hf. J. Heal Mass Trans/iir. Vol. 7, pp. 1353-1358.

Pergamon Press 1964.

Printed in Great Britain

ALLAN PHILIP COLBURN-THE
ROBERT
Departmentof Chemical Engineering,

L. PIGFORD

University of Delaware, Newark, Delaware, U.S.A.

(Recdived

14 August

COLBURN’S
early professional career has
been outlined by his good friend and co-worker,
Thomas Chilton, in a companion paper in thispublication. The two men collaborated directly ina number of important pieces of work which
contributed magnificently to the new field ofchemical engineering, in its adolescent stages in
the United States at the time. Theirs was a unique
opportunity to apply scientific tools to the many
new and intriguing problems of chemical manufacture afforded by the growth of an importantchemical company. Through them, and a few
others with similar insight, chemical engineering
became known to practicing engineers and to
students alike as a professional field unique.among the engineering branches in its opportunities to use the basic sciences, including
chemistry, and mathematics for a wide spectrumof problems characteristic of the chemical andpetroleum industries.
Thus, it was with a well-known reputation for
original work having practical significance that
Allan Colburn came to the University of
Delaware in 1938 to head a fledgling department
in what was then a small and unimpressive
college. Some have said that he made the change
so that he would be free to follow a less physicallydemanding schedule. Those who knew his workin these early days remember his almost boundless energy and his devotion to his new responsibilities, not only in his own department but inmany other affairs at his institution. Allan
Colburn’s father had been a school teacher; itappeared to Allan’s friends that he, too, had
found his place in the world. Even his plan totake a nap after lunch each day for the sake of his
recovery from illness was soon discarded infavor of the many new interests which he foundon the campus.
Naturally, there was much work that wasincomplete at the time of the transition fromindustry to teaching. The important papers
ALLAN

YEARS IN EDUCATION

1964)[IO, 121on the transfer-unit concept and its use intreating experimental data as well as engineering
design were yet to appear, but the thoughts
behind them quite clearly came from the industrial years. A new interest in thermodynamic properties of solutions, frequently pointed
out by Colburn as the key problem for the whole
field of distillation, had led to a series of studies
of vapor- liquid compositions in collaboration
with H. C. Carlson of the Du Pont Company.
Today their paper [6] is one of the most widely
quoted works in the field, for it set the stage for along series of papers by chemical engineers
throughout the world, a series which is far fromcompletion.
Professor Colburn’s interest in heat-transfer
problems appeared again soon in his university
work. Shortly after taking up his new duties hebecame involved as a consultant in several important investigations supporting the war effort.
One of these involved the need to provide better
air cooling of finned cylinders for aircraft engines.
The problem was to obtain nearly uniform
cooling around the circumference of the cylinder,
the air flow being confined to narrow passages
between the fins. The similarity to and differencesfrom heat transfer in exchangers with parallel
passages were pointed out in a publication with
Lemmon and Nottage [37] in 1945,
A related paper, published by the National
Advisory Committee for Aeronautics [23] wasconcerned with the influence of vapor bubble
formation on a hot surface, above the boilingpoint of a liquid which flows over the surface tocool it. The vapor bubbles cannot grow except
in the very thin layer of superheated liquid at thesurface itself, yet their appearance in this layer,
which accounts for the major resistance to heat
conduction, can greatly increase the cooling rate
-a problem of obvious importance for thedesign of liquid-cooled engine cylinders.
At about the same time the first of a series of

1353

1354

ROBERT

L. PIGFORD

papers on heat transfer in condensers began toappear. These undoubtedly have their origin in
Professor Colburn’s own doctoral thesis, doneat the University of Wisconsin under Professor
Olaf Hougen, but the work at the University of
Delaware was directed more toward the explanation of the heat-transfer coefficients than toward
discussing methods of computation in condenser
design. A paper with Millar and Westwater [2.5]had considered the transfer of heat to condensate
layers in the sub-cooling portion of a condenser.
A paper written with Carpenter, Schoenborn,and Wurster in 1946 [8] was concerned with theheat transfer and fluid friction effects in the thinannulus surrounding an experimental condenser
tube. Covering both laminar and turbulent flow
conditions, these authors showed how to apply
the heat transfer-friction analogy and how tomodify it for the viscous region. For these
conditions it had not been clear whether thehydraulic equivalent diameter, De, used tocorrelate the friction factors would also work forthe heat-transfer
problem, recognizing thatfriction effects occurred on both walls of theannulus and heat transfer was through one wall
only. The authors concluded that De,definedfor friction, ought to be used in the Nusselt
number for heat transfer, which was found to bea function of the Graetz number involving only
the mass-rate of flow rather than the linear
velocity. Heat-transfer studies on the same
apparatus were subsequently published with
Carpenter [7] in a paper which explored, perhaps
for the first time in a realistic way, the considerable infiuence of vapor velocity on rates ofcondensation inside vertical tubes. An earlier
paper by Colburn [9] had shown how the onset of
turbulent motion in the gravity flow of thecondensate layer could improve heat transfer
through it. The new work showed, however, thata turbulent vapor stream, adjacent to the falling
liquid film, could produce turbulence in the film
Reynolds numbers as small as 240. Under these
conditions the condensation
coefficient was
sometimes ten times the previously expectedvalues. The new results could be explained byassuming that the thermal resistance of the liquid
layer was really that of a laminar sub-layer having
the same thickness that such a layer would havein a tube filled with liquid, provided thewall shear stress was the same in both cases.
Thus, the key to the problem lay in the wellknown universal velocity distribution function.
These results and a review of other recent work[21] on condensation were presented by Professor Colburn as the James Clayton Lecture
at an international meeting on heat transfer in
London in 195 1.
Beginning in 1949, the first of a series of
papers on heat-transfer coefficients on the shellside of tubular heat exchangers appeared. It wascharacteristic of Colburn’s interests in heattransfer that the important practical problems
were given first place and this investigation.
which extended over nearly fifteen years until
Colburn’s death, was a good example of thirinterest. The work was supervised jointIy h>Colburn and his faculty colleague, Olaf Bergelin, but the progress on the project wasreviewed periodically by a Special Advisory
Committee of the Heat Transfer Division of theAmerican Society of Mechanical Engineers,
composed of engineers with a working knowledgeof the real problems involved and a keen interestin the usefulness of the results. In the first paper[39] data were presented from tests of an idealizedheat exchanger tube bundle involving flow of anoil directly across and perpendicular to the tubes.
Reynolds numbers from about 3 to 500 wereachieved, both friction and heat-transfer factors
being measured. Variations in tube diameter andspacing were explored in a number of subsequentstudies, culminating in Engineering Experiment
Station Bulletins published by the University of
Delaware in 1950 [4]. Highest coefficients wereobtained, for a given power loss, with smahV
closely packed tubes in staggered arrangements.
The Colburn ,j-factor method of correlation
proved to be best when the influence of thetemperature gradient through the fluid was
expressed with a function of the fluid viscosity.
More recently, the same series of publications
continued with the appearance in 1954 of apaper with Bergelin and Brown [2] on the heattransfer and frictional effects in a baffled shelland-tube exchanger specially designed to eliminate leakage of the shell fluid through the annuli
between baffle plates and the inside wall of theshell and between the tubes and the corresponding holes through the baffles. Although

ALLANPHILIPCOLBURN-THE

such an exchanger is too highly idealized forpractical use, its use in the program was anecessary step in the development of methods
for treating the shell-side phenomena quantitatively. The new measurements included values ofheat transfer and friction factors for the tubes
occupying the baffle window regions, where theshell fluid reverses its direction. The results are
summarized in a second Engineering Experiment
Station Bulletin 151.Finally, in another Bulletin[I], published after Professor Colburn’s death,but reflecting a considerable influence from his
earlier participation, data were published fromwork on still another shell-and-tube exchanger
in which various leakage paths could be opened
one at a time. The final result of the work was a
proposed method of separating the heat transfer
and fluid friction phenomena into component
parts, bearing in mind the subdivision of thetotal shell-side stream and the recombination of
the different streams at points along the heattransfer surface.
Professor Colburn’s work on the classification of vapor-liquid
equilibrium thermodynamic phenomena, begun earlier at Du Pont
and resulting in the now famous paper of Carlson
and Colburn [6], also continued at the University.
First, on the experimental side, two papers
written with his faculty colleague, E. M. Schoenbow, and their students [28, 291 describedlaboratory equilibrium stills useful for miscible
and immiscible liquid mixtures. The first still was
designed to avoid the problems associated withimperfect mixing of the liquid condensate which
was returned continuously to the boiler in apreviously popular apparatus, by continuously
recirculating a vapor stream through the equilibrium chamber until it reached a constantcomposition, The same idea has been adopted
by several other investigators more recently.
On the theoretical side Professor Colburn
became interested in the properties of ternaryand multicomponent, thermodynamically nonideal mixtures as a result of his work for the
U.S. Office of Rubber Reserve during the war.
The nation needed a domestic source of synthetic rubber to replace the natural product fromabroad and asked the chemical industry todevelop processes for producing butadienestyrene polymer. A key step in the process

YEARS

IN EDUCATION

1355

involved the separation of unsaturated butene
from saturated butane. This separation, difficult
because of the very small difference in boilingpoints of the compounds, was made possible byadding a third substance of low volatility to theliquid, causing it to form non-ideal mixtures inwhich the relative volatility of the two hydrocarbons would be considerably enhanced. The
first paper resulting from this work [38] reported
data on mixtures of the hydrocarbons, one at atime, with furfural. This was soon followed bydata on the ternary system n-butane-cis-2-butenefurfural [33, 481 resulting from work done
jointly with Colburn’s faculty colleague, J. A.
Gerster, and their students. Finally, the work
was extended to four components, including
water, in a paper written with Jordan, Gerster,and Wohl [36]. For a number of years thesedata were among the few sets in the chemicalengineering literature in which multicomponent
non-ideal interactions among the components inthe liquid had been reliably observed under theconditions important for extractive distillation.
Professor Colburn’s interest in the field was
genuine. Through this interest he influenced
many students and faculty friends whose work
continues to appear in our literature.
Professor Colburn’s friends at the University
recall that he sometimes mentioned that among
his different research interests his work in thefield of distillation seemed to him to be his best
accomplishment. This is born out by his contributions to thermodynamics of solutions and by
several publications, both experimental andtheoretical in character, which relate to theperformance and the design of distillation process equipment. In a sense these are a continuation of the studies of mass transfer begun at
Du Pont, yet they are also directed more specifically at the special characteristics of distillationequipment rather than to mass transfer ingeneral.
The first paper 1131in this series is entitled“The Calculation of Minimum Reflux Ratio in
the Distillation of Multicomponent Mixtures”.
It made available for the first time a shortmethod suitable for distillation column designfor fixing the minimum quantity of liquid reflux
to be fed to the top of a continuous fractionating
cohunn which handles solutions of three orI356

ROBERT

more compounds.
Mathematically,
the problem
had been known for some time, yet it was amark of Colburn’s
genius that he, possibly
before anyone else, recognized its essential parts
and indicated a logical way to solve it approximately. To some degree his procedure has now
been superseded by other methods suitable only
for high-speed computersand by the elegant
analytical method of Underwood [47]. Colburn’s
method was designed for use by the design
engineer who wants a quick answer and who
likes a method into which he can put his own
engineering judgement
as he proceeds. There isevidence that. even today in spite of otherdevelopments,
Colburn’s
method is still used.
It is remarkably
simple and appealingly
relatedto the real conditions occurring inside columns.
Anotheranalytical
study of fractionatingcolumns showed how mass balances could beapplied to the unsteadystate changes in thecompositionsof liquid held inside the column
during batch-wise removal of the more volatilecomponent.
Others more recently have also
shown how the inertia of the column may, undercertain conditions, make the efficiency of separation of the components
of a binary mixture
greater than if the hold-up
of liquid in thecolumnwere zero. However,ColburnandStearns were apparently the first to point it out[301.
A series of experimental
investigations
involved studies of azeotropic distillation[26, 291,
in which the essential
problemdependsontaking advantage
of certain non-ideal
solutionbehavior among the components.
The work on
extractive
distillationof saturated
and unsaturated hydrocarbons
with furfural culminatedin a paper [34] reporting some of the first data
available on the efficiencies of bubble-cap plates.
Owing to the increase in liquid viscosity brought
about by the addition of a high percentageoffurfural, it had been expected that the efficiencies
in this important
process might be very low. It
was encouraging
to find that they were on theorder of 50 to 60 per cent and, while smaller
than comparable
values encounteredin distillation of binary mixtures, were not SO low as tomake the whole operation unattractive.
The paper on extractive distillation had beenpreceded by another 1321 in which the relation-L.

PIGFORD

ship between plate efficiency and the diffusionat
resistances of the vapor and liquid phases had
been brought out. It seems not unlikely that
Professor Colburn’s
influence on more recent
investigations
into distillation
behavior
wasconsiderable,
including the cooperative
project
carriedout in three universities
under
the
sponsorshipof the American
lnstituteoi
Chemical Engineers, which acted on behalf of alarge group of American chemical and petroleum
companies.
Indeed,the correlationsof dataresulting from the cooperative
project bear aclose relationshipto the ideas originallyputforward by Professor Colburn.
His interest in the general disseminationof
informationabout
mass-transfer
processes isshown by Colburn’s contributions
to engineering
handbooks[14, 27, 401 and several papers of ageneral nature designed to make the generalengineering
public aware of advancesin theheld [I 5, 20, 241. Other miscellaneous
papersreportingexperimental
results of work withstudents and colleagues should also be mentioned[31, 42, 44, 451, as well as a paper concernedwith economic factors in engineering design [42].
We come finally to the part of Professor
Colburn’s work at the University of Delawarein which he may have had the deepest interestof all and which his close friends and associates
remember most vividly. This was his concern
for education itself.
During the war years he had prepared thecurriculum on chemical engineering for the U.S.
Army, in cooperation
with Professor
B. F.
Dodge of Yale [Jniversity.
Some of his ideas
were set forth in a short paper contributed
as apiece for a series on “Careers in Chemistry andChemical Engineering”
published by the American Chemical
Society [17]. In addition,
hecontributed
papers to professional
educationalsocieties on the teaching of the unit operation ofgas absorption[ll], on his organizationof hisgraduatecourseon distillation[16], about
graduate programs
suitable for engineers whoare employed in industry [19], and about thechallenges of engineering as a field 118, 221. The
first of these containedmuch new informationon the economically
optimumdesign of gas
absorbers which has subsequently
appeared in
textbooks [46] and handbooks [41].

ALLANPHILIPCOLBURN-THE

The recitation of these references does not dojustice to the iniluence of a great teacher.
Professor Colbnrn has left us a great traditionin engineering and applied science. He, morethan most teachers of his day, was abie to show
students through his own enthusiasm forengineering, through his quick, incisive thought,
through his modesty, and through his uncanny
ability to put aside the irrelevant to get to theimportant core of problems, that chemicalengineering is an exciting field of work and study.
Many engineers who occupy positions of responsibility today speak of the great influencewhich Dr. Colburn had on them, not only
through his classroom teaching, but also throughhis remarkable influence upon anyone who had
an opportunity to work alongside him on anengineering problem.
But this influence of the man was not only
because of his rare technical ability. It was also
because of his concern for people in all fields.
He was active in developing the University’s
Institute of Inter-American Study and Researchand its Institute for Human Relations, and hecontributed much to the postwar growth of the
University in many other ways. He was Directorof the Delaware Chapter of the Red Cross and amember of the Research Committee of theDelaware Branch, American Cancer Society.
His friends trusted and admired him for his
understanding heart, his quick sympathy, his
gentleness, his humility and his complete
unselfishness.
In February, 1955, Allan Colburn died.
Many honors came to him during his life andposthumously but his greatest honor is one thatcannot be recorded on parchment. It is theremarkable result of an unselfish life devoted tothe service of others.
REFERENCES

1. K. J. BELL, Cooperative research program on shelland-tube heat exchangers, Engineering Experiment
Station Bulletion No. 5. University of Delaware,
Newark, Delaware (1963).
2. 0. P. BERGELIN,G. A. BROWN and A. P. COLBURN,
Heat transfer and fluid, friction during flow acrossbanks of tubes-V.
A study of a cylindrical baffledexchanger without internal leakage. Trans. Amer. Sot.
Mech. Engrs 76, 841-850 (1954).
3. 0. P. BERGELINand A, P. COLBURN, Miscellaneous
overall coefficients of heat transfer, in Chemical

YEARS

IN

EDUCATION

1357

Engineers’ Handbook (J. H. Perry, Ed.), pp. 480-482,
3rd Edit. McGraw-Hill, New York (1950).
4. 0. P. BERGELXN,A. P. COLBURNand H. L. HULL,Heat transfer and pressure drop during viscous flow
across unbtied tube banks, Engineering Experiment
Station Bulletin No. 2. Univ. of Delaware, Newark,
Delaware (1950).
5. 0. P. BERGELIN,M, D. LEIGHTON,W. L. LAFFERTY
JR. and R. L. PIGFORD,Heat transfer and pressure
drop during viscous and turbulent Aow acrossbaffled and unbalTled tube banks. Engineering Experiment Station Bulletin No. 4. Univ. of Delaware,
Newark, Delaware (1958).
6. H. C. CARLSON and A. P. COLBURN,Va~r-squid
equilibria of nonideai solutions utilization of theoretical methods to extend data, Industr. Engng Chem.
34, 581-589 (1942).
7. F. G. CARPENTERand A. P. COLBURN,The effect ofvapor velocity on condensation inside tubes, General
Discussion on Heat Transmission, pp. 20-26. Inst.
Mech. Engrs (London) and Amer. Sot. Mech. Engrs(1951).
8. F. G. CARPENTER,A. P. COLBWRN,E. M. SCHOENBORNand A. WURSTISR,Heat transfer and friction ofwater in an annular space, Trans. Amer. inst. Chem.
Engrs 42,165-187 (1946).
9. A. P. COLBURN,Calculation of condensation with aportion of condensate layer in turbulent motion,
Industr. Enanp Chem. 26.432-434 (1934).
10. A. P. C&L%RN, The’ simplified calculationofdiffusional process. General consideration of twofilm resistances. Truns. Amer. Inst. Chem. Engrs 35,
21 l-236, 587-591 (1939).
11. A. P. COLBURN, Absorption of gases by liquids.
CollectedPapers on the Teachingof ChemicalEngineering. Amer. Inst. Chem. Engrs, New York (1940).
12. A. P. COLBURN.SimoIi~ed ~lculat~on of di~usion~
processes, Zndustr. Engng Chem. 33,459-466 (1941).
13. A. P. COLBURN,The calculation of minimum reflux
ratio in the distillation of multicomponent mixtures,Trans. Amer. Inst. Chem, Engrs 37,805-825 (1941).
14. A. P. COLBURN,Other methods of comminution andproduction
and applicationof metal powders,
Chemical Engineers’ Handbook (J. H. Perry, Ed.),
2nd ed., pp. 1982-1983; 2003-2007. McGraw-Hill,
New York (1941).
15. A. P. COLBURN,Heat transfer by natural and forced
convection. E~ineering Bulletin, Research Series
No. 84, Purdue University, Lafayette, Indiana (1942).
16. A. P. COLBURN,A graduate course in distillation,
Trans. Chem. Eng. Div. Amer. Sot. Engng Ed.,
Bucknell University, Lewisburg, Pa. (1947).
17. A. P. COLBURN,Training the undergraduate chemicalengineer, Chem. Engnn News, 28, 2513-2515 (1950).
18. A.-P. COLBURN,New frontiers for the engineering
auuroach, C/rem. Engna Pron., 44, 18-20 (1948).
19. A.-P. COLBURN,The graduate pr&ram at Delaware
as related to industrial employees in cooperativeeducation at the graduate level. Paper presented atmeeting of Div. the Graduate Studies. Amer. Sot.
Eng. Education (1950).

l??X
20. A. P. COLBURN,Azeotropic

ROBERTL.

PIGFORDand extractive distillation,
J. A. GERS~ERand A. P. COLBURN,Plate efficiencies
Canad. Chem. Process Industr. (1950).
in separate of Cs hydrocarbons by extractive distilla21. A. P. COLBURN, Problems in design and research ontion with furfural, Chem. Engng Prog. 45, 725-737
condensers for vapor mixtures (The James Clayton(1949).
Lecture). Proc. Inst. Mech. Engrs, Lond. M&448-458
35. C. A. JONES,E. M. SCHOENBORIX
and A. P. COI.B~K&,(1951).
Equilibrium still for miscible liquids. Data on ethy22. A. P. COLBURN, A challenge to engineering education.
lene dichloride-toluene
and ethanol-water
Irltfusrr,.
Proceedings, annual conventionof Assoc. Land
Engng Chem. 35, 666.-672 (1943).
Grant Colleges and Universities, pp. 183-185 (1952).
36. D. JORDAN,J. A. GERSTER,A. P. Co~stia% and K.
23. A. 1’. COLBURN,C. GAZLEYJR, E. M. SCHOENBORNWOHL, Vapor-liquid equilibrium of Cq hydrocarbon-and C. S. SUTTON, Effect of local boiling and air
furfural-water
mixtures, Chem. Z%gng Prog. 46:
entrainment
on temperaturesof liquid-cooled
601-613 (1950).
cylinders. Nat. Adv. Comm. Aeron. Tech. Note No.
37. A. LEMMONJR., A. P. COLBUKNand H. B. Nor-r~,t.
1498 (1948).
Heat transfer from a baffled-finned cylinder to air.
24. A. P. COLBURN,J. A. GERSTEKand C. PYLE, Some
Trulrs. Amer. Sot. Mech. Enws 67. 601-612 (19451.
recent developments
in fractional
distillation.
38. T. S. MERTESand A. P. COL&JKN,Binary mixtures ofProc. Fourth World Power Congress. Sect. 3B. Carlon-butane, isobutane, and 1-butene with furfural.
Colombo, Rome (1955).
Vapor--liquid equilibria and thermodynamic proper25. A. P. COLBURN,L. L. MILLARand _I.W. WESTWATER,
tics, Zndustr. Engng Chem. 39, 781-196 (1947).
Condenser-subcooler
performance and design. Trans.
39. G. A. OMOHUNDRO,0. P. BERC~ELIN
and A. P. C‘OLAnrer. Inst. Chem. Engrs 38, 447-468 (1942).
RIJRN,Heat transfer and fluid friction during viscous
26. A. P. COLBURN and J. C. PHILLIPS, Experimental
flow across banks of tubes. Trans. Artw. Sot. Mcch.
study of azeotropic distillation-useof trichloroEngrs 71, 27-34 (1949).
ethylene in dehydration of ethanol, Trans. Amer. ht.
40. R. L. PIGFORD and A. P. COLBURPU,
Piate etiiclcncic:,Chem. Engrs 40, 33-58, (1944).
for distillation columns and packed distillation
27. A. P. C~LBLJRNand R. L. PIGFORD. Sections oncolumns,in
ChemicalEngineers’
Handbook
general theory of diffusional operatidns (pp. 524(J. H. Perry, Ed.), 4th ed., pp. 610.-621. McGraw
559) and gas absorption (pp. 668-711). Chemical
Hill, New York (1950).
Engineers’ Handbook (J. H. Perry, Ed.). McGraw-HilI,
41. R. L. PIGFORU and R. E. EMMEKT,Section of gas
New York (1950).
absorption. in Chemical Engineers’ Handbook (J. H.
and D. SCHILLING,
Perry, Ed.), 4th ed. McGraw-Hill,
New York
28. A. P. COLBURN,E. M. SCHOENBORN
Equilibrium still for partially miscible liquids. Zndastr.
(1963).
42. CYRUS PYLE, A. P. COLBURN and H. K. Du~~:t.u,Engng Chem. 35, 1251-1254 (1943).
The selection
Factors controlling efficiency and capacity of sieve29. A. P. COLBURNand E. M. SCHOENBORN,
of separating agents for azeotropic and extractive
plate extraction powers, Zndustr. Engng Chem. 42,
distillation and for liquid-liquid extraction. Trans.
1042-1047 (1950).
Amer. Inst. Chem. Engrs 41, 421-43 (1945).
43. B. R. SARCHETand A. P. COLBURN,Economic pipe
size in the transportation of viscous and non-viscous
30. A. P. COLBURNand R. F. STEARNS.The effect ofcolumn hold-up on batch distillation. Trafzs. Amer.
fluids, Zndustr. Engng Chem. 32, 1249-1252 (1940).
44. E. M. SCHOENBORN
and A. P. COLBUKN, Rotameter
Znst. Chem. Engrs 37, 291-308. (1941); Discussion
calibration, Chem. Met. Engng 46, 414-415 (1939).
ibid., 37, 727-732 (1941).
45. E. M. SCHOENBORNand A. P. COL~URX, The flow
31. A. P. COLBURN and D. G. WELSH, Experimental
mechanism and performance of the rotameter, Trans.
study of individual transfer resistance in counterAmer. Inst. Chem. Engrs 35, 359-389 (1939).
current liquid-liquid extraction. Trans. Amer. Inst.
46. T. K. SHERWOOD and R. 1,. PIC;FORD,Absorption and
Chem. Engrs 38, 179-201 (1942).
Extraction, pp. 4.51-544. McGraw-Hill, New \‘ork
32. J. A. GERSTER,A. P. COLBURN,W. E. BONNETand(1951).
T. W. CARMODY,Plate efficiencies related to separate
47. A. J. V. UNDERWOOD, Fractional distillation olvapor and liquid resistances, Chem. Engng Prog. 45,
multi-component mixtures-calculationsof minimum
716-724 (1949).
reflux ratio, Inst. Petrol. 32, 614 (1946).
33. J. A. GERSTER,T. S. MERTESand A. P. COLBURN,
48. F. WELTY, J. A. GERSTER and A. P. Co~_au~h.
Ternary systems n-butane-l butene-furfural and isoVaoor-liauid relation in the system n-butane-cis-2butane-1-butene-furfuralvapor-liquid
equilibrium
buiene-firfural-water.
Indust;. Engng Chem. 43,
data. Zndustr. Engng Chem. 39, 797-804 (1947).
162-172 (1951).
34. E. W. GROHSE, R. F. MCCARTNEY,H. J. HAUER,