This review of fundamental work published since 1965 provides a wealth of information for all operations where the behavior of
gas bubbles or liquid drops is a controlling factor
BUBBLE AND DROP PHENOMENA BENJAMIN GAL-OR GEORGE E. KLINZING LAWRENCE L. TAVLARIDES
ubbles and drops are of common occurrence in many and biological systems and processes such as gas-liquid contacting, distillation, evaporation, aerosols, homogenizing and emulsifying systems, fermentation, flotation, liquid-liquid extraction, spray combustion, spray drying, direct-contact heat exchange, etc. T h e intrinsic behavior of all the different systems cited above can be thought of as following essentially the same basic principles-those which govern all the phenomena of bubbles and drops. Hence, it may be not only logical but also, perhaps, more practical to cover all these systems and processes under a unified approach to bubble and drop phenomena. I n recent years a n increasing amount of basic and applied research has been directed to cases involving single bubbles and drops and swarms of bubbles and drops entrained in various continuous moving phases. The numerous papers covering the advances in this field range from fundamental studies to descriptions of new processes and equipment. The purpose of this article is to review the references which are representative of the total contribution to the literature from 1965 through the first half of 1968. The authors feel that this review represents the majority of articles published in this area, but not the absolute total. The works are divided into general classifications; separate tables regroup these classifications. The tables note whether the work was experimental or theoretical in nature, whether bubbles or drops were studied, and whether the dispersed phase was liquid, gas, or solid. I t is believed that this review will serve as a valuable reference for the researcher in the general area of bubble and drop phenomena. Comprehensive reviews of the literature in this field u p to about 1965 are available (4aN, 30N, 37N).
B industrial
Mass Transfer
Numerous studies treat mass transfer in dispersions. I n the area of liquid-liquid extraction for single-drop systems, Brounshtein, Gitman, and Zheleznyak ( 7 6 A ) presented a mathematical treatment for mass transfer in spherical drops. Johns and Beckmann (36A) used a model based on the Hadamard stream function to extend the theory of solute extraction in viscous single-drop systems. These authors showed the dependence of the asymptotic Nusselt number on the Peclet number and of the diffusion entry region Nusselt number on the Peclet number, and the initial concentration profile. In the area of oscillating drops and mass transfer, Rose and Kintner (72A) developed a mass transfer model for vigorously oscillating single-liquid drops moving in a liquid field. They used the concepts of interfacial stretch and internal droplet mixing. Angelo, Lightfoot, and Howard ( 4 A ) developed a method for predicting rates of mass or heat transfer for oscillating drops. The primary result of this work may be considered as a generalization of the penetration theory. Wellek and Skelland (83A) modified the Handlos and Baron turbulence model for circulating and/or oscillating droplets by considering the effect of a finite continuous phase resistance in the boundary. Patel and Wellek (59A) extended this work to short contact times and to finite continuous phase resistances. Levich, Krylov, and Vorotilin ( 4 6 4 extended the Kronig-Brink relations for mass transfer from drops falling freely through a liquid to the region of large Peclet numbers. Conditions where the continuous phase resistance is of the same order as that in the dispersed phase were considered. They also solved the problem of unsteady diffusion from a moving drop for the case when the distribution of velocities in the conVOL. 6 1
NO. 2 F E B R U A R Y 1 9 6 9
21
TABLE I.
MASS TRANSFER
Liouid
Ref 87A 36A 4A 32A,51A,57A, 7QA 16A, 31A, 37A, 40A 5 8 A , 5 9 A , 72A, 83A 23A,45A,46A, 5ZA, 7 1 A I l A , 12A 57A 38A SA 26A 7OA 75A 54A 60A,64A,67A 28A 22A 4 7 A , 48A 68A, 60A QA 20A 43A 15A 14A 28A 7OA 42A 53A
Title Mass transfer in research and chemical technology Fundamentals of mass transfer in liquid-liquid extraction Penetration theory for surface strength a p lied to forming and oscillating Xrops Liquid-liquid extraction from swarms of drops Liquid-liquid extraction from drops Mass transfer from oscillating drops Liquid-liquid extraction from moving drops Liquid-liquid extraction from turbulent flow Mass transfer from particles in agitated systems Effect of concentration on transfer coefficients in liquid-liquid extraction Interfacial phenomena and mass transfer Influence of mass transfer on countercurrent liquid-liquid extraction Axial mixing in agitated liquidliquid extraction tower Mass transfer rate through liquidliquid interface Mass transfer in steady and pulsed continuous phases Gas-liquid absorption to a drop Mass transfer equations for bubble prodess Influence of transverse irregularity on efficiency of mass transfer in crosscurrent Mass transfer from single bubbles Mass transfer and velocity for rising bubbles Bubble motion and mass transfer in non-Newtonian fluids Absorption from bubbles of dilute gas Liquid phase mass transfer Supersaturation in simultaneous gas absorption and desorption Mass transfer in bubbling aeration Gas-liquid mass transfer in nozzleless Venturi absorber Surface composition effect on twophase flow Influence of diffusivity on liquid phase mass transfer in stirred vessel Effect of diffusivity on gas-side mass
T
D
L
T
D
L
ET
D
L
E
D
L
ET
D
L
ET
D
L
84A 24A 2A 74A 34A
ET
D
L
ET
D
L
T
D
LG
E
D
L
ET
D
L
5A-7A
E
D
L
25A
83A 13A 64A 44A 66A
E
D
L
33A
E
D
L
49A
E
D
L
39A
D BD
L LG
ET
T T
D
L
ET E
B B
L L
E
B
L
T
B
L
E T
B B
L L
T E
B B
L L
E
B
L
E
B
L
E
B
L
tinuous and dispersed phases conforms to the rule of Hadamard and Rybczinski. Photographic techniques were employed by Marsh and Heideger (524) to measure extraction rates from a drop in a liquid with controlling dispersed phase resistance. They observed that a 14-fold decrease in the transfer rate occurred during the first second after drop formation. Several treatments of mass transfer in a turbulent flow field have been made. Boyadzhiev and Elenkov ( 7 IA) applied Kolmogoroff’s theory of isotropic turbulence to describe the mass transfer process in liquidliquid dispersion systems. Middleman (55A) discussed rational methods of predicting the manner in which macroscopic agitation parameters enter into the correlation of mass transfer from particles in agitated systems; he, too, applied Kolmogoroff’s theory. Much experimental work involved liquid-liquid systems. Johnson and Raal (38A) analyzed mass transfer 22
Liquid
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
56A 18A 80A 21A 47A 62A 63A 3A 30A 81A 50A 7A 88A 17A 73A
Title transfer coefficient in bubble column Determination of diffusion coefficients of gases in water and solution rate of small stationary bubbles Longitudinal mixing in bubble reactor columns Radial mixing in two-phase countercurrent flow through packed column Gas absorption in horizontal cocurrent bubble flow Mass transfer in horizontal annular gas-liquid flow Gas absorption in stirred vessel Mass transfer in sparger contactor Contact time in atomizing scrubber Retention-time distribution and mass transfer in gas-liquid absorption Interfacial area and transfer coefficients for gas-liquid absorption Transfer coefficients and tray efficiencies in tray towers Liquid-liquid separation by bubble formation Gas-liquid mass transfer in cocurrent froth flow Unsteady-state absorption of 0 2 in cumene I m roved version of rate equation f% molecular diffusion in dispersed phase Mass transfer from single bubbles Mass transfer to spherical drops or bubbles Mass transfer in agitated tanks Gas interchange between bubbles and continuous phase Mass transfer coefficientsin liquidliquid systems Mass transfer to small drops Chemical absorption of gases by small drops Mass transfer across mobile interfaces Mass transfer from single bubbles under distillation conditions Absorption in gas-liquid dispersions Mass transfer and wake phenomena Cocurrent bubble flow of water and air Mass transfer and rise velocity of single bubbles Dissolving of stationary bubbles Single-drop unsteady convective diffusion
E
B
L
E
B
L
E
B
L
E
B
L
E
B
L
E E E E
B B B B
L L L L
T
B
L
E
B
L
E
B
L
E
B
L
E
B
L
T
D
L
E
T
B BD
L LG
T E
BD B
LG S
E
D
L
T T
D D
G G
E
D
L
E
B
L
ET E ET
DB D B
LGS L L
E
B
L
ET T
B D
I, G
using a Lewis-type extraction cell. Dunn, Lapidus, and Elgin (26A) studied the influence of mass transfer on the holdup of countercurrent liquid-liquid fluidized systems and the effect of solute on droplet coalescence. Bibaud and Treybal (IOA) measured axial mixing in both phases for a countercurrently operated, mechanically agitated extractor. Eddy axial diffusivities were correlated in terms of the variables studied. I n gas-liquid absorption to a drop, experimental and theoretical techniques were employed. Plit (6OA) developed generalized equations for mass transfer within small drops in contact with a gas medium of constant concentration. He assumed that the gas diffuses toward the center of the drop, forming a radial concentration gradient. Experimental work by Plit (63A) on the absorption of ammonia by large water drops was correlated by dimensional analysis. Rajan and Goren (67A) conducted an experiment to measure the absorption of
carbon dioxide gas by a series of drops moving down a vertical wire. Their proposed model assumes the gas is absorbed by almost stagnant liquid film between and covering the drops, that the film is subsequently mixed with a drop as it moves past, and that the dissolved gas is carried from the column in circulating loops of liquid within the drops. As part of the work done on mass transfer from moving gas bubbles, Redfield and Houghton ( 6 9 A ) conducted simultaneous dilatometric and photoelectric determinations for single bubbles of carbon dioxide rising in pure water and 10 different aqueous solutions of dextrose. Bubble drag coefficients and mass transfer coefficients were computed over a wide range of Reynolds numbers using various models. Barnett, Humphrey, and Litt ( Q A ) obtained instantaneous mass transfer coefficients for the absorption of carbon dioxide bubbles rising in an aqueous solution which was rheologically well described by the Ellis model. Mass transfer coefficients were initially high, but they decayed rapidly with bubble age. Li et al. (47A) determined liquid phase mass transfer coefficients for streams of bubbles of various gases rising in water. Danckwerts (2OA) studied the absorption into a liquid of a soluble gas from a mixture of insoluble and soluble gases. He noted that, for dilute soluble gas mixtures, the absorption rate is little different from that measured when a pure soluble gas is employed. Loudon, Calderbank, and Coward (48A) developed an analysis which removes several restrictions in Danckwerts’ analysis and demonstrates that his conclusions remain substantially valid. Data were presented from basic bubble-liquid contactors. Mehta and Sharma ( 5 3 4 studied the effect of diffusivity on gas-side mass transfer coefficients in an experimental bubble column. Scott and Hayduk (74A) obtained data on liquid phase-controlled absorption of gases in horizontal two-phase flow. Hughmark (34A) applied the momentum-mass transfer analogy to available data for mass transfer in horizontal annular gasliquid flow. Braulick, Fair, and Lerner (73A) conducted studies of the air oxidation of aqueous sodium sulfite solutions in simple bubble-contacting columns. Experimental work was described on mass transfer in foams. Weissman and Calvert (82A) developed an efficient gas absorption device for a stable aqueous foam moving in a horizontal duct, which could be used to study mass transfer performance. Heuss, King, and Wilke ( 3 3 A ) reported similar results for the absorption of ammonia and oxygen in horizontal cocurrent gasliquid froth flow.
AUTHORS Benjamin Gal-Or is Associate Professor, George E. Klinzing is Assistant Professor, and Lawrence L. Tavlarides is a Graduate Student in the Deflartment of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pa. Professor Gal-Or is also with the Department of Aeronautical Engineering , Technion-Israel Institute of Technology, Haifa, Israel.
Heat Transfer
Papers presented on heat transfer ranged from detailed studies of temperature profiles in drops to the effect of bubble size in nucleate pool boiling, boiling heat transfer and two-phase flow, and direct contact heat transfer. By measuring temperatures in drops, Head and Hellums (78B)developed a new technique for the study of heat transport from large single drops heated dielectrically while suspended motionless. They reported measurements of temperature distributions within circulating drops and drops with retarded circulation. Letan and Kehat (32B) described a simple method for continuous measurement of the temperature or concentration of drops of an organic liquid flowing in a continuous liquid medium. I n the area of heat transfer in two-phase flow, Kudirka, Grosh, and McFadden (26B) investigated airwater and air-ethylene glycol systems in forced circulation apparatus a t low gas-liquid ratios. Magrini (34B) presented a correlation for experimental data on heat transfer between heated horizontal cylinders and the gas-liquid mixcd fluids stream. Photographic studies of boiling thermal exchange and nucleate boiling appeared frequently. Gaertner ( 73B) studied saturated nucleate pool boiling using these techniques and concluded that any heat transfer model or design equation based on any single mechanism must be in serious error. Hsu (22B) conducted photographic studies on the gradual transition of nucleate boiling from the discrete bubble regime to the multibubble stage. Sideman, Hirsch, and Gat (52B) also analyzed direct contact heat transfer with change of phase employing these techniques. Sideman and Barsky (5OB), treating direct contact heat transfer, used the concept of local isotropy in turbulent agitation, together with the particular characteristics of volatile drops. They derived a correlation relating the specific power input to the temperature driving force and the heat flow rates for all conceivable mixing regimes. Labuntsov, Shevchuk, and Pazyuk (27B)analyzed mathematically and confirmed experimentally two models of a process for boiling liquid metals under different surface conditions. Borishanskii et al. (5B) presented a correlation of experimental data on heat transfer during the boiling of large volumes of alkali metals in steel tubes. Gal-Or and Walatka (74B) presented a theoretical analysis of some of the main interrelationships governing heat and mass transfer in dispersions. Qualitative and quantitative analyses of the effects of physical and operating parameters were considered for two domains. One domain was represented by a low dispersed phase holdup and a steady motion of swarms of bubbles with clean interfaces, the other by high dispersed phase holdup on fine dispersions with surfactants. Heat and Mass Transfer
Downing ( 3 C ) correlated rates of evaporation for drops of pure liquid evaporating in streams of high temVOL. 6 1
NO. 2 F E B R U A R Y 1 9 6 9
23
_
~
_
TABLE 11.
_
_
~
~
~
~
~
HEAT TRANSFER
Liquid
Ref
28B 9B
328 30B 368 48B 418 34B 23B,26B 208 18B
148 138, 77B,22B, 52B 49B
Title Energy transfer to bubbles during formation Energ balance for bubble column or gas Eft Sampling probe for measurement of temperature and concentration of organic drops Mixing effects in spray-column heat exchanger Axial dis ersion and heat transfer in liquid-$quid spray towers Heat transfer to bubble beds Heat transfer in liquid-film flow Heat transfer in two-phase fluid with gas phase generated by electrolysis Heat transfer in two-phase flow Heat transfer during bubbling on bubble-cap tray Temperature distributions in large drops a t low Reynolds numbers Heat transfer in multistage liquidliquid disperser Photographic studies of boiling
and/or Theor Bubbles Re
(T )
(B)
ET
B
L
51B
T
B
L
53B
E
D
L
E
D
L
E
D
LG
ET E E
B B B
L L L
ET E
B B
L
E
D
L
51B
T
D
46B
38B 15B
16B 11.9 8B
728
38 5B, 27B
35B,45B 50B,52B
58B 1B 10B 59B,63B 4B,258 60B
L
L
6 1 4 62B
65B 39B
E
B
L
B
L
Heat transfer in surface boiling at high system pressures and surface heat loads Number of active centers of va or formation and critical heat &livery Boiling from liquid interface Single center of vapor formation and frequency of vapor bubble separation Film boiling of spheroidal droplet Bubble diameter and frequency of removal Characteristic parameters in free convection nucleate boiling
E
B
L
E
B
L
Effects of interfacial instability on film boiling Heat transfer to water droplets on flat plate Heat transfer in boiling liquid metals
ET
318
E
298
ET
24B
1%
47B
Boiling heat transfer with electrical fields Nucleate pool boiling of water a t low pressure
Direct contact heat transfer with change of phase Bubble dynamics on hot surface Initial boiling of liquids during pulse heating Convective heat transfer between gasliquid mixture and wall Heat transfer in boiling ethanol Microconvection creation by vapor bubbles in boiling Nucleate boiling Boiling heat transfer and two-phase flow Film boiling on vertical surfaces Geometrical similarity of random distribution of spherical bubbles in saturated pool boiling Heat transfer from hot wall to water drops in spheroidal state Maximum heat flux and growth velocity of vapor bubbles in boiling Diffusion theory of evaporation of drops Peak and minimum heat fluxes Combustion of aniline droplets Review Heat transfer between two immiscible liquids Floating drops and liquid boules Evaporation kinetics of liquid droplets Thermodynamics of bubbles and drops Direct contact transfer between immiscible liquids in turbulent pipe flow Interfacial vibration on saturated boiling heat transfer Forced convection subcooled boiling heat transfer wiih H s 0 in electricall heated tubes at 100-550 Ib/in.Y Mechanism of heat transfer in spray column heat exchange Investigation of heat transfer during boiling of solutions in vertical tube under conditions of forced motion Contraction and acceleration of vapor bubbles in subcooled boiling Submerged heating surface with injected air bubbles Mechanism of dropwise condensation
54B
E
Thermal exchange and nucleate boil-
Title
E E
B B
L L
ET E
338 6B 648
448
79B 55B 428
438 378 21B
E
E
2B
T
perature air. Toei et al. (18C) conducted an experimental investigation on evaporation from a single drop in a stream of superheated steam and various steam-air mixtures. The data permitted calculations of heat and mass transfer coefficients. King and Scully (8C) studied film evaporation of drops from heated surfaces, obtaining time-weight curves of various liquids at different hot surface temperatures. Results were correlated in terms of heat conduction through the supporting vapor film.
40B
Experimental and theoretical approaches appeared in an attempt to elucidate this complex phenomenon. Several studies were presented on the absorption of carbon dioxide with chemical reaction. Eben and Pigford (80) determined experimentally the rate of carbon dioxide absorption into sodium carbonate-bicarbonate buffer solutions and a sodium hydroxide solution. Results were analyzed using the penetration theory. Kishinevskii and Armash (760)compared experimental data on the absorption of carbon dioxide by aqueous solutions 24
INDUSTRIAL AND ENGINEERING CHEMISTRY
T E
B B
L L
L
E
B
L
E E
B B
L L
ET ET
B B
L L
E ET
B B
L LS G
ET
D
E
B
L
T
D
G
E E ET E
B D BD D
L G
ET E
D D BD D
G LG
E
B
LG
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B
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ET
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L
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B
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ET
B
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ET
B
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ET
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G
T E
LO
L L
L
~
TABLE I I I .
HEAT AND MASS TRANSFER Liquid
Ref
IC 6C
5c
zzc Mass Transfer with Chemical Reaction
and/or and or Theor Bvbhes (T) (B) ET DB
3C, 8C, 12C,
13C, 76C, 78C,20C 21C
Title Mass and heat transfer to drops in mixer-settler Concentration distribution of nonvolatile solute in evaporating drop Coupled heat and multicomponent mass transfer in dispersions with size and residence time distributions Mass and heat transfer in gas-liquid contacting Evaporation of drops
D
L
T
D
G
T
DB
LO
E
B
L
ET
D
G
T
D
G
IOC,1lB, 15C, Bubbles in boiling 15B, 53B Mechanism of dropwise condensation 4C, 17C Laminar flame propa ation in droplet llC
ET
B
L
ET ET
D D
G G
7c
T
D
G
T T
D D
G L
T
D
G
ZC 9c 74c
Vaporization of water drops in mist by radiation
E
suspension of liquidgfuel Spontaneous condensation of drops in gas Rates of evaporation of sprays Mass of heat transfer in boundary layer Condensation controlled by heat transfer to large droplets
TABLE IV. MASS TRANSFER W I T H CHEMICAL REACTION
%? and/or
Ref 710
5D
75D 25G
210 130 2OD 240
160
18D 790
80 40
230 170
20 720 90 50
740
220 250
Tit18 Mathematical treatment of effect of particle size distribution on mass transfer in dispersions Mass transfer with rapid chemical reaction in a drop Mass transfer with chemical reaction from single gas bubbles Monte Carlo treatment for reacting and coalescing dispersed phase systems Performance of stirred reactors with dispersed phase mixing Reaction-accompanied mass transfer from fluid and solid spheres at low Peclet numbers Reaction-accompanied mass transfer between liquid phases E uilibrium yield in liquid phase reactor with f i g h surface-to-volume ratio Ex erimental check of equations for absorption Juring chemical reaction Mass transfer coefficients in chemi-absorption of gas by large drops Chemisorption from gas by large drops under countercurrent flow C o t absorption with chemical reaction Reaction of SO2 and 0%in aqueous solution o f MnSO4 Interaction of 1 2 and SOa during mass transfer in liouid-liauid extraction svstems Absorption of 0 2 into sulfite solution in agitated gas-liquid reactor Film model for ethylene dichloride formation Kinetics of absorption of Oa in aqueous solutions of cuprous chloride Rate of bromination of benzene droplets in agitated aqueous emulsion Chemical and physical limits on vapor phase diffusion flames of droplets Mass transfer with chemical reaction Extraction of second-order reaction Multicomponent mass transfer with reversible chemical reactions
.
.
Bubbler (B)
"ir and/or Gas
T
D
(GI L
T
D
L
T
B
L
T
BD
L
T
DB
L
ET
DB
L
E
D
L
T
B
L
E
B
L
E
D
G
T
D
G
E E
B
L
E
D
L
ET
B
L
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B
L L
ET
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L
T
D
G
E
B D
L L LG
E
E T
DB
of sodium hydroxide under different hydrodynamic conditions. These studies were based on a new model which uses stationary concentration field methods. Plit (790) developed three equations for mass transfer from the gas phase to large drops of liquid; the equations differ according to the principal location of the chemical reaction. For the problem of mass transfer with reaction in dispersions, Gal-Or and Hoelscher (700) proposed a mathematical model which accounts for interaction between drops or bubbles in a swarm by considering particle size distribution. Shain (270) modified an existing computer program to calculate the effect of coalescence and redispersion of drops on conversion in a stirred reactor when a second-order reaction is occurring in the dispersed phase. Spielman and Levenspiel (25G) treated a similar problem for reacting and coalescing dispersed phase systems using a Monte Carlo technique. Hydrodynamics
Photographic techniques used to view bubble collapse near solid boundaries were reported by Shutler and Mesler (706E). Collier and Hewitt (78E)reviewed experimental techniques of two-phase flow with emphasis on photography. Van der Walle, Verheugen, Haagh, and Bogaardt (720E)carried out experiments using acoustical means for determining void fractions in boiling water systems.
Bubbling in fluidized beds received the attention of researchers : Raso, Volpicelli, and Maitz (93E) used photographic techniques. Collins (79E) found that Davidson and Rowe's representation of a real bubble is valid. Work by Winter, Schugerl, Fetting, and Schiemann (727E)showed that the share of bubbles in the variance of residence time distributions is substantially smaller than that caused by the over-all nonuniformity of the gas velocity. Relative bubble velocities in gas-liquid contactors were presented by Gal-Or and Resnick (33E). The velocity of rising swarms of bubbles was analyzed by Marrucci (69E), who presented a cellular spherical model and gave an expression for the ratio of velocity of rise of the swarms to velocity of a single bubble. Mendelson (73E) examined wave theory to predict bubble terminal velocities. Brandt and Perazich ( 9 E ) experimentally recorded flow patterns around large gas bubbles and employed an empirical equation for volume change of a bubble moving in a liquid. Astarita and Apuzzo (4E) initiated bubble flow in non-Newtonian liquids. Heat transfer effects on the velocity of rise of bubbles were presented by Sideman (707E),who determined the velocity of rise with condensation and evaporation. Individual air bubbles in a turbulent water stream were photographed by Baker and Chao (6E). Bubble velocity was indicated as similar to rise velocity in quiescent liquids, and drag coefficients were found for a range of Reynolds numbers. Falling oscillating drops in a liquid were recorded by Schroeder and Kintner (703E). The frequencies and amplitudes of oscillations were varied. Wellek, Agrawal, and Skelland (725E) handled the case of nonoscillating drops falling in liquid media and found empirical relations to predict eccentricity over a wide Reynolds number range. Deformed drops in the Stokes region were studied by Matsunobu (77E). Internal drop circulation in the low Reynolds number region was examined by Horton, Fritsch, and Kintner (46E). Unsteady boundary layers on vibrating spheres were theoretically analyzed by Yeh and Yang (728E). Drop size, effective viscosity, and velocity distributions were determined and a criterion based on the first two was established to allow prediction of when a dispersion can be treated as a homogeneous single-phase fluid. Formation, Growth, and Collapse
Articles on drop formation ranged from drop formation in normal to highly viscous liquid-liquid systems. Andrews ( I F ) developed a heuristic argument to show why droplets form in one-dimensional classical fluids at sufficiently low temperatures. Rao, Kumar, and Kyloon (52F) studied the effect of volumetric flow rate, interfacial tension, viscosity, and capillary size on drop volumes for benzene drops formed in water and glycerine. Papkov, Iovleva, and Mikhailov (46F) analyzed equilibrium conditions of liquid flow from a nozzle and showed the existence of a critical nozzle diameter corresponding to the transition of drop formation to a continuous stream. Similarly, ManfrC (37E) applied a VOL. 6 1
NO. 2
FEBRUARY
1969
25
TABLE V.
HYDRODYNAMICS
Liauid
Ref 51E, 80E, 706E 47E, 52E, 53E, 7 1 IE, 174E 9E, S7E 7 E , 18E, 28E, 30E, 31E, 37E, 43E, SOE, 67E, 66E, 76E, 708E, 779E, 130E 7E
Re Cavitation Unsteady gas-liquid, liquidliquid systems Gas-liquid flow patterns Two-phase flow
74E
82E 27E 3SE 36E
ET ET
B BD
L GL
67E
ET ET
B BD
GL GL
42E
T
D
L
E
D
L
ET
D
LG
713E
E E
D BD
G LG
723E
65E 66E 7 10E
44E ET
BD
LG
E ET E ET ET
D B D B B
G LG L L L
E
B
L
ET
B
L
E
BD
L
E E
D D
G G
ET
B
L
ET ET
B B
L LG
T
D BD BD
G
105E
T T
64E 83E 57E 716E 721E 709E 87E 59E 23E QSE, l00E 45E 8E
175E LG
77E, 84E
T
B
L
T
BD
LG
T
D
L
T T
D D
G L
34E
T
B
L
47E
Two-phase non-Newtonian flow Bubble-driven fluid circulations
T
B
L
E
B
LG
Profile of a growing droplet
ET
D
G
Axial dispersion coefficient measiircment in two-phase flow
E
B
L
Shear deformation of drops Flashing flow from existing nucleation sites
generalized form of the Hagen-Poiseuille law to liquid extruded from a capillary tube in the form of drops. Linde and Sehrt (35F) studied Marangoni instability in drop formation using Schlieren photographic methods for n-butanol diffusing from water to ethanol. Vivdenko and Shabalin (77F) used high speed motion pictures to show that the breakup of a jet at a given cross section occurs without reversible oscillations. Wilcox and Tate (75F) investigated high intensity sound as a means of liquid droplet formation. Other articles were presented on the evaporation and growth of drops in a gaseous medium. Buehl and Westwater (3F), using photographic techniques, considered 26
73E 25E
Prediction of existence of two phases Momentum and heat trans61E, 92E fer in liquid-liquid dispersions 707E, 103E, 704E, 728E Drop vibration and oscillation 46E Circulation in drops 717E, 724E, 725E, 129E Size and shape of bubbles and drops 77E, ZOE, 36E, 59E, Bubble and drop motion 69E-77E, 73E, 89E, lOZE, 107E, 7263 Drop formation 122E 49E, 94E, 172E Bubble dynamics Dispersion hydrodynamics 98E Slip phenomena 68E, 79E 24E, 56E Electric and magnetic stress on gas bubbles 29E Mass transfer and liquid mixing Bubbles in fluidized bed 79E, 26E, 76E, SOE, 93E, 96E, 98E, 127E Mass transfer in pulsed 1 ?E, S5E column End effect in columns 132E Air entrainment in liquid 7OE spray 40E, 50E, 55E, 72E, Bubbles in boiling systems 95E, 7ZOE Mass transfer in gas jet 50E Bubble and drop motion 2E-4E, 6E, 12E, 15E, 33E Contact time in scrubbers 87E Polyphase flow 8SE Viscous incompressible flow 7SE around fluid spheres Gas bubbles in vibrating 97E liquid columns Particle retardation in 4SE oscillatory fluids Profile of a separatory drop39E let Drops falling in electric fields 131E 63E
Liquid
INDUSTRIAL A N D ENGINEERING CHEMISTRY
21E 86E 75E
54E 22E 5E 16E
Rise velocit of bubbles in tubes ancrrectangular channels Ap roach of a liquid drop to $at plate Drag coefficients of droplets accelerating through air Rising velocities of spherical cap bubbles Bubbles in fluidized beds Drag force on oblate spheroidal bubble Bubbles in fluidized beds Gas bubbles a t reduced pressures Entrainment in two-phase dispersed annular flow Translation of continuous phase in wakes of single rising drops Correction to Stokes law for a charged sphere Bubble velocity in liquid Shape of drop or bubble a t low Reynolds number Wall migration of fluid drops Dynamics of gas bubbles Stability of pulsating bubble in flowing fluid Nonlinear bubble oscillations Laminar separation bubbles Liquid drop dynamics Instability of charged droplets Drop formation at low velocities in liquid-liquid systems Translation of continuous phase in wakes of single rising drops Unsteady settling toward a flat plate Terminal velocity of circulating and oscillating drops Initial motion of a bubble in fluidized bed Velocity in a cylindrical container Unsteady toroidal bubble and its stability Small oscillations of viscous fluid droplet Hydrodynamics of ensemble of drops or bubbles in presence of surfactants Steady motion of spherical drop at high Reynolds number Pressure behind accelerated bubble Wakes behind two-dimensional bubbles Liquid entrainment a t high bubbling rates Vortex rings from drops falling into stationary bath
T
B
L
ET
D
L
E
D
G
E
B
L
T T
B B
L L
ET E
B B
L L
E
DB
LG
E
D
L
T
DB
L
E ET
B BD
L LG
E T T
D B B
L L L
T E E T
B B D D
L L G G
ET
D
L
E
D
L
ET
DB
L
E
D
L
ET
B
GS
ET
B
L
T
D
LG
T
DB
LG
T
D
L
ET
B
L
E
B
L
E
B
L
E
D
L
the growth of bubbles on a wall from a supersaturated liquid of the dissolved gas. Griffin and Coughanowr (76F) gave general methods for solving moving boundary value problems and, in one case, applied the method in spherical coordinates to the growth of spherical droplets in humid air. Portnov (47F) discussed mathematically the evaporation and growth of drops in a gaseous medium and presented solutions for various cases. Florschuetz and Chao (IOF) examined the mechanics of vapor bubble collapse under spherically symmetrical conditions to ascertain the relative importance of the effects of liquid inertia on the rate of collapse.
FORMATION, GROWTH, AND COLLAPSE
TABLE VI.
Liouid and/or and/or Theor Bubbler Solid (T ) (B) (SI B ET LS
and/or
Raf 78F 7F 3 7 F , 46F 52F 53F 3F, 76F, 47F 36F 35F 39F, 57F 66F 75F 77F 73F 4F 48F, 4QF 5F 79F 44F 45F 34F 56F 32F 75F 70F 76F 29F 2F 63F 7 7 F , 78F 37F 25F 57F 72F
Title Bubble initiation, growth, and departure in nucleate pool boiling Theory of dro formation in onedimensionaffluids Rheological aspects of drop formation Drop formation in liquid-liquid systems Molecular diffusion with moving boundary and spherical symmetry Evaporation and growth of drops in gaseous medium Cloud chamber droplet growth and formation Marangoni instability in drop formation-Schlieren techniques Dropwise condensation on solid surface (nucleation sites for) Energies of nucleation Liquid atomization in high intensity sound fields Mechanism ofjet breakup into large drops Spherical phase growth in superheated liquids Vapor pressure over solution droplets Shape of fluid drop a t fluid-liquid interface Mass transfer in li uid phase during formation of b u h l e s Mass transfer to drops formed at moderate speed Growth of air bubbles formed at orifice in water-fluidized beds Effect of orifice submergence on bubble formation Bubble entrainment by plunging laminar liquid jets Mechanism of bubble formation in fluidized bed Statistical analysis to describe bubble occurrence in two-phase flow Newtonian jet stability Mechanics of bubble collapse Evaluation of diffusion coefficients by following rate of bubble collapse Destruction of gas bubbles in boiling Bubble dynamics in boiling Bubble dynamics in general temperature fields Theoretical study of bubble dynamics in purely viscous fields Analogy between boiling and bubbling processes Bubble shapes in nucleate boiling Bubble formation a t boiling point of liquids Bubble formation on horizontal plate with periodically varying heat flux
T
D
L
ET E
D D
L L
T
B
LS
ET
DB
LG
Ref 74F, 59F, 65F, 69F, 79F 62F
E
B
L L
70F 30F
lZF, 27F 43F 9F
T
73F
E
L
28F 38F
E
GS
22F
T
L G
27F 74F 8F
E E
G
T
L
E ET
G L
ET
L
47F 50F 42F 26F
E
D
L
E
B
L
E
B
L
33F 1 IF
E
B
L
67F
23F
T
B
S
T
B
L
E E
D B B
G L L
E T T
B B B
L L L
T
B
L
E
B
L
E E
B B
L L
E
B
L
Coalescence and Breakage
Coalescence and breakage is a complex physical phenomenon which occurs in bubble and drop systems. T h e exact mechanism is far from clear. Hartland (7G-9G) has investigated the effects of drop shape, film thickness, and film rupture on the coalescence of a liquid drop a t a liquid-liquid interface. Valentas, Bilous, and Amundson (JOG) attempted to develop a mathematical model which relates a two-phase system to the distribution of droplet sizes, while Valentas and Amundson (29G) developed a model to relate breakage and coalescence of droplets to steady-state distribution of droplet sizes. Jeffreys and Hawksley (72G, 73G) reported the effect of physical properties on coalescence rate for hydrocarbon-water systems and theoretically analyzed these coalescence rates to verify experimental results.
Title
Growth rate of vapor bubbles in boiling liquids Generation and growth of bubbles in water boiling channels Visual studies of boiling at high pressures Boiling phenomena a t supercritical pressures Incipience of nucleate boiling in liquids Generation of bubbles and drops in boiling channels Boiling in thin film Nucleate boiling instability of alkali metals Deposits formed beneath bubbles during nucleate boiling of radioactive calcium sulfate solutions Superheating and nucleation behavior of n-pentane and n-hexane Dynamics of vapor bubbles in propane Bubble departure diameters a t subatmospheric pressure Change in interfacial tension during evaporation of N-propyl alcohol from aqueous pendant drop Permeability of soap films to gases Thermal equilibrium shapes Mechanism of boiling crises in pool boiling Bubble ,freguency, departure, and rise velocity in nucleate boiling Bubble departure from heated surface Bubble growth in boiling of water with surfactants Factors affecting which phase will disperse when immiscible liquids are stirred Draina e of solutions between foam bubbqes Turbidity as criterion of coagulation Mechanism of two-phase annular flow Problems of theory and energy computation of mass transfer process Gas absorption with simultaneous chemical reaction Growth of liquid drop Shape of sessile drop Drop size distribution Bubble frequency departure volumes Droplet size-age distribution on rate processes Bubble growth and collapse Mechanism of nucleate boiling
77F 64F 58F 55F 60F 24F 54F
6F 7F 67F 20F 68F
ET
B
E
B
L
E
B
L
ET
B
L
E
B
L
E E
B B
L L
E
B
L
E
B
L
E E
B B
L L
E
D
G
ET E E
B B B
LG LS L
ET
B
L
ET ET
B B
L L
E
D
L
ET
B
L
E ET T
D D DB
L G LG
T
D
L
T T E T T
D D D B D
G L L L L
E ET
B B
L L
Bubble growth rates at high Jakob numbers
ET
B
L
Nucleation site instability
E
B
L
Various effects on coalescence have been considered by many researchers-for example, porous media [Jordan (75G)1, surface diffusion [Nichols (Z7G)1, and electrical charge [Waterman (33G)l. Interfacial Area and Holdup
The determination of mass transfer rates and coefficients is intimately associated with the interfacial area of contacting systems. Absorption reactions to determine both terms were reported by Dulon and Harris ( 6 H ) . Good agreement with published data was obtained. Dilute aqueous solutions were utilized by Zieminski, Caron, and Rlackmore (32H) to find interfacial areas and the oxygen mass transfer coefficients in the presence of small quantities of organic compounds. These compounds had a profound effect on the transfer. I n liquid-liquid systems, interfacial area plays a vital VOL. 6 1
NO. 2
FEBRUARY
1969
27
~~
TABLE VII.
~
COALESCENCE AND BREAKAGE L&id
Re
Title Effect of physical and chemical parameters on coalescence 3G Drop coalescence in liquid-liquid systems 33G Effect of electrical charge on coalescence 25G Monte Carlo treatment for reacting and coalescing dispersed phase systems 22G Device for producing controlled collisions between pairs of drops 23G Effect of pipe diameter on maximum stable drop size in turbulent flow 13G, ZSG, Breakage and coalescence in dispersed phase 30G systems Coagulation constant of highly developed 6G aerosols Coalescence of two spheres by surface diffu21G sion 77G Coalescence and redispersion in packed beds 31G Motion of drops in viscous media 28G Critical dimensions of disintegrating drops 32G Coalescence in presence of surfactants Coalescence of gas bubbles in aqueous solu18G tions of inorganic electrolytes 34G Interaction of two-phase gas-liquid flow in Venturi 9G Film rupture in coalescence 8G Film thickness in coalescence 7G Drop shape in coalescence 20G Luminosity produced during coalescence o oppositely charged falling water drops 24G Coalescence in condensation Effect of porous material on coalescence 15G 1SG Approach of two identical rigid spheres 7 6G Transformation of a body with constant specific surface area ZG Size of drop in Venturi extractor Effect of mass transfer on coalescence 74G 3G Coalescence in liquid-liquid systemsreview 70G Coalescence frequency in tanks 26G Drop size distribution 1OG Measurement of coalescence frequency in agitated tank 4G, 25G Drop size distributions in strongly coalescing agitated liquid-liquid systems l G , 12G
ET
D
L
E E
L
T
D D D
L
E
D
G
E
D
L
T
DB
LG
E
D
G
T
B
L
E
L
ET E E
D D D D B
E
D
G
E E E E
D
L L
ET
E
D D D
L
L L L L
L G
G
T T
D D D D
L L
E ET ET
D D D
L L L
E E
D D DB
L L L
E
D
L
E
E
role, also. Mechanical agitation effects on an interphase surface, yielding a minimum agitation rate for uniform dispersions, were reported by Kovalev and Kagan (78H). The sedimentation method given by Gil’perin, Pebalk, Zarbovskaya, and Tsyurupa ( 7 7 H ) is a method for determining interfacial surface area in liquid extraction. I n gas-liquid systems, bubble columns and trays, orifices, and agitated reactors are a few contacting devices. Methanol, ethanol, and water systems were examined and contact area determined for a bubble column by Vevioroskii (27H). Dil’man and Aizenbud (5H) found the average bubble diameter to be independent of gas velocity, size of opening, and viscosity in a high bubbling layer. Holdup is another variable in bubble and drop systems which is difficult to treat. Porter (23H) concluded from his study on a gas absorption reaction system that the mean contact time of the gas in the liquid is sufficiently accurate for design purposes. Klinkenberg ( 76H) indicated methods of calculating residence time distributions with applications to liquid-liquid dispersions. Backmixing was studied by Retallick (24H) in a cascade of mixing vessels. A modification in calculation of the coefficient is seen for each backtrack. Liquid volume fractions are reported by Cravarala and Hassid ( 4 H ) for a two-phase adiabatic system with an empirical correlation for liquid volume fraction in circular geometries. Electric field effects on liquid-liquid settling were analyzed by Sjoblom and Goren (26H). The effectiveness of the settling process was determined, yielding residence times and dispersed phase volume fractions. Surfactants
TABLE V I I I .
ET E
B D
L
E E
B B
L
Surfactants can have drastic effects on the transport phenomena of drops. Mass transfer effected by surfactants around spheres was described by Lochiel (732), who presented equations which predict the effect of surface-active impurities on mass transfer across a spherical interface at creeping flow. Interfacial circulation due to surface-active agents in steady two-phase flow was studied by Kenning (91). Experimental work on the effect of surface-active substances on the size of droplets produced was performed by Kochetov and Klepikov
E
D
G
(701).
E E
B B
L
E ET E E
B B B D
E
L L
T
D B D
T
B
G
E E E
D D B B
G L L LG
INTERFACIAL AREA AND HOLDUP Exptl (E)
Ref 3H 9H lOH, 15H 8H 1H ZH, 27H, 28H 4H 5H 6 H , 1 7H, 3 2 H 7H 12H, 16H 13H, 3 0 H 17H, 18H, 20H, 24H 79H ZIH ZZH 23H 25H 26H 29H 31H
28
Title Packed bubble column Interfacial area and mass transfer in agitated liquid-liquid contactors Bubble size distribution Interfacial area in liquid-liquid contactors Formation of interfacial areas Contacting area on bubble trays and columns Liquid volume fraction in two phases Interfacial area in bubbling layers Mass transfer and area in contacting systems Physical properties and liquid level Axial mixing of liquids in beds Holdup and heat transfer Volume ratios in flow-type mixer Mechanics of spray column Gas holdup in fluidized bed Collision model in liquid-liquid packed column Contact time on absorption with reaction Aerosols Electric field and settling Surface renewal in gas-liquid reactor Polydispersed systems
Drops (D)
Liquid
and/or
and/or
Theor (T ) E E
Bubbles (B) B D
Gas (GI
E
T
(L)
and/br
L L L
L
L
Water droplet evaporation and the effect of surfaceactive substances on this process have been studied by Lyashev, Dukhin, and Deryagin (751) and Lyashev
L
(741).
L
L
L
L
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Aerosols
When drops are considered, aerosols hold a special place because of their size. A number of phenomena are exhibited by aerosols that are not shown by ordinary size drops. Goldschmidt (79.4 measured the aerosol concentration using the hot-wire anemometer. The size distribution of an aerosol was determined by Tokiwa and Ohki
(37J), who employed air-blast nebulization. Espenscheid, Willes, Matijevic, and Kerker ( 7ZJ) utilized light-scattering techniques to study size distribution of aerosols. Coagulation rates of aerosols are of great interest. Brock and Hidy (3J)analyzed theoretically the classical collision rate theory in reference to aerosol coagulation and obtained a result not in agreement with classical theory. Pulsating sound waves were used by Varlamov, Manakin, and Ennar (38J)to effect coagulation of water mist. A flow method employed by Fuchs and Sutugin (77J) yielded coagulation rates of uncharged NaCl aerosols. An excellent review of the formation of monodispersed aerosols is presented by Fuchs and Sutugin (76J). Sutugin (34J) has generated reproducible monodisperse aerosols of mean particle radius from 30 to 300A. Derjaguin, Storozhilova, and Ravinovich ( 6 J ) employed two new methods for measuring velocities of thermophoresis and their results contradict the formulas of Brock and Epstein.
Foams
Research in the foam area touched on fractionation, physical properties, and formation and collapse. The major work was carried out on foam fractionation. Lemlich ( 77K)analyzed theoretically bubble fractionation and showed how this process differs from foam fractionation and gas desorption. Leonard and Lemlich (78K) presented a model for foam fractionation, while Harper and Lemlich (73K) gave ranges of column operability for combined bubble and foam fractionation. Newson (ZOK) stated the principles that govern surfactant transfer in a continuous foam column and presented drop size distribution data. Aleksandrov, Gorechenkov, Khalif, and Baikova ( 7 K ) studied experimentally the relative densities of foamed liquid layers on sieve plates. The formation, properties, and breakdown of foams and emulsions were treated by Bikerman (3K). T h e formation of foamed polymers by a novel method was recorded by Hansen and Martin (72K), and the kinetics of foam decomposition was handled experimentally by Kruglyakov and Taube (74K), who presented the change in the specific surface of a foam.
TABLE I X .
and/or
Thcor (T )
Title
Ref 3I, 71 7 7I 41, 741, 751 21, SI,SI, SI 731
721 7 7I 701
7I 781 81
Influence of surfactants on creeping motion of bubbles and drops Velocity, pressure distribution, and retardation coefficients of falling drops Effect of surfactants on e%.aporationof drops Surface mobilit). and interfacial circulation in two-phase flows Effect of surfactants on mass transfer around spheres Shape and terminal velocity of slurry drops in air Dcsorption of surfactant3 from liquidphase boundary Effect of surfacranrs on dispersion of liquids Interfacial resistance to mass transfer in liquid-liquid systems-rcvicw Evaporation of liquid droplets containing surface impurities Effect of surfactants on rise velocities of ensembles of drops and bubbles
TABLE X.
Ref 7J 3J, 1 1 5 , 13J, 743, 7SJ, 21J, 32J, 38J SJ-SJ, 29J 70J 72J 75J, 47J 77J, 24J, ZSJ, 34J,47 J 79J 20J, 26J, 33J 22J 23J 25J, 30J, 31J, 37J 27J 40J 43 ZJ 36J 35J 55 78J
3K, 6K, 74K, 25K 4K 5K, 77K, 73K, 74K, 7 7K 7K 77K 72K 76K 78K, 7QK 20K, 26K,27K, 29K 22K 24K 28K 8K 2K 27K
T
D
E
D
ET
B
T E
D
G
E
DB
L
E
D
L
ET
D
L
T
D
G
T
DB
LG
Title Nucleation Coagulation of aerosols
E ET
Thermophoresis Diffuseophoresis Light scattering techniques Deposition in bed Monodispersions
ET ET E ET ET
Concentration by hot wire Generalities Thermal forces Compressed gases Size distribution
E
Generation from electrolytes Electrical neutralization Production of aerosols Noncontinuum regions Gravity settling of aerosols in tubes Formation of condensation aerosols Preparation and growth of sulfuric acid aerosols Unipolar diffusion of aerosol particles
E
T ET E
E
E T D D D
E E E
G G G
T
FOAMS
Title
Ref 23K
T
?$
and/or Bubblcs (B) DB
AEROSOLS
TABLE X I .
7K
Emulsions The general theory of coagulation of emulsions has been treated by Rice and Whitehead (7L). The particle size distribution in emulsions has been checked by who treated oil-water emulsions and correBecher (7L), lated the effect of preparation parameters on the initial size distribution. Rowe (QL)investigated the effect of emulsifier concentration and type in reference to particle size distribution in emulsions. Hazes which often occur in hydrocarbon liquids were attributed to water by Hermanie and Von der Waarden (4L).
SURFACTANTS
Dynamic foam columns Density of foams Formation, breakdown Reaction in foams Fractionation
ET
E ET E ET
Tray efficiencies Ion flotation Production Draining of liquids Interstitial flow Separation Gas content of foam Interstitial liquid flow in foam Flow characteristics of foams Studies on foam separation process Structural mechanical properties of foam Mass transfer and bubble sizes in cellular foams and froths ~
VOL. 6 1
NO. 2
~~
E E E E ET E E E
E E
B B
L L
E
B
L
~~~~~
FEBRUARY 1969
29
TABLE X I I .
Friedlander and Wang ( I M ) also used similarity solutions for the asymptotic behavior of the kinetic equations of coagulation.
EMULSIONS
3;‘
Ref IOL
2L 1L 7L 8L QL 3L, 6L 4L, 5L
Title Effect of saline electrolyte on particle sizes in fat emulsions Energy dissipation in emulsion drops in shear flow Initial size distribution in oil-in-water emulsions Theory of coagulation of emulsions Influence of electrolytes on electrokinetic mobility of emulsions Effect of emulsifier concentration and type on particle size distribution of emulsions Stability of emulsions General
TABLE X I I I .
and/or Theor Drops Li ui (2.) (B) E D L
(5)
T
D
L
E
D
L
ET
D
L
E
D
L
E
D
L
T
BROWNIAN M O T I O N
Ref
Title
Theor ( T )
Drops (D)
1M-3M
Coagulation
T
D
TABLE XIV.
GENERAL E&l
Ref. 7N 4 N , 22N 6N 8N S N , 25N, 26N
Title Aerosols Emulsions Photos of drops Interfacial renewal Adsorption layer on bubbles and drops 70.17 Liquid-liquid extraction 7lN Thermodynamics of gas suspension 72N Reactor design 13.17 Annular flow of air-water systems 14N, 15N, 32iV Boiling 77N Condensation and fog 18N Ultrasonics Bubble dynamics 1QN Dispersions 27N 24N, 2QN, 36N Heat and/or mass transfer Bubble breakage 27N Fluidization 28N 31N Interphase transfer Extraction with reaction 33N 34N Interfacial tension 35N Foams Fluid dynamics of multiphase systems 37N-40N Mixing systems 3QN 47N Jet disruption into drops 2ON Liquid-liquid spray column 5N Gas absorption from bubbles Mass transfer with chemical reactions 2N Power consumption and gas holdup 3N in pulsed column 7N Absorption of gases in liquids 16N Index to two-phase gas-liquid flow literature Conservation laws for two-phase flow 38N with change of phase
9’ry
and/or and/or Theor Bubbler (T) (B) D T ET D E D DB T DB ET ET
Gas (3) nndjor Solid
(SI G L L LG L
L
D B B D B D BD BD BD BD B B BD D D
G L G L G LG LG LG L L LS LG L L
ET ET ET E E ET ET
BD BD D D B BD B
LG LGS G L L LGS L
T
B
L
T E E E E ET ET ET ET E T
T T E
T
Brownian Motion
When the droplets under consideration are of s u e ciently small diameter, Brownian motion cannot be ignored. Hidy ( Z M ) presented a theory of coagulation of noninteracting particles in Brownian motion. Numerical solutions of the coagulation equations were made. Heterogeneity in particle size increased rates of coagulation. Hidy and Lilly ( 3 M ) discussed the classical solution of kinetics of coagulation and a similarity solution. 30
INDUSTRIAL A N D ENGINEERING CHEMISTRY
General
A number of general composite works have been published recently. A comprehensive treatment of the fluid dynamics of multiphase systems is given by So0 ( 3 7 N ) . The dynamics of bubbles, drops, and solid particles are considered. Various specialized reviews are available, such as that by Sideman, Hortacsu, and Fulton (36N), who analyzed mass transfer in gas-liquid contacting systems, and that by Kutateladze (23N), who investigated turbulent heat and mass transfer during physical and chemical conversions. Experimental results, design methods, and various mathematical models for gas-liquid dispersions were reported in a general treatment of bubble dynamics by Resnick and Gal-Or (3011’) . Heat transfer by boiling, with reference to the thermodynamics of surface phenomena, was dealt with by Gleim and Vilenskii (74N),while Nesis ( 2 7 N ) considered the mechanism of bubble break-off from a nonwettable horizontal plate. The application of ultrasonics to dispersion was reviewed by Horioka and Tatsuhara (18:V). Photographic techniques in liquid drop studies were described by Damon, Angelo, and Park ( 6 N ) . Adsorption on spherical particles and its relationship to bubble and drop mass transfer ability were studied by Dukhin and Buikov ( Q N ) . REFERENCES Mass Transfer (1A) Afschar, A. S., Diboun, M.,and Schugert, K., Chem. Eng. Sci., 23, 253, 267 (1968). (2A) Anderson, K. L., Stakke, 0. M., and Gilbert, R. E., IND.END. CHEM., FUNDAX., 5, 430 (1966). (3A) Angelo, J. B., and Lightfoot, E. N., A.1.Ch.E. J.,14, 153 (1968). (4A) Angelo, J . B., Lightfoot, E. N., and Howard, D. W., ihid., 12, 751 (1966). (SA) Asano, K . , Tokyo Institute of Technology, Bulletin 70, 1965. (6A) Asano, K., and Fujita, S., Soc. Cfiem. Engr., Japan, 4, 330 (1966). (7A) Asano, K., and Fujita, S . , ibid., p. 369. (8A) Bakker, C. A . P., Buytenen Van, P. M., and Beek, W. J., Chem. Eng. Sci., 21, 1039 (1966). (9A) Barnett, S. M., Humphrey, A. E., and Litt, M., A.I.Ch.E. J . , 12,252 (i966). (10A) Bibaud, R. E., and Treybal, R. E., ibid., p 472. (11A) Boyadzhiev, L., and Elenkov, D., Chem. Eng. Sci.,21,1955 (1956). (12A) Boyadzhiev L., Elenkov, D., and Kyuchoukov, G., Compt. Rend, Acad. BulgnreSci., 18, b35 (1965). (13A) Braulick, W. J., Fair, J. R., and Lerner, B. J., A.1.Ch.E. J.,11, 73 (1965). (14A) Brayinskii, L. N., Evilevich, M. A., and Pavlushenko, I. S., Protressy Khim. Tekhnol. Gidrodin. Teplo Massoperedacha Akad. N a u k SSSR, Old. Obrhch Tekhn. Khim. Sb. Stalei, 304 (1965). (15A) Brian, P. L. T., Vivian, J. E., and Matiatos, D. C., Chem. Eng. Sci., 22, 7 (1967). (16A) Brounshtein B. I . Gitman, I. R., and Zheleznyak, A. S., Dokl. Akad. Nouk S S S R , 162, 1336’(19653. (17A) Cable, M., Chem. Eng. Sci., 22, 1393 (1967). (18A) Cheh, H. Y . , and Tobias, C . W., IND.ENC.CHEM.,FUNDAM., 7, 48 (1968). (19A) Chittenden, D. H., and Spinney, D. U., J . Colloid Interfoc. Sci., 22, 250 (1966). GOA) Danckwerts, P. V., Chem. Eng. Sci., 20, 785 (1965). (21A) Davies, L., and Richardson, J. R., Brit. Chem. Eng., 12, 1223 (1967). (22A) Dil’man, V. V., Inter. Chem. Eng., 6, 297 (1966). (23A) Dil’man, V. V . , J . Eng. Phys. (USSR),8, 319 (1965). (24A) Dil’man, V. V., and Zhilyaeva, T. A,, Khim. Tekhnol. Topi. Mosel, 10, 36 (1965). (25A) Dorman, D . C., and Lemlich, R., Nature, 207, 145 (1965). (26A) Dunn, I., Lapidus, L., and Elgin, J. C., A.2.Ch.E. J., 11, 158 (1965). (27A) Dytnerskii, Yu. I., Kasatkin, A. G., and Kholpanov, L. P., Zh. Prikl. Khirn., 39, 92 (1966). (28A) Elenkov, D., and Boyadzhiev, Kr., Inter. Chem. Eng., 7, 191 (1967). (29A) Gal-Or, B., Hauck, J. P., and Hoelscher, H. E., Int. J . Heat M a s s Transfer, 10, 1559 (1967).
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~
.
I
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