NEW DEVELOPMENTS I N MASS TRANSFER D. M . H I M M E L B L A U
rbulent dffusi-
K. B.
BISCHOFF
interphase
mass transfer, and interfacial phenomena is reviewed
and pressure (40.4),i that the relation devel dict the self-diffusivitv for the rare gases was not suited for methane. Transport coefficients appeared quite sensitive to the details of shape of the intermolecular potential. An approximate expression for the self-diffusion coefficient of spherical molecules in liquids (as well as in solids and gases) was reported (9A, 70.4) based on the equation
his review of mass transpor T fundamentals covers the peria November 1960 to March 1963. It contains an extensive but not exhaustive bibliography and reviews mainly those accomplishmentsgenerally indicated by the topical subheadings.
I
-1
Molecular Diffusion
Molecular Basis of Diffusion in Liquids. Although statistical me-
.
chanical analysis of transport properties in liquids is more complicated than most other approaches, it does clarify the physical meaning of parameters which arise and sheds light on simpler theories. Bearman and others (2.4, 3.4)have been developing a unified statistical mechanical theory of transport processes in solutions based on Kirkwood’s work; also, they give a bibliography (2.4). The well-known equations of Eyring, Hartley, and Crank, and Gordon, although superficially unrelated, are all of equivalent validity and may be derived from the equations of statistical mechanics, if solutions are assumed regular (2.4). Bearman’s equations have been found (26A) to predict viscosity, self-diffusion coefficients ( *Z%), and mutual diffusion coefficients (*‘/g%) fairly well but not thermal conductivities (*50%). Another group (49A) have also been active in this area. Using certain moderately restrictive simplifying assumptions, Rice’s equation D = k t / t was tested (28A) where 5 is the frictional resistance to diffusion which can be related to measured macroscopic properties of the system. For 56 liquid-liquid systems, the predicted values at infinite dilution were only slightly poorer than those developed from the Wilke correlation. However, the concentration dependence of the diffusivity, while good for ideal solutions, was not particularly good for nonideal solutions. In measuring the self-diffusivity of rare gases and methane as a function of temperature 50
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
D
W-
=
kT/m
p(s)d(
in which p(s)
is the momentum correlation function. By an extension of Kirkwood’s analysis of diffusion in a dense fluid, the expression for p(s) was simplified (SA) while retaining certain qualitative features. Modest agreement was obtained between the predicted and experimental temperature dependence for the self-diffusion of neopentane. Methods are given (47.4)to calculate the effective diffusion coefficient for material in an inhomogenous media, such as mixed solids, suspensions, or emulsions. The same author (48.4) considered the problem of approximating the diffusion coefficients (and viscosities) of a solute in a suspension of solid particles. Diffusion in Gases. Ternary gas diffusion coefficients are predicted and measured for Krw-HeKr (52A), and HpNpC02 (77.4). An acoustic model of diffusion in gases is reported (29.4). Diffusion of 1, in COInear the critical point is discussed (374. Work on models for diffusivity is extended to dilute polar gas mixtures (364, and moderately good agreement is obtained with the available data. Variation of Diffusivity with Concentration. Of increasing interest are solutions for problems where variation of diffusivity with concentration is taken into account, bec-ause measurements and calculations based on an assumed constant diffusivity can be in substantial error. Because the Schmidt number for gases is usually
in the range of 0.5 < Sc < 3 while that for liquids is 100 < Sc < 1000, the problem of variable parameters must be handled somewhat differently for the two cases. A perturbation scheme is presented (47A) for solving the diffusion equation for systems of high Schmidt number when the density and diffusivity vary exponentially with mass fraction. An approximate integral equation is used to obtain solutions for flow in a laminar boundary layer past arbitrary shapes (23A). Equations are developed for the composition dependence of the ratios of the friction and diffusion coefficients by use of statistical mechanics for binary liquid solutions ( 3 A ) . One-dimensional solutions are given for various boundary conditions and variations of D (ZOA, 24A, 55A). Some graphical and numerical methods are presented (22A) to develop concentration gradients. Ternary Diffusion. Some theoretical and experimental aspects of ternary diffusion have been reported using a Gouy-diffusiometer in the NaCI-KCl-H20 system (76A, 58A) and H20-NazSOd-H&304 system (57A) ; a porous diaphragm cell in hydrocarbon systems (25A); a similar cell in the ideal toluene-chlorobenzenebromobenzene system ( 5 A ) . The relations between the various binary and ternary diffusion coefficients are discussed and evaluated in these articles. New Correlations for Diffusion Coefficients. Two new correlations were proposed for gas diffusion in a binary system at low pressures; one was a semitheoretical equation (6A) and the other a reference substance method (43A). A method is presented (27A) for correlating isothermal diffusion coefficients as a function of molecular weight in dilute liquid systems and also in binary gas systems. An equation is derived (45A) for dependence of the diffusion coefficient on temperature, pressure, and concentration, based solely on molecular volume, latent heat of vaporization, coordination number, and energy of one bond in the liquid. New Experimental Techniques to Measure Diffusion. Several novel experimental methods of measuring diffusion coefficients are reported. A theoretical analysis of G. I . Taylor is used to develop an apparatus similar to a gas chromatographic column without packing to measure gas diffusion coefficients (78A). “Cold” neutron scattering is used to measure diffusion in pure liquids (44A); a good review of the entire subject is available in a British document ( 7 2 4 ) . A simple device for measuring diffusion coefficients in liquefied gases is described ( 7 A ) . T h e Kirkendall effect in gases is discussed (37A), and used to get absolute rather than relative diffusion coefficients (35A). Miscellaneous. Some other interesting work on diffusion briefly noted is : -Behavior of dzyusion coejicients in binary liquids near the critical temperature of the solution (53A) -Use of a generalized form of the Stefan-Maxwell equation to uppoximately predict dzyusion in multicomponent condensed systems (33A) -A reueiw of the dzyusion of small molecules in solidpolyinel r. (75A)
-A signzjicant variation with concentration of the dzfusion coejicient of carbon dioxide gas in water (42A) -A review of the dzyusion of single ions in low concentration through high concentrations of electrolytic solutions (.38A) -A review of the methods of calculating concentrations in dzyusion processes (77A) -D$usion of solutes in slurries and in non-Newtonian &ids (7A)
Thermal and Pressure Diffusion. A general treatment of thermal and pressure diffusion in gas mixtures is presented (32A). T h e temperature dependence of the thermal diffusion coefficient for He, Ne, and Ar and significance in terms of intermolecular potentials are described (57A). Also, other gas mixtures were investigated (27A). Thermal diffusion coefficients for binary gas mixtures are related to the approximate calculations of Chapman and Cowling (50A). T h e connection between thermal diffusion coefficients and the thermodynamic properties of binary mixtures for both low and high pressures are given (30A). Thermal diffusion was studied in binary liquids (39A), and in laminar flow of a liquid in a horizontal duct (544). Analysis and operation of thermal diffusion columns received considerable attention and some pertinent articles appear (4A, 8A, 73A, 79A, 34A, 46A, 56A). T h e theory of irreversible thermodynamics is used to calculate composition of an open system of reacting gases on which a temperature gradient was imposed (74A); in this case mass separation can take place. Turbulent Diffusion and Dispersion
Basic Turbulent Diffusion. This section is not intended to be a comprehensive review of turbulent diffusion. Only those articles of rather direct interest to chemical engineers, taken mostly from chemical engineering journals, have been covered. For more details about the fluid mechanical aspects of turbulent diffusion, “Applied Mechanics Reviews” should be consulted. A detailed theory of turbulent diffusion has been developed (42B). It was found from consideration of the probability distribution of the displacement of a n element from its initial position that the eddy diffusivity is proportional to time for short times and approaches a constant value, lu,, for t >> l / v , ( I = macroscale; u, = r.m.s. turbulent velocity). For diffusion of two elements, the diffusion coefficient for long times was found to be sensitive to the form of the energy spectrum that was assumed. Relationships between Lagrangian and Eulerian statistical properties are considered (35B). Information on turbulent diffusion in empty tubes (5B, 37B, 57B) and a novel experimental method (44B) involving the use of very fine smoke particles for measuring turbulent diffusion properties are presented. T h e effect of solids on turbulent flow in a pipe is considered (3lB). Theoretical estimates of turbulent diffusion in porous media have been developed (45B, 48B), and much information of this type has been summarized in a VOL. 5 5
NO. 1 0
OCTOBER 1 9 6 3
51
-
4
b
Most applications of mathematical models of diffusion and
monograph (478). Use of turbulence theory to predict particle size in stirred tanks is discussed by Shinnar and Church (508). Axial and Radial Dispersion. The concept of axial dispersion in empty tubes with laminar flow as originally developed by Taylor is still under intensive investigation. Experimental work with gases (70B)indicates that the theory might not be valid for this case. Other work with liquids (4B) indicates agreement between theory and experiment. Detailed numerical comparisons between the approximate solution of Taylor and the results of solving the full partial differential equation are discussed (44 2 7 9 . The Taylor model was extended to flow with a pulsating velocity (3B). Several papers give experimental measurements of axial dispersion for turbulent flow in an empty tube (58B,3 3 4 74B). Data for packed beds are given (ZB, 8B, 34B, 52B). A detailed theory concerning axial dispersion in packed beds is discussed (25B). Axial dispersion in two-phase flow in packed beds is a more recent area of interest. Experimental data have been obtained (78B,ZSB). A theory and data for a predictive model are given (23B, 248). The nonsteady state behavior of a packed gas absorber was determined (26B). Axial dispersion has also been recently measured in other types of equipment. A rotating disk column was used (55B, 56B). A novel type of reactor that consists of an empty tube with rotating Screens was proposed (39B). It was found that the rotating screens greatly decreased the amount of axial dispersion and backmixing. An extensive set of calculations for a step input to a system with axial dispersion is given (7219). Experimental data for radial dispersion in a packed bed at low flow rates of gases are given (43B). The use of radial dispersion to calculate more accurate mass transfer coefficients between solid and fluid streams is discussed (77B). Reviews of the status of axial and radial dispersion are presented ( Z B , 28B). A generalization and comparison of the various dispersion models that have been proposed are given (7B). Applications. Most applications of the various diffusion and dispersion models to date have been to chemical reactors. A general review of chemical reactions with diffusion is available (47B),and effect of using simplified (208) and proper (68) boundary conditions is discussed for chemical reactors with axial dispersion. General perturbation solutions for small amounts of axial dispersion were determined (2QB). A new model for reaction flow systems which consists of a series of interconnected stirred tanks has been proposed (77B) as an alternate to the usual diffusion equation. It was felt that this type of model would have computational advantages. 52
INDUSTRIAL AND ENGINEERING C H E M I S T R Y
Solutions of the equation for axial dispersion with chemical reaction are given (7B)for optimum yields. The combined effects of mass and heat dispersion with reaction are discussed (76B),and considerable difficulty was experienced with the numerical solution. However, a different numerical procedure for a similar problem was used apparently without difficulty (73B). Solutions for wall reaction with radial dispersion are given (QB, 49B). General dispersion effects are considered (408). The mathematics of reaction in a laminar flow system have been rather extensively developed (75B, 32B, 46B, 53B, 5 4 4 57B). Some special applications to polymerization reactions are considered (27B). Experimental data on a baffled reactor (308) and for reaction between a turbulently flowing fluid and a dissolving solid (36B)are presented. A complex set of reactions in a fluidized bed is discussed (79B),and general computational procedures for combined heat and mass dispersion in packed beds are given (388). The effects of axial dispersion on the mass transfer in a pulsed extraction column were studied (SOB).
-
General Mixing Processes in Flow Systems
Distribution of Residence Times. The use of chisquared distributions to represent experimental residence time distribution data for certain types of mixing systems is discussed (7C). The use of moments of the diseibution of residence time curve for fitting mathematical models has often been used. The usual practice is to use the first two moments to find the model parameters and then use the higher moments to differentiate between models. It has been shown ( 4 K ) that the higher moments of many of the commonly used models are quite similar so that differentiation between them might not be possible. The relationship between lifetime distribution and age distribution is derived (77C). An analog computer to automatically calculate the moments from experimental residence time data was invented (74C). An interesting and potentially useful extension of the residence time concept is discussed (32C) in which a describing variable other than time was used. The event space distribution function of this variable was then developed for certain systems. Another extension is considered ( 4 0 in which the inlet stream was allowed to have an age distribution.
D . M . Himmelblau is an Associate Professor and K . B. B i s c w is an Assistant Professor in the Departmmt of
AUTHORS
C h u a l Engineering, T h University of Texas, Austin 12, Tex.
,
dispersion to date have been to chemical reactors Determinations of the distribution of residence times for various systems are presented: a falling film (7C); fluidized bed solids (72C) and gas (73C); a series of stirred tanks (47C); flotation cells (15C); and trickle beds (33C). The relationships in solid-fluid chemical reactors are considered (28C, 42C, 43C). Mathematical Models and Experimental Data. Some general characteristics of mathematical models consisting of interconnected flow regions are given (79C). A summary of some of the models that have been previously used was published (8C). Various types of models are proposed for representing real stirred tanks (7OC, 35C, 47C). A probe for measuring concentration fluctuations in flow systems was constructed (76C) and then later used in a stirred tank (23C). The mean concentration was found to be essentially constant throughout the vessel. Flow patterns in stirred vessels are presented (26C). An experimental technique in which the particle size of a dispersion would be used to characterize agitation is proposed (36C). The description of mixing in two-phase flow in stirred tanks has begun to receive some quantitative attention. The rate of coalescence of droplets has been measured (ZZC) . A comprehensive theoretical development to consider the effect of coalescence and redispersion of drops on processes occurring in a stirred tank is presented (6C). Experimental measurements based on this model were then performed (27C). A novel method of mixing with an electrostatic field was described (5C), and a model was developed and tested experimentally for mixing in a jet stirred reactor ( 2 C ) . The characterization of mixing in a fluidized bed is still in progress. Various models have been developed and then tested with experimental data (77C, 21C, 25C, 39C). Various aspects of macroscopic and microscopic mixing have been measured (3C, 29C, 30C, 34C). Applications. Again, most of the applications have been to chemical reactors. General discussions of the use of flow models in predicting the operation of chemical reactors are given (78C, 37C, 38C), and a comparison between the dispersion and tanks in series models as applied to chemical reactions is reported (2OC). The direct use of distribution of residence time information for reactors is presented for fluidized solid regeneration (37C) and heterogeneous gas-solid noncatalytic reactions in a fluidized bed (46C). The effect of contacting on catalytic reactions in fluidized beds was studied (9C, 24C). The effect of mixing and nonideal flow patterns on the operation of heat exchangers is discussed (45C, 44C) * Interphase Mass Transfer
Models for Interphase Mass Transport. A new
model called the “random eddy” model for mass transfer from a turbulent fluid to an interface is described ( 1 9 0 ) , and several different types of surface renewal models were developed (330). A theoretical and experimental study of multicomponent mass transfcr between a liquid film and a turbulent gas phase was carried out ( 4 3 0 ) . A simplified model for the hydrodynamics of a stirred vessel was set up (370),and the resulting velocity distributions were used to predict the ratio of the mass transfer coefficient divided by the kinematic viscosity; the results were 35 to 50y0low but the technique of modeling has promise. A mixing model is described for transport near a boundary ( 2 8 0 ) . Ability of the Danckwerts, Higbie, and Delta models for gas absorption to predict carbon dioxide absorption with chemical reaction in packed columns is compared (7.20). The predicted values based on transient laboratory data from a wetted wall column (340) are within about f10% of the experimental values. Interphase Mass Transfer From Drops and Bubbles. Effect of a number of easily measurable parameters on mass transfer from single rising bubbles was investigated (250). Absorption of small spherical bubbles in water was used to determine the diffusion coefficients of some difficult (very slightly soluble) to measure gases (220). Eight characteristic dimensionless parameters were isolated (240)for isothermal bubble growth in a Newtonian fluid from the general equations of change. Other related work on single bubbles appeared ( 7 0 , 5 0 ) . The interesting case of mass transfer between a growing or contracting drop, or bubble, for both steady and unsteady state conditions was analyzed (6D), and some approximate relations for the diffusional flux were developed. Effects of surface active agents on interphase mass transfer from drops are reviewed (380), and some current conflicts in transport models are examined. From correlations for falling drops in water it was concluded (410) that the high mass transfer coefficient could not be explained by internal circulation or surface tension effects. They suggested instead that the effect was due to interfacial agitation (caused by hydrodynamic turbulence) in the rear of the drop. Mass transfer accompanied by a rapid chemical reaction in a drop was analyzed ( 7 6 0 ) . The effect of oscillation on mass transfer in liquid drops was described ( 9 0 ) . Simultaneous Mass Transfer and Chemical Reaction. The nonlinear differential equations which arise from simultaneous absorption and reaction of two gases in a liquid were solved numerically (200, 350). Investigations of absorption of a single gas plus chemical reaction in a liquid which are primarily experimental in nature are shown in Table I. (Continued on next page) ‘401. 5 5
NO. 1 0
C I C T ~ R F R l o r ( ?
=?
!I
,
i
Manv4 svstems with both absorption and reaction have been studied 4 TABLE I
'w __
-
Tmnrfcr
&=Pma
Lipid
GUS
co2
Aq. NaOH, NarCOa NasSOd
Wetted wall col. Packed col.
450
c o x
750
co,
Stirred veacl Wetted wall col.
740
"8
ID
COI
Aq. NaOH, ",OH Aq. monoethanolamine Water, aq. HAC, water Water, MeOH, aq. NaOH
20
GO*
Aq. monoethanolamine
Jet
400
Clr
Aq. NaOH, HISOI Water
Jet Wetted wall col.
Aq, NaOH Aq. HISO,
GI. of spherca
1.20, 341
cos
Clr
H atoms Watmpltu rcamgw.
b
Single aphcre
lnkdacial Phenomena
C m f h w bubbling.
Table I1 summarizes articles on absorption of a single gas plus chemical reaction in a liquid which are primarily mathematical and/or theoretical in nature. TABLE I
Sm U Type of &&ion ~U 320 AfB=C S* 260 lrrcv., 1st order 30 U Irrev., 1st order 780 U Imv., 1st order Ref.
40
U
440
S,U
460
S
Zero ardcr Zero order, 1st order lrrcv., 1st order
230
*
370 360
S
U
Tjpe of Aflm&s
i m A
-
Quigwnt fluid
N
Agitated tank
A
String of balls
A A
Film and well mixed fluid Plug flow Quiescent fluid
A A A
Irrev., 1st order
Turbulent boundary layer Film penetration
Infinitely rapid Irrev., 2nd order
Padred column Quiescent fluid
A A A
-
a Prnrdosrmdy r f o f i . b Far liquid-liquid or gar-liptd trawfo. S= s t d y rfotr; V = unrfrody rtotc; N = n u m c a l rolculotion; A =
rmolyticol solution.
Effect of concentration on the standard interphase mass transfer coefficient for CO2 absorption and desorption in water is small ( 7 7 0 ) . The standard assumption that equilibrium exists at the interface in gas absorption (without reaction) was verified (730). Mass transfer with rapid, homogeneous, irreversible reactions was studied for dilute turbulent and nonturbulent systems (420). Vaporization, Condensation, and Sublimation. Various solutions are compared ( 2 7 0 ) for heat and mass 54
Interfacial Phenomena. Since the Sternling and Scriven article on surface driven flows, other experimental work has been reported, including some excellent photographs of polygonal cells and other phenomena (72.5) ; the related Mnard cells (those generated by thermal convection) and how well the experimental observations fit the simplified Sternling theory are discussed. Effects of diffusion on the growth of interfacial instability of argon-bromine mixtures falling into helium was examined @E). A theoretical development and some experimental results are presented ( 7 9 for the development of instability in an interface for two mutually immiscible liquids with solute diffusing across the interface. Other authors (5E, 7 E ) considered the effect of surface active agents on the velocity of rise of drops and bubbles. Problems of coalescence and phase separation are interpreted in terms of surface phenomena (8.5, IOE, 74E). Equations for the unsteady state vaporization from a liquid drop covered by an insoluble liquid film were derived (3E). Schl'm e n photographs were used (16.5) to study convection currents generated by evaporative cooling in a water tank. Concepts of interfacial turbulence as developed by the Russians are reviewed @E), and effects of surface phenomena on transport processes are reviewed (75E). Articles discussing "interfacial resistance" appeared for eas-liauid stirred vessels (6.5). liauid-liauid stirred .~ vessels (77E),liquid-liquid jets (73E), and interfacial films and with surface active agents in liquid-liquid stirred vessels (2E).
I pO'aryphy
0,
-
Disk col.
transfer in vaporization from porous materials. The accommodation coefficient for evaporation into a vacuum was measured (270) as a = 0.05 for glycol. For sublimation from several organic solids, a ranged from 1.00 to 0.15 (390). Both pairs of investigators took careful account of the temperature of the surface. Numerical calculations on the nucleation of drops consisting of the order of 100 or so molecules were carried out (700) for the classical liquid-drop theory. Thermodynamics and kinetics of vapor condensation are described (290)for media with complete absence of foreign materials, including walls.
INDUSTRIAL AND ENGINEERING CNEMISTRY
0
1
~
I ,
I
Olhw Recent Work
Mass Transfer in Boundary Layer Flow. A number of new similarity integrals for temperature, concentration, and vortex fields both for compressible and incompressible flow are presented (SF). Evans and Spaulding have written a detailed series of papers delineating the velocity equation for laminar boundary layer flow'when mass transfer takes place in either direction through the boundary. References to the entire series of articles and related material are available
( 7 F ) . A review of mass transfer cooling, including transpiration cooling, film boiling, and ablation is given ( 7 7F). Methods of irrei-ersible thermodynairics are applied to the vaporization of a liquid accompanied by heat transfer (76F). Boundary layer diffusion (and heat transfer) with high transfer rates over planes and wedges are reported (29F). Other articles of interest are (7F, ?OF,28F). Simultaneous Mass a n d Heat Transfer. Experiments with macroscopic and local combined heat and mass transport from spheres in turbulent air streams indicate that the macroscopic Nusselt number is greater than for mass transfer alone (32F). The analogy between steady-state heat and mass transfer in a laminar fluid was used (3F) to estimate the average Nusselt number for particles of arbitrary shape from a knowledge of the Nusselt number at Pe = 0. Thermal decomposition of calcium carbonate for spherical and cylindrical particles by a quasi-steady state treatment was predicted with good results (27F). A theoretical analysis of mass and heat transfer plus chemical reaction at the front of a blunt body is available (2OF), and a theoretical treatment of transient mass and heat transfer for unsteady-state energy or diffusion from a rotating disk in a revolving fluid is given (22F). Mass and heat transfer in fixed and fluidized beds is reviewed ( 7 2 F ) . General Books and Reviews. Reviews on mass transfer appear (73F, 74F, 3OF), and a large annotated bibliography on gas-liquid and liquid-liquid interfaces is available (27F). A bibliography of the 320 papers presented at the 1961 Minsk Conference on Heat and Mass Transfer was prepared ( 9 F ) . Books by Tyrrell (37F) and portions of the translations of the books by Lykov and Mikhaylov (17F) and Levich (7527) will be of definite interest. Miscellaneous. “Nonequilibrium thermodynamics” was used to treat macroscopic combinations of mas?, momentum, and energy flow (SF, 6F). Spalding (26F) used H-x diagrams to show how predictions of mass transfer rates from an interface at which chemical equilibrium did not prevail require only small changes in the standard calculational procedures. A complex system of chemical reactions can be uncoupled for intraparticle diffusion and reaction in a porous catalyst (33F). Fluctuations in mass transfer rates to small electrodes in the viscous sublayer was studied in order to investigate flow disturbances near the wall (241;). Additional work of interest is -A siudy of rippling and its efect on gas absoiption (ZF) -Extraction of nitric acid by TBP-n-hexane solvent in a stirred reactor (23F) -Mass transfer from .solid spheres to air (25F) -Liquid mass transfer from apacked bed of spheres (33F) --Liquid mass transpr from cast solids in an agitated cessel (78F) -Several papers concernzng coeficients for the transport of mass, momentum, and energy (7QF) -Mechanism OJ gas phase mass tranfer in grid packing of various shapes (4F)
B I BLl OG RAPHY Molecular Diffusion (IA) Bagrov, M. M., Ukr. Fiz. Zhur. 6 , 486 (1961). (2A) Bearman, R. J., J . Phys. Chem. 6 5 , 1961 (1961). (3A) Bcarman, R. J., J . Chem. Phys. 32,1308 (1960). (4A) Brock, J. R., Chem. Eng. Sci. 13, 207 (1961). (SA) Burchard, J. K., Toor, H. L., J . Phys. Chem. 66, 2015 (1962). (6A) Chen, N. H., Othmer, D. F., J . Chem. Eng. Data 7, 37 (1962). (7A) Clough, S. B., Read, H. E., Metzner, A. B., Behn, V. C., A..I.Ch.E. J . 8, 346 (1962). (8.4) Crownover, C. F., Powrrs, J. E., A.1.Ch.E. J . 8, 166 (1962). (9A) Douglass, D. C., J . Chem. Phys. 35, 81 (1961). (10A) Douglass, D. C., McCall, D. W., Anderson, E. W., J . Chem. Phys. 34, 152 (1961). (11A) Duncan, J. B., Toor, H. L., A.1.Ch.E. J . 8, 38 (1962). (12A) Egelstaff, P. A., “Neutron Scattering Studies of Liquid Diffusion,” Atomic Enrrgy Research Establishment, Doc. AERE-R4043, May 1962. (13A) Frazier, David, 2nd. Eng. Chem. Proc. Design Deuelop. 1, 237 (1962). (14A) Frie, W., Maecker, H., Z. Physik 162, 69 (1961). (15A) Fujita, Hiroshi, Fortschr. Hochpolymer-Forsch 3, 1 (1961). (16A) Fujita, Hiroshi, Gosting, L. J., J . Phys. Chem. 64, 1256 (1960). (17A) Galvez, E. M., Zon 21, 568 (1961). (18A) Giddings, J. C., Seager, S. L., J . Chem. Phys. 33, 1579 (1960) ; 2nd. Eng. Chem. Fundamentals 1,277 (1962). (19A) Grasselli, Robert, Frazier, David, 2nd. Eng. Chem. Proc. Design Deralop. 1, 241 (1962). (20A) Greenfield, Harvey, J . SOC.Indust. A$@. Math. 10, 424 (1962). (21A) Grew, K. E., Mundy, J.N., Phys. Fluids 4, 1325 (1961). (22A) Hall, R. C., Can. J . Chem. Eng. 38, 154 (1960). (23A) Hanna, 0. T., J. P. L. Tech. Rept. 32-204, Dec. 28, 1961. (24A) Heaslet, M. A., Alksne, Alberta, J . SOC.Indust. Appl. Math. 9, 584 (1961). (25A) Holmes, J. T., Olander, D. R., Wilke, C. R., A.1.Ch.E. J. 8, 646 (1962). (26A) Horrocks, J. K., McLaughlin, E., Trans. Faraday Soc. 58. 1357 (1962). (27A) Ibrahim, S. H., Kuloor, N. R., Brit. Chem. Eng. 6 , 862 (1961); 5 , 795 (1960). (28A) Kamal, M. R., Canjar, L. N., A.2.Ch.E. J . 8, 329 (1962). (29A) Kotin, Leonard, Mol. Phys. 4, 401 (1961). (30A) Kotousov, L. S., Zhur. Tekhn. Fiz. 31, 89 (1962). (31A) Krichevskii, I. R., Kazanova, N. E., Lifshits, L. R., Inzh.-Fiz. Zhur., Akad. Nauk Belorussk S.S.R. 3, 117 (1960). (32A) Laran.jeira, M. F., Physica 26, 409 (1960). (33A) Lightfoot, E. N., Cussler, E. L.,’Rettig, R . L., A.1.Ch.E. J . 8, 708 (1962). (34A) .L,yko;, A. V., Zikharev, E. A., Inzh.-Fiz. Zhur. 12, 22 (1961). (35A) Mason, E. A., Phys. Fluids 4, 1504 (1961). (36A) Mason, E. A., Monchick, L., J . Chem. Phys. 36, 2746 (1962). (37A) Miller, L., Carman, P. C., Trans. Faraday SOC.57, 2143 (1961). (38A) Mills, R., Rev. Pure A#@. Chem. 11, 78 (1961). (39A) Mizushina, T., Ryuzo, I., 2nd. Eng. Chem. Fundament& 2 , 102 (1963). (40A) Naghizadeh, Jamshid, Rice, S. A., J . Chem. Phys. 36, 2710 (1962). (41A) Olander, D. R., Znt. J . Heat Mass Transfer 5 , 765 (1962). (42A) Onda, K., Chem. Eng. (Japan) 24, 918 (1960). (43A) Othmer, D. F., Chen, D. T., 2nd. Eng. Chem. Fundawentnls 1, 249 (1962). (44A) Palevsky, H., in “Inelastic Scattering of Neutrons by Solids and Liquids,” p. 265, I.A.E.A., Vienna, 1962. (45A) Ponomarev, V. V., Alekseeva, T. A., Zhur. Fiz. Khim. 35, 800 (1961). (46A) Powers, J. E., IND.ENG.CHEM.53, 577 (1961). (47A) Prager, Stephen, J . Chem. Phys. 33, 122 (1960). (48A) Prager, Stephen, Physica 29, 129 (1963). (49A) Rice, S. A., J . Chem. Phys. 33, 1376 (1960). (50A) Saxena, S. C . , Dave, S. M., Rev. Mod. Phys. 33, 148 (1961). (51A) Saxena, S. C., Kelley, J. G., Watson, W. W., Phys. Fluids 4, 1216 (1961). (Continued on next page) VOL. 5 5
NO. 1 0 O C T O B E R 1 9 6 3
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(52A) Srivastava, B. N., Paul, R., Physzca 28, 646 (1962). (53A) Sundelof, L. O., Arkiu fb’r Kemi 15, 317 (1960). (54A) Turner, J. C. R., Chem. Eng. Sci. 17, 95 (1962). (55A) Tsang, T., J . Applied Phys. 32, 1518 (1961). (564) Vichare, G. G., Powers, J. E., A.Z.Ch.E. J . 7, 650 (1961). (57A) Wendt, R. P., J . Phys. Chem. 66, 1279 (1962). (58.4) Woolf, L. A., Miller, D. G., Costing, L. J., J . Am. Chem. Soc. 84, 317 (1962). Turbulent Diffusion a n d Dispersion (1B) Adler, J., Vortmyer, D., Chem. Eng. Sci. 18, 99 (1963). (2B) Ampilogov, I. E., Stoyanovskii, I. M.! Zh. Fiz.Khim. 36,1552 (1962). (3B) Aris, R., Proc. Roy. SOC.A259, 370 (1960). (4B) Bailey, H. R., Gogarty, W .B., Zbid., A269, 352 (1962). (5B) Baldwin, L. V., Walsh, T. J., A.I.Ch.E. J . 7 , 53 (1961). (6B) Bischoff, K. B., Chem. Eng. Sci. 16, 131 (1961). (7B) Bischoff. K. B., Levenspiel, O., Ibid., 17, 245, 257 (1962). (8B) Blackwell, R. J., Rayne, J . R., Terry, TV. M., J . Petrol. Technol. 11, 1 (1959). (9B) Boettger, G., Fetting, F., Chem. Ing. Tech. 34, 834 (1962). (1OB) Bornia, A., Coull, J., Houghton; G., Proc. Roy. Soc. A261, 227 (1961). (11B) Bradshaw, R. D., Bennett, C. O., A.I.Ch.E. J . 7, 48 (1961). (12B) Brenner, H., Chem. Eng. Sci. 17, 229 (1962). (13B) Carberry, J. J., IYendel, M. M., A.1.Ch.E. J . 9, 129 (1963). (14B) Carter, D., Bir, W.G., Chem. Eng. Progr. 58, 40 (1962). (15B) CambrC, P., Appl. Sci.Res. A9, 157 (1960). (16B) Coste, J., Rudd, D., Amundson, N. R., Can. J . Chem. Eng. 39, 149 (1961). (17B) Deans, H. A,, Lapidus, L., A.I.Ch.E. J . 6, 656 (1960). (18B) de Maria, F., White, R. R . , Zbid., p. 473. (19B) de Maria, F., Longfield, J. E., Butler, G., IND.EWG.CHEM. 53, 259 (1961). (20B) Fan: L. T., Ahn, Y. K., Ind. Eng. Chem. Proc. Design Decelop. 1, 190 (1962). (21B) Farrell, M. A., Leonard, E. F., A.I.Ch.E. J . 9, 190 (1963). (22B) Froment, G. F., Belg. Chem. Ind. 24, 619 (1959). (23B) Glaser, M. B., Litt, M., A.I.Ch.E. J . 9, 103 (1963). (24B) Glaser, M. B., Lichtenstein, I., Zbid., p. 30. (25B) Gottschlich? C. F., Ibid., p. 88. (26B) Gray, R. I., Prodos, J. W., Ibid., p. 211. Nagata, S., Chem. Eng. (Japan) (27B) Harada, M., Eguchi: W.. 26, 583 (1962). (28B) Hofmann, H.: Chem. En?. Sci. 14, 193 (1961). (29B) Houghton, G., Can. J . Chem. Eng. 40,188 (1962). (30B) Hovorka, R. B., Kendall, H . B., Chem. Eng. Progr. 5 6 , 58 (1960). (31B) Kada, H., Hanratty, T. J., A.I.Ch.E. J . 6, 624 (1960). (32B) Krongelb, S., Strandberg, M. W. P., J . Chem. Phys. 31, 1196 (1959). (33B) Lee, J. C., Chem. Eng. Sci. 12, 191 (1960). Geankoplis, C . .J., A.I.Ch.E. J . 6 , 591 (1960). (34B) Liles, A. I\’,, (35s) Lumley, J . L.; Appl. Sci. Res. A10, 153 (1961). (36B) Meyerink, E. S. C.: Friedlander: S. K.. Chem. Eng. Sci.17, 105 (1962). (37B) Miller, E., Wohl, K., A.1.Ch.E. J.8, 127 (1962). (38B) Nagata, S.: Hashimoto, K., Taniyama, 1.; Nishida, H . Chem. E q . ( J n p a n ) , 26, 569 (1962). (39B) Pa\vlowski: J., Chem. Ing. Tech. 34, 628 (1962). (40B) Zbid., p. 684. (41B) Prager, S., Chem. Eng. Progr. Symposium Ser. No. 25. 55, 11 (1959). (42B) Roberts, P. H., J . FluidMech. 11, 257 (1960). (43B) Roemer, G., Dranoff, J. S.:Smith, J. M., Ind. Enp. Chem. Fundamentals 1, 284 (1962). (44B) Rosenweig, R. E., Hottel. H. C., Williams: G. C., Chem. Eng. Sci. 15, 111 (1961). (45s) Saffman, P. G., J . FluidMech. 7, 195 (1960). (46B) Schechter, R. S., Wissler, E. H., Appl. Sci. Res. A9, 334 (1960). (47B) Scheidegger, A. E., “Physics of Flow Through Porous Media,” Macmillan, New York, 1960. (488) Scheidegger, A. E., Can. J . Phys. 39, 1573 (1961). (49B) Schmidt, H. J., Chem. Ing. Tech. 34, 841 (1962). (50B) Shinnar, R., and Church, J. M., IND.ENG.CHEM.52, 253 (1960) ; Smoot, L. D., Babb, A. L., Ind. Eng. Chem. Fundamentals 1, 93 (1962). (51B) Sparks, R. E., Hoelscher, H . E., A.I.Ch.E. J . 8, 103 (1962). 56
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
(52B) Stoyanovskii. I. M., J . A@l. Chem. (USSR) 34, 1863 (1961). (53B) Vignes, J. P., Trambouze, P. J.. Chem. Eng. Sci. 17, 73 (1962). (j4B) Walker, R. E., Phys. Fluids 4, 1211 (1961). (55B) Westerterp, K. R., Landsman. P., Chem. Eng. Sei. 17, 363 (1962). (56B) Westerterp, K . R., Meyberg, W. H . . Ibid., p. 373. (57B) M’issler, E. H., Schechter, R. S.,Appl. Sei. Res. A10, 198 (1961). (.58B) Yablonskii, V. S., Asaturyan. A. Sh., Khizgilov, I. Kh,, Intern. Chem. Eng. 2 , 3 (1962). General Mixinq Processes in Flow Systems (1C) Asbjdrnson, 0. A , , Chem. Eng. Sci. 14, 211 (1961). (2CI Bartok. W., Heath. C. E., Weiss, M. A.? A4,1,Clz.E. J . 6, 685 (1960). (3C) Cairns: E. J., Prausnitz, J. M., Ibid.. p. 554. ( 4 0 Cha. L. C., Fan. L. T., Can. J . Chem. Eng. 41, 62 (1963). (5C) Cropper, W. P., Seelig, H . S.. Ind. Eng. Chem. Fundamentals 1 , 48 (1962). (6C) Curl, R . L., A.2.Ch.E. J . 9, 175 (1963). ( 7 C ) de Baun, R. M., Katz, S., Chem. En?. Sci. 17, 97 (1961). (8C) Eguchi, W.,“Preprints 25th .4nniversary Congr.,” The Society of Chemical Engineers, Japan. p. 296, Gordon and Breech, Neiv York. 1961. (9CI Gomezplata, A , Shuster, IV. W.. A.I.Ch.E. J . 6, 454 (1960). (10C) Gutoff, E. B.; Ibid.. p. 347. (11C) Hanratty,T. J.. Chpm. Enq. Sci. 17, 57 (1961). (12C) Hull, R . L., von Rosenberg, A. E., IND.ENG.CHEm 52, 989 (1960). (13C) Huntley. A. R.? Glass, W., Heigl, J . J., Ibid., 53, 381 (1961). (14C) Hyman, R., Corson. LIT. E., Ind. En?. Chem. Proc. Design Decelop. 1, 92 (1961). (15C) Jowett, A , , Brit. Chem. En?. 6 , 254 (April 1961). (16C) Lamb, D. E., Manning, F. S., T.Vilhelm. R. H.: .4.I.Ch.E. J . 6, 682 (1960). (17C) Lanneau. K. P.. Trans. Inst. Ch. E q r . (London) 38, 125 (1960). (18C) Levenspiel, 0.: “Chemical Rcaction Engineering,” J . Wiley, New York. 1962. (19C) Levenspiel. 0.:Can. J . Chem. Eny. 40, 135 (1962). (20CI Levenspiel, O., Chem. Enq. Sci.17, 576 (1962). (21C) Lewis, W. K., Gilliland. E. R.. Glass. W., A.I.Ch.E. J . 5 , 419 (1959). 122C) Madden. A. J.. Damerell. G. L.. Ibid.. 8. 233 (1962). (23C) Mannini, F. S:, Wilhelm; R. H.; Ibid.; 9; 12 (1963). (24C) Massimilla, L., Johnstone, H. F.: Chem. Eng. Sei. 16, 105 (1961). (ZjC) May, W. G., Chem. Eng. Progr. 55, 49 (Decembrr 1959’1. (26C) Metzner. A. B., Taylor, .I. S., A.2.Ch.E. J . 6, 109 (1960). (27C) Miller, R. S., Ralph, J. L., Curl, R . L., Towell, G. D., Ibid., 9, 196 (1963). (28C) Moudr?, F., VanFEek, V., Coll. Czech. Chem. Comm. 27, 2477 (1962). (29CI Muchi, I.: Mamuro, T., Sasaki, K . , Chem. Enr. (Japan) 25, 747 (1961). (30C) Muchi: I., Mukaie, S., Kamo, S., Okamoto, M.. Ibid., p. 764. (31C) Petersen, E. E.: A.I.Ch.E. J . 6,488 (1960). (32C) Rudd, D. F., Can. J . Chem. En~g.40, 197 (1962). (33c1) Schiesser: W. E., Lapidus, L., A.Z.Ch.E. J . 7, 163 (1961). (34C) Schugerl, K., Merz, M., Fetting. F.. Chrm. Eng. Sci. 15, 1 (1961). (3SC) Sinclair, G. G., A.I.Ch.E. J . 7 , 709 (1961). (36C) Sullivan, D. M., Lindsey, E. E.. Ind. Eng. Chem. Fundamtntals l, 87 (1962). ( 3 7 C ) Trambouze, P. J., Rev. inst. franz.pCtrole 15, 1948 (1960). (38C) Trambouze, P. J., Genie Chimique 84, 189 (1960). (39C) Van Deemter: J. J., Chem. Eric. Sci.13, 143 (1961). (40C) Zbid., p. 190. (41C) Van De Vusse, J. G., Chem. Eng. Sci.17, 507 (1962). (42C) VanEEek, V., Coll. Czech. Chem. Comm. 2 5 , 2395 (1960). (43C) Van;Eek, V., Mondr?, F., NimeEek, J., Coll. Czech. Chem. Comm. 27, 1081 (1962). (44C) Vincent, G. C., Hougen, J. O., Dreifke, G. E., Chem. Eng. Progr. 57, 48, July (1961). (45C) Watson, E. L.: McIGllop, A. A , , Dunkley, \f’. L.: Perry. R. L., IWD.ENG.CHEW52,733 (1960).
(46C) Yagi, S., Kunii, D., Chem. Eng. Sci. 16, 364 (1961). (47C) Zelmer, R. G., Chem. Eng. Progr. 58, 37 (1962).
P
..
Interphase Mass Transfer (1D) Astarita, Giovanni, Ric. Sci. Rend., Ser. A 1, 177 (1961). (2D) Astarita, Giovanni, Chem. Eng. Sci. 16, 202 (1961). (3D) Astarita, Giovanni, Beek, W. J., Chem. Eng. Sci. 17, 665 (1962). (4D) Astarita, Giovanni, Marrucci, Guiseppe, Znd. Eng. Chem. Fundamentals 2, 4 (1963). (5D) Baird, M. H . I., Davidson, J. F., Chem. Eng. Sci. 17, 87 (1962). (6D) Beek, W. J., Kramers, H., Zbid., 16, 909 (1962). (7D) Bowman, C. W., Johnson, A. I., Can. J . Chem. Eng. 40, 139 (1962). (8D) Brian, R. L. T., Vivian, J. E., Habib, A. G., A.Z.Ch.E. J. 8 , 205 (1962). (9D) Constan, G. L., Calvert, Seymour, Zbid., 9, 109 (1963). (10D) Courtney, W. G., J . Chem. Phys. 36, 2009, 2018 (1962). (11D) Czapski, Gideon, Jortner, Joshua, Stein, Gabriel, J. Phys. Chem. 65, 956, 960 (1961). (12D) Danckwerts, P V., Kennedy, A. M., Roberts, D., Chem. Eng. Sei. 18, 63 (1963). (13D) Delaney, L. J., Eagleton, L. C., A.Z.Ch.E. J . 8, 418 (1962). (14D) Dhillonn, S. S., Perry, R. H., Zbid., p. 389. (15D) Emmert, R. E., Pigford, R. L., Zbid., p. 171. (16D) Fujinawa, K., Nakaike, Y . , Chem. Eng. (Japan) 25, 274 (1961). (17D) Gibbs, R. K., Himmelblau, D. M., Znd. Eng. Chem. Fundamentals 2, 55 (1963). (18D) Gill, \Y. N., Nunge, R . J.. Chem. Eng. Sci. 17, 683 (1962). (19D) Harriott, Peter, Zbid., p. 149. (20D) Hatch, T. F., Pigford, R . L., Znd. Eng. Chem. Fundamentals 1, 209 (1962). (21D) Heideger, W. J., Boudart, M., Chem. Eng. Sci. 17, 1 (1962). (22D) Houghton, G., Ritchie, P. D., Thomson, J. A., Chem. Eng. Sci. 17, 221 (1962). (23D) Huang, C. J., Kuo, C. H., A.I.Ch.E. J . 9, 161 (1963). (24D) Langlois, W. E., J . Fluid Mech. 15, 111 (1963). (25D) Leonard, J. H , Houghton, G., Chem. Eng. Sci. 18, 133 (1963). (26D) Lightfoot, E. N., A.I.Ch.E. J . 8, 710 (1962). (27D) Lykov, A. V., Int. Chem Eng. 3, 195 (1963) ; Inth.-Fiz. Zhur. No. 10, 12 (1962). (28D) Marchello, J . M., Toor, H. L., Znd. Eng. Chem. Fundamentals 2, 8 (1963). (29D) McDonald, J. E., Am. J . Phys. 30, 870 (1962); 31, 31 (1963). (30D) Novella, E. C., Sala, A. L., Simo, J. B., Anales Real Soc. Espan. Fis. Quim, Ser. B 5 8 , 277 (1962). (31D) Olander, D. R., Chem. Eng. Sci. 18, 123 (1963). (32D) Onda, K., Sanda, E., Takeuchi, H., Chem. Eng. (Japan) 26, 984 (1962). (33D) Perlmutter, D. D . , Chem. Eng. Sci.16, 287 (1961). (34D) Roberts, D., Danckwerts, P. V.: Zbid., 17, 961 (1962). (35D) Roper, G. H., Hatch, T. F., Pigford, R. L., Ind Eng. Chem. Fundamentals 1, 144 (1962). (36D) Scriven, L. E., A.I.Ch.E. J . 7 , 524 (1961). (37D) Secor, R. M., Southworth, R. W., Zbid., p. 705. (38D) Schechter, R. S., Farley, R. W., Brit. Chem. Eng. 8, 37 (1963). (39D) Sherwood, T . K , Johannes, Conrad, A.ZCh.E. J . 8, 590 (1962). (40D) Spalding, C. W., Zbid., p. 685. (41D) Thorsen, G., Terjesen, S . G., Chem. Eng. Sci. 17, 137 (1962). (42D) Toor, H. L., A.I.Ch.E. J . €470 (1962). (43D) Toor, H. L., Sebulsky, R. T., Zbid., 7 , 558 (1961). (44D) Van der Vusse, J. G., Chem. Eng. Sci. 16, 21 (1961). (45D) Vassilatos, G., Trass, O., Johnson, A. I , Can. J . Chem. Eng. 40, 210 (1962). (46D) Vieth, W. R., Porter, J. H., Sherwood, T. K., Znd. Eng. Chem. Fundamentals 2, 1 (1963). (47D) Yagi, S., Inoue, H., Chem. Eng. Sci. 17, 411 (1962). Interfacial Phenomena (1E) Aranow, R. H., Witten, I.., Phys. Fluids 6, 535 (1963). (2E) Davies, J. T., Mayers, G. I
