K. B . B I S C H O F F
D. M. H I M M E L B L A U
ANNUAL REVIEW
SURVEY OF M A S S T R A N S F E R
.
Colorimetric methods f o r determining residence times in
highly-localized
micromixing are
among the nouel techniques f o r estimating age distributions in open systems.
The term “res-
idence time,” is being replaced by a new terminology.
his review, which covers the period of 1963 and the
Tfirst half of 1964, is meant to be relatively complete
for chemical engineering interests, but not exhaustive. A few selected papers and some of general interest are briefly described in the text, but most of the work is classified by subject into tables with short descriptions as to its nature and scope. I t is hoped that this method will provide a review that is more comprehensive than previous reviews. Molecular Diffusion
Matrix methods for solving multicomponent diffusion problems are described both by Stewart and Prober (56A), and by Toor (59A). Both start with the premise from irreversible thermodynamics that the diffusion fluxes and forces (chemical potential gradients) are linearly related, and the mass balances are linearized by using small perturbations in parameters about a reference state. The mathematical statements involving sums of fluxes are uncoupled from each other and stated in terms of differential equations for binary diffusion. Stewart and Prober include applications to and examples for processes without flow and with forced convection, and provide a comparison with experimental data for ternary gas flow over a flat plate. Toor uncouples the linearized equations both by algebraic and by matrix methods, and gives an example of diffusion between two phases with different diffusion coefficients in each phase. The nonlinear problem of isothermal diffusion through
a mixture of two non-Newtonian fluids and an elastic solid is examined by Green and Adkins ( I A , 2 I A ) . Attention is confined to constitutive equations which express partial stresses and the diffusive force in terms of kinematic quantities measured at the current time t. Dunlop ( I 6 A ) defined a set of frictional coefficients for isothermal multicomponent diffusion which prove to be identical with relations previously proposed by Lamm, Onsager, Klemn, Laity, and Bearman. These frictional coefficients can be computed for binary and ternary diffusion from experimental thermodynamic and diffusion data. Other theoretical microscopic studies of multicomponent diffusion were given by (73A, 57A). Also of interest is a brief exchange of correspondence concerning correlations for gaseous diffusion (9A, 53A). While having their lighter side, the letters do carry a valuable message to all those engaged in research. Other selected recent work in molecular diffusion is listed in Tables A-1 through A-5. Turbulent Diffusion and Dispersion
Basic Turbulent Diffusion. A comprehensive review of turbulent diffusion will not be given-only those articles of direct interest to chemical engineers will be covered. A careful consideration of averaging conservation laws in pipes was given by Birkhoff (6B). Kelly (49B) formulated in great detail the balance equations for seven variables used to describe the state of a flowing fluid. Lee and Brodkey (53B) and Seagrave and Fahien (78B) present comprehensive data for turbulent diffusion in round pipes. Lamb and Wilhelm (52B)have discussed the statistical variations in local concentration patterns caused by the packed bed structure. Prager (685’) has shown how bounds can be put on the properties of two-phase media by a variational approach using geometric correlation functions. These two articles could lead to a better understanding of the structure of two-phase media. Hinze (43B) and Standart (85B)have considered the fundamental formulation of mass, momentum, and energy balances in heterogeneous flow systems. Axial and Radial Dispersion. Table B-3 lists general work and reviews in this area. Bear (4B) discussed the general tensor form of dispersion in porous media. Scheidegger (76B) developed a theory and Giddings and Robison (28B) studied the failure of other theories VOL. 5 6
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DECEMBER 1 9 6 4
61
for predicting dispersion. Harleman, Mehlhorn, and Rumer (33B) showed that dispersion can be well correlated with the more commonly measured permeability. Coats and Smith (72B) and Deans (75B)considered the effect of dead and pore volume on dispersion. Gabor, et al. (23B, 24B) studied lateral solids and gas mixing in fluidized-packed beds. Quite a bit of dispersion data for various types of processing equipment has become available. Van Andel, Kramers, and deVoogd (95B) have shown that axial dispersion in empty tubes is greatly decreased by curving the tube in a helical fashion. Chemical Reactor Applications. Biskis and Smith (8B) found that pulsing the fluid feed to a fixed bed reactor improved its performance. The effect is probably caused more by interparticle diffusion than by axial dispersion, but the method is very interesting. Liu and Amundson (57B) discussed the effect of axial dispersion on the complicated problem of packed bed
TABLE A-1.
GASEOUS DIFFUSION
m
T or
c.
p, atm.
27A
25 to 85
1
5 A , 79A 3ZA 40A
25 to 90 60 to 120 25 to 110
1 to 150 17 to 157
29A 30A
12 to 55 25
65 to 300
1 ,
Ref.
1
38A
20
1
55A
15 to 65 -200 to 100
1
62A
XA 4 7 A , 48A
64A
Ref.
c.
25 25 25 15 to 35 25 25 25
7ZA 43A 28A 75A
25
various 0 to 100 25
7 7A
__
L I Q U I D DIFFUSION
T, O
4 to 200
46A 67A 45A 3A 49A 77A 60A 25A 4A 33A
2A 42A
T or Ea
System Ethane in n-decane He, Hi, 0 2 , COS, CsHa in water COz in aqueous salt solutions Gases in NHa, water, butadiene Various gases in CCla Self-diffusion in benzene-cyclohexane n-Octane-n-dodecane Sucrose in ternary aqueous solutions Hexane-hexadecane Self-diffusion of COz, HCOa-, COS- in aqueous solutions Effective diffusion of counter ions in potential field Kinetic treatment for liquids Cubic cell model for self-diffusion Hydrodynamic (frictional) analysis for n-alkanes in CCla Analysis of boundary condition at end of open capillary Ternary liquid with reaction Modified free volume theorv for self-diffusion
a T = theoretical study; E = experimental inustigation.
62
TABLE A-3.
System He-air, He-COS, air-COz, A-CO, A-Hz, A-He Hz in cyclohexane Binary or self-diffusion for many gases Naphthalene in CzHa, COz Dl-Hz, Dz-Ni, NHs-Hz, CONz, etc. Hz-COz, Hz-Kr, Hz-CChFz, etc. NHa-Et20 Binary diffusivities for polar polyatomic molecules estimated from viscosity measurements Irreversible thermodynamics applied to water vapor Semitheoretical correlation to predict gas diffusion in air Modified model of Kubu, Yokota, Nakajima
a T = theoretical study; E = experimental investifation
TABLE A-2.
reactor stability. Rosner ( 7 0 B , 7 1 B ) gave a comprehensive analysis of many convective diffusion effects on chemical reactions. Tichacek (93B) and Adler and Vortmeyer ( 7 B ) calculated the loss in selectivity caused by axial dispersion. Mickley and Letts (59B) have analyzed dispersion effects on yields for the general case of a nonisothermal reactor with both radial and axial gradients. Mass Transfer Applications. Miyauchi and Vermeulen (67B) presented a comprehensive analysis of the effects of axial dispersion on two-phase operations. Wilburn (707B) gave a set of modified solutions of the same type but with different boundary conditions that are more typical of many actual types of equipment. Houghton (45B) showed how an analytical solution can be obtained for certain types of nonlinear adsorption with axial dispersion. Miscellaneous Applications. Some other applications are summarized in Table B-8.
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
NEW EXPERIMENTAL TECHNIQUES AND APPARATUS
Tofiic
Ref.
Cell to permit set-up of sharp interfaces in L-L diffusion Measurement in diaphragm cell with very viscous liquids Self-diffusion in a capillary by scintillation techniques Diffusion in gels Diffusion of ions by diffraction methods Modified capillary cell for liquid-liquid diffusion
34A 26A
7A, 2OA 37A 7 8A
50A
TABLE A-4.
T H E R M A L DIFFUSION AND DIFFUSIONT H E R M 0 EFFECTS
Ref.
Topic
63A 51A 39A 37A 74A 23A,36A,47A 54A, 58A 52A
Theoretical analysis for sign and magnitude of thermal diffusion in gases and liquids Soret coefficientsfrom unsteady state measurements Chapman-Cowling second approximation for binary gas Thermal diffusion theory from microscopic viewpoint Diffusion and thermal diffusion in H r K r mixtures Inversion temperature in isobaric separation of CO Thermal diffusion columns Diffusion-therm0 effects in boundary layer Application of temperature gradient to liquid concentration gradient Book: Thermal Diffusion in Gases (in German) Thermal diffusion-a review
6A
ZZA 70A, 44A
a T = theoreticol analysis; E = cxperimenlal rtudJ.
TABLE A-5.
Ref.
24A 35A
Topic
'
~
MISCELLANEOUS
Relation between diffusion and sedimentation in fluid mixtures Status of the theory of diffusion in solids
B. Bischof is Assistant Professor of Chemical Engineering, University of Texas, Austin, Texas. D. M . Himmelblau is Associate Professor of Chemical Engineering at the same university. They have prepared I e E C ' s M a s s Transfer Review since 7962. AUTHOR Kenneth
General Mixing Processes in Flow Systems
Age Distribution Functions. Naor and Shinnar (46C) have proposed a new age distribution function termed the “intensity function” which is essentially the exit age distribution divided by the internal age distribution and is a measure of the probability of a fluid dt). element of age t leaving the system in time (t, t Its major utility is that it is sometimes more sensitive to stagnancy-dead space and bypassing-than the usual distribution functions. Orcutt, Davidson, and Pigford (50C) used a “reaction time distribution” which may be more meaningful than the age distributions for characterizing chemical reactors. Behnken, et al. (3Cb) presented a fundamental study of particle growth processes which should be useful in predicting the behavior in these systems. Harada, Arima, Eguchi, and Nagata (78C) made a start on the very difficult and important problem of micromixing in flow systems. They developed a coalescence-type model which could be used to interpolate between segregated flow and perfectly mixed flow. LaRosa and Manning (32C) used a known second order chemical reaction as a measure of micromixing. Schwartz (67C) devised an optical method for measuring micromixing in fluids. A novel “time reaction” method was proposed by Denbigh, Dombrowski, Kisiel, and Place (7OC) and used by Danckwerts and Wilson (8C) which permits visual observation of the fluid staying in a (transparent) vessel longer than a given time. A starch-iodine solution that changes color sharply after a certain length of time was used. The method should be very useful for obtaining semiquantitative micromixing information. White (69C) estimated the size of various errors in residence time distribution measurement. Age Distribution Function Applications. Moore and Hesler (44C) gave some information on residence time distributions in an evaporator used to process heat sensitive material where fluid elements with long holding times must be avoided. Rothfeld and Ralph (55C) argue from their data that pulse and step measurements are equivalent in trickle-phase reactors contrary to some previously available data. Grieves, Milbury, and Pipes (76C) showed the effects of short circuiting in a biochemical reaction-the activated sludge process. Adler, Long, Rooze, and Weinstein ( I C ) illustrated the effects of mixing on a variety of chemical reaction schemes. Mixing in Stirred Tanks. Rosenweig (54C) derived an idealized turbulent diffusion theory. Van de Vusse (66C) has further discussed his mathematical model and Yoshitoshi, Ichiro, Yasuhiko, Kazumi (72C) extensively investigated the use of a similar model involving circulation paths throughout the vessel. Holmes, Voncken, Dekker, and den Hartog (23C, 67C) obtained detailed experimental data for use with the van de Vusse type model. Biggs (4C) studied the effect of various parameters on the mixing time. Mayer and Rippel (40C) made residence time and contacting studies. Funda-
+
-
mental turbulence measurements were performed by Rice, Toor, and Manning (53C) and Yamanato and Nagata (77C). Foraboschi and Lelli (73C, 34C) have found an interesting case of thermal instability of the residence time distribution in a tank with heating/cooling coils. The presence of a temperature difference between coil and tank fluid apparently rather drastically changes the flow patterns. Mixing in Fluidized Beds. Ruckenstein (60C) has developed a theory to predict mixing in a homogeneous fluidized bed (no bubbles). DeMaria and Longfield (9C) measured point age distributions which enabled them to calculate some aspects of micromixing. In particular, mean age and variance contours throughout several fluidized beds were reported. Metcalfe (41C) used residence time distributions from various internal points to subdivide the unit into various mixing zones. Baerns, Fetting, and Schiigerl (3Cu) measured radial and axial gas mixing. Rowe (56C) discussed the effects of mixing on gas-solid reactions using his previous extensive work. Other Mixing Applications. Bryer (6C) discussed a novel impeller design for agitated systems based on aerodynamic principles that sheds uniform vortices that persist throughout the system. This scheme should lead to more uniform mixing conditions. Gould (74C) used a similar method to improve the mixing in ducts. Miller, Fredrickson, Brown, and Tsuchiya (43C) developed a device for efficiently growing algae utilizing the mixing caused by secondary flow (Taylor vortices) between two rotating cylinders. Interphase Mass Transfer
Olander (330) has modified his earlier model of mass transfer in a stirred vessel by accounting for transfer in the core of the mixing region. A simplified limiting model was also examined in which the liquid in effect rotates as a solid body. Both models were compared to some limited experimental data for transfer cells with no separators at the interface, with reasonable agreement. Unsteady state transport across a stagnant fluid interface under a large flux has been analyzed by Szekely ( 4 8 0 ) . T h e velocity in the one-dimensional mass balance originated only by diffusion and was time dependent. Methods of expressing the velocity in terms of the flux, and solving the mass balance for an infinite media and a moving boundary were described. A variational procedure was presented by Prager ( 3 9 0 ) to handle the complex problem of calculating interphase mass transfer in suspensions (or similar random twophase media). Upper bounds were obtained on transfer rates for certain specific cases in terms of the void-size distribution. The effect of concentration on mass transfer in liquidliquid systems was discussed by (340, 75D). A summary of a number of previously unpublished investigations into interphase mass transfer accompanied by a fast reaction (GOz into monoethanolamine) was given by Astarita, Marrucci, and Gioia ( 3 0 ) . Four different VOL. 5 6
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DECEMBER 1 9 6 4
63
TABLE
B-I.
TURBULENT DIFFUSION GENEOUS FLUIDS
I
Ref.
IN
HOMO-
TABLE B-7.
Subject
Subject
11B
Lagrangian similarity hypothesis applied to diffusion in turbulent stream flow Diffusion measurements in Lake Huron Detection of conductance fluctuations Universal spectra of scalar fields Vertical diffusion in lower atmosphere Diffusion in a stratified fluid Calculation of Lagrangian correlation in stationary homogeneous turbulence Local turbulent mass transfer to pipe wall Turbulent transfer in mass transfer entry region
138 26B 27B 298 37B 748
36B 978
TABLE 8-2.
11
Reference 3B 42B 468 488 828 838
TURBULENT DIFFUSION I N HETEROGENEOUS FLOW SYSTEMS Subject Vertical particle diffusion in a horizontal water pipe Turbulent flow of suspended particles Behavior of particles in a sinusoidal velocity field Sand rransporr studies using radioactive tracers Effect of electrification of a flowing particulate system Concentration and mass flow distributions of parricles
General discussion of axial mixing effects in extraction columns Diffusion and back flow models for two-phase axial dispersion Graphical calculation methods for extraction with axial mixing Dynamic behavior of a pulsed extraction column with axial dispersion Axial dispersion in ion exchange Effect of axial dispersion on gas absorption with chemical reaction Effects of fluid mixing on dynamics of cross-current contacting
25B 62B 69B 39B 38B,40B 60B 978
TABLE B-8.
Sumerical solution methods Waste dispersion in tidal waters Waste dispersion in streams Salt water intrusion in porous media with axial dispersion Miscible displacement in soils Scaling laws for porous media dispersion Interpretation of model experiments for porous media dispersion Design of laboratory models for porous media dispersion Stability of miscible displacement with dispersion Effect of transverse dispersion on miscible displacement fingering Miscible displacement in a mulriphase system
1'
668
818 928
~
~
~
~
TABLE C - I . TABLE 8-3.
Subject Fluorescent tracers for dispersion measurement
I
Reference
i
I
5C 36C, 68C
70C
TABLE B-4.
DISPERSION I N POROUS M E D I A
1
34B 478 54B 67B 80B, 84B 102B 7038
35c 62C 37C, 64C
Longitudinal and lateral dispersion in isotropic media Diffusion in porous alundum Liquid dispersion in packed bed Studies in packed columns Axial dispersion in packed column Convection in a saturated POTOUS media a t large Peclet number Mixing layer flows in a saturated media
I ,
33C 45C
izI
I
;:z
1
Reference 2B
78 378 148 78B, SOB 86B, 87B, 89B 1OOB 638 798 39B QB 16B 648
Measurement of molecular diffusion coefficients using capillary dispersion Prediction of dispersion for empty tubes with return bends Axial dispersion of liquid on a column of spheres Tracer measurements in turbulent boundary layer Axial dispersion in bubble columns Axial dispersion in rotaing disk contactors Mixing on valve trays and in downcomers Mixing on sieve trays Axial dispersion in pulsed extraction column Axial dispersion in spray extraction tower Mixing in tidal estuary Dye dispersion studies in natural waters Axial dispersion in Delaware River model
AGE D I S T R I B U T I O N
Residence time distribution in a cylindrical vessel Residence time distribution of powders in an open circuit ball mill Residence time distribution in bubble columns Use of residence time distribution information in calculating chemical reactor output
M I X I N G I N STIRRED.TANKS
Reference 39c 2c 7c 1 lC 7 7C
38C 48C
52C 12 c 15c 57C
Subject Pumping capaciry of impellers Liquid-liquid systems Hysteresis effects when changing impeller location Contacring efficiency measured by mass transfer Residence time distribution of gas in a gas-liquid contactor Determination of drop size in liquid-liquid systems Effect of mixing conditions on precipitation Propeller pumping and solids fluidization Agitation of liquid systems requiring high shear Batch miying of viscous liquids Review
M I X I N G I N FLUIDIZED BEDS
TABLE C-4.
I
Reference TABLE B-6.
CHEMICAL REACTOR APPLICATIONS
Reference
Subject
79B, 22B
Axial dispersion with molar expansion of reacting fluid Frequency response relations with axial dispersion Axial dispersion with heterogeneous (adsorption) reaction Transients with axial dispersion
20B
44B 55B 588 IOB, 32B, 51B, 98B 75B 77B
64
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
APPLIED
Subject
TABLE C-3.
DISPERSION I N EQUIPMENT Subject
Subject A general method of using moments to find model parameters Discussion of dead space in combined models for characrerizing flow systems General residence time distribution proposed to correlate experimental data Optically tagging individual particles Sensitive probe for dynamic water vapor measurements Reviews
TABLE C-2.
Subject
TABLE 8-5.
AGE D I S T R I B U T I O N FUNCTIONS
DISPERSION IN GENERAL
Reference 218
MISCELLANEOUS APPLICATIONS Subject
I
88B 7 7B 50B 73B 5B 308 418 728
~~~
Reference
MASS TRANSFER APPLICATIONS
79C, 3OC, 59C, 63C, 65C 47c 57C, 58C
TABLE C-5.
1
1
Subject Solids mixing measurements Backmixing measurements Basic studies of bubbles in fluidization
OTHER M I X I N G APPLICATIONS
Reference
Subject
24C 21C, 28C, 31C, 42C, 4QC
Mixing two fluids in a closed conduit .Mixing using jets
TABLE D - I .
INTERPHASE TRANSFER, GENERAL
Ref.
Apparatus and Process
Wediaa
Rotating disk with high flux Ions diffusing and adsorbing on solid simulating a porous media Bubble mixed interface Countercurrent extractor, variable void fraction Overcoming variation of interphase transfer coefficient in packed column Theories for wetted wall column Two-phase stratified laminar flow between parallel plates Efficiency of chromatographic columns Limiting mechanisms in agitated vessel Effect of free surface and bubbles In pulsed column Effect of electrolytes on absorption Development of average driving force for countercurrent equipment Gas absorption a t rotating wetted wall Theoretical analysis for ordinary diffusion combined with pressure diffusion
S-L s-L
TABLE D-4. MASS TRANSFER TO AND FROM DROPS, BUBBLES, AND SMALL SOLID PARTICLES
T or ~
11D 400 490 580 270 510 530 360 220 40 560 130 520 60
a G = gds; L, =,liquid; S = solid. study; A = applzcation gzven.
b
Ref. 470
D
L
L-L L-L 0-L
590 230 540
D D
L L L
G-L G-L
310
D
L
160
D D
G-L
70 80
G-L
140 20 430
B B B, D
440 25D 260 300
s
L
S S S, D
G G L, G
180
S
incompressible
G-L G-L G-L
T = theoretical analysis; E = experimcntal
SIMULTANEOUS MASS TRANSFER AND C H E M I CA L REACT I O N (Primarily Experimental)
Ref.
I
Transfer Equipment
100
0
240 410
Stirred tank
170 320 27 0
Stirred tank Stirred tank Falling film
TABLE D-3.
Phases
Type of Reaction
Process
Ab
U
irrev., 1st order
A
570
U
irrev., 1st order
120
s
550
U
irrev. 1st order (rapid) rev. 1st order
500
U
General time independent velocity and boundary conditions Solid particles, moving boundary Two reactants, constant fluid velocity, thin reaction zone Application of Eyring theory to interphase coefficient Two immiscible liquids, 2 components
380
S
350
u
ID 200
50
1QD
S
u, s u u
--
irrev., infinitely rapid; irrev. and rev., 2nd order pseudo 1st order 2nd order; also infinitely rapid nth order mth, n t h
mth,
order
nth order
A e B ; B-C Simultaneously
a S = sfcad stale; U = unsteady state. or analog carcuttion.
L = liquid; G = gas.
Tofiic
A
Freezing of drops exposed to vacuum Interface shapes on crystallization Diffusion limited vaporization of metals Molecular theory of freezing Condensation on flat surface from supersaturated vapor
3QE QE 26E 37E 15E 16E 17E 21E 3E 14E 2E 29E 38E 12E ZOE 40E 22E 28E
G
290
u a
b
Diffusion controlled zone melting Interfaces during melting and freezing Variables affecting crystal growth Sublimation of solids
39E 32E 27E 1QE 7E 11E 4E 33E 6E 1E
SIMULTANEOUS MASS TRANSFER AND CHEMICAL REACTION
S or
__
drop; E = bubble; S = solid partirlc.
TABLE E-I. VAPORIZATION, CONDENSATION, SUBL I M A T I O N , FREEZING AND M E L T I N G
(Primarily Theoretical)
Ref.
B
Problem Fal!ing drops with and without oscillation Comparison of models Coalescence in turbulent flow field Effect of interfacial tension caused by concentration gradient Monomer to dimer conversion at interface Evaporation of l p charged water droplets Growth of droplet in saturated media COz rising in water Simultaneous heat and mass transfer Effect of surface tension Theoretical analysis for complete range of Re Natural convection mass transfer Mass transfer in turbulent air stream Effect of free convection a t sphere Theoretical analysis for nonspherical shapes Boundary. laver . analvsis
Ref.
Solid Is into I- in aqueous solution COP into aqueous COa-2 COa into aqueous COS-' COz into aqueous monoethanolamine COz into COS-* with glycine COz into aoueous NaOH Aqueous H + and Na + with Dowex 50 C o r into aqueous NaOH COz into diethanolamine Brg into alkaline solutions
420 450 90
460
1
D
G G L L L L, G
a
TABLE D-2.
Other Phase L or Gb
Eb
0
Condensation coefficient of water Condensation of water on droplets from svpersaturated vapor Molecular theory applied to condensation Condensation in laminar flow inside tubes Evaporation from porous cylinder wall Evaporation coefficient of various liquids Evaporation from drops in steady and unsteady state Evaporation from porous plate with laminar flow Evaporation and absorption in flow over flat plate
T = theoretical analysis; E
SIMULTANEOUS HEAT AND MASSTRANSFER
TABLE E-2.
N A A
Ref.
1 2 -Sor Ub U
Countercurrent and cocurrent gas absorption Absorption, 2 reactants
A
Laminar tubular flow; reaction A at wall Film and penetration models, 2 reactants Penetration model, 2 reactants Reaction at flat electrode with diffusion
A
A
A
N A
A = analytical solution; N = numerical
= cxpcrimentolstudy.
E or
~
S S
T, E
13E
L
S
T, E
23E
L
S
T
25E 31E
L
T
S U
T T
30E 36E
T
S
T, E
T
S
E
5E
T
S
T, E
%
a c
ProcesJ
To
T, E T, E
Mass and heat transfer in gas absorption Falling laminar film in vertical tube Gas passing through porous walls Calculation of enthalpy from interference measurements on gas or liquid Drying of porous materials in terms of boundary layer analysis for flat plate Incompressible gas flow over axisymmetric body Use of film and penetration theories in gasliquid transfer Transpiration cooling Correlation for heat and mass transfer to pipe wall Effect of chemical reaction on rate of heat transfer between gas and wall
L = Iaminarj%w; T = turbulent pow. b S = steady rtatc; U = unsteady E = experimental study; T = theoretical analysis.
VOL. 5 6
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DECEMBER 1 9 6 4
rtate
65
types of apparatus were compared for the same reactions: a batch absorber, a wetted wall column, a string of spheres, and a packed column. For different ratios of COz/amine, different reaction mechanisms prevailed, and comparisons were made to the theoretical performance for each type of apparatus. Lebeis (280) has surveyed the relative merits of the film and penetration theories as applied to equipment design. Three methods are presented to calculate mass transfer rates by an unsteady state analysis. He suggested that contact times be determined experimentally, and offered a method to take account of the variability of the rate coefficient with time. Popovich, Jervis, and Trass (370) analyzed five mechanisms which had been proposed in the literature for mass transfer during drop or bubble formation by use of a common general function describing the variation of drop area with time. All models were based unsteady state diffusion theory with different assumptions concerning the process hydrodynamics. A general equation to calculate interphase transfer was proposed and some brief data on liquid-liquid transfer were compared with the various models. Other recent work is shown in Tables D-1 through D-4. Simultaneous Heal and Mass Transfer
Earlier theoretical work on transient interfacial heat and mass transfer in multicomponent vapor-liquid systems was extended by Yang and Clark (41E). Source theory was applied to the phase change across the interface with a step change in gas phase pressure. Numerical and exact solutions compared favorably. El’perin (7UE) analyzed the process of heat and mass TABLE F-I. ~
INTERFACIAL PHENOMENA ~~
Ref.
Ward and Quinn (15F) modified a laminar liquid jet so that the jet could be operated in another liquid to measure the magnitude of the “interfacial resistance”. The resistance, if any, was found to be extremely small, while the diffusivities of each phase agreed w7ell with those measured in other experiments or calculated from semi-empirical theories. Ruckenstein and Berbente (77F) have set forth in a quantitative fashion the conditions needed for interfacial turbulence when isothermal diffusion and a first order chemical reaction take place in one phase. The criteria of stability differ from the case without reaction. Other work is listed in Table F-1. Pore Diffusion in Solids
Mason et al. (QG) have extended their model of pore diffusion visualizing the solid phase as “giant” stationary molecules in a statistical mechanics type treatment. Robertson and Smith (74G) have proposed a model to predict the diffusion in alumina pellets. Rothfield (15G) presents a method for calculating the effective diffusion coefficient from counter-diffusion data. Wakao and Smith (77G) used their model to predict effectiveness factors for chemical reactions and Rao, Wakao, and Smith (13G) give data to support the model. TABLE H - I .
MASS TRANSFER I N BOUNDARY LAYER FLOW
System
73F 8 F , 74F 9F 72F 4F IF 6F 2F 7F 3F, 5F
TABLE G - I .
Reference IG 5G 6G ZG, 4G, 77Gj l Z G , 78G 7G
8G 3G, 70G 76G
66
Interfacial Phenomena
~~
Effect of surface tension gradient along bubble on mass transfel coefficient Interfacial tension gradients and droplet behavior Droplet motion caused by surface active agents Effect of surface active agents on velocity of rising air bubbles Drops in liquid-liquid systems and effect on mass transfer rates Effect of interfacial tension on nucleate boiling Effect of surface films on gas absorption in turbulent cell Effect of glycine on gas absorption in liquid jet Effect of surfactants on solid-liquid mass transfer Theory of surface turbulence and potential barriers in liquid extraction Effect of interfacial tension in packed extraction column
7OF
s
transfer in homogeneous and heterogeneous reacting systems by Lykov’s concepts as well as by irreversible thermodynamics. The effect of viscosity and friction forces on kinetics was described. Other work on simultaneous heat and mass transfer including phase changes is listed in Tables E-1 and E-2.
i
PORE DIFFUSION IN SOLIDS Subject
Flow and diffusion measurements Quali’ative model of penetration 01 gas into liquid Network model Reaction with pore diffusion Pore diffusion in ion exchange resins Adsorption rates and pore diffusion Gaseous isotope separation through porous wall Gaseous isotope separation through porous wall with imposed electric field
E = experimental study.
T = theoretical analysis.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Solution A or ArQ
Ref. 7H 28H
A
4H 35H 2H 1QH 2OH
A
13H 34H 26H
A A A
Process Porous plate with surface chemical reaction Effect of large concentration gradientsnear catalyst surface on apparent kinetics Similarity solutions to heat and mass transfer
A, N
Mass transfer with moving interface High speed laminar couette flow .4lteration of gas composition and velocity by surface reaction Dissociated flow with first order surface reaction Predicting mass transfer from two dimensional surfaces Perturbation solution for flow past wedge
A A A, S
A = analyt‘cal solutio?; AJ = numerical rolulzon.
TABLE H-2.
Ref. QH 7H 30H 8H 21H 37H
1
E or Ta T
T E T
T E
~
MASS TRANSFER I N ELECTRIC FIELDS
Process Forced and natural convection at flat electrodes Diffusion, convection, adsorption through double layer Natural convection from sFheres and horizontal cylinders Different diffusion coefficients in bulk and near electrode Irreversible thermodynamics applied to polarized diffusion layer Mechanical vibration of electric double layer
TABLE H-3.
Topic
Ref. 17H 27H 17H 32H 14H 23H 7OH 22H 24H 25H 18H 31H 16H 5H 12H 38H 39H 29H 33H 36H 75H 6H 3H 30Ha 19Ha
RELATED REVIEWS AND BOOKS
Carbon dioxide removal processes Convective diffusion effect on surface catalyzed reactions Drop phenomena in liquid extraction Electrodialysis Formation and coalescence of drops and bubbles Problems in heat and mass transfer Diffusion of gases physically adsorbed on solids Isothermal diffusion Liquid-liquid extraction Mass transfer Mass transfer between phases Mass transfer and critical phenomena Mass transfer and interfacial phenomena Mass transfer in applied electrochemistry Mass transfer in solid metals Stability of liquid films; coalescence of drops and bubbles T h e role of diffusion in catalysis (book) Convective mass transfer (book) Diffusion and membrane technology (book) Fundamentals of mass transfer (book) Interfacial phenomena (book) Momentum, heat and mass transfer (book) Physiological applications of tracer studies (book) Dispersion and mixing in chemical reactor design (book)
No. Refs. 112 84
82 33 108 33 39 244 21 30 103 51 61 30
Miscellaneous
Table H-1 lists articles of interest dealing with mass transfer in boundary layer flow while Table H-2 lists those concerning mass transfer in electric fields. Various reviews and books in the field of mass transfer are shown in Table H-3. B I BLl OG RAPHY Molecular Diffusion (1A) Adkins, J. E., Arch. Rat. Mech. Anal. 15, 222 (1964); Phil. Trans. 256, 30’1 (1964). (2A) Albright, J. G., J . Phys. Chem. 67, 2628 (1963). (3A) Bartholome, E., Gerstacker, H., Scuola Arione Pt. 7 , 61 (1963-64). (4A) Bidlack, D. L., Anderson, D. K., J. Phys. Chem. 68,206 (1964). (5A) Bondarenko, A. G., Golubev, I. F., Gan. Prom. 9, 50 (1964). (6A) Brock, J. R., Proc. First Symp. Less Common Means Separation, Birmingham, 1963, p. 77, T h e Institution of Chemical Engrs., London, 1964. (7A) Brown, D. S., Tuck, D . G., Trow. Faroday Soc. 60, 1230 (1964). (EA) Cary, J. W., J. Phys. Chem. 67, 126 (1963). (9A) Chen, N. H., Othmer, D. F., IND.END.CHEM.FUNDAMENTALS 3, 279 (1964). (10A) Clusius, K., J . Chim. Phys. 60, 163 (1963). (11A) Collins, D. A,, Watts, H., Australian J . Chem. 17, 516 (1964). (12A) Coriell, S. R., Jackson, J. L., J . Chem. Phys. 39,2418 (1963). (13A) Cussler, E. L., Lightfoot, E.N., A.2.Ch.E. J . 9, 702, 783 (1963). (14A) de Vries, A. E., Haring, A,, Z . Naturforschung 19, 225 (1964). (15A) Dewan, R. K., Van Holde, K. E., J. Chem. Phyr. 39,1820 (1963). (16A) Dunlop, P. J., J . Phys. Chem. 68,26 (1964). (17A) Gergely, J Tamas, J Vertes, A., Lengyel, S., M a y Kem Folyoirat 70, 55 (1964); Acta Acad.Sc7. Hung 39,423 (1963) (Pub. 16664) (in’English). (18A) Gokhshtein, Ya. P., Zh. Fiz. Khim. 37, 2640 (1963). (19A) Golubev, I. F., Bondarenko, A. G., Gor. Prom. 8, 46 (1963). (20AI . , Gosman. A,. Chem. Listv, 56., 1445 (1962). (21A) Green, A. E., Adkins, J. E., Arch. Rat. Mech. Anal. 15,235 (1964). (22A) Grew, K. E., Ibbs, T. L., “Physikalische-Chemische Trenn- und Messmethoden. Bd. 7., Thermodiffusion in Gasen,” Deut. Verlag Wissenschaften, Berlin, 1962. (23A) Grigor’ev, V. B., Smirnov, N. I., Zh. Prikl. Khim. 36, 2228, 2687 (1963). (24A) Haase, R., in “Ultracentrifugation in Theory and Experiment,” pp. 13-28, ed. Williams, J. W., Academic Press, New York, 1963. (25A) Henrion, P. E., Trans. Faraday SOC.6 0 , 75 (1964). (26A) Hollander, M. V., Barker, J. J., Oak Ridge Radioisotope Conf., Res. Appl. Phys. Sci. Eng., p. 52, TID-7688, U.S.A.E.C., 1963. (27A) Holsen, J. N., Strunk, M. R., IND.ENO. CHEM.FUNDAMENTALS 3, 143 (1964). (28A) Houghton, G., J . Chem. Phys. 40, 1628 (1964). (29A) Iomtev, M. B., Tsekhanskaya, Yu. V., Zh. Fir.Khim. 38,896 (1964). (30A) Ivakin, B. A., Suetin, P. E., Sou. Phys.-Tech. Phys. 8, 748 (1964).; Zh. Tekhn. Fin. 33, 1007 (1963). (31A) Kelemen, F., Bota, F., Neda, A,, Acad. Rep. Populare Romine, Studii Cercctari Fin. 14, 583 (1963). (32A) Khazanova, N. E., Linshits, L. R., Khim. Prom. 579 (1963). (33A) Kigoshi, K., Hashitani, T., Bull. Chem. Soc. Japan 36, 1372 (1963). (34A) Killmann, E., Chem. Ingr. Tech. 36, 378 (1964). (35A) Lazarus, D., AGARDograph No. 62, 65 Univ. of Illinois, Urbana, Ill. (1963). (36A) Los, J., Velds, C. A,, RGmber E Proc First Symp Less Common Means Separation, Birrmngham, 1963, p. ‘?he Inst. of Chem.‘Engrs., London, 1964. (37A) Mason, E. A., Islam, M., Weissman, S., Phys. Fluids 7, 1011 (1964); 174 (1964).
Gib.
I
,
85,
(38A) Miller, L., Carman, P. C., Trans. Furoday Soc. 60, 33 (1 964). ENG.CHEM.FUNDAMENTALS 2, 102 (1963). (39A) Mizushina, T., Ito, R., IND. (40A) Mueller, C. R., Cahill, R. W., J . Chem. Phys. 40,651 (1964). (41A) Nafikov, E. M., Usmanov, A. G., Tr. Karansk. Khim. Tekhnoi. Inst. 36 (1963). (42A) Naghizadeh, J., J . Appl. Phys. 35, 1162 (1964). (43A) Panchenkov, G. M., Int. Chem. Eng. 4, 440 (1964). (44A) Powers, J. E., p 1-98 in “New Chemical Engineering Separation Techniques,” ed. H. M . .&Goen, h i l e y , New York, 1963. (45A) Ratcliff, G. A., Holdcraft, J. G., Trans.Znstn. Chcm. Engrs. 41,315 (1963). (46A) Reamer, H. H., Lower, J. H., Sage, B. H., J. Chem. Eng. Data 9, 54 (1964). (47A) Reinhold, G., Z. Physik. Chem. (Leiprig) 224, 384 (1963). (48A) Roberts, J., Brit. Chcm. Eng. 8, 753 (1963). (49A) Ross, M., Hildebrand, J. H., J . Chem. Phys. 40, 2397 (1964). (50A) Saraf, D. N., Witherspoon, P. A., Cohen, L. H., Science 142, 955 (1963). (51A) Saxena, S. C., Joshi, R. K., Indian J. Phys. 37,235 (1963). (52A) Schaaffs, W., Naturivissenschaften 51, 83 (1964). 3,278 (1964). (53A) Scott, D. S., INn. ENO. CHEM.FUNDAMENTALS (54A) Sparrow, E. M. Minkowycz W. J. Eckert, E. R. G., A.Z.A.A. J. 2, 652 (1964); J . Heat TraAsfcr 81C, 311’(1964): (55A) Srivastava, B. N., Srivastava, I. B., J . Chem. Phys. 38, 1183 (1963). 3, 224 (1964). (56A) Stewart, W. E., Prober, R., IND.ENO. CHEM.FUNDAMENTALS (57A) Sundelaf, L. O., Slidervi, I., Ark. Kemi 21, 143 (1963). (58A) Tewfik, 0. E., Eckert, E. R. G., Jurewicz, L. S., A.Z.A.A. J . 1, 1537 (1963) (59A) Toor, H. L., A.2.Ch.E. J. 10, 448 (1964); 10, 460 (1964). (GOA) Van Geet, A. L., Adamson, A. W., J . Phys. Chem. 68, 238 (1964). (61A) Vivian, J. E., King, C. J., A.2.Ch.E.J. 10,220 (1964). (62A) Weissman, S., J . Chcm. Phys. 40, 3397 (1964). (63A) Zhuravleva, V. P., Znt. Chem. Eng. 4, 128 (1964). (64A) Zwanzig, R., J . Chem. Phys. 40, 2527 (1964). Turbulent Diffusion and Dispersions (1B) Adler, J., Vortmeyer, D., Chem. Eng. Sci. 19, 413 (1964). (2B) Bailey, H. R., Gogarty, W. B., Sot. Petrol. Eng. J . 3, 256 (1963). (3B) Barnard, B. J. S., Binnie, A. M., J . Fluid Mech. 15, 35 (1963). (4B) Bear, J., J . Geophys. Res. 66, 1185 (1961). (5B). Biggar, J. W., Nielsen, D. R., Soil Sci. SOC.Am. Proc. 26 (2), 125 (1962); cf. tbtd. 25, 1-5 (1961). (6B) Birkhofl, G., J . Math. Anal. App. 8, 66 (1964). (7B) Bischoff, K. B., A.Z.Ch.E. J . 10, 584 (1964). (8B) Biskis, E. G., Smith, J. M., A.Z.Ch.E. J . 9, 677 (1963). (9B) Bowden, K. F., Int. J . Air Water Poll. 7, 343 (1963). (9Ba) Carberry, J. J., Chem. Process Eng. 44, 306 (1963). (10B) Carra, S., Stabilini, M., Chim. Ind. (Milan) 44, 851 (1962). (11B) Cermak, J. E., J . Fluid Mech. 15, 49 (1963). (12B) Coats, K . H., Smith, B. D., SOC.Petrol. Ens. J. 4, 73 (1964). (13B) Csanady, G. T., J . Fluid Mech. 17, 360 (1963). (14B) Davar, K. S., Cermak, J. E., Int. J . Air Waterpoll. 8, 339 (1964). (15B) Deans, H . A,, Sot. Petrol. Eng. J. 3, 49 (1963). (16B) Diachishin, A. N., J . Sanit. Eng. Diu. ASCE 89, 29, SA1 (1963). (17B) Ibid., 23, SA4 (1963). (18B) Dil’man, V. V., Aizenbud, M . V., Zhilyaeva, T. A,, Khim. Prom. 1963 (9), 705. (19B) Douglas, J. M., Bischoff, K. B., IND. ENG. CHEM.PROCESS DESIGNDEVELOP. 3, 130 (1964). (?.OB) Fan, L. T., Ahn, Y. K., Chem. Eng. Prog. Symp. Ser. 59, 91, No. 46 (1963). (21B) Feuerstein, D. L., Selleck, R. E., J . Sank Eng. Div. ASCE 89, 1, SA4 (1963). (22B) Foraboschi, F. P., Chim. Ind. (Milan) 43, 1275 (1961). (23B) Gabor, J. D., A.2.Ch.E. J. 10, 345 (1964). 3,60 (1964). (24B) Gabor, J. D., Mecham, W. J,, IND.ENG.CHEM.FUNDAMENTALS (25B) Gerster, J. A,, Chem. Eng. Prog. 59,79, Nov. (1963). (26B) Gibson, C. H., Schwarz, W. H., J . Fluid Mech. 16, 357 (1963). (27B) Ibid., p. 365. (28B) Giddings, J . C., Robison, R. A,, Anal. Chem. 34, 885 (1962). (29B) Greenfield, H., Appl. Sci. Res. A12, 327 (1964). (30B) Greenkorn, R. A,, IND.END. CHEM.56, No. 3, 32, (1964). (31B) Grigg, H. R., Stewart, R. W., J . Fluid Mech. 15, 174 (1963). (32B) Grosjean, C. C., Froment, G. F., Med. Kon. Vlanmse Acod. Wet. 24, No. 1 (1962). (33B) Harleman D R. F., Mehlhorn, P. F., Rumer, R. R., Proc. ASCE, J . Hyd. Diu. 89, HYZ (i96j). (34B) Harleman, D. R. F., Rumer, R. R., J . Fluid Mech. 16,385 (1963). (35B) Harris, E. K., Znt. J . Air Water Poll. 1,799 (1963). (36B) Ibid., 8, 421 (1964). (37B) Harrison, D., Lane, M., Walne, D. J., Trans. Inst. Chem. Eng. (London) 40, 214 (1962). (38B) Hashimoto, I., Deshpande, K. B., Thomas, H . C., IND.ENG.CHEM.FUNDAMENTALS 3,213 (1964). (39B) Hazlebeck, D. E., Geankoplis, C. J., ibid., 2, 310 (1963). (40B) Helfferich, F., Chem. Zng. Tech. 34, 269 (1962). (41B) Heller, J. P., A.2.Ch.E. J . 9, 452 (1963). (42B) Hino, M., J . Hydr. Diu. ASCE 89, 161, HY4 (1963). (43B) Hinze, J. O., Appl. Sci. Res. A l l , 33 (1962). (44B) Hofmann, H., Astheimer, H. J., Chem. Eng. Sci. 18, 643 (1963). (45B) Houghton, G., J . Phys. Cham. 67,84 (1963). (46B) Ibid., Proc. Roy. SOC.A271, 33 (1963). 2, 189 (1963). (47B) Huang, J. H., Smith, J. M., IND.END.CHEM.FUNDAMENTALS (48B) Hubbell, D. W., Sayre, W. W., J. Hydr. Diu. ASCE 90, 39, HY3 (1964). (49B) Kelly, P. D., Znt. J . Eng. Sci. 2, 129 (1964). (50B) Krenkel, P. A,, J . Water Pollution Control Federation 34, 1203 (1 962). (51B) Kubota, H., Akehata, T., Kagaku Kogaku 28, 284 (1964). 2, 173 (52B) Lamb, D. E., Wilhelm, R. H., IND.ENG. CHEM.FUNDAMENTALS (1963).
VOL. 5 6
NO, 1 2
DECEMBER 1 9 6 4
67
(53B) Lee, J., Brodkey, R. S., A.I.Ch.E. J . 10, 187 (1964). (54B) LeGoff, P., Ind. Chim. Belge. 27, 1009 (1962). (55B) Lelli, U., Chim. Ind. (Milan) 46 (3), 263 (1964). (56B) Levenspiel, O., Bischofl, K. B., Adu. Chcm. Eng. 4, 95 (1963). (57B) Liu, s. L., Amundson, N. R., IND.ENCI.CHEM.FUNDAMENTALS 2,183 (1963). (58B) Lorenz, M. G., Ind. Eng. Chem. Process Dcsign Deuelop. 2, 88 (1963). (59B) Mickley, H . S., Letts, R. W. M., Can. J . Chem. Eng. 41, 273 (1963); 42, 21 (1964). (60B) Miura, Y., Hirota, S., Nakajima, M., Kagaku Kogaku 27, 815 (1963). (61B) Miyauchi, T., Vermeulen, T., IND.ENC. CHEM.FUNDAMENTALS 2, 113 ( 1963). (62B) Ihid., p. 304. (63B) hltitzenberg, A,, Chem. Ing. Tech. 34, 542 (1962). (64B) O’Connor, D. J., Int. J . Air Water Poll. 7, 1073 (1963). (65B) Perkins, T. K., Johnston, 0. C., Soc. Pet. Eng. J. 3,70 (1963). (66B) Perrine, R . L., ibid., p. 205. (67B) Pfannkuch, H. O., Rev. Inst. Franc. Petroie 18, 215 (1963). (68B) Prager, S., Chem. Eng. Sci. 18, 227 (1963). (69B) Rod, V., Brit. Chem. Eng. 9, 300 (1964). (70B) Rosner, D. E., A.I.A.A. J . 2, 593 (1964). (71B) Ihid., Chem. Ens. Sci. 19, 1 (1964). (72B) Pozzi, A. L., Blackwell, R., Fundamcntalr J. Sot. Pet. Eng. J . 3, 20 (1963). (73B) Rumer, R . R., Harleman, D. R . F., J . Hydr. Diu. ASCE 89, 193 HY6 (1963). (74B) Saffman, P. G., Appl. Sci. Res. A l l , 245 (1963). (75B) Satterfield, C. N., Yeung, R. S. C., IND. ENC. CHEM.FUNDAMESTALS 2, 257 (1963). (76B) Scheidegger, A. E., J . Geophys. Res. 6 6 , 10 (1961). (77B) Schmidt, H. J., Int. J . Heat Mass Trans. 6 , 719 (1963). (78B) Seagrave, R. C., Fahien, R . W., U. S. At. Energy Comm. IS-419, 135 pp. (1 961). (79B) Sehnel, G. A,, Babb, A. C., IXD. ENG. CHEY.PROCESS DESIGNDEVELOP. 3, 210 (1964). (80B) Shestopalor, V. V., Kagarov, V. V.,Blyakhman, L. I., Int. Chem. Eng. 4, 17 (1964). (81B) Slobod, R. L., Thomas, R. A,, Sac. Pet. Eng. J . 3, 9 (1963). (82B) Soo, S. L., IND.ENO.CHEM.3, 75 (1964). (83B) Soo, S. L., Tresek, G. J., Dimick, R . C., Hohnstreiter, G. F., Ibid., 3, 98 (1 964). (84B) Stahel, E. P., Geankoplis, C. J., A.I.Ch.E. J . 10, 174 (1964). (85B) Standart, G., Chem. Eng. Sci. 19, 227 (1964). (86B) Stainthorp, I . P., Sudall, N., Trans. Inst. Ch. E . (London) 42, T198 (1964). (87B) Stemerding, S., Lumb, E. E., Lips, J., Chem. Ing. Tech. 35, 844 (1963). (88B) Stone, H . L., Brian, P. L. T., A.I.Ch.E. J.9, 681 (1963). (89B) Strand, C. P., Olney, R. B., Ackerman, G. H., A.I.Ch.E. J . 8,252 (1962). (90B) Tadaki, T., Maeda, S., Kagaku Kogaku 28, 270 (1964). (91B) Takamatsu, T., Nakanishu, E., ihid., 27, 932 (1963). (92B) Thomas, G. H., Countryman, G. R., Fatt, I., Soc. Pel. Eng. J . 3, 189 (1963). (93B) Tichacek, L. J., A.I.Ch.E. J . 9, 394 (1963). (94B) Turner, J. C. R., Brit. Chem. Eng. 9, 376 (1964). (95B) van Andel, E., Kraniers, H., de Voogd, A,, Chem. Eng. Sci. 19, 77 (1964). (96B) van Shaw, P., Hanratty, T. J., A.I.Ch.E. J . 10, 475 (1964). (97B) van Shaw, P., Reiss, L. P., Hanratty, T. J., A.I.Ch.E. J . 9, 362 (1963). (98B) von Rosenberg, D. U., Durrell, P. L., Spencer, E. H., Brit. Chem. Eng. 7 , 186 (1962). (99B) Watjen, J. W., Hubbard, R . M., A.I.Ch.E. J . 9, 614 (1963). (100B) Welch, N. E., Durbin, L. D., Holland, C. D., ihid., 10, 373 (1964). (101B) Wilburn, N. P., IND. ESG. CHEWFUNDAMEXTALS 3, 189 (1964). (102B) Wooding, R . A., J . Fluid Mech. 15, 527 (1963). (103B) Ihid., 19, 103 (1964).
(25C) Kaldi, P., Blickle, T., Veszpremi i’egyzp. Egyet. Korlemen. 6 (3), 251 (1962) (Pub. 1963). (26C) Kaufman, A,?IND.END.CHEM.FUNDAMENTALS 1, 104 (1962). (27C) Kaye, B. H., Sparrow, D . B., Ind. Chemist40 (4), 200, (51,246 (1964). (28C) Kiser, K. hi.,A.I.Ch.E. J . 9, 386 (1963). (2% Koelbel, H., Langeman, H., Platz, J., Dechemn Monograph 41, KO.642-660, 225-43 (1962). (30C) Kondukov, N. B. Kornilaw A N. Skacbko, I. M., Akhromenkov, A . A,, Kruglov, A. S., Int. C&m. Eng. 4,’43‘(19;4). (31C) Kurosawa, A., Kagaku Kogaku 28, 380 (1964). (32‘2) LaRosa, P., Manning, F. S., Cun. J . Chem. Eng. 42,65 (1964). (33‘2) Lau, W .T. F., Chem. Eng. Sci. 18, 243 (1963). (34C) Le& U., Foraboschi, F. P., Am. Chim. Roma 52, 391 (1962). (35C) Lemlich, R., Manoff, M., A.I.Ch.E. J . 9, 426 (1963). (36C) Levenspiel, O., Can. J . Chem. Eng. 41, 132 (1963). (37C) Levenspiel, O., Bischoff, K . B., Ado. Chem. Eng. 4, 95 (1963). (38C) hladden, A. J., McCoy, B. J., Chem. Eng. Sci. 19, 506 (1964). (39C) hlarr, G. R., Johnson, E. F., A.I.Ch.E.J. 9, 383 (1963). (40‘2) Mayer, F. X., Rippel, G. R., Chem. Eng. Prog. Symp. Ser. 59, 84, No. 46 (1963). (41C) Metcalfe, T. B., Chem. Eng. Prog. 60, 71, Feb. (1964). (42C) hliller, D . R., ihid., 58, 77, April (1962). (43C) hliller, R . L., Frederickson, A. G. Brown. A . H., Tsuchiya, H. hl., IND. ESG. CHEWPROCESS DESIGN DEVELOP. i,134 (1964). (44C) hloore, J. G., Hesler, W. E., Chem. Eng. Prog. 59, No. 2,87 (1963). (45C) Mori, Y., Jimbo, G., Yamazaki, M., Kagaku Kogaku 28, 204 (1964). (46C) Naor,. P... Shinnar., R.., IND.ENG.CHEM.FUNDAMENTALS 2.278 119631. (47C) Ogasawara S. Kihara IM., Nishigama, M., Shirai, T., Morikawa, K., Kagaku Kogaku is, i 9 (1964): (48’2) O’Hern, H . A,, Rush, F. E., IND.ENG.CHEM.FUNDAhiENTALS 2, 267 (1963) (49C) Okita, N., Oyama, Y., KaEnku Koqaku 27,252 (1963). (50C) Orcutt, J. C., Davidson,-J. F., Pigford, R. L., Chem. Eng. Prog. Symp. Ser. 58, 1, No. 38 (1962). (51C) Parker, N. H., Chem. Eng. 71, 165 (June 8, 1964). (52C) Porcelli, J. V., hIarr, G. R., IND.END.CHEM.FUNDAMENTALS 1, 173 (1962). (53’2) Rice, A. W.,Toor, H. L.: Manning, F. S., A.I.Ch.E. J . 10, 225 (1964). (54C) Rosenweig, R . E., ibid., 10, 91 (1964). (55C) Rothfield, L. B., Ralph, J. L., zbid., 9, 852 (1963). (56C) Rowe, P. N., Chem. Eng. Prog. 60, No. 3, 75 (1964). (57C) Ihid., Chem. Eng. Sci. 19, 75 (1964). (58C) Rowe, P. N., Partridge, B. A,, ibid., 18, 511 (1963). (59C) Rowe, P. N., Sutherland, K . S., Trans. Inst. Chem. Eng. (London) 42, T 5 j (1964). (60C) Ruckenstein, E., IND.ENG.CHEkf. FUNDAMENTALS 3, 260 (1964). (61C) Schwartz, L. M., Chem. Eng. Sci. 18, 223 (1963). (62C) Strunk, M . R., hlitrovic, M. V., Bunch, D. W., A.I.Ch.E. J . 10, 418 (1964) (63C) Talmor, E., Benenati, R . F., ibid., 9, 536 (1963). (64C) Turner, J. C. R., Brit.Chem. Eng. 9, 12 (1964). (65C) Vakhrushev, I . A., Erokkin, G. S., Int. Chem. Eng. 3, 333 (1963). (66C) van de Vusse, J. G., Chem. Ing. Tmh, 35, 215 (1963). (67C) Voncken, R. M., Holmes, D . B., den Hartog, H . W., Chem. Eng. Sci. 19, 209 (1964). (68C) White, E. T., Can. J . Chem. Eng. 41, 131 (1963). (69C) Ibid., J . Imp. Coll. Chem. Eng. Soc. 14, 72 (1962). IXD.ENC. CHEM.FUXDAMENTALS 2, 287 (1963). (70C) Wolf, D., Reswick, W., (71C) Yamanato, K., Ito, hl., Naaata, S., Kaeaku Kozakn 27,662 (1963). (72C) Yoshitoshi, O., Ichiro, I . , Yasuhiko, T., Kazumi, S., Refit. Tokyo Inst. Phys. Chem. Res. 39, 183 (1963). I
_
Interphase Mass Transfer
General Mixing Processes i n Flow Systems (1C) Adler R. J., Long, W. M . , Rooze, J., Weinstein, H., Proc. 6th World Pet. Cong. SeLt. VII, paper 19, Frankfurt Main, (1963). (2C) Arima, K., Eguchi, W., Nagata, S., Kognku Kogaku 28, 162 (1964). (3Ca) Baerns, M., Fetting, F., Schiigerl, K., Chem. Ing. Tech. 35, 609 (1963). (3Cb) Behnken, D. W’.,Horowitz, J., Katz, S., IND.ENC. CHEM.FUNDAMENTALS 2, 212 (1963). (4C) Biggs, R. D., A.1.Ch.E. J . 9, 636 (1963). (5’2) Bischoff, K. B., Cun. J . Chem. Eng. 41, 129 (1963). (6C) Bryer, D. TY., Brit. Chem. Eng. 7, 332 (1962). Holland, F. A,, A.I.Ch.E. J . 10, 274 (1964). (7C) Chapman, F. S., Urban, W., (8C) Danckwerts, P. V., Wilson, R . A. M., J.FluidMech. 16, 412 (1963). (9C) de hlaria, F., Longfield, J. E., Chem. Eng. Prog. Symp. Sei. 58, 16, No. 38 (1962). (1OC) Denbigh, K. G., Dombrowski, N., Kisiel, A. J., Place, E. R., Chem. Eng. Scz. 17, 573 (1962). (11C) Engel, A. J., Hougen, 0. A,, A.2.Ch.E. J . 9, 724 (1963). (12C) Fondy, P. L., Bates, R . L., ibid., 9, 338 (1963). (13C) Foraboschi, F. P., Lelli, U., Chim. Ind. (Milan) 43, 1279 (1961). (14C) Gould, R. W. F., Brit. Chem. Eng. 7, 667 (1962). (15C) Gray, J. B., Chem. Eng. Prog. 59, S o . 3, 55 (1963). (16C) Grieves, R . B., Milbury, W-. F., Pipes, W.O., Int. J . Air Water Poll. 8, 199 (1964). (17C) Hanhort, J., Kramers, H., Westerterp, K . R., Chem. Eng. Sci. 18, 503 (1963). (18C) Harada, M., Arima, K., Eguchi, W., Nagata, S., Mem. Fuc. Eng. Kyoto Univ. 24, 431 (1962). (19C) Hayakawa, T., Graham, W., Osberg, G. L., Can. J . Chem. Eng. 42, 99 (1964). (20C) Hedden, K., Chem. I g . Tech. 34, 139 (1962). (21C) Hidy, G. M., Friedlander, S.K., A.I.Ch.E.J. 10,115 (1964). (22C) Hoelscher, H . E., ibid., 9, 569 (1963). (23C) Holmes, D. B., Voncken, R . M., Dekker, J. A,, Chem. Eng. Sci. 19, 191 (1964). (24C) Johnston, A. K., Stewart, D. B., IND. END.CHEM.PROCESS DESIGNDEVELOP. 3, 5 (1964).
68
INDUSTRIAL A N D ENGINEERING CHEMISTRY
(1D) Alwitt, R. S., Kapner, R . S., A.I.Ch.E. J . 10, 417 (1964). (2D) Anderes, G., Chem.-Ingr.-Tech. 34, 597 (1962). (3D) Astarira, G., hlarrucci, G., Gioia, F., Chem. Eng. Sci. 19, 95 (1964). (4D) Bretsznajder, S., Pasiuk, W., Bull. Acad. Polon. Sci., Ser, Sci. Chim. 10, 639 (1962). (5D) Brian, P. L. T . , A.I.Ch.E. J . 10, 5 (1964). (6D) Brock, J. R., J . Chim. Phys. 59, 703 (1962). (7D) Buikov, hl. V., Koll. Zh. 25, 9 (1963). (8D) Calderbank, P. H., Lochiel, A. C., Chem. Eng. Sci. 19, 485 (1964). (9D) Clarke, J. K. A,, IND.ENG.CHEM.FUNDAMENTALS 3,239 (1964). (10D) Cowherd, C., Hoelscher, H. E., ibid., 2, 272 (1964). (1lD) Emanuel, A. S., Olander, D. R., Int. J . Heat Mars Tranrfcr 7, 539 (1964). (12D) Firedlander, S. K., Keller, K. H., Chem. Eng. Sci. 18, 365 (1963). (13D) Gel’perin, N. I., Pebalk, V. L., Zh. Vses. Khim. Obshchestun im. D. I. Mendeleeua 8, 595 (1963). (14D) Gianetto, I. A,, Demalde, P., Chim. 2nd. (Milan) 45, 173 (1961). (15D) Gibbs, R . K., Lazarraga, I,, Himrnelblau, D. M., Brit. Chem. Eng. 8, 538 (1963). (16D) Gokhale, K.R., Indian J . Phys. 37, 450 (1963). (17D) Goodridge, F., Taylor, ht. D., Trans.FnrudaySoc. 59, 2868 (1963). Chem. Eng. Sci. 18, 457 (1963). (18D) Grafton, R. W., (19D) Groden, C. hl., Aylward, G. H., Hayes, J. W.,Australian. J . Chem. 17, 16 (1964). (20D) Hikita, H., Asai, S., Chem. Eng. (Japari) 27, 823 (1963); also Int. Chem. Eng. 4, 332 (1964). (21D) Hobler, T., Int. Chem. Eng. 3, 339 (1963). (22D) Howarth, W.J., Chem. Eng. Sci. 18, 47 (1963). (23D) Ibzd., 19, 33 (1964). (24D) Jeffreys, G. V., Bull,A. F., Tranr.Inrt. Chem. Engrs. 42, T118 (1964). (25D) Jones S J R Smith W. Paper Third Congr. European Fed. Chem. Engrs., LoAddnB55 ?1962), s;e Flel Abstract Current Titles 3, Abst. No. 5915, 1962. (26D) Kitaura, Y., Tanaka, H., Chem. E n g . (Japan) 27, 567 (1963). (27D) Ksenzenko, V. I., Erofeeva, K. A , , Khim. Prom. 1964, 207. (28D) Lebeis, E. H., Glnie Chimique 90, 57 (1963).
(29D) Lightfoot, E. N., A.Z.Ch.E. J . 10, 278 (1964). (30D) Lochiel, A. C., Calderbank, P. H., Chem. Eng.Sci. 19,471 (1964). (31D) Nitsch, W., Naturmissenschaften 50, 300 (1963). (32D) Nunge, R . J., Gill, W. N., A.I.Ch.E. J.9,469 (1963). (33D) Olander, D. R., C h m . Eng. Sci. 19, 275 (1964). (34D) Olander, D. R., Reddy, L. B., Ibid., p. 67. (35D) Pearson, J. R. A,, Appl. Sci. Res. A l l , 321 (1964). (36D) Perrett, R. H., Purnell, J. H., Anal. Chem. 35, 430 (1963). (37D) Popovich, A. T., Jervis, R. E., Trass, O., Chem. Eng. Sci. 19, 357 (1964). (38D) Porter, K. E., Trans. Inst. Chem. Engr. 41, 319 (1964). (39D) Prager, S., Chem. Eng. Sci. 18, 227 (1963). (40D) Prokhorov, V. M., Koll. Zh. 25, 60 (1963). (41D) Rehm, T. R., Moll, A. J.,Babb, A. L., A.2.Ch.E. J . 9,760 (1963). (42D) Richards, G. M., Ratcliff, G . A,, Danckwerts, P. V., Chem. Eng. Sci. 19, 325 (1964). (43D) Ruckenstein, E., Zbid., p. 131. (44D) Schiiltz, G., Int. J . Heat Mass Transfer 6 , 873 (1963). (45D) Sharma, M. M., Danckwerts, P. V., Chem. Eng. Sci. 18,729 (1963). 3, 195 (1964). (46D) Smith, J. G., Dranoff, J. S., IND.END.CHEM.FUNDAMENTALS (47D) Skelland, A. H. P., Wellek, R. M., A.I.Ch.E. J . 10, 491 (1964). (48D) Szekely, J., Chem. Eng. Sci. 19, 51 (1964). (49D) Szekely, J., Int. J . Heat Mass Tramfcr 6 , 417 (1963). (50D) Zbid., p. 1077. (51D) Tadaki, T., Maeda, S., Chem. Eng. (Japan)(English ed.) 1,24 (1963). (52D) Takamatsu, T., Takahashi, T., Nakajima, T., Tanaka, K., 2nt. Chem. Eng. 4, 173 (1964). (53D) Tang, Y. P., Himmelblau, D. M., A.I.Ch.E. J.9,630 (1963). (54D) Valentine, R . S., Heideger, W. J., Can. J.Chem. Eng. 42,43 (1964). (55D) Voipio, A,, Suomen Kemistilehti 35B, 197 (1962) (in English). (56D) Ibid., 36B, 79 (1963); (in English). (57D) Vyrodov, I. P., Russ. J . Phys. Chem. 37, 37; 212 (1963); also Zh. Fiz. Khim. 36, 78 (1963). (58D) Wilburn, N. P., IND.ENC.CHEM.FUNDAUENTALS 3,189 (1964). (59D) Zheleznyak, A. S., Brounshtein, B. I., Zh. Prikl. Khim. 36,2437 (1963). 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J. 10,115 (1964). (16E) Hill, P. G., Witting, H., Demetri, E. P., J . Heat Tranrfer 85C, 303 (1963). (17E) Isachenko, V. P., Tcploencrgetika 9, 81 (1962). (18E) Jamieson, D. T., Nature 201, 583 (1964). (19E) Jepsen, D. W., Somorjai, G. A., J . Chem. Phys. 39, 1665 (1963). (20E) Kobayashi, K., Chem. Eng. (Japan) 29, 826 (1963). (21E) Liboff, R. L., Phys. Rev. 131, 2318 (1963). (22E) Lykov, A. V., Znt. J . Heat Mass Transjer 6 , 559 (1963). (23E) Ibid., Teplo-i Massoperenos, Peruoc Vses. Soveshch., Minsk, 1961 3, 21 (1963). (24E) Modine, A. D., Parrish, E. B., Toor, H . L., A.2.Ch.E. J . 9, 348 (1963). (25E) Motulevich, V. P., Fir. Gdzodinam. Teploobmen i Termodinam. Gar. Vysokikh Temperatur, Akad. Nauk SSSR, Energ. Inst.’ 1962, 171. (26E) Nabavian, K., Bromley, L. A,, Chem. Eng. Sci. 18, 651 (1963). (27E) Palermo, J. A., Grove, C. S., A.2.Ch.E. J . 10, 351 (1964). (28E) Schlunder, E. U., Chem. Z g . Tech. 36, 484 (1964). (29E) Zbid., 2nt. J. Heat Mass Transfer 7, 49 (1964) (30E) Staub, F. W., Flathers, A. E., Chem. Eng. Prog. Symp. Ser. No. 41, 59, 145 (1963). (31E) Takamatsu, T., Hiraoka, M., Tanaka, K., 2nt. J . Heat Mass Transfer 7, 621 (1964). (32E) Thomas, L. J., Westwater, J. W., Chem. Eng. Prog. Symp. Ser. No. 41, 59, 155 (1963). (33E) Turkdogan, E. T., Grieveson, P., Darken, L. S.,J. Phyr. Chem. 67, 647 (1963). (34E) Tewfik, 0 . E., Int. J . Heat Mars Transfer 7, 409 (1964). (35E) Tewfik, 0. E., Yang, J. W., ibid., 6 , 915 (1963). (36E) Wasan, D. T., Wilke, C. R., ibid., 7, 87 (1964). (37E) Wegener, P. P., Pouring, A. A,, Phys. Fluids 7, 352 (1964). (38E) Wieber, P. R., A.I.A.A. J . 1, 2764 (1963). (39E) Wilcox, W. R., Wilke, C. R., A.Z.Ch.E. J . 10, 160 (1964). (40E) Wright, P . G., Proc. Roy. Sac. Edinburgh A66, 65 (1961-1962). (41E) Yang, W. J., Clark, J. A,, J . Heat Transfer 86C, 443 (1964). Interfacial Phenomena (1F) Davies, J. T., Kilner, A. A,, Ratcliff, G.A., Chem. Eng. Sci. 19, 583 (1964). (2F) Ghosh, D. N., Perlmutter, D. D., A.2.Ch.E. J . 9,474 (1963). (3F) Gosse, J., Vigliecca, L., Reo. Inst. Franc. Petrola Ann. Combust. Lipuides. 17, 1328 (1962). (4F) Hovestreijdt, J., Chem. Eng. Sci. 18, 631 (1963). (5F) Jackson, M. L., Holman, K. L., Grove, D. B., A.2.Ch.E. J . 8,659 (1962). (6F) Jeffreys, G. V., Bull, A. F., Trans. Inst. Chem. Engr. 42,T118 (1964).
(7F) Kishinevskii, M. Kh., Kornienko, T. S., Zh. Priki. Khim. 36, 1008 (1963). (8F) Levich, V. G., Kuznetsov, A. M., Dokl. Akad. N o d SSSR 146,145 (1962). (9F) Okazaki, S., Bull. Chem. Sac. Japan 37, 144 (1964). (10F) Ruckenstein, E., Chem. Ens. Sci. 19, 505 (1964). (11F) Ruckenstein, E., Berbente, C., Chem. Eng. Sci. 19, 329 (1964). (12F) Sawistowski, H., Goltz, G. E,, Trans. Instn. Chem. Engrs. 41, 174 (1963); Chem. Ing. Tech. 35, 175 (1963). (13F) Schechter, R. S., Farley, R. W., Can. J . Chem. Eng. 41,103 (1963). (14F) Valentine, R. S., Heideger, W. J., IND.END.CHEM.FUNDAMENTALS 2, 242 (1 963). (15F) Ward, W. J., Quinn, J. A., A.I.Ch.E. J. 10, 155 (1964). Pore Diffusion i n Solids (1G) Ash, R., Barrer, R . H., Pope, C. G., Proc. Roy. Sac. A271, 1, 19 (1963). (2G) Auer, W., Bakemeier, H., Detzer, H., Krabetz, R., Chem. Int. Terh. 36, 774 (1964). (3G) Breton, J., Massignon, D., J . Chim. Phys. 60, 294 (1963). (4G) Butt, J. B., A.2.Ch.E. J . 9, 707 (1963). (5G) Chernenko, A. A., Chizmadzhev, Yu. A,, Dokl. Akad. Nauk SSSR 151, 392 (1963). (6G) Fatt, I., Third Congr. European Fed. Chem. Engrs., London, C63 (1962). (7G) Hering, B., Bliss, H., A.2.Ch.E. J . 9, 495 (1963). (8G) Masamune, S., Smith, J. M., ibid., 10, 246 (1964). (9G) Mason, E. A,, Evans, R. B. 111, Watson, G. M., J . Chcm. Phys. 38, 1808 (1963), cf. C A 57, 9238b. (10G) Massignon, D., J . Chim. Phys., 60, 267 (1963) (in French). (11G) Rao, M. R., Smith, J. M., A.I.Ch.E. J . 9, 485 (1963). (12G) Ibid., 10, 293 (1964). 3, (13G) Rao, M. R., Wakao, N., Smith, J. M., IND.ENC. CHEM.FUNDAMENTALS (1 964). (14G) Robertson, J. L., Smith, J. M., A.Z.Ch.E.J. 9, 342 (1963). (15G) Rothfield, L. B., A.Z.Ch.E. J. 9, 19 (1963). (16G) Verdler, J., Weil, L., Morin, H., J . Chim. Phys. 60, 289 (1963). ENC.CHEM.FUNDAMENTALS 3, 123 (1964). (17G) Wakao, N., Smith, J. M., IND. (18G) Weisz, P. B., Goodwin, R. D., J . Catal. 2 , 397 (1963). Miscellaneous (1H) Avduyevskiy, V. S Obroskova, Ye. I., Izevert. Akad. Nauk SSSR, Mekh. Mashin. No. 5., 3 11962):) . (2H) Beek, W. J., Bakker, C. A. P., Appl.Sci. Res. A12, 139 (1963). (3H) Bennett, C. O., Myers, J. E., “Momentum, Heat, and Mass Transfer,” McGraw-Hill Book Co., New York, N. Y., 1962. (4H) Berkovskii, B. M., 2nt. Chem. Eng. 4, 499 (1964). Jr., Vermeulen, (5H) Davies, J. T. in Aduan. Chem. Eng., Drew, T. B., Hoopes, J. W., T., ed., Academic Press 4, 1-50 (1963). (6H) Davies, J. T., Rideal, E. K., “Interfacial Phenomena,” 2nd ed., Academic Press, 1963. (7H) Delahay, P., Natl. Acad. Sci.-Natl. Res. Council, Publ. No. 942, 183 (1963) (8H) Rangarajan, S. K., Doss, K. S. G., J . Electroanal. Chem. 5 , 114 (1963). (9H) Elder, J. P., Wranglen, G., Electrochem. Tochnol. 2 , 34 (1964). (10H) Field, G. J., Weller, K. R., Watts, H., Rev. Pure Appl. Chem. 13,2 (1963). (11H) Hoogendoorn, J. C., Trans. Inst. Chem. Engrs. (London) 41, 264 (1963). (12H) Ibl, N., Chem.-Zng.-Tech. 35, 353 (1963). (13H) Inger, G. R., Int. J. Heat Mass Transfer 6 , 815 (1963). (14H) Jackson, R., Trans. Inrt. Chem. Engr. 42, CE 107 (1964). (15H) Kafarov V. V “Fundamentals of Mass Transfer. Systems Gas-Liquid, Vapor-LiquiJ, Liqu6-Liquid.” Gos. Izd. “Vysshaya Shkola,” Moscow, 1962. (16H) Khazanova, N. E., Rott, L. A,, Znzh.-Fit. Zh., Akad. Nauk Belorursk. SSR 6 , 123 (1963) (17H) Kintner R C. in Aduan. Chem. Eng., Drew, T. B., Hoopes, J. W., Vermeulen, T., ed., Academic Press 4, 51 (1963). (18H) Kling, G., Feind, K., in “Fortschr. Verfahrenstech.,” Miessner, :H,, ed., Verlug Chcmie, 5, 1-24 (1962). (19H) Knuth, E. L., Int. J . Heat Mass Tranrfer 6 , No. 1, 1083 (1763). (19Ha) Kramers, H., Westerterp, K. R., “Elements of Chemical Reactor Design and Operation,” Academic Press, New York, 1963. (20H) Kulgein, N. G . , Phys. Fluids 6 , 1063 (1963). (21H) Laity, R. W., J . Phys. Chem. 67, 671 (1963). (22H) Lamm, Ole, in Aduan. Chem. Phyr., Prigogine, I., ed., Interscience, New York, 6 , 291 (1964). (23H) Lykov, A. V., Teplo-i Mnssoperenos, Peruoc Vses. Soueshch., Minsk, 1961 3, 9 (1 963). (24H) Oberg, A. G., Jones, S.C., Chem. Eng. 70,No. 15, 119 (1963). (25H) Olney, R. B., Miller, R. S., in “Modern Chemical Engineering,” p. 89, Reinhold, New York, 1963. (26H) Prober, R., Stewart, W. E., Int. J . Heat Mass Transfer 6, 221 (1963). (27H) Rosner,D. E., A.I.A.A. J . 2 , 5 9 3 (1964); alsoseeA.I.Ch.E.J.9,321 (1963). (28H) Rosner,D. E.,Chem. Eng.Sci. 19, l(1964); A.I.Ch.E. J. 9, 321 (1963). (29H) Satterfield, C. N., Sherwood, P. K., “The Role of Diffusion in Catalysis,” Addison-Wesley, Reading, Mass. 1963. (30H) Schuetz, G., Intern. J . Heat Mass Transfer 6 , 873 (1963). (30Ha) Sheppard, C. W., “Basic Principles of the Tracer Method,” Wiley, New York, 1962. (31H) Sherwood, T. K., Natl. Acad. Sci.-Natl. Res. Council, Publ. No. 942, 211 (1963). (32H) Solt, G. S., Wegelin, E., Chapman, C. V. G . , Brit. Chem. Eng. 8, 485 (1963). (33H) Spalding, D . B., “Convective Mass Transfer-An Introduction,” Blackwell, B. H. ed., McGraw-Hill, New York, 1963. (34H) Spalding, D. B., Chi, S. H., Znt. J.Heat Mars Transfer 6 , 363 (1963). (35H) Suponitski, A. M., 2nt. Chcm. Eng. 3,478 (1963). (36H) Tuwiner, S. B., “Diffusion and Membrane Technology,” Reinhold, New York, 1962. (37H) Watanabe, A., J . Elatrochem. Sac. 110, 72 (1963). (38H) Wever, H., Angew. Chem. 75, 309 (1963). (39H) Zuiderweg, F. J., Chem.-Ingr.-Tech. 36, 290 (1964). I
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