ANNUAL REVIEW
Mass Transfer Special interest tables, with brief descriptions of the nature and scope of the work covered
gas pairs, the following improved correlatibn had the lowest error:
in the literature during the past year, highlight the revieze, his review covers the period immediately following that covered by the last annual review [IND.ENG. CHEM.57, 54 (1965)] and is in essentially the same format to provide continuity. Although the review is relatively complete for chemical engineering interests, it is by no means exhaustive. A few selected papers are discussed, but the bulk of the review consists of special interest tables with brief descriptions of the nature and scope of the reported work.
T
MOLECULAR DIFFUSION The volume of published literature on molecular diffusion in the gas phase has decreased somewhat in the last year, whereas the literature dealing with diffusion in the liquid phase has increased. Of significance, mainly by its absence, is the lack of any new contributions concerning prediction and calculation of liquid diffusivities from molecular models. Fuller, Schettler, and Giddings (77A) compared nine methods of estimating gaseous diffusion coefficients : Those of Gilliland ; Andrussow ; Hirschfelder, Bird, and Spotz; Wilke and Lee; Chen and Othmer (2 equations) ; Slattery and Bird; Arnold; and Fuller, Schettler, and Giddings. O n the basis of 340 diffusivities of binary 32
INDUSTRIAL A N D ENGINEERING CHEMISTRY
where T = K., M = molecular weight in gramlmoles, = pressure in atmosphere, and V , are special diffusion volumes reported in the article. Another comparison of methods of estimating gaseous diffusivities was given by Saxena and Saxena (55‘4). The determination of diffusion coefficients in the liquid phase by detection of concentration gradients or the concentration field itself is well known. The methods of Rayleigh, Gouy, and Lamm all rely on the formation of interference fringes. A new interferometer has been described (67A) with an appreciably greater sensitivity to changes in refractib e index than previous instruments. Concentrations as low a s 0.0170 of electrolyte are now feasible. Board and Spalding (5A) point out in regard to another experimental technique, namely diaphragm cells, how an unmeasured amount of transport originating from a pressure gradient can be superimposed on top of a supposedly diffusion process. The pressure gradient originates from the unequal transfer in the cell. A special cell which more closel>-’ represented the diffusion process model was designed, tested on dimethyl acetamide-water, and found to yield improved results. Duda and Vrentas (72A) developed a method of calculating the ( N - 1)2 independent diffusion coefficients from the appropriate number of Xi-component “free-
p
D. M. HIMMELBLAU K. B. BISCHOFF
diffusion” experiments-i.e., experiments in which one dimensional diffusion takes place from a n initially sharp boundary between two solutions of different concentrations. The key to economic experimentation is to choose the terminal compositions in one experiment so that the diffusion path intersects the diffusion paths of as many of the other experiments as possible. Pictures of liquid thermal diffusion processes have been taken by Norberg (45A) using a Rayleigh type interferometer. The device permits a n examination of the entire range of concentration in the cell. The nature and prevention of the convective disruption of thermal diffusion are discussed and evaluated. Other recent work on molecular diffusion is listed in Tables A-1 to A-5. Turbulent Diffusion and Dispersion
T .
Fundamental Studies. Basic descriptions of the dynamics of multiphase flow systems were provided by So0 (7ZB). Houghton (37B) investigated theoretically particle and fluid dispersion in homogeneous (nonaggregative) fluidization using the methods of turbulent diffusion. Quantitative aspects of liquid jets in vessels were studied by McNaughton and Sinclair (57B). A very comprehensive set of calculations for the classical problem of laminar dispersion in a round capillary were performed by Ananthakrishnan, Gill, and Barduhn (7B) where the limits for applicability of the Taylor-Aris and pure convection limiting cases were delineated. Lighthill (46B) has provided a theory for the case between the above two limits, which completes the picture in this type of system. Patterson and Gloyna (5233) have given extensive results for open channel dispersion in rivers. Axial and Radial Dispersion. A very comprehensive statistical study of the structure of packed beds was made by Debbas and Rumpf (20B). Among other things,
they found that definite bed nonuniformities are caused by certain modes of packing. Le Goff and Prost (27B) have begun the construction of relatively simple mathematical models to represent porous media structure. Whitaker (82B) has discussed the proper types of geometrically averaged flow variables to use and Stewart (75B) has indicated how far one can progress in the analytical prediction of transport phenomena for very slow flows in porous media. Evans and Kenney (22B) studied gas dispersion at low Reynolds numbers and found that the dispersion coefficient is not strictly linear in the velocity as is usually assumed, and this may be the cause for the van Deemter equation not always being satisfied in gas chromatography applications. Another complication occurs for small ratios of tube-to-particle diameter, and Sternberg and Poulson (74B) have presented data for this case. I n the important area of two-phase flow in packed beds, Sater and Levenspiel (69B) have given data for both gas and liquid axial dispersion along with tentative correlations. Jameson (35B) has devised a cell model for trickle beds. Bibaud and Treybal (5B) and Miyauchi, Mitsutake, and Harase (53B) have measured and correlated longitudinal dispersion in rotating impeller extraction towers. Longitudinal mixing of liquid in bubble reactors was determined by Argo and Cova (3B) and then used to predict suspended catalyst distribution by Cova (76B). Chemical Reactor Applications. A further extension of his method for uncoupling complex reactions with diffusion was given by Toor (78B). The prediction of conversion for second-order reactions in well defined turbulent flow fields was accomplished by Vassilatos and Toor (87B). Van Cauwenberghe (72B) discussed boundary conditions and Crider and Foss (78B) presented detailed computations for transient chemical VOL. 5 8
NO. 1 2
DECEMBER 1 9 6 6
33
reactions with axial dispersion. Detailed calculations for nonisothermal complex reactions with axial dispersion were given by Marek and HlavAcCk (48B), and Pawlowski (59B) developed a general treatment for chemical reactions with dispersion. Other Applications. A detailed study of axial dispersion effects on adsorption in fixed beds was given by Chao and Hoelscher (73B), and Cooney and Lightfoot (75B) presented efficient calculation methods for the “asymptotic” transport region. Dunckhorst and Houghton (27B) considered axial dispersion effects on chromatography.
TABLE A-I. Systelr or
General Mixing Processes in Flow Systems
Age Distribution Functions. Bell and Rabb (7C) and Klinkenberg (26C) have discussed how to determine moments of the residence time distribution of the cell model with backflow. Klinkenberg also showed how the calculations can be made much simpler by reversing the order of some of the mathematical manipulations. Bischoff and McCracken (8C) provided calculations from an idealized model and also arialysis of experimental data to test the actual usefulness of several of the proposed methods for interpreting tracer tests in flow systems. Goldish, Koutsky, and Adler (79C) demon-
GASEOUS DIFFUSION
1
Tobic
Optical measurement of Hz-Kr; Ar-Kr; He-Ar, air, SFc, Kr Isothermal isobaric coefficients for Hz-COz, Hz-Ar, HeCOz, He-Ar Diffusion of Hz-Ar, K r , Dn-Kr; Tz-Kz; in a temperature field Self-diffusivity correlation Mulricomponent isothermal isobaric diffusion coefficient matrix Use of binary thermal conductivity to predict diffusivity Diffusion near the critical point Self-diffusion in capillaries Modification of Fair and Lerner correlation
I
1
T Or Ea
i
~~
E
Ref. (76A)
( 3 2)~ E
(4ZA)
~
TABLE A-3. L I Q U I D DIFFUSION (Primarily Theoretical Studies and Reviews) Topis
a T = theoretical study, E = experimental investigation.
TABLE A-2. L I Q U I D DIFFUSION (Primarily Experimental Data and Methods) S)stem
Technique a
Temp.,
-
C.
I
Correlation of diffusivities of metals in Hg Correlation for predicting concenrration dependence of binary diffusivities when one component is associated by H-bonding Variation of diffusiviry with concenrration i n binary Time-dependent solutions to low-order BBGKY model for dense fluids Theory of the “ time-lag” method of measuring diffusivities Effect of bulk flow caused by diffusion in transient diffusion with variable diffusivity Relation between activation energy for self-diffusion and the melting temperature Iterative least square method for Gouy interferometer data Numerical solution of diffusion equation in infinite media
(4711) ( 744 1
(774)
Ref.
~~~
n-Octane and 1-heptanol in homomorphic liquids Cyclohexane-benzene Acetone-benzene-CClr CCla-cyclohexane Chloroacetic acid-HzO Acetone in CsHs, BuAc, toluene, kerosine; four acids in H 2 0 PrOH-toluene Kr-MeCO, CHCla HOAc-Hz0 HC1-Hz0 KC1 in H 2 0 , hleOI1 MeOH-H20 CH4, CZH6, C3Hs, CaHx in Hz0 N a + in M e O H , E t O H , P r O H solutions in H z 0 H20-KC1-NaC1; test Onsager relations HzO-KC1-sucrose Hz, CHa i n KC1, hlgclz, hlgSOa solutions HzO-mannitol-NaCI HsPOr-Ca (HzP04)-HzO Glycerol-HzO COS, NzO-HzO HzO through n-hexadecane, squalene HzO in aqueous solutions KNO8, LiZSO Self-diffusion of H s 0 in alkaline chlorides Self-diffusion of CsHs-cyclohexane, others Self-diffusion of AcOMe, AcOEt, E t O H , hexane Self-diffusion i n liquid ethane NaI i n P r O H . iso-PrOH. BuOH. ethylene glycol COz, 0 2 in hemoglobin
dc
10, 25, 55
dc i dc
25 25, 35
dc dc Ney
cc
30 25 10-40 25 25 25 25 25-43
dc
25
dc, i
25 25
C C
dc
i 1
dc 1j
cc
25-65 25 25 25 18-75 25-45 10-45 25
dc
25
cc
15-45
S
Lamm. draw
34
E
(69.4) (374) (2281
T = theoretical studv, E = experimental investigation.
TABLE A-5. 155-298’ K. 25
c = conductometric, cc = capillary cell, dc = diaphra~tncell or porousjt, Rayleigh interferometer, ij = Inminarjet,s = spin echo method. a
CsHs-MeOH system a t 25’ C. Cyclohexane-n-heptane and others a t 3 5 O C. CC14 in CsHs a t 25’ C. Validity of theory in thermal diffusion columns for iso-
MISCELLANEOUS
Topic
i
=
GGUYor
INDUSTRIAL AND ENGINEERING CHEMISTRY
Measurement of diffusion in gases or liquids by elution curve from tube Diffusion in solids (a review) Determination of molecular size parameters Model for diffusion in glassy polymer
Ref.
(16.4) ~
(6.4) (63A ) (77A)
strated a novel flash photolysis method to introduce a tracer into a flow system without any disturbances. Curl and McMillan ( 7 0 2 ) discussed the accuracy in residence time distribution methods required to obtain meaningful values of mean residence time. Their analysis seems to resolve the differences in results reported by other investigators of trickle bed reactors. General Population Balances. The development of more general population balances, which include age distributions, has recently been very active. The basic treatments of Hulburt and Katz and of Randolph were reported in last year’s review; several diverse applications will now be discussed. Shain (46C) extended the treatment of Curl for coalescence and reaction in dispersed-phase perfectly macro-mixed chemical reactors. A complementary study of breakage in similar systems (without reactions) was by Valentas, Bilous, and Amundson (57C). Matz (35C) and Beckmann and Matis (6C)discussed crystal size and polymer length distributions and effects of the residence time distribution. Reid (43C)showed how population balances could give a quantitative description of batch grinding.
Age Distribution Function Applications. The effects of age distributions on the selectivity of complex reactions were discussed in a general way by Wei (58C)and for a recycle model by Gillespie and Carberry (77C). These calculations begin to show how this very important problem can be treated. Kuchler and Troltenier (29C) and Tadmor and Biesenberger (52C) have presented similar results for the specific case of polymer molecular weight distributions. Silveston (47C) has shown how certain theorems of Laplace transform theory can aid in the calculation of conversions in segregated flow. Mixing in Stirred Tanks. Aiba, Suzuki, and Kitai
(IC)have given results of mixing time studies witk nonNewtonian fluids, a n important and somewhat neglected area. Wolf and Manning (62C) measured flow patterns, and Sykes (50C) reported particle circulation times. A detailed experimental and theoretical study of turbulence levels in stirred tanks was performed by Cutter (77C). Mixing in Fluidized Beds. Echigoya et al. (73C) presented results of the application of tracer test information to the prediction of chemical reaction behavior. Two types of tracer were used: nonadsorbable and adsorbable. Since the reactants are adsorbed, it would seem that the latter type of tracer results should be used for reaction calculations, and the authors indeed report that the best predictions were made in this way. Thus, until methods for combining adsorbtion and reaction kinetics information with tracer data are formulated, care should be used in applying the usual inert tracer studies to reactor design. A comprehensive study of gas mixing in fluidized beds with screen packing was provided by Winter, Schugerl, Fetting, and Schiemann (60C,67C). Kang and Osberg (24C) investigated longitudinal particle mixing in a similar system. Both studies indicated that the screens can greatly modify the mixing behavior. The funda-
mental mechanisms of solids mixing were described by Rowe et al. (442)in terms of bubble motion.
INTERPHASE MASS TRANSFER The enhancement of interphase mass transfer by waves in falling films has been a popular topic in the past year. I n early studies of interphase mass transfer with the aid of vertical wetted wall columns, the penetration model did not represent the process too well in longer columns because of ripples a t the interface. I n turn, rippling itself and the velocity profiles in falling films have been subjected to intensive study. Attempts to make analytical predictions of interphase mass transfer across rippling layers have been carried out by Whitaker and Jones (660)and Ruckenstein and Berbente (520). The former made a classical perturbation analysis of the Orr-Sommerfeld equation for selected cases while special attention was paid to the effect of a n insoluble monolayer at the interface. The latter introduce the theoretical velocity :profile of Kapitza into the mass balance with poor results, although a n empirical adjustment of the velocity profile gives better results. Other investigators have made experimental measurements on the rate of transfer of gases in wavy falling films (220, 320) and horizontal layers (330). Huang and Kuo (200) extended their work on mathematical models for mass transfer accompanied by chemical reaction from first-order reactions to more complex reactions. I t was found that the predicted effects of the chemical reaction are quite sensitive to the mechanism postulated, except in cases in which the diffusivities of the reactant and product are nearly equal. Diffusion with reversible reaction, the film theory, surface renewal theory, and the film-penetration theory are compared, and for mass transfer with a first-order reversible reaction it was concluded that the film-penetration model was the most general. Barnett, Humphrey, and Litt ( 4 0 ) studied the absorption of COz bubbles in non-Newtonian aqueous solutions of sodium carboxymethylcellulose. Bubble shape transitions, from ellipsoidal to spherical, were shown to play an important role in the total interphase mass transfer; these transitions became more significant as the liquid became more non-Newtonian in character. Correlations were also presented for drag coefficients. Tables D-1 through D-4 list other work in the area of interphase mass transfer.
SIMULTANEOUS H E A T A N D MASS TRANSFER Some of the most difficult mass transfer problems to treat mathematically are those of phase change in which the phase boundary moves. These processes are known as moving-boundary or free-boundary problems. Griffin and Coughanowr ( 7 7E) presented two analytical methods for solving such problems in general: (a) Riemann-Volterra integration, useful for quiescent phases, which leads to nonlinear integro-differential equations VOL. 5 8
NO. 1 2 DECEMBER 1 9 6 6
35
(b) the method of “intermediate integrals,’’ a method for solving problems involving convection normal to the moving boundary, which yields a differential equation for M hich a solution is difficult to obtain They conclude that probably the most efficient method of solving a moving-boundary problem involving convection is to use numerical methods at the beginning. They give several references to such methods. Each of the three techniques is demonstrated by application to evaporation from a flat surface. Buevich ( 6 E ) examined the specific problem of a heterogeneous reaction at a spherical surface with a moving interface and obtained analytical solutions for first- and secondorder reactions. A numerical method for the calculation of the temperature field outside a freezing front on a n isothermal cylinder was given by Tien and Churchill
(27E). Methods of predicting mass and heat transfer under large concentration and temperature gradients were investigated both theoretically and empirically by Ranz and Dickson (21E) for a completely turbulent boundary layer on a flat plate. Approximate solution of the bound-
TABLE
B-1.
BASIC TURBULENT D I SP E RS IO N Subject
_
INTERFACIAL PHENOMENA Jeffreys and Lawson ( Q F ) studied the effect of mass transfer into and out of drops on the rate of coalescence of single drops at a plane interphase. A progressive decrease in drop stability was observed as the transfer rate from drops increased, whereas a progressive increase in stability was observed as the transfer rate into drops increased. The analysis of stability at a n interface between two immiscible liquids has been extended by Smith ( 7 Z F ) . Some of the anomalies in the model with convective instability engendered by gradients of surface tension
AND TABLE B-5.
TQ
E07
_
Turbulent diffusion in empty tube Eddy diffusion in air-water wetted wall column Particle trajectory in vertical oscillating fluids Brownian enhanced diffusion through dispersoids Turbulent pipe flow of solids in air Mixing in turbulent jets Laminar dispersion of non-Newtonian fluid in round capillaries Time variable axial dispersion a
DIFFUSION
ary layer equations formed the basis of the correlation of data. Tables are given of theoretical correction factors to be applied to the dimensionless mass (and heat) transfer coefficients for various cases of Sc and Pr. The empirical results seemed to agree well with the predictions, and simplified rules are suggested for engineering purposes. Other work, including phase transitions, is shown in Tables E-1 and E-2.
_
~
E T
Probability model for continuous chromatography Gas absorption with dispersion Dispersion, mass transfer, and stability o f miscible displacement fronts Nonmiscible disulacement
T E,T
~
E, T
I
T
1
’
Subject
EST
~
OTHER APPLICATIONS
Ref.
TABLE C-1.
E, T
Eo7T
Ref.
~
T ~
( 708) (YB, 245, 6 2 8 )
E, T
T
(148)
T
(4QBl
AGE D I S T R I B U T I O N FUNCTIONS
E = experimental znuestigation, T = theoreticoi study.
TABLE B-2.
DISPERSION I N POROUS M E D I A
Subject
I
Variation of local void fraction Liquid axial dispersion Effective heat transfer properties Radial dispersion in countercurrent flow 4xial dispersion in trickle bed Flow dirtribution
!
E07T
E E E,T E E
Ref. (778) (42B, 5ZB, 65B) (178, 7 1 8 ) (2B (645
~
I
R T D of gas in bubble column Collision model for dispersed phase in liquid-liquid packed bed R T D measurement from chemically reacting tracer R T D of solid particlee in’flow system Resolving R T D with hybrid computer Comparison of cell and dispersion models for packed bed R T D in multistage system?
E, T E, T
(27C) (28C)
T T T
~
i
(37C) (36C) (37C) (QOC) (56C)
T
1
T
a E = exprimental inuertiEation, T = lheoretical study.
TABLE C-2.
AGE D I S T R I B U T I O N FUNCTION APPLICAT IONS E or T
Subject
1
Ref.
Backflow cell model with first-order reaction Recycle model for reactor calculations Dynamic rcsponse equations for combined models with first-order reaction Effect of mixing on photochemical reactors Extraction with back-mixing
Subject Turbulent wake of cylinder with turbulent diffusion Inlet region Various calculation methods and results with dispersion Laminar flow with diffusion Laminar flow pyrolysis reaction with diffusion Laminar flow of non-Newtonian fluid with diffusion External flow fields
36
-1 I
:YTT
T
I
T
~
T
TI
Ref. (688 1
(8B) (255, 395, 4?5,44B, 558, 575, 6 0 B ) ( 6 5 , 7 5 , 32B, 33B) (79B) (548) (635)
INDUSTRIAL A N D ENGINEERING CHEMISTRY
TABLE C-3.
M I X I N G I N STIRRED TANKS
Subject Gas residence timc distribution in gas-liquid system Dynamic studies with first-order reaction Flow patterns Mixing with Two-stage agitator Mixina with uaddles
1_____ EorT 1
Ref. (15C)
E. T
(54C) (55C)
are discussed, and the role of small gravity waves was described. The dynamic equations for both phases are taken into account. Other articles are listed in Table F.
PORE DIFFUSION IN SOLIDS
Y,
A computational model for predicting the properties of catalyst pellets based on a convergent-divergent pore array was given by Foster and Butt (72G). Satterfield and Saraf (39G) found some extremely interesting results by measuring the pore diffusion through successive layers of a catalyst pellet. The effective diffusivity varied quite strongly at different locations, which casts doubt on the accuracy of applications assuming constant values. With highly absorbable molecules, especially in very small pores, the problem of surface diffusion arises. This is a diffusion mechanism in addition to the fluid phase and is not entirely clear as yet. Weaver and Metzner (48G) have developed a theory to begin explanation of it. Extensive results for micropore diffusion in glass were given by Hwang and Kammermeyer
TABLE C-4.
G-1. The problem of predicting existence of multiple steady states for nonisothermal reactions in porous catalysts is made difficult by the fact that the mathematical model is of the distributed parameter type for which little background exists. Wei (50G) and Gavalas (74G) have recently shown how some aspects can be calculated without too much complication. Shen and Smith (43G) considered the case of pore diffusion with a gas-solid reaction occurring. Bischoff (3G) showed that transverse gradients across the capillary can be safely neglected for most types of catalyst. As in all areas of reactor design, consideration of the behavior of complex reaction systems is increasingly important and Butt (5G) has given a n extensive treatment with the additional complexity of nonisothermal conditions. A large number of other cases have been recently discussed as shown in Table G-2. Some other applications with pore diffusion are given in Table G-3.
M I X I N G I N FLUIDIZED BEDS
I
Subject
Eor T
1
Ref.
E E, T
Gas mixing in fluidized bed with sieve plates Axial dispersion of spheres fluidized with liquid Mixing in nonhomogeneous fluidization Solids mixing Lateral solids mixing
TABLE C-5.
(20G). There is currently great interest in diffusion through polymeric films and the use of membranes for desalination. Some references are given in Table
(760 (250 (45C (ZC, 23C, 38C, 3QC) (34C)
T E, T E
OTHER M I X I N G APPLICATIONS
1
Subject Statistical treatment of solid mixing Mixing of powders Solid mixing in rotating cylinder Dielectrophoretic process for liquid-liquid mixing Mixing in spray heat exchanger Mixing of highly viscous liquids Computer simulation of sedimentation in the ultracentrifuge
E or T E, T
E
E, T E E E, T
E, T
1
Ref. (22C) (4C, 47'2)
(74C, 4%) (27C) (33C) (57C) (9C) Phases
Ref.
COz into H z 0 H a 0 into Hz, N2, 0 2 ; NHa from NHaOH Cln into N a O H 0 2 into NaHSOa HzS and COz in OH- solution COz i n O H - solutions SOa, NzOa in HzO, HzSOa AcOH to CHCla-H20 1% in O H -
(260)
Transfer Equrpment
TABLE D - I .
GENERAL INTERPHASE TRANSFER Mediaa
Apparatus and Process Review and comparison of 1 2 theories of interphase mass transfer Absorption of Oz into the blood Effect of concentration level in NHa absorption by turbulent water Prediction of packed column absorption coefficients from laboratory data on stirred tanks (for COz) Models for transfer across a free interface in stirred vessel Effect of direction or mass transfer on liquid mixing Enhancement of mass transfer by pulsation and ultrasonic waves Dissolution of HBz into non-Newtonian liquid Dissolution from cylinders in laminar flow Dissolution from inside of pipe in turbulent
Rotating d r u m Wetted wall column Sieve tray Wetted wall column Tank Wake in flow uast cylinder
G-L G-L G-L G-L
E
L-L, G-L
E
1 1
a
tion.
G = g a s , L = liquid, S = solid.
b
(390) (56D) (380) (30) (580) (QD)
(540) (530)
(270, 2 9 0 )
(730)
G-L, S-L
TABLE D-3. SIMULTANEOUS INTERPHASE TRANSFER AND CHEMICAL REACTION (Mathematical Analyses)
s-L
Tvbe of Reaction
s-L s-L
flow
Controlled leaching from salt cavities Transfer in channels with porous walls Transfer of HBz and acetanilide into HzO Examination of renewal models for turbulent process near boundary Relation between renewal models and instability theory in fluidized bed
Stirred tank Liquid jet
s-L s-L s-L
T = theoretical study, E = experimental invesliga-
-~
Heterogeneous First order at wall First order, irreversible Zero order "Newton's law of cooling" It wall -. -~. First order First order, second order
1"Ua"'l
Process
S S S
Laminar flow in packing Laminar flow in tube Diffusion to plane electrode Boundary layer, laminar and turbulent Laminar flow in annulus
S
S
1 1 U
U
Laminarflow Prediction of gas absorption
a S = steady state, U = unsteady state. calculation.
VOL. 5 8
lANobll
1
A A
Ref.
(400)
(450)
A = analytical solution, N = numerical
NO. 1 2
DECEMBER 1 9 6 6
37
TABLE D-4. MASS TRANSFER FROM AND T O DROPS, BUBBLES, AND SMALL PARTICLES
'
,
System
Othcr 1 1 Phase $1
D B
o; Sa'iL or
-I
TABLE F.
Rel.
INTERFACIAL PHENOMENA
~
Unstead>-state mathematical analysis at low R e D L Extraction of HOAc from aqueous solutions by L EtOAc Modification of Handlos and Baron turbulence i mode! D I L Extraction from spherical drops, organic-€120 D L Extraction from falling and ricing drops in propionic acid-HzO-CCla D L iMathematical analysis for single drop at low R D L D Mathematical analysis for oscillating drop L D Water drops to 2-ethylbutyric acid (in mixer) L Mathematical analysis of absorption and reacn tion in large drops G D Oscillating drops in vertical air stream G D G Evaporation of water drops D G Mathematical analysis for small drop hlathrmatical analysis of absorption during B L bubbling aeration S HBz to water, naphthalene to air L, G S G Evaporation from porous sphere S L Single particles and packed beds in rising flow S I, Mathematical analysis of leaching Marhematical analvsis of mass transfer from a sinele sDhere S. B L, G
Topic
I D
1
Ref.
Potential barrier for liquid-liquid interfacial transfer and appropriate boundary conditions Laminar jet to detect interfacial resistance Suppression of water evaporation by surface films Moire pattern study of tranrfer across a liquid-liquid interface Schlieren photographs of interfacial turbulence Effects of surface films in damping eddies at a free surface Maraneoni inrtabilitv in drops
TABLE G-1.
( 7 7.77) (73F)
~
'
1
( Z F , 8F 7OF) (4P) ( 7 F , 5F) (3F, 7 F ) (6F)
PORE DIFFUSION
Subject
1
(240, 2 8 0 )
Capillary-orifice model Measurement of effectire pore diffusion by gas chromarograph Values of diffusivity Surface diffusion Binary liquid flow in micropores Pore diffusion in glass membranes Diffusion through films and membranes
~~~
*D
=
L
drop, B = buhble. S = solid particle.
=
liqmd, G = gar.
E = expeiimenial investigation, T = theoretical study.
TABLE E - I . PHASE TRANSITIONS (Vaporization, Condensation, Sublimation, Freezing, and Melting) T
To+ Frost formation on vertical flat plate at -310' F. Formation of ice crystals from supersaturated \cater vapor Optical method used to dctect film between condensing drop and surface Sratistical mechanical contributions to free energy of formation of nucleus Effect of absorbed particles on accommodation coefficients Nucleation of drops from supersaturated vapor Sublimation of naphthalene from rorating cone Melting, vaporization with material immediately removed Evaporation of drops in terms of molecular parameters Surface evaporation from leading edge in laminar boundary layer Interferometer study of free convection from p-dichlorobenzene Evaporation coefficients of solids Evaporation of CCla at stagnation point on cylinder Effect of surface evaporation of crystal on diffusion (Br2 in KBr) Schlienen optical methods to study liquid evaporation Review of heat conduction and diffusion with phase change 1157 refs.)
TABLE
G-2.
PORE DIFFUSION EFFECTS ON CH E M I CAL REACTIONS
E'
"i
E T
T, E T
T
E F T T
T
Sublrct
Eor T
Large pellets Annular pellcts Consideration of all resistances Thermal effectiveness factor Miscellaneous reactions Selectivity Catalysr fouling Adsorption kinetics Particle geometry effect with adsorption kinetics h-onisothermal Iionisothermal with volume change
E E, T T T
Ref.
E,'r T T T T T T
E
E E
TABLE G-3.
APPLICATIONS W I T H PORE DIFFUSION
Subject
E E
Pore diffusion in ion exchange resins Drying of porous solid? Porous electrodes
TABLE H - I .
Eo7 T
Ref.
E, T
( S G , SG, 32G) (77G, 37G, 38G)
MASS TRANSFER I N BOUNDARY LAYER FLOW Proms
~ Vertical blowing of gas onto liquid surface , Flow between rotating parallel diaks Gas flow part blunt object Use of nonstationary heat and mass sources Parallel and countercurrent air-water flow Application of irreversible thermodynamics to gas-suspension flowGas flow in tube with reaction
'
_
E T, E
S
T
S U S
S
T T T
I
_ L, T L, T
_
1 1
(76E) (75E) (ZE, 5E)
U
Boundary layer on moving flat surface with suction, in_ ~ jection H e a t and mass tranrfer in compressible gas over porous plate Free and forced convection a t verrical plate Non-Newtonian fluid on flat plate As mptotic expansion solutions for heat and mass tranrJer Diffusion and reaction at solid surface Displacement effect with mass transfer Combustion on porous surfaces-a review
A
(2211, 2 J " )
A = analytical solution, A' = numerical solution, E = exjertmentnlsludy.
I
MISCELLANEOUS Articles of interest dealing with mass transfer in boundary layer flow-are listed in Table H-1. Various books and reviews related to the field of mass transfer are given in Table H-2. Table H-3 lists miscellaneous articles. 38
INDUSTRIAL A N D ENGINEERING CHEMISTRY
K . B. Bischof is Associate Professor and D.M . Himmelblau is Professor of Chemical Engineering, University of Texas. They haaeprepared INEC's annual reoiew of M a s s Transfer since 7962. AUTHORS
1
REFERENCES
(41A) Marcinkowsky, A . E,, Phillips, H . O., Kraus, K. A., J . Phys. Chem. 69, 3968 (1965). (42A) Mason, E. A., Weissman, S., Phys. Fluids 8 , 1240 (1965). (43A) Miller, D. G., J . Phys. Chem. 69, 3374 (1965). (44A) Nienow, A. W., Brit. Chem. Eng. 10, 827 (1965). (45A) Norberg, P. H . , Abhandl. Deut. Akad. Wiss. Berlin, Kl. Med. 1 (1964) (Eng.). (46A) Oishi, Y., J . Chem. Phys. 43, 1611 (1965). (47A) Oshcherin, B. N., Z h . Fir.Khim. 39, 1835 (1965). (48A) Panchenkov, G. M., Ageev, E. P., Korytin, A. A., Zbid., 40, p. 234 (1966). (49A) Prabnudesai, R . K . , Powers, J. E., Ann. N . Y.h a d . Sci. 137, 8 3 (1966). (50A) Rathbun, R. E., Babb, A. L., IND.ENC. CHFM.Pnocms DESIQNDEVELOP. 5, 273 (1966). (51A) Robinson, R . L. Edmister, W. C., Dullien, F. A. L., IND.ENG. CHEM. FUNDAMENTALS 5, 74 6 9 6 6 ) . (52A) Rodwin, L., Harpst, J. A., Lyons, P. A., J . Phys. Chem. 69, 2783 (1965). (53A) Saxena, S. C . , Joshi, R . K . , J . Sci. Znd. Res. 24, 518 (1965).; 25, 54 (196Li). (54A) Saxena, S. C., Mathur, B. P., Rev. M o d . Phys. 38, 380 (1966). (55A) Saxena, M . P., Saxena, S. C., Indian J . Pure Appl. Phys. 4, 109 (1966), (56A) Schatzberg, P., J . PolymerSci., P t . C, No. 10, 87 (1965). (57A) Shroff, G. H . , Shemilt, L. W., J . Chem. E n g . Data 11, 183 (1966). (58A) Sparrow, E. M . , Scott, C. J., Forstrom, R . J., Ebert, W. A , , J . Heat Transfer 88C, 321 (1965). (59A) Srivastava, B. N., Saran, A., Physic0 32, 110 (1966). (6OA) Steil, L. I., Thodos, G., Can. J . Chem. Eng. 43, 186 (1965). (61A) Stillinger, F. H., Suplinskas, R . J., J. Chem. Phys. 44, 2432 (1966). (62A) Stromberg, A. G., Zakharova, E . A . , Z h . Fiz. Khim. 40, 81 (1966). (63A) Sundelof, L . O., Arkiu. Kemi 25, 1 (1965) (Engl.). (64A) Szekely, J., Trans. Faraday Soc. 61, 2679 (1965). (65A) Takamatsu, T. Hiraoka M., Tanaka, K., Inoue, Y., Osugi, A., Kagaku Kognku 28, 755 (196k); 3, 65 11965) (Engl.). (66A) Thomas, W. J., Adams, M . J., Trans. Faraday Soc. 61, 668 (1965). (67A) Thomas, W. J., Nicholl, E. McK., Applied Optics 4, 823 (1965). (68A) T o o r , H . L.,Seshadri,C.V.,Arnold,K. R., A.1.Ch.E. J . 11,746,755 (1965). (69A) Tyrrell, H . J . V., Firth, J. G., Zaman, M . , J . Chem. SOC.1965, p. 3613. (70A) Uminski, T., Dera, J., Kupryszewski, G., Acta Phys. Polon. 28, 1 7 (1965) (Engl.). (71A) Vieth, W. R., Sladek, K. J., J. Coll. Sci. 20, 1014 (1965). (72A) Vignes, A . , IND.ENC. CREM.FUNDAMENTALS 5 , 189 (1966). (73A) Viswanath, D. S., Zndian J. Technol. 3, 295 (1965). (74A) Wade, C. G., Waugh, J . S., J. Chem. Phys. 43, 3555 (1965). (75A) Weissman, S., Symp. Thermophys. Properties, Papers, 3rd, Lafayette, Ind. 1965, p. 12. (76A) Witherspoon, P. A , , Saraf, D . N., J . Phys. Chem. 69, 3752 (1965). (77A) Youssef, A., Hanna, M. M., Migahed, M. D., Z . Naturforsch. 20a, 655 (Engl.).
Molecular Diffusion
Turbulent Diffusion and Dispersion
(1A) Ageev, E. P., Panchenkov, G. M., Deev, M. A., Z h . Fiz. Khim. 40,229 (1966). (2A) Andreev, G. A , , Zbid., 39, 2586 (1965). (3A) Beronius, P., Enberg, R., Z. Physik. Chem. (Frankfurt) 46, 373 (1965). (4A) Birkett, J. D., Lyons, P. A., J . Phys. Chem. 69, 2782 (1965). (5A) Board, W. J., Spalding, S. C., A.Z.Ch.E. J . 12,349 (1966). (6A) Borel, J . P., Phys. StalusSolidi 13, 3 (1966). (7A) Byers, C. H., King, C. J., J . Phys. Chem. 70, 2499 (1966). (8A) Chien, K . Y . ,Intern. J . Heat M o s s Transfer 8, 1507 (1965). (9A) Cullinan, H. T., T o r r , H . L . , J. Phys. Chem. 69, 3941 (1965). (10A) Cussler, E. L., Dunlop, P. J., Zbid., 70, 1880 (1966). 5, 69 (1966). (11A) Duda, J. L., Vrentas, J . S., INO.ENC.CHEM.FUNDAMENTALS (12A) Duda, J. L., Vrentas, J . S., J. Phys. Chem. 69, 3305 (1965). (13A) Dunlop, P. J., Zbid., p. 4276. (14A) . . Dunn. R . L.. Hatfield.. J. D... Zbid.. D. 4361. (15A) Edwards, 0. W. Dum, R . L., Hatfield, J. D., Huffman, E . O., Elmore, K. L., Zbid., 70, 217 (1966). (16A) Fedorov, E . B., Ivakin, B. A., Suetin, P. E., Z h . Tekhn. Fiz. 36, 569 (1966). (17A) Fuller, E. N,, Schettler, P. D., Giddings, J. C., IND.ENC. CHEM.58 (5), 18 (1966); 5 8 ( 8 ) , 81 (1966). (18A) Gandhi, J. M . , Saxena, S. C., Proc. Phys. Soc. 87, 273 (1966). (19A) Garland, C. W., Tong, S., Stockmayer, W. H . , J . Phys. Chem. 69, 2469 (1965). (20A) Gruen, F., Walz, D., Helv. Phys. Acta 38, 207 (1965). (21A) Gubbins, K . E., Bhatia, K . K., Walker, R . D., A.Z.Ch.E. J . 12, 548 (1966). (22A) Guczi, L . , Tyrrell, H . J. V., J . Chem. Soc. 1965, p. 6576. (23A) Hala, S., Kuras, M., Landa, S., Ropa Uhlie 7, 227 (1965). (24A) Harpst, J . A., Holt, E., Lyons, P. A , , J . Phys. Chem. 69, 2333 (1965). (25A) Holt, E. L., Lyons, P. A., Zbid., p. 2341. (26A) Huber, J. F. K., van Vught, G., Ber. Bunsenges. Physik. Chem. 69, 821 (1965). (27A) Jones, J. R., Rowlands, D. L . G . , Monk, C. B., Trans. Faraday Soc. 61, 1384 (1965). (28A) Kamal, M . R., Canjar, L. N . , Chem. Eng. Progr. 62, 82 (1966). (29A) Khazanova, N. E., Lesnevskaya, L. S., Z h . Fiz.Khim. 40, 76,464 (1966). (30A) Kim, H . , J . Phys. Chem. 70,562 (1966). (31A) Korsching, H., Z . Naturjorsch. 20a (7), 968 (1965). (32A) Kosov, N. D . , Kurlapov, L. I., Z h . Tekhn. Fiz. 35, 2120 (1965); SOU.Phys.Tech. Phyr. 10, 1623 (1966) (Engl.). (33A) Kotousov, L. S., Z h . Tekhn. Fir. 35, 2215, 2221 (1965); Sov. Phys.-Tech. Phys. 10, 1698, 1702 (1966) (Engl.). (34A) Krishnan, K . S., Laddha, G. S., (Trans.), Indian Chem. Engr. 7, 83 (1965). (35A) Kulkarni, M . W.? Allen, G. F., Lyons, P. A,, J . Phys. Chem. 69, 2491 (1965) (36A) Kulkarni, M . V., Lyons, P. A., Zbid., p. 2336. (37A) La Force, R . C . , Trans. Faraday SGC.62, 1458 (1966). (38A) Leontovich, M., Z h . Eksperim. i Teor. F i z . 49, 1624 (1965). (39A) Lightfoot, E. N., Cussler, E. L., Chem. Eng. Progr. Symp. Ser. 61, (58) 66 (1965). (40A) Lund, L . M . , Berman, A. S., J. Appl. Phys. 37,2489,2496 (1966).
(1B) Ananthakrishnan, V., Gill, W. N., Barduhn, A . J., A.I.Ch.E. J . 11, 1063 (1965). (2B) Anderson, K . L., Stokke, 0. M . , Gilbert, R . E., IND.ENC. CHEM.FUNDAMENTALS 5, 430 (1966). (3B) Argo, W. B., Cova, D. R.,IND. ENC.CHEM. PROCESS DESIONDEVELOP. 4, 352 (1965). (4B) Banks, R . B., Jerasate, S., Proc. A m . SOC. Ciuil Eng. 88 HY3, 1 (1962). (5B) Bibaud, R. E., Treybal, R . E., A.Z.Ch.E. J. 12, 472 (1966). (6B) Brauer, H., Schliiter, H., Chem. Zng. Tech. 37, 1107 (1965). (7B) Zbid., 38, 279 (1966). (8B) Brauer, H . W., Fetting, F., Zbid., p. 30. (9B) Brittan, M . I . , Woodburn, E. T., A.Z.Ch.E. J . 12, 541 (1966). (10B) Brodkey, R . S., Zbid., p. 403. (11B) Bunch, D. W., Strunk, M . R.,Zbid., 11, 1108 (1965). (12B) Cauwenberghe, A. R . van, Chem. Eng. Sci. 21, 203 (1966). (13B) Chao, R., Hoelscher, H . E., A.Z.Ch.E. J . 12, 271 (1966). (14B) Cooney, D. O., IND.ENC. CHEM.FUNDAMENTALS 5 , 426 (1966). (15B) Cooney, D. O., Lightfoot, E. N., IND.END.CXEM.PROCESS DESIGNDEVELOP. 5 , 25 (1966). (16B) Cova, D. R., Zbid., p . 20. (17B) Crider, J. E., Foss, A. S., A.Z.Ch.E. J. 11, 1012 (1965). (18B) Zbid., 12, 514 (1966). (19B) Danilychev, I. A., Planovskii, A. N., Chekov, 0. S., Znt. Chem. E n g . 6 , 272 (1966). (20B) Debbas, S., Rumpf, H., Chem. Eng. Sci. 21, 583 (1966). (21B) Dunckhorst, F. T., Houghton, G., IND.END. CHEM.FUNDAMENTALS 5, 93 (1966). (22B) Evans, E. V., Kenney, C. N., Trans. Znst. Chem. Eng. 44, T189 (1966). (23B) Fan, L. T., Wang, C. B., Pmc. Roy. SGC.A292, 203 (1966). (24B) Flatt, P., Chem. Zng. Tech. 38, 254 (1966). (25B) Froment, G . F., Genie Chim. 95, 41 (1966). (26B) Gegner, J. P., Brodkey, R . S., A.Z.Ch.E. J . 11, 817 (1966). (27B) Goff, P. Le, Prost, G., Genie Chim. 95, 1 (1966). (28B) Herrmann, H . , Chem. Zng. Tech. 38, 25 (1966). (29B) Houghton, G., Can. J. Chem. Eng. 44, 90 (1966). (30B) Houghton, G., Chem. E n g . Sci. 21, 469 (1966). (31B) Houghton, G., IND.END.CHEM.FUNDAMENTALS 5, 153 (1966). A.Z.Ch.E. J . 11, 938 (1965). (32B) H ~ u C-J., , (33B) Hudson, J . L., Zbid., p. 943. (34B) Huesmann, K., Chem. Ing. Tech. 38, 293 (1966). (35B) Jameson, G. J., Trans. Znst. Chem. Eng. 44, T198 (1966). (36B) Kaminskii, V. A., Partsakhashvili, G. L., J . Appl. Chem. (USSR)37, 1944 (1964). (37B) K a n , S.V., et a l . , Znt. Chem. Eng.6 , 260 (1966). (38B) Kirillov, V. A , , Khudenko, B. G., Zbid., p. 509. (39B) Kobayashi, T., O’Shima, E., Inoue, H . , Kagoku Kognku 30, 348 (1966). (40B) Komasawa, I., Hisatani, S., Kunugita, E., Otake, T., Ibid., p. 450.
TABLE
H-2.
BOOKS AND REVIEWS RELATED TO MASS TRANSFER No. of
Topic
Ref.
Reviews Dimensional analysis and interphase transport Estimation of heat and mass transfer coefficients H e a t and mass transfer bibliography H e a t and mass transfer review Heterogeneous catalysis and transport processes Mass transfer in gas-liquid contacting systems Mass transfer theory Unit operations, heat transfer, fluid flow Waste water and water pollution control
Ref.
46 12 110 29 54 33 71
Books Chemistry and physics of interfaces Convective heat and masn transfer Liquid mixing and processes in stirred tanks Mass transfer and absorbers Mass transfer through a mobile interface Surface interactions between metals and gases Theory of energy and mass transfer (revised ed.)
Topic
Ref.
Mass transfer in impinging turbulent free radical wall jet Mass transfer in semiconductor technology Mathematical treatment of effect of particle size distribution on mass transfer in suspensions Parametric pumping for separating fluid mixtures Dielectrophoretic process for liquid mixiug Concentration polarization in reverse osmosis Diffusion and heat conduction within a flowing media Unsteady unidirectional diffusion with multicomponent reactions
(8.W (75H)
.
L
(77H) (34H) (78H) (6H, 73H) (32H) (33H)
VOL. 5 8
NO. 1 2
DECEMBER 1 9 6 6
39
(41B) Kubota, H . , Ikeda, M., Kshimura, Y., Ibid., 29, 611 (1965). (42G) Kunugita, E.,Otake, T., I b i d . , 30, 144 (1966). (43B) Lee, E. S., Chem. Eng. Sci. 21, 143 (1966). (44B) Leung, P. K., Quon, D., Can. J . Chem. E n g . 44, 26 (1966). (45B) Levine, M. M . , Chernick, J., Nature 208, 68 (1965). (46B) Lighthill, M . J., J . Inst. M d h . Appl. 2, 97 (1966). (47B) Malenge, J.-P., Gosse, J., Genie Chim. 94, 170 (1965). (48B) Marek, M., HiavBcek, V., Ckem. Eng. Sci. 21, 493: 501 (1966). (49B) Marle: C., Pottier, J., Genie Chim. 94, 125 (1965). (50B) Mason, G., Clark, W., Nature 207, 512 (1965). (51B) McNaughton, K . J . , Sinclair, C-G., J . Fluid M e c h . 25, 367 (1966). (52B) Miller, S. F., King, C. J., A.I.Ch.E. J . 12, 767 (1966). (53B) Miyauchi, T., Mitsutake, H., Harase, I., Ibid.,p . 508. (54B) Novosad, Z., Ulbrecht, J.; Ckem. Eng. Sci. 21, 405 (1966). (55B) Ohki, Y., O’Shima, E., Inoue, H., Yagi, S., Kagaku Kogaku 30, 341 (1966). (56B) Oroveanu, T., Rev. Roumnine Sci. Tech., Serie Mrchan. A p p l . 10, 1365 (1965). (57B) Pao, Y-H., Chem. Eng. Sei. 20, 665 (1965). (58G) Patterson, C . C . ; Gloyna, E. F., Proc. A m . Soc. Civil Eng. 91, 17 (1965). (59B) Pawlowski, J., Ckem. Ing. Tech. 38, 69 (1966). (GOB) Rennhack; R . , Ibid.: p. 711. (61B) Rippel, G. R . : Eidt, C. M., Jordan, H . B., I N D .ENG.CHEM.PROCESS DESIGN DEVEI.OP. 5 , 32 (1966). (62B) Rod, V., Brit. Chem. Eng. 11, 483 (1966). (63B) Rosner, D . E., Chem. Eng. Sci. 21, 223 (1966). (64B) Ross, L. D., Chem. Eng. Prop. 61, No. 10, 77 (1965). (65B) Rumer, R . R., Proc. A m . SOL.Civil Eng. 88HY4, 147 (1962). (66B) Rutgers, R., Chem. Eng. Sci. 20, 1079 (1965). (67B) I b i d . , p. 1089. (68B) Saidel, G. h l . : Hoelscher, H. E., .I.I.Ch.E. J . 11, 1058 (1965). (69B) Sater, V. E., Levenspiel, O . , IND. ENC.C H E M . FUNDAMENTALS 5 , 86 (1966). (70B) Sciance, C. T., Crosser, 0. K . , A.1.Ch.E. J.12, 100 (1966). (71B) Seidel, H.-P., Chrm. Ing. Tech. 37, 1125 (1965). 4, 426 (1965). (72B) Soo, S. L., I N D .ERG. CHEM.FUNDAMENTALS (73B) Soo, S. L., Trezek, G. J., Ibid., 5 , 388 (1966). (74B) Sternberg, J. C . , Poulson; R . E., Anal. Ciiem. 36, 1492 (1964). (75B) Stewart, \V, E . , in: “Selected Topics in Transport Phenomena,” Chem. Eng. Prog. Symp. Sci. 6 1 (58) (1965). (76B) Templeman, J. J., Porter, K . E , , Chem. Eng. Sci. 20, 1139 (1965). DESIGN DEVELOP. (77B) T h a d u n i , M. C . : Pccbles, F. N., I N D .ENG.CHEM.PROCESS 5, 265 (1966). (78B) Toor, H . L., Cham. Eng. Sci. 20, 941 (1965). (79B) Trombetta. M. L . , Hoppel, J., A.I.Ch.E. J . 11, 1041 (1965). C Q ~J.. Chem. Eng. 44, 1 3 (1966). (808) Turner, G. .4., (81B) Vassilatos, G . , Toor, H. L., A.1.Ch.E. J . 11, 666 (1965). (82B) Whitaker, S., Chem. Eng. Sci. 21, 291 (1966). General Mixing Processes i n Flow Systems (1C) Aiba, S., Suzuki, K., Kitai, S., J . Fermentalion Technol. (Japan) 43, 948 (1965). (2C) Alfke, G . , Baerns, M . , Schugerl, K., Shiemann, G., Ckem. Ing. Tech. 38, 553 (1966). (3C) Ambwani, D . S . , A d l e r , R . J., A . I . C k . E . J. 12, 612 (1966). (4C) Ashton, M . D.: Valcntin, F. H . H., Trans. Inst. Chem. Eng. 44, T166 (1966). (5C) Baldwin, J . T . , D u r b i n , L . D . , Can.J. Chem. Eng. 44, 151 (1966). (6C) Beckmann, G . , Matis, H . , Chem. Zng. Tech. 38, 209 (1966). (7C) Bell, R . L . , Babb, A . L., Chem. E n g . Sci. 20, 1001 (1965). ( 8 C ) Bischoff,K . B., McCracken, E. A., INn. ENC.CHEM.58 (7),18 (1966). (9C) Cox,D. J., Arch. Biochem. Biophys. 112, 249, 259 (1965). (1OC) Curl, P.. L., McMillan, M. L.,.4.I.Ck.E. J . 12, 819 (1966). (11C) Cutter, L. A., Ibid.: p. 35. (12C) Douglas, J. M., Chem. Eng. Sa. 20, 1142 (1965). (13C) Echigoya, E.,e l a / . , Kagaku Kognktc 29, 892 (1965). (14C) Fraiman, R. S., Makevnin, hl. P., Chem. Pet. Eng. (Russ. travel.) No. 3, 197 (1965). (15‘2) Gal-Or, B., Resnick, W., I N D .E N D .CHEM. Pnocess DESIGNDEVELOP. 5 , 15 (1966). (16C) Gazanchiyanrs, M .G., hlartyushin, I . G., Planovskii: A. X., Int. Ckem. Eng. 6 , 217 (1966). (17C) Gillespie, B., Carberry, J. J , >I N D .ENG.CHEM.FUNDAMENTALS 5 , 164 (1966). (18C) Gillespie, B. M., Carberry, J. J., Ckem. Eng. Sci. 21, 472 (1966). (19C:) Goldish, L. H . , Koutsky, J . A , , Adler, R . J., I b i d . , 20, 1011 (1965). (20C) Hill, F. B., Felder, R . hi.; A.I.Ch.E. J . 11, 873 (1965). 5, 204 (1966). (21C) Holland, B. O., I N D .ENG.CHEM.FUNDAMENTALS ~ (22C) Hyun K . S., Marc de Chazal, L. E . , IND.ESC. C H E M . P R O C E SDESIGN DEVELOP. ’5, 105 (1966). (23C) Jinescu, G., Teoreanu, I., Ruckenstein, E . , Can. J . Ckem. Eng. 44, 73 (1966). (24C) Kang, W.A . , Osberg, G. L . , Ibtd., p. 142. (25C) Kennedy, S . C., Bretton, R . H., A.I.Ch.E. J . 12, 24 (1966). (26C) Klinkenberg, A , , I N n . ENG.CHEM.FUNDAMENTALS 5 , 283 (1966). Ckem. Ing. Tech. 38, 564 (1966). (27C) KGlbel, H . , Langemann, H., Stein, H . W., (28C) Komazawa, I., Kunugita, E.,Otake, T., Kagaku Kognkii 30, 237 (1966). (29C) Ktichler, L.,Troltenier, V., Chem. Ing. Tech. 38, 439 (1966). (30C) Landau, J., Prochazha, J., Lutovsky, Z., Collectton Czech. Chem. Commun. 31, 1 9 9 2 (1966). (31C) Lelli, V . , I N D .ENO.CHEM.FUSDAMENTALS 4, 360 (1965). (32C) Lelli, V., Salvigni, S., Ing. Chim. I l n l . 1, 15 (1965). (33C) Letan, R . , Kehst, E . , A.I.Ch.E. J . 11, 804 (1965). (34C) Lochiel, A . C., Sutherland, J. P . , Chem. Eng. Sci. 20, 1041 (1965). (35C) M a t z , G . , Ckem. In,?. Tech. 38, 431 (1966). (36C) Molerus, O . , Zbid., p . 137. (37C) Moser, J. H., Cupit, C . R . , Chem. Eng. Prug. 62 (6), 60 (1966). (38C) M u d , L., Prochazha, J., Genie Chtm. 95, 25 (1966). (39C) M u d , L., Steidl, H . , Ibid.: 93, 161 (1965).
40
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
(40C) Olbrich, T.V. E , , Agnew, J. B.:Potter, 0 . E., Trans. Inrt. Chem. Eng. 44, T207 (1966). (41C) Poole,K . R., Taylor, R . T . , Wall, G. P . , I b i d . , 43, T261 (1965). (42C) Prochazka, J., Landau, J., Collrction Czech. Chem. Commun. 31, 1685 (1966). (43C) Reid, K . J., Ckem. E n g . Sci. 20, 953 (1965). (44C) Rowe, P. N , , et ai., Trans. Inst. Chem. E n g . 43, T271 (19651, FUNDAMENTALS 5, 139 (1966). (45C) Ruckenstein, E., IND.ENG.CHEM. (46C) Shain, S. A . , A.I.Ch.E. J . 12, 806 (I 966). (47C) Silveston, P . L . , Con. J . Chem. Eng. 44, 119 (1966). (48C) Souhrada, F., Prochazha, J., Landau, J., Collectton Czech. C h m . Commun. 31. 1695 (1966). . , (49C) Sugimoto, M . , Endoh, K . , Tanaka. T . , Kngnku Kogoku 30, 427 (1966). (5OC) Sykes, P., Chem. Eng. Sci. 20, 1145 (1965). ( 5 l C ) Sykora, S., Coilection Czech, Chem. Commun. 31, 2664 (1966). (52C) T a d m o r , Z . , Biesenherger, J. A , , IND. EKG. CHEM.FUNDAMENTALS 5, 336 (1966). (53C) Takeda, K., Hoshino. T., Kagaku Kogoku 30, 544 (1966). (54C) Taniyama, I., Sato, T., I b i d . , p. 354. (55C) Tone, S., Orake, T.. Ibid.,p . 439. (56C) Valchar, J., Brit. Chem. En!. 10, 532 (1965). (57C) Valentas, K. J . , Bilous, O., Amundson, K . R . , I N n . EKG. CHEM.FUNDAMENTALS 271 (1966). (58C) It’ei. .I. Can. : J . Chem. E*g. 44, 31 (1966). (59’2) Wen, C . Y., Chung, S. F . , Itid., 43, 101 (1965). (60C) Winter, O., Schugerl, K . , Fetring, F., Schiemann, G . , Ckem. Eng. Sci. 20, 823 (1965). (61C) Ibid.,p. 839. (62C) Wolf. D., Manning, F. S . , Can..J. Chern. E n g . 44, 137 (1966). I n t e r p h a s e Mass Transfer (ID) Aliev, R . Z Romankov P. G . Medvedev A. A . Protsersy Khim. Tekhnol Gidrodinam., re&- i itiassoper~dackn,k k a d . N a u k h S R , 0;d. OLshch. i Tekhn. Khim:: Sb. Statei, 138 (1965) (Russ.). (2D) Astarita, G., IND.E N G .CHEM.FUNDAMENTALS 5 , 14 (1966). (3D) Astarita, G., Gioia, F., Ibid., 4, 317 (1965). (4D) Barnett, S. M . , Humphrey, A . E., Litt, M . , A . Z . C h . E . 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Miscellaneous (1H) American Chemical Society, “Chemistry and Physics of Interfaces,” American Chemical Socicty, Washington, D. C . , 1965. (2H) Anastasijevic, P., Afgan, N., N u k l . Energija 2, 8 (1965) (Croat.). (3H) Arkharov, V. I., Gorbunova, K . M., “Surface Interactions Between Metals and Gases,” Consultants Bureau, New York, 1966. (4H) Batievskii, A . L . , Mosse, A . L., Tarasevich, I,. I., Teplo-.i iMossoobmen Tel s Okruzhayushchei Gar. Sredoi, Akad. N a u k Belorussk. SSR, Zn.rt. Teplo- i Massoobmena, 168 11965). (6H) Brian, P. L. T., I N D .ENC.CHEhf. FUNDAMENTALS 4, 439 (1965). (7H) Cocquere, M. A. T. “Unit 0 erations, Heat Transfer Fluid Flow,” in R e p . Progr. Appl. Chem. 19, 2 i 3 (1964) PH. S. Rooke, ed., Staples Printers, Rochester, England). (8H) Dawson, n. A , , Trass, O., Can. J . Chem. Eng. 44, 121 (1966). (9H) Erickson, L. E., Fan, L. T . , Fox, V. G., I N D .ENG.CHEM.FUNDAMENTALS 5 19 (1966). (10H) Fannelop,T. K . , A . I . A . A . J . 4, 1142 (1966). (11H) Gal-Or, B., Hoelscher, H. E., A.I.Ch.E. J . 12, 499 (1966). (12H) Gill, W. N., del Casal, E., Zeh, D. W., Int. J . Heat M a s s Transfer 8, 1135 (1965). (13H) Gill, W. N., Tien, C., Zeh, D. W., IND.ENC.CaEhi. FUNDAMENTALS 4, 433 (1965). (14H) Goddard, J. D., Acrivos, A . , J . Fluid Mech. 24, 339 (1966). (15H) Grove, A. S., I N D .E N G .CHEM.58 (7), 49 (1966). (16H) Hobler, T . , “Mass Transfer and Absorbers,” Pergamon, New York, 1966. (17H) Hobler, T., Intern. J . Heat Mass Transfer 8, 841 (1965). END.CHEM.FUNDAMENTALS 5,204 (1966). (18H) Holland, B. O., IND. (19H) Holland, F. A., Chapman, F. S . , “Liquid Mixing and Processing in Stirred Tanks,” Reinhold, New York, 1966. (20H) Kays, W . M., “Convective Heat and Mass Transfer,” McGraw-Hill, New York, 1966. (21H) Krusenstierna, 0. von, I V A (Zngeniorsuetenskapsakad.) Medd., No. 140, (1964) (Swed.) (22H) Libby, P. A , , Liri, T. M., Phys. Fluid 9, 436 (1966). (23H) Lightfoot, E. N., Massot, C., Irani, F.: Chem. Eng. Progr., Syrnp. Ser. 61 (58), 26 (1965). (24H) Luikov, A. V., Mikhailov, Yu. A,, “Theory of Energy and Mass Transfer,” rev. ed., Pergamon, Oxford, 1965. (25H) Makarevicius, V., Tamonis, M., LietuL,os T S R M o s k I u Akad. Darbai, Ser. B, 153 (1965). (26H) Okun, D . A., et nl., J . Water Pollution Control Federation 37, 887 (1965). (27H) Rozen, A. M., Krylov, V. S., Khim. Prom. 42, 51 (1966). (28H) Sergeev, G . T . , Smol’skii, €3. M., Znzh.-Fiz. Zh., Akad. Naiik Belormsk. S S R 9, 163 (1965). (29H) Sideman, S . , Hortasa, O., Fulton, J. W., I N D .ENC.CHF,M.5 8 (7), 33 (1966). (30H) Skelland, A. H. P., A.Z.Ch.E. J . 12, 69 (1966). (31H) Stewart, W. E., Chem. Eng. Progr., Symp.Ser. 61 (58), 16 (1965). (32H) Szekely, J., Chem. Eng. Sci. 20, 1063 (1965). (3313) Toor, H . L . , Zbid., p. 941. (34H) Wilhelm, R . H., Rice, A . W . , Bendelius, A . R . , I N D .ENG. CHEM.FUNDAMENTALS 5, 141 (1966). (35H) Zeh, D . W . , Gill, W . N., Chem. Rng. Progr., Symp. Ser. 6 1 (59), 19 (1965).
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