design tech-

Unit Operations Laboratory Experiments
1. Fluid flow
a. Friction factor for fluid flow in pipes
b. Newtonian and non-Newtonian fluid behavior
c. Venturi and orifice meter measurements
2. Heat Transfer
a. Free and forced convection systems
b. Drop and film condensation
c. Double pipe heat exchangers performance
3. Mass transfer
a. Liquid-liquid extraction
b. Filtration of aqueous slurries.
4. Combinations of heat and mass transfer
a. Distillation
b. Evaporation
c. Humidification
d. Drying
5. Chemical kinetics
6. Unsteady-state operations
a. Mixing coupled with titration
b. Stirred-tank cooling

niques (methods), are strongly emphasized. An
algorithmic method for report design is taught in
order to convey the step-by-step procedure re-
quired for predictably successful writeups. Sen-
tence structure presentations are adopted from
recent results in linguistics. Enabling students to
describe relationships between sentences ("good"
and "bad" ones, ones linked together by para-

Charles W. Brewer has attended Rice University, The University of
Texas, and The University of Utah. He has taught at The University of
Texas, Bemidji State College, and Texas Tech. He has been employed
by International Telephone and Telegraph, Johnson Space Center, and
NCR Corporation. At Texas Tech, he directs the Technical and Profes-
sional Writing Program, a program developed to offer interdisciplinary
coursework in three areas of engineering. The program also offers con-
tinuing education for various industries and organizations in Texas, in-
cluding the AIChE. (L)
Richard Wm. Tock is an Associate Professor in ChE at Texas Tech
University. He received his B.S., M.S., and Ph.D. degrees in ChE at
the U. of Iowa where he also taught for several years following gradu-
ation. His industrial experience includes serving as a Research Engi-
neer in the Central Research Division of Monsanto Company and vari-
ous consulting services. (R)

graphing, ones having the desired effects on read-
ers, etc.) is a primary objective. Report format
for memorandum, letter, and formal reports is
adopted from American Chemical Society publica-
tion specifications.
Grading reports is like real-world evaluation of
engineering work based on the twin criteria of
effectiveness and efficiency in achievement of com-
munications objectives. Misspelled words, for ex-
amples, are not frowned on for reasons of social
unacceptability or instructor disapproval; they are
disparaged because they are not effective or ef-
ficient in a report's achieving objectives among
persons who recognize them as misspelled words.
Classwork and grading procedures are supple-
mented by conferences with students. The con-
ferences are designed to provide tutorial teaching
and provide additional rapport between ChE stu-
dents and technical-writing teachers.
Three types of reports are required in the
course in order to simulate the complete spectrum
of writing required of professional engineers.
Formal reports correspond to well documented
communications for wide distribution throughout
a company, an industry, or a profession. Memo-
randum (short-form) reports correspond to col-


Three types of reports
are required in the course in order to
simulate the complete spectrum of writing required
of professional engineers.

league and management oriented communications
within an organization. Letter reports correspond
to contract related communications between two
organizations. Differences and similarities among
audiences of the three reports-as well as format
and language differences and similarities-are
stressed as key materials in report design.

IN GENERAL THE FIRST few semesters of the
program were qualitatively evaluated by the
professors involved in the instruction. Simple im-
provement in an individual student's performance
seemed to suggest that the added emphasis given
to technical communication was indeed ac-
complishing its goal. This achievement was not
without conflict, however. Initially some students
were unhappy with the added time spent in the
technical-writing class and the additional assign-
ments. Many students also expressed strong feel-
ing about having their papers graded by two dif-
ferent professors and on two different bases: for
technical content and for communication effective-
ness and efficiency. Nor did all the voiced dissent
come from the students. There was some disagree-
ment among the faculty during the initial stages
of the program concerning the proper format and
style to be followed in the reports. Fortunately,
time and compromise have brought solutions to
most of these early conflicts. Now a manual of
instruction is being developed to help formally
establish the program. In addition, several other
engineering departments have begun similar
technical-communications instruction within their
own courses.
Even though the new program appeared to be
successful, it was deemed desirable to have some
additional evidence of its success. Moreover, it
was felt that some input from graduates of the
program would be helpful in developing an even
more effective program in communication skills.
Consequently, a short questionnaire was developed
and mailed to department graduates from the
preceding eight years. These alumni included
graduates from the last two years who had had
the benefit of the new instructional program, as
well as those from earlier years who had not ex-

perienced any formalized instruction outside of
that supplied by the ChE faculty of the depart-
ment. The following six questions to be answered
"yes" or "no" were asked of each person in this
1. Did you receive all your undergraduate education at
Texas Tech?
2. Do you feel the technical writing instruction you
received at Texas Tech was adequate to meet the
responsibilities of your job?
3. Do you consider writing ability to be essential to the
performance of your job?
4. Do you feel a course in technical communication
should be required for all B.S. engineering gradu-
5. Has your company ever offered to provide instruction
for improving communication skills of its engineer-
ing employees?
6. If Texas Tech offered an off-campus course in com-
munication skills at or near your plant location,
would you attend?
The results of the questionnaire are summarized
in the following graph. Of the 211 questionnaires
mailed, 135, or 64 percent, were returned. For
comparative purposes the responses were sep-
arated into two classifications: (a) those alumni
who had only departmental emphasis given to
their technical writing skills while attending
Texas Tech and (b) those alumni who graduated

100 -

90 -


7n 5


during the last two years and received the new
instructional program developed by the English
Department. The latter group composed 19 percent
of the total responding population.
The response to Question 1 indicates that stu-
dents at Texas Tech are following a national trend
by obtaining some of their education at local or
area schools before getting their final degree at a

at their convenience. On the surface it might ap-
pear as though the responses to Question 6 are not
compatible with those of Question 2. One interpre-
tation is that the increased emphasis on technical
communication by the program has tended to make
more students aware of their deficiencies. Hence
they would aspire to do more work in this area to
improve their abilities. There is also a certain de-

The groups were then assigned four experiments to be carried out
during the semester. These included the standard heat and mass transfer studies,
those experiments which gave a combination of heat and mass transfer, a kinetics experiment
and a system to elucidate mixing operations.

greeof aturtio whch mst e asignd t th

state institution such as Texas Tech. This pattern
of switching schools means that the final degree-
granting institution has an added responsibility to
their graduates. The students must be exposed to
those basic fundamentals which will enable them
to succeed. In the case of communication skill,
competency is all too often inferred from tran-
scripts and is rarely tested. Thus graduates may
be ill prepared to meet their job requirements with
respect to communication unless the university
takes specific steps to prepare them.
Question 2 responses appear to support the
general assumption that the program has had a
positive impact. Thus, 62 percent of the people
who had the new course felt it was adequate. How-
ever, a nearly equal 58 percent of those who didn't
have the benefit of the new program felt that they
still had received sufficient instruction. Question 4
might also be taken as proof of the program's suc-
cess. In this case 76 percent of those in the course
felt that a general program for all B.S. candidates
was desirable while 84 percent of those not in the
program felt it was. This implied that those having
the new instructional program found it to be suf-
The answers to Question 3 indicate that the
overwhelming majority of graduates feel their
writing ability is essential to job performance.
Apparently their companies do also, since for both
populations (a and b) more than 50 percent of the
responses to Question 5 indicated that they had
been offered some form of additional instruction
in writing. The 135 respondents worked for a total
of 58 companies, 26 of which offered the additional
Finally, Question 6 seems to indicate that at
least 40 percent of all the graduates are still
willing to take more instruction if it were offered

gree of maturation which must be assigned to the
earlier graduates of the population.

ALTHOUGH THE GENERAL response of the
questionnaire was judged to be supportive of
the new program, some unsolicited written re-
sponses were even more enlightening. These are
included in the Appendix in an abridged form. In
addition to these longer comments there were sev-
eral penciled replies. In general these were in
reference to the necessity of good communication
skills, and almost exclusively of the short letter
form. Longer formal reports seemed to be within
the purview of graduate degree holders and those
in research groups. There were also comments en-
couraging the development of communication
skills for transfer of technical information to the
nontechnical person.
Finally, response from the technical writing
faculty also seems to strongly support the pro-
gram. Their observations include the following
* The senior unit-operations laboratory students, because
of their level of maturity and their background in rig-
orous studies, grasp the material more rapidly and
thoroughly than younger, less experienced students.
* The students are more highly motivated to learn writing
procedures and techniques within the "applicative-ori-
ented" context of unit-operations laboratory than are
students in "stand-alone" technical writing courses.
* The "engineered approach" to writing used in the pro-
gram dispells doubts and poor attitudes toward writing
that may have resulted from less rigorous writing
coursework undertaken during freshman college years or
in public-school classroom.
In summary, responses to the questionnaire
and responses of instructors indicate that the new
emphasis on technical communication appears to


be accomplishing its intended goal. In addition, it
has provided some valuable insights into some new
directions the program might go in order to be
more meaningful for the new engineer on the
job. O


Abridged Responses to the Questionnaire
"Tech writing at work is far different and less involved
than those unit ops reports. I've written letters to spend
$15 million since I've been at work and have never written
more than two pages per project."
"Tech writing: no need to emphasize technical aspects
. . . concentrate on freshman English, basic grammar and
sentence structure."
"For your information I now supervise the efforts of
some twenty Chemical, Civil, Mechanical and Petroleum
Engineers in our area office. I have found that the majority
of the engineers on my staff, particularly those having just
graduated from college, are weak in communication skills.
I have also found that only about 50% of an engineer's
total efforts are spent in technical analysis, the remaining
50% of an engineer's time is normally spent in "sales" of
his ideas to his supervisors. As a result I feel that com-
munication skills are of vital importance in the producing
"I feel a course in written communication is justified,
however I differ with the title "Technical Communication."
Since most reports (or letters) are written to management,
or with the intent of informing management, too much em-
phasis on the technical points can tend to confuse. I re-
ceived most of my writing "training" while getting my
MBA (whether popular or not). During this time I was
forced to word both written and oral communications in
terms nontechnical personnel could understand and relate
to. In my opinion, writing could more easily and effectively
be given by a department not so closely related to the de-
tailed technical aspects."

1. Weissenstein, C., Presenting Yourself in Writing,
Chem. Eng. News, Jan. 26, 1959, p. 3.
2. Marschner, R. F. and J. O. Howe, How to Train People
to Write Better Reports, The Oil and Gas Journal,
March 27, 1961, p. 94.
3. English Journal 61, March, 1972, p. 389.
4. Why Can't Johnny and Jane Write, English Journal 65,
Number 8, Nov. 1976, p. 36.
5. Where is Technology Leading Communications? IEEE
Trans. on Engineering Writing and Speech, Special
Issue, Vol. EWS-12, No. 12, Washington I.E.E.E.,
August, 1969.
6. Morris, M. D., Why Engineers Can't Write, Engineer,
Sept.-Oct. 1969, p. 15.
7. Minty, H. K., Why Can't Engineers Write? Research/
Development, Jan. (1968), p. 26.
8. Meyers, M., Diatribe of a Technical Editor, Chemical
Engineering, Oct. 7, 1968, p. 194.
9. Report of Departmental Chairmen, AIChE, B.Ch.E.
Curriculum 1957, 1961, 1968, 1972, 1976.

Continued from page 39
students in their courses. In contrast to the usual
classroom experience Churchill exposes students
to lousy data, teaches data handling techniques,
encourages critical evaluation and skepticism, and
makes error analysis a reality. It becomes clear
why rates of change are associated with deriva-
tives and process rates are not. Adoption of his
approach might even help to eliminate the wide-
spread notion that the rate of a chemical reaction
is equal to (-dC/dt) !
The book is liberally studded with quotations
such as, "No generalization is wholly true, not
even this one." My favorite came in Chapter 12
after an immoderate series of 24 batch system
integration (including 11 different ones in
kinetics) : " 'One more such victory and I am lost.'
Pyrrhus." The quotations were almost universally
unpopular with the students, probably because
they interfere with the most rapid search for the
key to a homework problem solution. However a
mature reader will find meaning (and frequently
amusement) in nearly every one.
At the end of the course five students said they
liked the book, three said they did not, and nine ex-
pressed no opinion. Two years later the same
seventeen students were surveyed. There were
eight respondents, all of whom thought the book
was important or potentially valuable. Seven of
them still had their copies, and three had used
them on their jobs. Virtually all users will be in-
convenienced by the absence of a nomenclature
section. The units might be described as "early
American traditional." Churchill could do all of
us a favor, (and better demonstrate the coherence
of the rate concept in diverse applications) if he
would produce an SI edition.
It is easy to recommend the book to currently
practicing individuals for self study. It is even
pleasant bedside reading. For the most part the
subject matter is familiar, but it appears in a new
and interesting context which should increase
understanding considerably. Unfortunately the
implementation of routine use of this book in con-
ventional undergraduate curricula is awkward at
best. It could serve well as a text for a senior
elective course. A colleague suggested using it
in a seminar to introduce new graduate students
to data handling and analysis in the determination
of rates from experimental measurements. Ulti-
mately, this review urges you to use your imagina-
tion to get its vital message through to chemical
engineering students. O


Create, construct and control
your career with MILLIKEN

We provide an expanding range of opportunities
to accelerate your managerial and professional
career development.
Milliken's commitment to technological leader-
ship in providing new products, processes and
equipment is exemplified by the Millitron' ma-
chine, a computer controlled, jet-injection dyeing
system created and developed by Milliken engi-
neers and scientists for the production of multi-
colored carpet, rugs and upholstery products.
The men and women we need have open
minds, open enough to let us expose you to the
details of the Milliken challenge. When we select
each other, horizons broaden for both of us.
Call or write:
College Relations Dept.
S Post Office Box 1926
MI KLL I KEN Spartanburg, SC 29304
Phone (803) 573-2508

An equal opportunity employer.

00 curriculum




Brigham Young University
Provo, Utah 84602

FOR A NUMBER OF YEARS students gradu-
ating with a bachelor's degree in chemistry
have found themselves facing rather poor employ-
ment prospects. Often students who desire a career
in applied chemistry enter chemistry programs in
four-year colleges and smaller state universities
where no ChE curriculum is offered in order to be
close to home or, perhaps, the tuition is lower.
Traditional chemistry curricula cannot satisfy
their needs. In order to achieve their real desires
many of these students should be in a ChE pro-
gram. Some ChE departments are developing
special programs to offer a form of graduate ChE
education to chemistry graduates [1, 2].
A few years ago the ChE Department at
Brigham Young University (BYU) became
aware of this dilemma faced by chemists as in-
creasing numbers of applications for admission to
graduate ChE programs were received from dis-
satisfied BS chemists. Under normal circumstances
such applicants could not be admitted directly to
our graduate ChE program because they lacked
appropriate undergraduate ChE background
training. This meant that for a BS chemist to ob-
tain a MS degree in ChE, two academic years were
required plus a summer for research and thesis
writing. The first academic year was devoted to
elementary undergraduate subjects. This is es-
sentially the approach taken by Texas Tech [2],
and is what Cussler [1] refers to as a remedial
program. The prospect of two full additional years
of school frequently served as a deterrent and few
students undertook such a program.


W E DECIDED TO DEVISE a program which
would shorten the time required for a BS
chemist to obtain a MS degree in ChE without

sacrificing quality or soundness of training. We
saw such a program both as an opportunity for
chemistry graduates to gain a masters degree in
ChE and as a service to many surrounding-area
four-year college chemistry departments by pro-
viding a way for their industrially-oriented stu-
dents to gain the further training they needed and
desired. We also recognized it as a potential source
of good first year graduate students to supplement
the regular class of new ChE graduate students.
In order to maintain quality and a fundamental
basis for such a program the chemist must be
taught fluid mechanics, heat and mass transfer,

BS ChE (BS Chemist

Core Ch E Unoergraduate ChE
Graduate Courses Prerequisites
18 Credits 22 Credits

Minor Courses
Core Ch E
9 Credits Graduate Courses
18 Credits

Minor Courses
6 Credits
9 Credits

33 Credits )Research/Thesis

6 Credits

Normal time= 24 months 55 Credits

FIGURE 1. Flow chart for traditional MS degree pro-
gram starting from BS degrees in Chem-
ical Engineering and Chemistry (Remedial


A- ""*I -- -_ _
Richard W. Hanks is a professor in and Chairman of the Chemical
Engineering Department at Brigham Young University where he has
been a faculty member since 1963. He is author of numerous papers
in transitional and turbulent fluid mechanics and solution phase
equilibrium thermodynamics. Professor Hanks received his B.E. degree
from Yale University in 1957, and his Ph.D. from the University of
Utah in 1960. He has served as graduate coordinator of the Chemical
Engineering Department at BYU for a number of years, was the initiator
of this program, and handles all the recruiting activities. (L)
John Oscarson graduated from BYU in 1968 then did graduate
work at the University of Michigan 1971-74 after serving in the mili-
tary. His interests are transport phenomena and separation. He has
taught the summer course the three years it has been offered. (R)

and separations technology, as well as kinetics,
plant design and process synthesis and control.
This training must be at the same level that is
normally given regular ChE undergraduates who
enter the graduate courses so that the chemists
can successfully compete with ChE's.
The traditional MS degree course outline for
a BS ChE and a BS chemist following the remedial
track are illustrated in flow chart form in Figure
1. Clearly the problem for the chemist lies in the
22 semester hours of remedial undergraduate ChE
prerequisites. These consist of: 1) a three-
semester, 9-credit-hour series in unit operations
(fluid mechanics, heat and mass transfer, and
separations technology) spanning the junior year
and part of the senior year of the undergraduate
curriculum; 2) a two-semester, 4-credit-hour unit
operations laboratory taught in the senior year;
and 3) a three-credit-hour course in kinetics and
reactor design and a six-credit-hour series of con-
current two credit-hour courses in plant design,
process synthesis, and process control taught in
the senior year.
In February 1976, the university granted the
ChE department permission to undertake a new
program which allows properly prepared BS chem-
ists to obtain a MS degree in ChE in the normal 12

months plus one summer, or 15 months. The way
this is accomplished is illustrated in flow chart
form in Figure 2.
The key to shortening the time frame for the
BS chemists lies in two modifications of the tradi-
tional program: (1) a special preparatory unit
operations class, and (2) the minor. We recog-
nized that chemists in their BS program take ad-
ditional advanced level courses in chemistry, and
sometimes physics and mathematics, beyond the
usual physical chemistry requirement at which
undergraduate ChE's normally stop. Most gradu-
ate students in ChE take their 9-credit-hour minor
requirement in a "supporting field" arrangement.
In this situation the minor courses may be drawn
either from a single department or from a number
of departments, and may range from upper di-
vision undergraduate to graduate courses in the
supporting departments depending upon the stu-
dent's preparation and degree of specialization.

(BS Chemist

Special Summer Core Ch E
Course in U.O.
and Graduate
Laboratory Courses
6 Credits 18 Credits

Undergraduate ChE
Courses in Kinetic
Plant Design, Pro-
cess Synthesis/
Control in Lieu
of Minor
9 Credits

6 Credits

M.S. Ch E
33 Credits + Normal Time = 15 months
6 Prereq.

FIGURE 2. Flow chart for special MS degree program
for well-prepared chemists.

We decided to devise a
program which would shorten the
time required for a BS chemist to obtain a MS
degree in chemical engineering without
sacrificing quality or soundness
of training.


In developing this program we had
to face the problem of what to teach a chemist to
bring him "up to speed" in a short period of time....

Thus, the advanced level chemistry and other tech-
nical courses usually taken by a senior chemist are
generally equivalent to the supporting field minor
frequently taken by a graduate ChE.
We decided to replace the usual 9-credit-hour
minor requirement with 9 credit-hours of senior-
level ChE courses formerly required as prereq-
uisites (see Figure 1). Specifically, the courses
chosen for this purpose were undergraduate ki-
netics, plant design, process synthesis, and process
control (the latter two being open to both under-
graduates and graduates).
This left only the unit operations and labora-
tory sequences to be dealt with. To cover this ma-
terial we introduced a special 8-week, 6 credit-hour
course taught from June through August which all
entering BS chemists must take as a prerequisite
to their graduate program. This special high-
intensity course, which is described in more detail
below, gives chemists the conventional unit opera-
tions course and laboratory all in one massive dose.
This course is considered a remedial undergradu-
ate preparation which must be passed before a
chemist actually enters the M.S. program.


ENTRY TO THE NEW MS program must be
through the special summer class. Chemists
must also be properly prepared by having had a
3 credit-hour course in ordinary differential equa-
tions and a beginning course in FORTRAN pro-
gramming as undergraduate students. If a chem-
istry student has not had these prerequisites, he
or she must take them as remedial provisional re-
MS Course Outline for BS ChE Student

672, 673, 676
675, 681
Minor Electives


*See Table 4 for explanation of course numbers

Ch E

33 Credits )
FIGURE 3. MS ChE degree program compatible with
either a BS ChE or BS Chemistry degree.
Normal time is 12 months for BS ChE stu-
dent, 15 months for BS Chemist (may take
19 months if not prepared in math and
computer programming).

quirements in addition to the usual graduate load.
This usually necessitates an additional semester of
With the introduction of the special summer
course and some slight modifications in the way in
which some of the core graduate courses are
taught and sequenced to better accommodate both
types of entering students, we have finally devised
the MS program outlined in Figure 3. This flow
chart shows that the program is compatible with
either a BS ChE or BS Chemistry degree as a
starting point. Table 1 shows the typical course
outline followed by the BS ChE student. Table 2
shows the corresponding course distribution taken
by the properly prepared BS chemist. Table 3
shows a typical course outline for a BS chemist
who requires remedial mathematics and computer
work. Table 4 gives a brief description of each of
the courses listed by number in the previous
Some concern has been expressed [1, 4] that
students graduating from programs which at-


tempt [1, 2] to retrain chemists may not really
ChE's. We believe that we have successfully co
with and overcome this objection in our progr
A chemist who successfully completes our
gram will graduate having had precisely the s;
graduate ChE course work and thesis experi
obtained by any undergraduate ChE who c
pletes the regular MS degree program. The ch
ist will also have had the complete senior 3
ChE curriculum as well as the junior year 1
operations and about half of the senior year
operations lab courses. He will have had e
physics, mathematics, and general education tr
ing and superior chemistry training. The p
where a difference occurs is that the chemist
not have had the usual undergraduate course
electrical circuits and engineering mechanics.
this extent they are slightly less broadly expo
to engineering than the usual ChE undergradu
We do not perceive this as being a critical
ficiency. We believe that chemists who gradi
from our program are adequately trained in

MS Course Outline for
Properly Prepared BS Chemistry Student

672, 673, 676
478, 681
464,550, 551



6 12 13

*See Table 4 for explanation of course numbers.

and can be viewed essentially as MS ChEs wil
strong minor in Chemistry.

of a program such as ours is the recruit
effort. In order to generate a reasonable size cl
we initiated recruiting activities at all four-3
colleges in the state of Utah and a few in sele
neighboring states. Personal visits are made
chemistry departments where junior and sei
undergraduate chemists are interviewed and
program is presented and explained. In ordei
present the program effectively, we prepare
slide presentation which describes career op]

r be
s in

MS Course Outline for
BS Chemist Requiring Remedial Math/Computer Work

673, 676,672
478, 681
464, 550, 551
Math 321
CS 131


3 3

1 1

6 13


3 3


3 3

13 6 8

*See Table 4 for explanation of course numbers.

ate. tunities in the chemical industry. The presentation
de- outlines the differing roles of the chemist and the
uate ChE, presents current job offer statistics and
ChE starting salary data for both, and outlines the
BYU special program. This lecture is presented to
both junior and senior chemistry majors, usually
in a physical chemistry class. The usual response
of chemistry department chairmen, especially in
smaller schools, has been to request that it also be
/SU presented to freshman chemistry classes as a
career-guidance service. This we have done. In
3 addition to these activities we mail notices to a
large number of chemistry departments and indi-
vidual students as listed in the ACS lists of stu-
dents recommended for graduate work.
All participants in the special summer class are
5 expected to provide their own financial support.
8 Our experience with all classes taught to date indi-
cates that this is not a deterrent factor. The ChE
department faculty decided that this special sum-
Sa mer course should also serve as a screening
mechanism to sift out marginal students. There-
fore, all students entering the summer program
are considered to be provisional students and are
not admitted to full degree seeking status until
g they successfully pass the special course with a
, grade of B or better. Once a student successfully
ass passes the special summer course, he is admitted

r to

In order to maintain quality
and a fundamental basis for such a
program the chemist must be taught fluid mechanics,
heat and mass transfer, and separations technology,
as well as kinetics, plant design, and process
synthesis and control.


Brief Course Descriptions
464 Undergraduate plant design
478 Undergraduate kinetics
550 Process Synthesis
551 Process Control
672 Advanced Fluid Mechanics
673 Heat/Mass Transport
675 Advanced Thermodynamics
676 Advanced Separations
677 Creativity
681 Advanced Kinetics/Catalysis
691R Graduate Seminar
693R Special UO Course for Chemists
699R MS Research/Thesis
CS 131 Elementary FORTRAN Programming
Math 321 Ordinary Differential Equations

to full degree seeking status and is treated exactly
as any other graduate student. He is fully eligible
for all forms of department financial aid.
An administrative concern for any program
such as this is its cost to the university. Some pro-
grams [1], because of the heavy use of scholarship
subsidies, auxilliary text material production, and
administrative and faculty costs are relatively ex-
pensive. Our experience to date has indicated a
much lower cost for our program. Because no
student financial aid is given, the principal costs
are for recruiting, which is nominal, and faculty
and administrative costs. This program costs the
ChE department something between $5000 to
$6000 per year.

IN DEVELOPING THIS program we had to
face the problem of what to teach a chemist to
bring him "up to speed" in a short period of time
so that he could successfully compete with ChE
undergraduates in the advanced level courses. One
possible approach, used by Carnegie-Mellon [1],
is to give the chemists a brief introduction to each
topic in the full undergraduate curriculum with-
out going into detail or depth in any topic. In ad-
dition to lack of substantive depth, this approach
creates the additional problem of what to use for

text material [1] necessitating the writing and re-
production of large amounts of hand-out ma-
terials, thus increasing costs. We chose not to take
this route. Rather, we elected to develop a sub-
stantive course in unit operations in which the
chemists could learn the fundamentals of fluid
mechanics, heat and mass transfer, and separation
technology at a level and depth commensurate
with undergraduate ChE's. The special summer
course which we have developed seems to ac-
complish this objective.
A second objective which this course must meet
is to help the chemist overcome what might best be
described as a "culture shock", which all seem to
experience in making the transition from chem-
istry to ChE. Chemists do not approach problems
in the same manner as do ChE's. The heavy em-
phasis on quantitative results, the need to make
assumptions, and the necessity for manipulation
of multiple systems of units are foreign concepts
for most chemists and mastery of these skills is
difficult for all and mildly traumatic for some.
Most students generally accomplish this transi-
tion reasonably well during the first weeks of the
In order for the course to succeed both the in-
structor and the students must reconcile them-
selves to the idea that it requires full-time effort.
Students are not allowed to register for any other
courses and are permitted to engage in part time
employment only in extreme circumstances.
The course is structured around the classical
unit operations approach and closely follows the
text Unit Operations of Chemical Engineering,
3rd Edition by McCabe and Smith [3]. This text
has proved quite satisfactory for this course. Hav-
ing a text available greatly helps the students and
also reduces the overall costs of the program by
eliminating the need for reproducing large
amounts of handout materials. Table 5 contains a
listing of the chapters and topics from the text
which are covered during the course and the ap-
proximate amount of time spent on each. Short
chapters are covered in one day while longer chap-
ters require two days. As can be seen, all the ma-
terial on fluid mechanics and heat transfer in

We further believe that graduates of our program can legitimately
classify themselves as ChE's because they have had exactly the same graduate
coursework and thesis experience that regular ChE's do plus most of the technical
undergraduate experiences. They are not just "warmed over" chemists.



LI a

sections 2 and 3 of Reference three, and most of
the material on mass transfer and separations
processes in section 4 is covered. Section 5 on
grinding, mixing and solids handling is omitted.
The class consists of from two to three hours
of lecture each day starting at 8:00 A.M. Three or
four homework problems are assigned each day
which require most of the student's time following
the lecture classes. The instructor frequently as-
sists students in his office during this time. At
4:00 P.M. the class meets together with the in-
structor and a graduate teaching assistant for a
problem solving session that may last from one to
two hours.
Starting about the third week of the course one
day a week is devoted to the laboratory. On lab
day no lecture is held and students spend six hours
in the lab. They see this as a welcome break from
the routine of lectures and problem sessions of the
other four days. In the laboratory the students are
divided into two-man teams. Each team performs
one experiment in each of the three subject study
areas: fluid mechanics, heat transfer, and separa-
tions. Since there are a large number of experi-
ments available in the BYU undergraduate unit
operations lab and a small number of student
teams, no two teams perform the same experi-
ments. Each team is required to report orally to

Topics Covered in Class

Material & Energy Balances
Fluid Statics
Introduction to Fluid Flow
Flow of Incompressible Fluids in Ducts
Flow of Compressible Fluids
Flow Past Immersed Bodies, Settling,
Packed Beds, etc.
Pumping & Metering of Fluids
Mixing and Stirring Fluids
Conductive Heat Transfer
Fundamentals of Heat Transfer in Fluids
Heat Tranfser to Fluids w/o Phase Change
Heat Transfer to Fluids with Phase Change
Radiative Heat Transfer
Heat Exchangers
Phase Equilibria, Diagrams, etc.
Equilibrium Stage Operations
Leaching & Extraction
Multicomponent Distillation
Gas Absorption

2-3 HR.

... chemistry majors can successfully
complete our program ... and are well qualified
to go on to doctoral degree programs in ChE at
reputable schools or go to work in industry.

the combined class on the experiment which they
performed and to prepare written reports which
are graded. This activity allows all students to
become acquainted with each experiment and pro-
vides a good experience for the students preparing
and giving the reports. This schedule is main-
tained for the remainder of the eight-weeks


rpHE PACE OF THE summer course is very
Demanding but student morale is generally
quite high and the students develop a sense of
achievement. Most students negotiate the chemis-
try to engineering culture shock quite well and are
able to compete successfully with their regular
ChE colleagues in subsequent graduate courses.
About 80% of those starting in the program suc-
cessfully complete it. To date we have had four
graduates of this program accepted into doctoral
ChE programs-two at BYU and two at other
schools. Offers of employment have been about as
frequent and as lucrative as those to regular ChE
graduates. Indeed, some recruiters, notably from
pharmaceutical companies, have specifically asked
to see Biochemistry majors in the program. Thus,
it seems that the students, who complete this pro-
gram are about as well qualified as regular MS
ChE graduates to compete in the graduate school
and job markets.
As with all programs, we have encountered
some problems. The most serious problem is keep-
ing the students from feeling overwhelmed during
the summer course. Because of the large volume of
material presented very rapidly, the students feel
like they are always running behind trying to
catch up. This problem is best handled by en-
couragement from the instructor and generous
amounts of personal help. The class is limited in
enrollment to 10-12 students so that the instructor
can give the necessary amounts of personal help.
Another problem arises when students enter
the program without prior background in ordinary
differential equations or FORTRAN computer
programming. This does not particularly cause
problems during the special summer course. The


difficulties arise in the graduate fluid mechanics
and thermodynamics courses which follow. As a
result, poorly prepared students must follow a
more protracted schedule shown in Table 3. About
half of our students have encountered this prob-
lem. We are attempting to counteract this dif-
ficulty through our recruiting program by counsel-
ling junior chemistry majors who anticipate seek-
ing admission to our program to take courses in
ordinary differential equations and FORTRAN
computer programming before they graduate.
Our experience to date indicates that chemistry
majors can successfully complete this program for
an MS ChE degree and are well qualified to go on
to doctoral degree programs in ChE at reputable
schools or go to work in industry. We believe that
the combination of the intensive special unit op-
erations course coupled with the full undergradu-
ate senior year of ChE courses as a "supporting
fields" graduate minor makes our program some-
what unique among the several programs now in
existence. We further believe that graduates of
our program can legitimately classify themselves
as ChE's because they have had exactly the same
graduate coursework and thesis experience that
regular ChE's do plus most of the technical under-
graduate experiences. They are not just "warmed-
over" chemists. In our view this program repre-
sents a marriage of the best parts of both
worlds. D]

1. Cussler, E. L., Chem. Eng. Education, 11 (4), 176 (Fall
2. Bethea, R. M., Heichelheim, H. R., and Gully, A. J.,
Chem. Eng. Education, 11 (4), 181 (Fall 1977).
3. McCabe, W. L., and Smith, J. C., Unit Operations of
Chemical Engineering, 3rd. Ed., McGraw-Hill, New
York, 1976.
4. Cussler, E. L., private communication to authors, 1977.


April 25-27, 1979 Mexico City
For complete program and registration information write
to: John P. Klus, University of Wisconsin-Extention, De-
partment of Engineering & Applied Science, 432 North
Lake Street, Madison, WI 53706

M OREnews

Lloyd Berg reports that at least two chemical
engineering department heads completed 26-mile
marathons during 1978. Lloyd Berg of Montana
State ran the Governor's Cup race in Helena and
Tom Owens of North Dakota University completed
the Grand Forks run. Any other department
heads? Any other chemical engineering faculty?

The Department of Chemical Engineering at
Iowa State University is pleased to announce that
Dr. Maurice A. Larson has been selected as the
new Department Chairman. Dr. Larson is cur-
rently Anson Marston Distinguished Professor in
Engineering and has been a member of the Chem-
ical Engineering faculty at Iowa State since 1958.

ii books received


Continued from page 19
Solar Cooling and Heating: Architectural, Engineering
and Legal Aspects, edited by T. Nejat Veziroglu. Hem-
isphere Publishing Corp., Washington, D.C. 20005. Three
Volumes, $120
The Chemical Bond, by J. N. Murrell, S. F. A. Kettle, and
J. M. Tedder. Wiley, New York. 1978. 310 pages, $27.
Recent Developments in Boiling and Condensation, by
E. R. F. Winter, H. Merte, Jr., and H. M. Herz. Verlag
Chemie International, New York. 1977. 106 pages paper-
back $16.
Thermal Efluent Disposal from Power Generation, edited
by Zoran P. Zoric. Hemisphere Publishing Corp., Washing-
ton, D.C. 20005. 1978. 375 pages, $40.
Two-Phase Transport and Reactor Safety, edited by T. N.
Veiroglu and S. Kakac. Hemisphere Publishing Corp.,
Washington, D.C. Four volumes, 1416 pages.
Fuel Economy of the Gasoline Engine, edited by D. R.
Blackmore and A. Thomas. Halsted div. John Wiley, New
York. 1977. 268 pages.
Two-Phase Flows and Heat Transfer, edited by S. Kakac
and F. Mayinger. Hemisphere Publishing Corp., Washing-
ton, D.C. Three volumes, 1469 pages.
Engineering Fundamentals: Examination Review, 2nd ed.,
by D. G. Newnan and B. E. Larock, Wiley-Interscience,
New York. 1978. 503 pages, $21.95
Combustion and Incineration Processes: Applications in
Environmental Engineering, by W. R. Niessen. Marcel
Dekker, New York. 1978. 384 pages, $35
Integrodifferential Equations and Delay Models in Popula-
tion Dynamics, by J. M. Cushing. Springer-Verlog, New
York. 1977. 196 pages $8.30
Technical Data on Fuels, ed by J. W. Rose and J. R. Cooper,
1977. Halstead Divison of J. Wiley, New York. 343 pages


1ILI1111 P"s"�~-L""I"""�~�4~-"�*r"~~




at FMC

Loran Schillinger
B.S.Ch.E. from Montana State University in 1975...
joined FMC's Industrial Chemical Group plant at
Pocatello as a process engineer in the technical
department ... involved in pilot project working with
a fluid bed dryer to see whether a byproduct from
the plant's production process could be used to fuel
this vessel... worked with production, maintenance
and engineering groups to gain better production
efficiency throughout plant ... promoted to unit
foreman, supervised hourly workers in the
preparation department ... now planning analyst in
the Phosphorus Chemical Division at Industrial
Chemical Group headquarters ... responsibilities
include working on economic analyses of plant
expansion to ensure that they are consistent with
the Division's long-range plan; also conducts
feasibility studies on the effect of proposed
marketing changes on plant production equipment
... says, "What really impresses me about FMC is
the fact that a person is judged both on technical
competence and on ability to work with others."

As one of the nation's largest producers of chemicals,
FMC calls upon chemical engineers to make an
important contribution to the company's profits and
growth. Because of our diversity, we offer an unusually
broad range of career opportunities for top-flight

You can choose to apply your skills to a number of
rewarding projects-from applied research to on-line
production management.

We've highlighted the careers of two of our people to
give you an idea of how they've grown professionally,
what they're doing now, and how they feel about
working with FMC. If you're looking for an organization
that will give you immediate technical challenge and
long-term career growth and flexibility, we invite you to
consider FMC.

If the challenges and opportunities we've described
match your interests, a career with FMC-an equal
opportunity employer-might prove to be a rewarding
experience, both for you and for us.

For more information, see our representative on
campus or your Placement Director. Or, write to:
Manager, Training & Development, FMC Corporation,
Industrial Chemical Group, 2000 Market Street,
Philadelphia PA 19103.


Mary Ann Pizzolato
B.S.Ch.E. from Rutgers University in 1976 ... joined
Industrial Chemical Group's Carteret plant as a
process engineer ... worked as engineer for the
acid plant-did troubleshooting, process review and
some pilot and new project work ... promoted to
assistant area supervisor in production department
.. works directly with area supervisor to ensure
high quality and maximum production levels ... likes
having the opportunity to gain experience working
with management and hourly workers ... believes
that "with the pressure to get production out as
scheduled, you have to learn to work well with these
groups-it's the best kind of on-the-job-training."

PROCTER & GAMBLE is looking for

in R&D/Product

This organization is responsible for the
creation and improvement of new and
existing products, together with developing
the associated technology advances and
solving technical problems.
While this organization encompasses the full
range of scientific and engineering
backgrounds, the primary need at the BS/MS
level is for Chemical Engineers and
MBAs with a chemical or engineering
undergraduate degree.
Your initial responsibilities in the organization
would be primarily technical, with varying
degrees of interactions with P&G's
Engineering, Manufacturing and Marketing
divisions. As you advance, your career could
evolve along technical and/or management
routes. This evolution will include progressive
assignments, exposure to other divisions, and
in many cases a transfer to another
R&D/Product Development division, or
where appropriate to an Engineering,
Manufacturing or Marketing division.
The R&D/Product Development organization
is headquartered in Cincinnati, consists of
over 20 divisions, focuses on U.S. consumer
and industrial products, conducts P&G's basic
research, and provides technical support for
our international operations and technical
centers. (This technical support includes
international travel by certain of our
U.S.-based division personnel.)

If you are Interested In this area, please send
a resume to:
The Procter & Gamble Company
R&D BS/MS Recruiting Coordination Office
Ivorydale Technical Center
Spring Grove and June Avenues
Cincinnati, Ohio 45217