KENNETH B. BISCHOFF DAVID M. HIMMELBLAU
annual review
Mass Transfer New knowledge of daffision and dispersion phenomena as well as their injuence on chemical reactions afects the directions o f progress in applied chemical technology his review covers the period immediately following
Tthat covered by the last annual review [IND.ENG. CHEM. 56, 61 (1 964) ] 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, while the bulk of the review consists of special interest tables with brief descriptions as to the nature and scope of the reported work.
Molecular Diffusion
A generalized method of predicting diffusivities of nonpolar gases (up to temperatures of 10,OOOo K.) has been presented by Mathur and Thodos (37A). The method is applicable to 11 monatomic and diatomic gases both in their molecular and dissociated states. Robinson and coworkers (51A) re-examined the experimental determination of diffusion coefficients by diaphragm cell methods, and provided a new set of equations to obtain the diffusivity regardless of volume changes during diffusion. Also refer to Helfferich (19A). Tests of the final relation on the ethanol-water data of Dullien indicated good agreement. A modification of the Eyring rate concept for viscosity and diffusion was used effectively by Garner and Metzner (144) to predict diffusivities in viscous solvents. Lisnyanskii and Vuks (33A) in effect tested the use of Onsager coefficients, rather than diffusion coefficients, in examining the variation of diffusivity with concentration in polar liquid systems. A quasicrystalline model of a dilute ternary liquid system was proposed by Lane and Kirkaldy (31A) in which diffusion was assumed to occur by interchange of species on neighborhood lattice sites. Experimental verification of the proposal with ternary electrolytic solu54
INDUSTRIAL A N D ENGINEERING C H E M I S T R Y
tions was fairly good. From a study of the methane-nbutane system, Longwell and Sage (344) concluded that the diffusion coefficient defined by Chapman and Cowling for mixtures showed the least variation among a number of coefficients studied, and was reasonably simple in application to binary hydrocarbon systems. I t should prove advantageous in other nonideal solutions. Sandler and Dahler (52A) examined the well known but neglected case in which the assumptions about the diffusion flux lead to the telegrapher’s equation rather than the diffusion equation. Solutions of the two equations were compared and shown to yield essentially the values for most cases of interest. Certain other interesting features of the telegrapher’s equation are also reported. Other selected recent work on molecular diffusion is listed in Tables A-1 to A-5. Turbulent Diffusion a n d Dispersion
Basic Turbulent Diffusion. As in previous years, only articles of direct interest to chemical engineers will be covered. Two extensive experimental works appeared during the past year. The first by Martin and Johanson (36B) considered the statistical turbulence TABLE A-1. Ref.
T or Ea
Temp., C.
,
17-197 29 Various 0-120 25-60
GASEOUS DIFFUSION Pressure, Atm.
S>sstern o r Topic
1 10-6-10-8
1 1
1 1
80
1
iI a
~
H2, He, CO1, SFain many gases Xe in He, Ne, Ar, K r H?O in air He, .4r, X e pairs n-Hexane in methane, 3-methyl-pentane Kirkendall effect in .4r, He, Hz pairs Confirmed flat profile in Stephan diffusion tube for Bz-air Hydrocarbons in air Diffusion in straight tube by Taylor experiment Effective diffusion coefficient in boundary layers Diffusion near consolute point in tern a r y Diffusion in critical region Prediction of self-diffusivities by use of Enskog relationships Prediction of self-diffusivities
T = lheoretical stud?, E = experimental investigation.
characteristics of liquids in pipe flow. Correlations with Reynolds number were presented for the turbulence intensity, Eulerian and Lagrangian integral scales, and the eddy diffusivity. The second, by Baker and Chao (5B), was concerned with the motion of a heterogeneous system consisting of air bubbles in water flowing in a vertical pipe, Their results indicated that the average relative bubble velocity was the same as the rise velocity through a quiescent liquid. Axial and Radial Dispersion. A comprehensive review of many types of “dispersion” processes by Klinkenberg (29B) should be mentioned here. A theoretical extension of the classical Taylor diffusion in round pipes was made by Fan and Hwang (77B) for the case of an Ostwald-de Waele fluid in laminar flow. The axial dispersion was reduced for pseudoplastic and enhanced by dilatant materials. Mathematical solutions for the axial dispersion model with arbitrarily time varying velocity and dispersion coefficient were provided by Bischoff (8B) and Turner (60B). Data supporting the predictions of Taylor diffusion for laminar gas flow in a circular tube were presented by Evans and Kenney (76B). Mickley and coworkers (37B) have studied flow patterns in packed beds by making standard turbulence parameter measurements. One of the major findings was that the eddy diffusivity in the voids is much smaller than either the axial or radial dispersion coefficient and thus there is no direct connection between the two. New data on gas dispersion in packed beds were given by Sinclair and Potter (57B). A discussion of the importance of “dead end” pores in porous media dispersion was given by Coats and Smith (74B). Prost and LeGoff (48B) have presented a novel scheme of measuring longitudinal and lateral electrical conductivities of gas-liquid flow in packed beds. It is hoped that information on the internal flow patterns can be obtained from the data. Koutsky and Adler (30B)have performed an extremely detailed study on the reduction of axial dispersion in flow through helical pipes. This agrees with other work reported in last year’s review and is apparently caused by the secondary flow patterns existing in flow through helical pipes. Hoogendoorn and Lips (25B) present valuable new axial dispersion data for gas-liquid countercurrent flow in large packed beds. Chemical Reactor Applications. Several important fundamental papers were published. Amundson and Raymond (3B, 4B, 57B) considered a general treatment of the stability problem for distributed parameter models with dispersion. Keeler et al. (27B) showed that the statistical turbulent diffusion theories of Toor were able to give good predictions for a reaction carried out under the classical conditions of approximately isotropic homogeneous turbulence behind a grid. For simple systems, in which the turbulence characteristics can be readily predicted or correlated, this method can be used instead of the more general but less detailed residence time distribution. McGuire and Lapidus (35B) performed extensive cal-
TABLE A-2.
LIQUID DIFFUSION
[Primarily Experimental Data a n d Methdda) Temp.,
Ref.
O
c.
System ~~
~~
C o n , CzHa, CsHs, 1-butene in water with liquid jet
6-65 18 25 25 25 25
25 25 16
25
25
20 25 25 100-1 71 25
COz, CzHa in highly viscous solutions Effective binary coefficients of COz in EtOH-HnO, Bz-Tol, CCla-BZ Effect of COz concentration on diffusion coefficient in HzO Four coefficients for sucrose-glycine-water Four coefficients for sucrose-KC1-water with Gouy diffusiometer EtaN-H20-PhOH near critical point Bz and naphthane derivatives in HzO, dioxane, glycol CzHaClz in CeHs, EtOAc, CzHaClz by radiotracer Hydroquinone in various electrolytes by Philpot-Svenson oblique slit method Effect of concentration in nonideal, nonassociating systems such as Cr-Cs, Cs-Ciz, etc., by interferometer Monocarboxylic acids in H z 0 hy Gouy interferometer Alcohols in CCla in spin echo method Numerous cations in HzO by spin echo method Tracer and electrochemical diffusion coefficients of aromatics in various solvents Concentration effect in MeOH-Hz0 and other systems by schlieren knife-edge method Eight common binary systems restudied by moire patterns Radioactive tracer from porous frit in electrolytic media n-Butane, n-decane to 600 p.s.i.a. New diaphragm cell Effect of concentration in polymer solutions Errors in capillary method of measurement Three-beam interferometer
TABLE A-3.
LIQUID DIFFUSION
(Primarily Theoretical Studies)
-
Topic Quantum effect in diffusion of gases in liquids Review of diffusion of dissolved gases in liquids (145 refs.) Calculation of molecular friction constant for self-diffusion Isothermal ternary diffusion in terms of four coefficients Change of De with temperature of short-chain normal paraffins Estimation of coefficients for strong and weak electrolytes Moment method of evaluating coefficients in free boundary experiments Departures from Einstein equation for molten salts Isothermal diffusion in fluids with “glasslike” transition Multicomponent cross terms explained by relaxation process ( 6 8 A ) Prediction with temperature of diffusivities by semiempirical methods for Galkanes ( 2 5 A ) Review of diffusion processes (26A) Diffusion processes in liquid under influence of accoustical field ( 6 0 A ) Isothermal diffusion in nearly monodispersed system (494) Discussion of temperature dependence of activation energy of diffusion ( 3 8 A ) Prediction of self-diffusivities of pure liquids
I
Ref.
Tor Ea
System or Topic
___-I__
(5A)
E
(44A) (76A)
E E
(7A)
(24A) (22A) (39A) (45A) (54A) (63A)
_- Ref. (71A) (8A) (57A)
E T, E E E
T, E T
Thermal diffusion and diffusion coefficient for liquid NHs a t its b.p. by pulsed neutron technique Systems of isotopes of Ne-CHI pairs from 12O to 179O C. a t 1 atm. Application of wave front shearing interferometry in electrolytic solutions COz with Ar, Kr, X e Correct equation and use of swing separator [Trennscbaukel) Six univalent electrolytes at 25O C. Use of decrease of luminescence of adsorption in gas phase Analysis of parasitic backmixing in thermal diffusion column Gas phase analysis A bibliography covering period 1957 to June 1963
-
Topic
Theory of time lag method of measuring diffusion coefficients Consistent scheme for analysis of multicomponent diffusion by general flux equations Approximate solution to three-component diffusion
VOL. 5 7
NO. 1 2
DECEMBER 1 9 6 5
55
E
Ref.
07
Subject
T a
i Eddy diffusion of turbulent flow of suspension of fibers
E
(gB
(348,528,
E,T
Turbulent mixing in jets
(208)
E, T E, T
Horizontal mixing in sea Turbulent mixing of ocean outfalls
(428)
E
Diffusion from continuous source in wind
638)
(70~)
DISPERSION IN GENERAL
TABLE B-2.
1
Ref.
(28)
~
1
~
i
(268)
Subject
El?r
General, similarity methods for solution of dispersion mode equations of Taylor diffusion predictions Review of dispersion
culations for the transient operations of a packed bed chemical reactor with both intra- and interparticle diffusion. The computer calculations were extremely lengthy for the completely detailed case and the authors tried several simpler, approximate models. Unfortunately, many of the important features of the more rigorous solutions seemed to be lost in the approximate solutions and so the usefulness of the latter are not clear for these types of calculations. Other Applications. Bransoin and Trollope ( I IB) have considered the effect of axial dispersion on the process of crystallization. Asymptotic solutions to the transient fixed bed exchange equations for a step input of solute have been derived by Cooney and Lightfoot (15B). Schowalter (53B)presented a theoretical study of the stability of porous media flow with dispersion. An interesting study of the movement of a solute in the washing of a packed bed with dispersion taken into account was given by Sherman (55B). General Mixing Processes in Flow Systems
____ E E (438) T (228)
(248)
E
(45B)
,
(468) E
Lateral solid mixing in packed, fluidized beds Radial dispersion in packed beds with non-Newtonian fluids Flow through deformable porous media Longitudinal dispersion of countercurrent liquid-liquid flow in packed bed T u b e banks as model for packed bed
TABLE B-4. Ref.
Ep
~
E (398)
(588)
TABLE B-5. Ref.
~
E+r
~
(78, 328) (798, 4 0 8 ,
568) (278)
1
Subject
Longitudinal mixing in RDC Axial dispersion in pulsed perforated plate column 1 Longitudinal mixing in gas bubble columns
CHEMICAL REACTOR APPLICATIONS Subject
~
I
T
Axial and radial dispersion effects
T T T
1338) (678) (648) (738)
DISPERSION IN EQUIPMENT
T E. T
Chemically nonequilibrium flows Use of chemical affinity in convective diffusive calculations Boundary layer flow \+ith catalytic surface Chemical reaction in entrance region of pipe Diffusion and surface reactions Review of mass transfer effects in catalytic reactors
____ (388) (598) (68)
0
56
~
’
I
E, T
T E
Longitudinal dispersion with gas absorption and chemical reaction in packed bed Effect of fluid mixing on dynamics of mass transfer operations Radial miscible displacement
E = experimental investigation, T = theoretical
stud^.
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
Age Distribution Functions. A useful treatment of general “population balance” models was given by Randolph (52C). The age distribution is just one property of a group or population of molecules (or other entity) that can be handled by this method. Many other previous applications such as crystallization, microorganism growth, and catalyst activity were shown to be special cases of the general relations, which were derived by the methods used in the kinetic theory of gases. Hulburt and Katz (27C) used a similar approach for a specific problem. Also, Zuber (78C) gave a general formulation for flow patterns and diffusion in dispersed, two-phase systems. Sinclair and McNaughton (64C)showed how residence time distribution functions of a complex system of vessels could be combined to give the over-all system response. Age Distribution Function Applications. A general method of using direct age distribution function information to compare the performance of different types of chemical reactors was presented by Murphree and coworkers (42C). The idea was to compare the required holding time of the actual reactor to a plug-flow reactor for equal conversion and rate constant. The arbitrary conversion level is chosen in the range of interest for the desired final application, and thus a reasonably good estimate of the expected efficiency of the real reactor is obtained without assuming any specific mixing models. The effect of the residence time distribution on microbial kinetics was investigated by Goda and Nakanishi (2OC). Experimental residence time distribution data were obtained for flow sedimentation basins by Argaman and Rebhun (3C), for special reactor tubes by Kusunoki (35C), and for a ball mill by Mori and associates (4OC).
AUTHORS David M . Himnielblau is Professor and Kenneth B. Bischoj is Assistant Professor in the Chemical Engineering Department, Universitji of Texas. They have prepared ItYEC’s annual review of -Mass Transfer since 1962.
Mixing in Stirred Tanks. Further extensions of his fundamental studies of the turbulence in isotropic mixers were given by Corrsin ( I 7C). This latest development considers the effect of the molecular diffusivity in terms of the Schmidt number. Kim and Manning (32C) also presented experimental and theoretical work on turbulence levels. Data on mixing in large-scale tanks were provided by Stemerding et al. (69C). Worrell and Eagleton (75C) showed the effects of segregation on mixing in stirred tanks. Also, four letters concerning an apparent misinterpretation of some previous segregation experiments (reported in last year’s review) were published (8C). Spielman and Levenspiel (66C) gave a Monte Carlo treatment for reacting and coalescing dispersed phase systems in perfectly mixed tanks. This method was simpler for problems of this type than deriving the population balance partial differential equations and then solving them by differences. Mixing in Fluidized Beds. One of the major areas of interest in mixing studies continues to be fluidized beds. I t is known, especially for the most common gassolid fluidization, that “bubbles” form and cause most of the unique features of fluidized beds. Thus, much recent work has been centered in this area and has been organized by Davidson and Harrison (73C). Their elementary theory for the formation (stability) and motion of the bubbles has been extended by Jackson (30C), Pigford and Baron (48C),and, most rigorously, by Murray (43C, 44C). Anderson and Jackson ( I C ) have compared the stability theory of Harrison et al. with the fully developed bubble motion theory. Rowe and coworkers (57C, 58C) have measured further aspects of the bubbles, and de Kock and Judd ( I 5 C ) discussed the flow patterns within bubbles. Hassett (22C) has argued that really three “phases” exist : bubble, region above bubble, region with no bubbles. However, Davidson and Harrison (72C) state that a well designed gas entrance grid (with relatively high pressure drop) leads again to the two-phase concept which has been commonly used in the past to represent fluid bed mixing. The above theories do not yet lead to a working model, and a comprehensive set of direct measurements of mixing, especially applied to chemical reactions, has been given by Heidel et al. (23C). Rowe (56C) has given a n approximate theoretical calculation method for the prediction of chemical conversion based on the bubble model, and Pyle and Rose (50C) have considered other aspects of this. Ishii and Osberg (29C) have compared a reaction in fixed and fluid beds. It has been suggested that a tapered bed would be more uniformly fluidized, and Littman (36C) has measured solid mixing for this case. Finally, a special symposium on fluidization has been published (78C). Other Mixing Applications. An interesting illustration of the use of rather mathematically complicated theoretical equations for a practical problem was given by Hoftyzer (26C). His study was concerned with the best type of liquid distribution system to use for twophase countercurrent operations. Previously developed
TABLE C - I .
AGE DISTRIBUTION FUNCTIONS
/ E l or Subject
T O
E T T
T
Degree of mixing of liquids using optical method R T D in multistage system with recycle Models consisting of series of stirred tanks with short circuiting and backflow Mixing patterns and RTD predictions
E = experimental invertrpation, T = theoretical study.
TABLE C-2.
M I X I N G IN STIRRED TANKS Subject
Effect of separated layer in liquid-liquid systems Mixing with turbine and helical screw agitators Experimental verification of perfectly mixed model for well agitated tank rcactor Mixing characteristics of two-stage agitator Mathematical models Mixing and heat transfer Solid-liquid reaction mixing effects Fluid blending Turbulent diffusion in agitated vessel
equations for flow distribution based on a diffusion or random motion analogy were used with various entrance conditions to show the somewhat surprising result that about six liquid jets are almost as good as perfectly uniform distribution. The wetting of packing of various locations in a bed was also studied in the same work. Randolph (57C) showed the effects of mixing in crystallization processes. Interphase Mass Transfer
Attempts to predict interphase mass transfer for a wide variety of pseudopractical devices and laboratory experiments are described in this section. Work dealing with small and large scale commercial equipment is not discussed. Because of the inherent limitations in the modeling of interphase transfer, practically all investigations can lead at best to qualitative prediction techniques. Merson and Quinn (370) developed a new contacting device in which a thin layer of one liquid immersed in another liquid flowed horizontally and radially outward from a central source. The experimental data obtained were reproducible, but were not well represented by a simple steady state diffusion model. A stagnant interface existed and, with some liquid pairs, interfacial turbulence was noted. The well known relation for the additivity of phase resistances was discussed by both Szekely and by King. Szekely ( 4 9 0 ) examined the relation for the two-film theory, a bubble-stirred interface, various surface renewal models, and independently stirred liquids, and concluded that, for certain of the models, the relation is not exact, but, for all practical purposes, effective. King ( I 9 D ) considered deviations from the additive relation for two countercurrent flow models and, with the aid of numerical solutions of the mathematical models, demonstrated that material differences exist (as shown by graphs in the original reference). T o the many studies which exist of mass transfer from VOL. 5 7
NO.
12
DECEMBER 1 9 6 5
57
TABLE 6-3. M I X I N G I N FLUIDIZED BEDS Ref
E or T
TABLE D-2. SI MULTANEQUS INTERPHASE TRANSFER AND CHEMICAL REACTlON (Primarily Experimental)
Subpct
........... Backmidng Mixing in fixed and fluid beds Solid mixing Particle flow patterns R T D of solids in fluid and moving beds with continuoqs solids flow Solid sire segregation R T D of solids in multistage bed Analog model Flow patterns near solid obstacle Liquid-solid bed expansion Three-phase fluidization Comparison of gas bubble velocity in fluid bed and ordinary fluid Engineering aspects Reviews
Ref.
Transfer Equipment
~_,I_
.................................
SO:! irltu aqueous XdOH
'
1
(530) (230) (750)
Rapid mixing tee Vertical glass cylinder , J e t ; wetted wall culuniii ...............
,
1
.I____
GO2 from aqueous NaHCO3 solutions Aqueous COz irith aqueous bases Bz, HAC into aqueous N a O H C o z into aqueous N a O H _._I_, ................
TABLE D-3. SIMULTANEOUS INTERPHASE TRANSFER AND CHEMICAL REACTION (Primarily Mathematical Analyses) ....I.---__._x__._
--__
T j p e of Reaction
Ref.
Ref.
1
E or T
Rapid; first order; others Order of 0 and 1 ; A B+ First order Second order
OTHER M l X i N G APPLICATIONS
1
l_ll".l
N o r Ab
Process .............
TABLE C-4.
..
Phases
..
Gas absorption
A
+
Subject Blender geometry for solids mixing Solid mixing in tumbler mixer Mixing in double cone blenders Radiotracer analysis OS catalyst flow distribution Flow patterns in electrical precipirator Use of mixing tanks to siiiooth paper stock variations Flow patterns around ordered array of spheres Expressions for degree of solid mixing Review of mixing
S + A - - B Two steps: A 4B-C-,C+ B(1 + n j t h ordei
S a
S = steady r t n t e , U = unsteady stale.
b
N = nuniaricnl or nnolog colcuialion, A =
analyticai solution.
TABLE D-1.
GENERAL iNTERPHASE TRANSFER Apparalus and Procesr
Concentration profile of tracer in solid on evaporatiod under nonlinear boundary conditions Solution to moviny: boundary problem in cylindrical cuordinates Diffusion from aqueous solution into gel Dissolution from rotating disk with both laminar and turbulent conditions Use of electrochemiluminescence to measure mass transfer .rates Effect of vibration and oscillation on transfer from cylinder Use of penetration theory to model dissolution of multiparticulate solids Effect of solution contaminants on dissolution rate from s h g l e crystal face Absorptlbn of alcohol vapors on wetted Cu pipe Air-NHs jet impinging on H 2 0 with p H indicator Effect of sonic vibrations on transfer in welted wall column Absorption of COz in open rectangular channel for laminar flow Aljsorption of gases from streams of bubbles into water compared with penetration theory Extension of surface renewal model Concentration polarizarion effect a t membrane in water desalinization Demonstration of analogy between heat and mass transfer a G = gas, L = liquid, S = solid. tifJI2.
b
' 1
I _
Medias
$7- 0, Eb
S-G
r
MASS TRANSFER FROM AND T O DROPS AND SMALL SOLID PARTICLES Other Phase
I S-L
E, T
1
r
L
E
L L
E
L L, G G G
L or Gb
E, T
I i,
I'
L S-L
E
G-L G-L G-L
E E E
L, G G
E
L.
L
E
I
$%stem .......... ..- ............. Extraction of organics in n-heptane by rising drop Extraction from freely falling drops Transfer from swarms of large drops Droplet growth from supersaturated solutions Unsteady diffusion from moving diop Gas absorption by Salling drop Condensation growth in humid air Naphthalene spheres to water in packed and fluidired beds Dissolution of sinale of hvdroxvbenzoic acid " ssheres . in warer Math analysis of diffusion into sphere Over-all transfer coefficients frurn spheres correlated by dimensionless relations hlath analvsis of surface reaction on mhere immersed (n large concenrration an8 temperature gradients Math analysis of dissolution of sphere 1 Math analysis of transfer from ion exchange particle Marh analysis of dissolution of polydispersed powders Transfer frorn arrays of benzoic acid spheres to water stream _I-.__
s-L
S S
T
i '
E, ?' G-L
E
I
_-._I,.__
T = theoretical itudJ, E = experimental inaesliga-
both rigid and internally circulating spheres in a flowing media, Redfield and Houghton ( 4 1 8 ) have added a comprehensive investigation of desorption from rising single C 0 2 bubbles in water. Various relations, including those of Levich, Boussinesq, Chao, Griffith, etc., are compared with experimental data over a wide range of Reynolds numbers (0.02 to 5000). At both low and high Reynolds numbers the drag coefficients were fairly well correlated, but the mass transfer results agreed less 58
TABLE D-4.
INDUSTRIAL A N D ENGINEERING C H E M I S T R Y
a
.
c
L, G L
I
I
-. ... - ... L = liquid, C = gas.
..I.._.__.
U = drop, S = soiidparticie.
6
-_.I,____ ~
...... -
favorably with all of the correlations derived from models in thc literature. Simultaneous Heat and M a s s Transfer
A paper by Hasson and associates ( 6 E ) presented various theoretical solutions for the condensation of water vapor on cylindrical jets, plane sheets of uniform thickness, and fan spray sheets. Comparisons were rnade of the local N U number L I S . the GZ number for the special
conditions of constant ambient temperature. Vulliet (27E) gave a n analysis of the thermodynamics and mechanics of the vaporization process in the continuum regime in which the kinetic energy of the vapor (vapor velocity) is appreciable compared to the thermal energy of the molecules. T h e hydrodynamic boundary conditions and the balance equations are combined with the principles of irreversible thermodynamics to obtain the interphase transfer flux. Because chemical vapor deposition finds many industrial applications, a timely summary of the state of the art has been given by Oxley (76E). The process is characterized by the deposition of solid material from a gas by chemical reaction. As a rule of thumb, gas phase diffusion is important in the condensation process a t intermediate pressures (10 to 760 mm.), the reaction rate controls a t low pressures ( < l o mm.), and convective transport controls at high pressures (>1 atm.). However, suitable adjustment of other process variables can modify these categories. Other work, including phase transitions, is shown in Tables E-1 and E-2.
TABLE E-1.
Ref.
Topic
~
Nucleation in crystal growth controlled by diffusion Thermophoretic formation of crystals from flowing saturated fog Nucleation of solid in undercooled melt Molecular interpretation of freezing process Sublimation of solid COZdisk in hot air Sublimation of ice from porous materials Effect of chemical reaction on sublimation (or evaporation) of small solid (or liquid) particle Capillary condensation in wedge-shaped pore Hypothetical mechanisms in vacuum condensation Condensation coefficients Molecular analysis of condensation Turbulent film condensation based on Nusselt model Theory of evaporation and condensation in slip-flow and freemolecular regimes Vacuum evaporation from solid surfaces Evaporation of liquid drops in another liquid Vaporization of spherical solid into gas Evaporation coefficient and recoil pressure of biphenyl Evaporation of small droplets into flowing air a
T = theoretical study, E = experimental inuestigation.
TABLE E-2.
Interfacial P h e n o m e n a
T h e buildup of films of surface active agents in even the cleanest of apparatus is well known, but has been studied systematically for the first time by Merson and Quinn (13F) in a two-phase horizontal apparatus. Stagnation a t the interface and film growth for various experimental conditions was illustrated graphically. Interfacial resistance was discussed by Goodridge and Robb (5F). Using a stirred tank, they examined the change of interfacial resistance with temperature and interpreted the results in terms of a n energy barrier, sieve, and hydrodynamic effect. Mason and Princen (7227) analyzed mathematically the permeability of soap films in bubbles to a number of gases a t various temperatures. The exact shape of the bubble was taken into account, as well as changing gas composition for multicomponent gases.
(27E) (26E)
E E
(78E, 7 Q E ) T E (75E)
SIMULTANEOUS HEAT AND MASS TRANSFER
S U, S
T L
S
L
S
TABLE F-1. Ref. (2F)
I
(76F)
1
1
Transfer from single sphere lo-< R e < I O 4 Fluid heated from below with concentration gradient Fluid to particle heat and mass transfer rates Various shaped bodies with pulsating air flow
INTERFACIAL PHENOMENA
1
Pore Diffusion in Solids
A scheme for calculating the pore structure and gaseous diffusion properties of catalyst pellets was given by Johnson and Stewart (76G). I t is based on the "dusty-gas" model of Mason et al. (see last year's review) and appears to give good results. Gorring and DeRosset (8G) have devised a convenient experimental method for the determination of the effective diffusivities of porous material with adsorption occurring. Masamune and Smith (79G, 20G) have made a theoretical and experimental study of this same problem. Luikov (78G) has given a n extensive review of the field of heat and mass transfer in porous media. Aris (2G) and Bischoff (4G) both gave essentially identical derivations for the effectiveness factor for general reaction rate forms. A new modulus was defined such that the same plot for effectiveness factor can be used for all cases and complete new calculations need not be performed each time. Petersen (24G) used the same approach to develop a general criterion for the impor-
PHASE TRANSITIONS
(Vaporization, Condensation, Sublimation, Freezing, and Melting)
Topic Effect of surfactants on C O Babsorption in bubble column and in vibrating column Relation of liquid phase mass transfer coefficient and miscelle concentration Instability in liquid-liquid and gas-liquid forced convection transfer Mathematical anal sis of effect of surface active impurities on transfer from solid spleres and drops Interfacial resistance Retardation of evaporation of liquids from capillaries Continuum analysis of mixture a t moving surface Effect of diffusion o n drop coalescence Mathematical analysis for Marangoni effect in flowing films Retardation of evaporation by monolayers
tance of pore diffusion for reactions. Pore diffusion effects on the selectivity of complex reactions were studied by Butt (6G), and Gunn and Thomas (70G) gave a n interesting treatment of the effects of pore diffusion for multifunctional catalyst systems. A book by Petersen (25G) centered its interest on chemical reactions with diffusion. Miscellaneous
Articles of interest dealing with mass transfer in boundary layer flow are listed in Table H-1, while Table H-2 lists those concerning mass transfer in electric fields. Various reviews and books in the field of mass transfer are shown in Table H-3. V O L 57
NO. 1 2
DECEMBER 1 9 6 5
59
TABLE G - I .
PORE DIFFUSION
BIBLIOGRAPHY Molecular Diffusion
Gas diffusion Gaseous diffusion in natural zeolite-relation to crystalline disorder Thermal diffusion of gases Moisture transmission Diffusion with pressure gradient New method of calculating pore properties
( I G , 72G, 75G) (5'3
(9G) (ZlG, 28G-30G) (ZZG, 37G) (260)
E = experimental investigation, T = thearetical study.
TABLE
G-2.
PORE DIFFUSION EFFECTS ON CHEMICAL REACTIONS
Ref.
EorT
Subject
~
Miscellaneous catalytic reactions Combustion reaction Soncatalytic reaction Effectiveness factor with surface diffusion Effectiveness factor with pressure gradient Effectiveness factor with gas volume change
TABLE H-1.
MASS TRANSFER I N BOUNDARY LAYER FLOW
1-1 through turbulent and laminar boundary layers
1
I Isothermal diffusion in laminar boundary layer of variable
A ~
N
A E A, N
density Multicomponent diffusion in laminar boundary layer Concentration profile including thermal diffurion Diffusion from line source in turbulent boundary layer Flow over cylinder with mass removal
.4 = analyfical solufion, E
TABLE H-2.
1
(79H) (ZH) (6H)
!
T T
i
E
I
(ZOH)
~
E
MASS TRANSFER I N ELECTRIC FIELDS
Consideration of maximum detectable electrodiffusion coefficient Diffusion-electrical theory of Dorn effect Mass transport to rotating disk electrode Electrochemical diffusivities of naphthalene, anthracene, biphenyl ~~
a
= experimentel study, it' = numerical solution.
~
E = experimental inuesttgatzon, T = fheoretzcal sfudy.
TABLE H-3.
RELATED REVIEWS AND BOOKS N o . of
Topic Ablation in hot gas stream Absorption from gas mixtures Analogy between heat and mass transfer in packed beds
I
60
I
99 99
27
Crystal growth mechanisms Diffusion and reaction in catalyst pores Diffusion in electrolyte Diffusion in strained systems Dissolution rates Evaporation retardation by monolayers Extraction, solid-liquid
17 70 33 16 74 33 22
Mass transfer engineering computations Mass transfer trends
32 12
Mixing effect in chemical reactor design Nucleation in condensation Nucleation of crystals from solution Nucleation and freezing of supercooled water Waste water and water pollution control for 1963
33 36 14 1280
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
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Mixing Processes in Flow Systems
Interphase Mass Transfer
(1C) Anderson, T. B., Jackson, R., Chem. Eng. Sci. 19, 509 (1964). (2C) Angelino, H., Charzat, C., Williams, R., Ibid., p. 289. (3C) Argaman, Y., Rebhun, M., Israel J . Tech. 2, 228 (1964). (4C) Arima, K., Eguchi, W., Nagata, S., Kagaku Kogaku (English ed.) 2, 172 (1964). (5C) Botterill, J. S. M., Brit. Chem. Eng. 10 ( l ) , 26 (1965). (6C) Brit. Chem. Eng. 9, 461, 541 (1965). (7C) Cahn, D. S., Healy, T. W., Fuerstenau, P. W., IND.END. CHEM.PROCESS DESIGNDEVELOP. 4, 318 (1965). (8C) Can. J . Chem. Eng. 42, 282 (1964). (9C) Carley-Macauly, K. W., Donald, M. B., Chem. Eng. Si. 19, 191 (1964). (1OC) Chapman, F. S., Holland, F. A., Trans. Inst. Chem. Eng. 49, T131 (1965). (11C) Corrsin, S., A.Z.Ch.E. J. 10, 870 (1964). (12C) Davidson, J. F., Harrison, D., Chem. Eng. Sci. 20, 172 (1965). (13C) Davidson, J. F., Harrison, D., “Fluidised Particles,” Cambridge U. P., 1963. (14C) Dawkins, G. S., Purdue Univ. Eng. Bull., Ext. Ser., No. 115, 562 (1963). (15C) d e Kock, J. W., Judd, M . R., Trans. Inst. Chem. Eng. 43,T78 (1965). (16‘2) Eckhoff, R . K., Chem. Ens. Sci. 19, 835 (1964). (17C) Eliashberg, V. M., Burovoi, I. A., A.I.A.A. J. 1, 1264 (1963). (18C) “Fluidisation,” SOC.Chem. Ind., London, 110 pp. (1964). (19C) Glass, D. H., Harrison, D., Chem. Eng. Sci. 19, 1001 (1964).
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(19D) King, c. J., ISO. ENG.CHEX. FVNDAMEKTALS 4, 125 (1965). (ZOD) Kishinevskii, M . Kh., Zh. Prik!. Khim. 38, 103 (1965). (21D) Kishinevskii, M. Kh., Denisova, T. B., Zbid., 37, 1544 (1964). (22D) Kishinevskii, M. Kh., Kornienko, T. S., Ibid., p. 844; 36, 1869, 2681 (1963). (23D) Ibid., 37, 1285 (1964). (24D) Krichevskii, I . R., Tsekhanskaya, Yu. V., Poluprod. dlya Szntera Poliamidov, Khim. i Tekhno!. Produktov Organ. Sinteza 1963, p, 91. (25D) Kubie, G., Collection Czech. Chem. Commun. 29, 3020 (1964). (26D) Kukurechenko, I. S., Shokin, I. N., T T . ~Mosk.Khtm.-Tekhno!. Inst. 1963, p. 197. (27D) Levich, V. G., Krylov, V. S., Vorotilin, V. P., Dok!. Akad. N a u k SSSR 160, 1358 (1965). (28D) Ibid., 161, 648 (1965). (29D) Li, P. S., West, F. B., Vance, W.H., Moulton, R . W,, A.I.Ch.E. J. 11, 581 (1 965). 4, 129 (30D) Marsh, E. D.: Heideger, W. J., I N D . ENG. CHEhi. FUKDAMENTALS (1965). (31D) Merson, R. L., Quinn, J. A., A.I.Ch.E. J . 10, 804 (1964). (32D) Mullin, J. Mi., Cook, T. 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FUNDAMENTALS 3, 380 (1964). (19E) Pfeffer, R., Happel, J.,A.Z.Ch.E. J . IO, 605 (1964). (20E) Philip, J. R., J . Chem. Phys. 41, 911 (1964). (21E) Rowe, P. N., Claxron, K . T., Lewis, J. B., Trans. Inst. Cham. Engrs. (London) 43, T14 (1965). (22E) Rubinshtein, R . h‘,, Postnikov, I. V., Vasil’ev, I. G., Zauodsk. Lab. 30, 806 (1964). (23E) Sideman, S., Hirsch, G., Israel J . Techno/. 2, 234 (1964). (24E) Sideman, S., Taitel, Y . , Int. J . Heat .%{ass Transfer 7, 1273 (1964). (25E) Spalding, D. B., Christie, F. A,, Ibid., 8, 511 (1965). (26E) Turner, J. S., Ibid., p. 759. (27E) Vulliet, rt’. G., J . Chem. Phys. 41, 521 (1964). (28E) Wright, P. G., Trans. Faraday Sot. 60, 1889 (1964). Interfacial Phenomena (1F) Beloborodov, V. V., Tr. Vses. Nauchn. Issied. Inst. Zhirou 1963, p. 145. (2F) Boyadzhiev, L., Balarev, C., Comfit. Rend. Acnd. Bulgare Sci. (English transl.) 17, 937 (1964). uk SSSR 155, 644 (1964). (3F) Deryagin, B. V., Kurgin, Yu. S., Doki. Akad (4F) Deryagin, B. V., Nerpin, S. 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INDUSTRIAL A N D ENGINEERING CHEMISTRY
(9F) Lochiel, A. G., Can. J . Chem. Eng. 43, 40 (1965). (10F) hlacKay, G. D. M., Mason, S. G., Koll-Zeit 195, 138 (1964). (11F) Maroudas, N. G., Sawistowski, H.?Chem. Eng. Sci. 19, 9 1 9 (1964). (12F) ,Mason, S. G.: Princen, H . M., J. ColloidSci. 20, 353 (1965). (13F) Merson? R. L., Quinn, J. A,, A.I.Cii.E. J.11, 391 (1965). (14F) Morikawa, A,, Keii, T., Chem. Eng. Sci. 20, 255 (1965). (15F) Rukenshtein, E., Inzh.-Fiz. Zh. No. 7 , 116 (1964); Int. Chem. Eng. (English transl.) 5 , 88 (1965). (16F) Shukla, R . N.. Kulkarni, S. B., Gharpurey, M. K., Biswas, A. B., J . Appl. Chem. 14, 236 (1964). (17F) Slattery, J. C., Chem. Eng. Sci. 19, 453 (1964). P o r e Diffusion i n Solids (1G) Alder, H., Promotionsorb (Zurich), 3270 (1962). 4, 227 (1965). (2G) Aris, R., 1x0. ENC. CHEM. FUNDAMEKTALS (3G) Auer, IV., Bakemeier, H., Detzer, H., Chem. Ing. Tech. 36, 774 (1964). (4G) Bischoff, K . B., A.Z.Ch.E. J. 11, 351 (1965). (5G) Brandt, W. W-., Rudolff, W., 2. Physik Chem. 42, 201 (1964). (6G) Butt, J. B., Can. J . Chem. Eng. 42, 211 (1964). (7G) Caretto, L. S.: Nobe, K., Preprints, Div. Petrol. Chem., ACS Meeting, April 4, 1965, 10 (2), 25 (1965). (8G) Gorring, R . L., DeRosset, A. J., J . Catalysis 3, 341 (1964). (9G) Goshchitsky, B. N., Izrailevich, I. S., Dokl. h a d . A‘auk USSR 147,817 (1962); English rransl. JPRS-18180; OTS-63-21343. (10G) Gunn, D. J., Thomas, 1%‘. J., Chem. Eng. Sci. 20, 89 (1965). (11G) Hawrin, P., Murdoch, R., Ibid., 19, 819 (1964). (12G) Hewitt, G. F., Sharratt, E. W., “ f l u r e 198, 952 (1963). (13G) Hugo, P., Chem. Eng. Sci. 20, 187 (1965). (14G) Ibid., p . 385. (15G) Imre, K., Kouya, J., Imre, J., Acta Uniu. Debrecen. Ludouico Korsutk. Nom., Ser. Phys. Chem. 9, 17 (1963). (16G) Johnson, M. F. L., Stewart, Vv‘. E., J . Cafalysis4, 248 (1965). 4, 102 (1965). (17G) Krasuk, J. H., Smith, J. M., IND.ENG.CHEM.FUNDAMENTALS (18G) Luikov, A. V., Advan. Heat Transfer 1, 123 (1964). (19G) Masamune, S., Smith, J. AM,, A.I.Ch.E. J . 11, 34 (1965). (20G) Ibzd., p. 41. (21G) Osinski, 4.,Gar, Woda Tech. Sanit. 38, 384 (1964). (22G) Otani, S., Wakao, N., Smith, J. M., A.I.Ch.E. J . 11, 439 (1965). ( 2 3 G ) Ibid,, p. 445. (24G) Perersen, E. E., Chem. Eng. Sci. 20, 587 (1965). (25G) Petersen, E. E., “Chemical Reaction Analysis,” Prentice Hall, 1965. (26G) Rebinder, P. A,, Shchukin, E. D., Margolis, L. Ya., J . Phys. Chem. (L’SSR) 154, 1 (1964). (27G) Schneider, P., Mitschka, P., Collection Czech. Cham. Commun. 30, 146 (1965). (28G) Wakabayashi, K., Kopaku Kognku (English ed.) 2, 121 (1964). (29G) Ibid., p. 132. (30G) Zbid., p. 146. (31G) Wakao, N., Otani, S., Smith, J. M.: A.Z.Ch.E. J . 11, 435 (1965). (32G) Weekman, V. W., Gorring, R. L., J . Catalysis 4, 260 (1965).
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