Advances in mass transfer fundamentals published during I968 -69
THOMAS M. REGAN ALBERT GOMEZPLATA
Mass Transfer TABLE I-A.
he format of this review is the same as we used in our last T Annual Review [IND. ENG. CHEM.,60, 53-62 (1968)l. I n addition to summarizing the mass transfer literature, selected
GASEOUS DIFFUSION IT or Ea
System or Topic
Predicting diffusion coefficients of nonpolar and polar gases Cop-Kr, HzNz,He-02, CHd-COz, CH4CaHlo, He-Hp; 20°C, 3OOC; Pfrom 1-25 atm. Neon-noble gas pairs, 0°-1200C, 1 atm. twobulb H20 in argon, N2, and CH4; 10-100°C; low P, modified Stefan Cyclic steady-state diffusion Transition regime under reduced P
Reference
T
( 8 A1
E
( 2 0 A1
E
(27A)
E E,T T,E
(3OA) (39A) (47A)
* T is theoretical; E, experimental.
papers in supporting areas have been cited. sented in each section of the review.
Tables are pre-
Molecular Diffusion
Brokaw ( 8 A ) presented methods for predicting viscosity, thermal conductivity, and diffusion coefficients of nonpolar gases and their mixtures based on a modified Stockmayer potential. His methods have engineering usefulness and do not require a detailed knowledge of the kinetic theory. Prausnitz et al. ( 3 0 A ) made use of the collision integral based on the Kihara spherical core potential function to calculate the diffusivities of water in nonpolar gases. Several investigators ( 6 A , 20A, 2 7 A ) reported their work on gaseous diffusion with the noble gases. Hoshino and Sat0 ( 7 7 A )point out several interesting observations on the difference between macro- and microviscosity in the discussion of their work with the diffusion of sodium chloride and sucrose in polymer solutions.
TABLE Il-A. LIQUID DIFFUSION (Primarily Experimental Data and Method) System
Noble gases in
HzO
S02-HpO Alcohols and amides in HzO 0 2 in blood
Technique
Mass spectrometrical determination through a water column Radioactive tracer Capillary cell Unsteady state with electrode monitor Moirt pattern
Sodium chloride and sucrose in aqueous solutions of polyvinyl alcohol and polyvinylpyrrolidone Microinterferomo-Glucose in aqueous careter boxymethylcellulose and carboxypolymethylene
Temperature OO,
25O, 50' C
21 OC 4, 12.5, 24.8, 37OC
37OC
23OC
System
Technique
Temperoture
Electrophoresis NaNOs-CsNOa Optical diffusDodecane-hexaometer decane-hexane ; toluene-c hlorobenzene-bromobenzene Mach-Zehnder Several solutes in diffusometer hexane and carbon tetrachloride Photographically Triethylene glyrecorded intercol-water ferograms Diaphragm cell Ethylene glycolwater-KC1; ethanol-waterKC1 Rayleigh optical Poly sodium styrenesulfonate in NaCl solutions Sodium polyacry- Gouy interferometer late-NaC1-HzO
VOL. 6 2 NO.
2
45OOC 25OC
25°C
30, 45, 65OC
25OC
25OC
25 " C
FEBRUARY 1970
41
TABLE I l l - A . LIQUID DIFFUSION
TABLE I-B.
Subject
Ion transport controlled by both the concentration gradient and liquid junction potential in a Stokes Cell at 25OC Viscosity and the intradiffusion coefficient in multicomponent systems Phenomenological coefficients Transport in concentrated 1 :1 electrolytes Analysis of multicomponent diaphragm cell data Kinetics and diffusion in ion-exchange Mutual diffusion coefficient Hydrodynamic theory in multicomponent diffusion Reaction and diffusion in open systems Concentration dependence of transport coefficients in multicomponent mixtures Transient ordinary and forced diffusion Effect of linear dependence among driving forces on the independence of the fluxes Self-diffusivity from free volume theory Liquid-side mass transfer coefficients in ionexchange Correlation of diffusion coefficients for paraffin, aromatic, and cycloparaffin hydrocarbons in water
TABLE IV-A.
Subject
(7A) ( 2 A1 (3A, 7 A , 3 4 A )
(944 ) (77.4) (79A) (26A, 2 8 A ) (22A) ( 37A) (36A) (37A1
(@A)
(57'4)
Thermogravitational
Reference
(5-4)
'5Nz-l4Nz NaCl, KCl, Z2NaC1, 22Nain KCl
Diaphragm cell
(3344) (78A)
Hydride-Hz and hydride-hydride n-Heptane-n-hexadecane
Twin bulb Diaphragm cell
(72'4) (38A)
CC14-benzene, cyclohexanebenzene C H 3 0 H with CC14, benzene, and cyclohexane Diphenyl in benzene urea in water Neon-xenon
Flow cell
(47A)
Flow cell
( 4 2)~
Flow cell
(4344 1
Trennschaukel
(45A)
EXPERIMENTAL TECHNIQUE Method
TABLE 1 1 4 3 .
Re/erence
E
(77B, 27B,, 30B)
E,T
(43B, 46B)
E
(7B)
E,T
(5B, 22B)
E
(26B, 39B)
E
(20B1 (7B, 78B, 38B)
E,T
DISPERSION I N POROUS MEDIA TorE
Reference
T E
(4B, 29B) (ZB, 4 2 B )
Axial dispersion of gases in packed beds (G-S) Axial dispersion of liquid in fixed and fluidized beds (L-S) General dispersion Dynamics of packed bed with interphase heat and mass transfer Transport in nonisothermal packed beds Liquid distribution in packed beds
TABLE Ill-B.
E
T T E T,E
DISPERSION I N EQUIPMENT
Subject
Axial dispersion : Pipelines (note and replyj Multiphase systems (S-G) (G-L) Elbows Liquid in perforated-plate columns (L-L) Gas in gas-liquid reactors Response analysis on distillation plate Determination from experimental data
T or
E
Reference
( 2 3 )~
T E
(27B) ( 6 B , 24B)
E
(IIB)
E
(32%) (37B) (74B) (73B, 3 3 B )
E T T
Reference
Solid spheroids in a wind tunnel Wedge interferometer
(4A) ( 73A)
Chromatography for surface diffusion Bubble collapse
(35A) (504
TABLE IV-B.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
CHEMICAL REACTOR APPLICATIONS Subject
O n design and operation of jet stirred reactor Axial dispersion model Accuracy Optimal design Small and large Peclet numbers Applicability Limit or small axial diffusivity Thermodynamic significance boundary conditions Parametric study of first order, irreversible exothermic reaction in a flat slab catalyst a
42
Tkeoreiicol, T , or ExperimentaZ, E
Subject
Technique
Carbon-tetrachloride-cyclohexane; carbon-tetrachloride-ethyl alcohol
Newtonian jet stability, viscoelastic stability, and jet length Mixing and local concentrations in turbulent jets Dispersion mechanisins in laminar flow Laminar velocity profiles and dispersion in developing flows Wall region velocities, turbulent velocities, and eddy viscosity Nondisturbing flow visualization technique Velocity distribution and gas dispersion in transitional and turbulent flow
( 4 0 )~ (46A1
THERMAL DIFFUSION
Syrtern or Topic
TABLE V-A.
BASIC TURBULENT DIFFUSION AND DISPERSION
Reference
T is theoretical; E, experimental.
Tor Ea
Reference
E
(70B)
T T T T T
(3B)
T
(47B)
T
(75B)
(28B) (9B) (36B, 4 5 B ) (44B)
Bartelt and Horne ( 3 A ) have shown that the extra phenomenological coefficients introduced by using dependent fluxes are determinate by a simple proof based on entropy production. The coupling between the concentration gradient and liquid junction potential for a ternary ionic system has been discussed by AIbery, Ryan, and Totterdel ( 7 A ) . For diffusion in a binary mixture, Loflin and McLaughlin (26A) showed that the mutual diffusion coefficient follows from the Bearman theory when a geometricmean relationship between certain friction coefficients is assumed.
TABLE I-C.
AGE DISTRIBUTION FUNCTIONS Tar E
Subject
Residence time distribution (RTD) Analysis using Laguerre functions Transfer functions Digital resolution Determination in flow systems I n semi-infinite reactors Liquid phase of trickle flow reactors Of drops in spray column (L-S) Packed fluidized bed (G-S) Stochastic models Estimation of parameters Nonideal mixed-flow vessel Frequency response of back-flow cell model
T T T
Reference
(lSC,32C) (33C) (19'2)
TABLE-I-D.
GENERAL INTERPHASE MASS TRANSFER Subject
Reference
Primary Theoretical Mass transfer to rear of cylinder Problems in scale-up Dynamics of distributed parameter system in laminar flow Diffusion-controlled adsorption processes Primarily Experimental Effect of large-scale roughness (G-L) Turbulent promoters in packed beds Tangential feed to wetted-wall column Liquid jet column Horizontal cylinders with transverse vibration Wall of stirred vessel Annuli a t high Schmidt number Packed columns Effective interfacial area Two-phase cocurrent downflow (G-L) Effect of surface interaction (G-L) Solute and inert particles
( 11 2 0 ) (1300)
(1460) (70)
(300) (240, 540) (220 1
(570, 1160, 7 3 3 0 ) (1470) (7020) (2301
Design Methods
M I X I N G I N STIRRED TANKS
TABLE Il-C. Subject
Jet mixing vessel Thoroughness and time of homogenization Impulse response, dead space, backmixing and non-integral values for stirred tanks in series model Minimum stirring rates (G-L)
TABLE Ill-C.
T a7 E
Reference
T,E (29C) E (9C, 77C,31C)
T
(4C-7C)
E
(3C)
M I X I N G I N FLUIDIZED BEDS
Subject
Tor E
Reference
Incipiently fluidized bed Theory and measurement of contact time distribution Influence of distribution (G-S) Effect of bubbles on conductivity of particles (G-S) Bubbling bed model
E,T
(74C, 28C)
T,E E
(22C, 2 3 C ) (24C)
TABLE IV-C.
E
T
(26C) (36C)
OTHER M I X I N G APPLICATIONS
Subject
Liquid mixing on perforated tray Distillation with constant molar enthalpy Liquid extraction columns Packed fluidized beds Cold shot reactor Review of mixing
T a7 E
Reference
E
(73C)
T
(2OC) (27C, 30C)
T,E E
E
(15C) (20 (25C)
Albert Gomezplata is Professor and Thomas M . Regan is Associate Professor in the Department of Chemical Engineering, University of Alaryland, College Park, M d .
AUTHORS
Optimum operation of extractor Solvent extraction Adiabatic gas absorption
Hydrodynamic theory was used by Kett and Anderson (22A)in multicomponent systems to develop generalized expressions for the fluxes of each component relative to the volume-average velocity. Both the diffusion coefficients, Dli, and the phenomenological coefficients, L,,,are included. Schonert (36A) expanded the phenomenological coefficients for multicomponent mixtures in a Taylor series with respect to concentration. This technique is very useful in discussing cases where one component is very dilute. The diffusion coefficients for paraffin, aromatic, and cycloparaffin hydrocarbons in water have been correlated over a temperature range of 2' to 6OoC by Witherspoon and Bonoli ( 5 1 A ) with the Wilke-Chang empirical equation. I n their continuing studies of thermogravitational thermal diffusion, Beyerlein and Bearman ( 5 A ) found that when results are extrapolated to 0' to remove reservoir effects, results agree with flow cell and pure thermal diffusion techniques. They report a to vary with A T for the systems CClr-cyclohexane and CClaethyl alcohol. Using a quasi-lattice model for liquid structure, Shieh (38A) has proposed a theory relating thermal diffusion of linear alkanes to segmented motion. His theory was tested by employing tracer techniques and a modified Stokes cell and gave good agreement with equilibrium thermodynamics and non, 43A) conequilibrium expressions. Story and Turner ( 4 7 ~ 442A, tinued their flow-cell studies of thermal diffusion. Wise and Houghton (50A) presented an interesting new technique for determining the diffusion coefficient of slightly soluble gases in liquids by microscopically following the collapse of small stationary bubbles. VOL. 6 2
NO. 2 F E B R U A R Y 1 9 7 0
43
Turbulent Diffusion and Dispersion
I n laminar flow through tubes, Arai, Saito, and Maeda ( 1 B ) reported on the mechanism of laminar dispersion in the range where axial molecular diffusion appears. Gill et al. (22B) found less dispersion in developing fields than in fully developed flow and explain this observation in terms of the differences in velocity of the fluid particles on a plane perpendicular to the main direction offlow.
TABLE Il-D. SIMULTANEOUS INTERPHASE TRANSFER AND CHEMICAL REACTION Subject
Reference
A nondisturbing flow visualization technique using a photochromic dye which is irradiated to produce a colored trace has been used by Frantisak, Palade de Iribarne, Smith, and Hummel (20B) to study mean velocities and wall shear stresses in laminar and turbulent flow. Brinkworth and Smith ( 7 B ) report velocity distributions and eddy viscosity in the core of turbulcnt flow, while others (26B, 3 9 B ) report on velocity and eddy diffusion in the wall region. An unusually large number of experimental studies of dispersion
TABLE I l l - D . TRANSFER T O AND FROM SINGLE DROPS, BUBBLES OR SOLID PARTICLES
General Method to evaluate effect of film and pore diffusion Digital simulation of naphthalene oxidation Diffusion-controlled rate mechanism Transfer from single spheres to stagnant liquid Selectivity in stirred tanks General analysis for multiphase systems Surface reaction on wedge shaped surface Gas absorption, instantaneous, firstorder and second-order reaction Analysis based on two-film theory Continuous flow system with firstorder reaction (based on R T D ) Penetration model with large heat effects (1st order) Laminar boundary layer for wedge flow (1st order) Multiplicity of steady states in boundary layer Uniqueness of large distributed parameter system Maximum temperature rise in gassolid reactions Fluidized beds Wetted-wall column Carbon dioxide-water and sodium hydroxide Packed column Sieve plate
Continuous-flow stirred tank
Hydrogen sulfide-aqueous ammonia Carbon dioxide-carbonate bicarbonate solution containing hypochlorite catalyst Sodium thiosulfate and hydrogen peroxide Nitration of toluene with mixed acid
Effect of turbulence Large Reynolds and Peclet numbers Creeping flow when trace of surfactant is present Diffusion and distortion effects in drops Bubble drag and transfer in nonNewtonian fluids Isothermal bubble dissolution Bubble formation in viscous liquids
(560 (7490) ( 7230)
( 720 )
( 7 780)
(200)
Local rates from solid bodies of revolution Drops Pulsating (water-xylene) Free convective effects (methyl acetate or 2-ethoxy ethyl acetatedistilled water) Surface impurities Coalescence and effect of impurities Rates inside liquid drop Dimpled and skirted drops Formation from cylindrical jet Experimental method to suspend and measure transfer Bubbles Comparative study on experimental methods Terminal velocity, shape and path Growth in superheated liquids Effect of chemical additives Transfer with and without reaction Large or cap bubbles Interaction in fluidization Coalescence in fluidized beds Wake Stability of trailing gas envelope Gas interchange Solid particles Simultaneously rotating and translating sphere Dissolution by isothermal free convection Orientation, and shape and oscillation on settling velocity Electrochemical technique Suspension in vertical tube Transfer Review Bubble and drop phenomena a
44
T T T T
(1660) (370, 7500)
T T
T,E Primarily Experimental
Review Inter-intraphase diffusion and reaction
Reference
Primarily Theoretical
(660)
Single gas bubbles
T o r Ea
Subject
Primarily Theoretical
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
T is theoretical; E, expenmental.
(7010)
(1220) ( 6 2 0 , 1240) (520) (16D, 7360) (7390) (9801 ( 7000)
(1340, 7570) (1550, 1560) (1440) (5001 (1540)
(7 740) (1310)
(7430, 1600) (69D) (320) (130, 7580) (370)
TABLE IV-D. Subject
General heterogeneous flow
TRANSFER BETWEEN A CONTINUOUS PHASE AND A DISCONTINUOUS PHASE OF DISCRETE PART I CLES Tor E
Reference
T
(380,390,990, 7200) (1650)
Dynamics of particulate sysT tems T Effect of surfactants Agglomeration by population T balances Determination of interfacial E area (G-L) Interaction effects T E Spacial distribution (S-L) Agitated tanks Segregation of dispersed phase E (L-L) T,E Suspension of solids Correlation for suspended solids E.T E Gas dispersion Interfacial area with slow E reaction Effect of rate on holdup and E interfacial area Power consumption (G-L) E T Drop size distribution E Drop size by encapsulation E Liquid extraction rates Stage contactors Solid distribution in two-stage E system Cell model ( R T D ) for column T with plates Holdup and axial distribution in pulsed sieve-plate column E (L-L 1 Oxidation-reduction reactions E (L-L) Bubble columns E Suspension of solids E Bubbles from porous plate Solid concentration profiles for E slurry reactor Pressure drop in perforated T pipe distributors E Bubbles from perforated plate E Gas holdup and axial mixing Concentration gradient in mulE tiple stages E Application of two-film theory E Liquid film coefficient
3
'
(1510) (390)
(80,640) (870,1420) (360,370, 1650) (840)
(1180) (1100)
(170,630,1710, 1130) (1280) (1420) (860) (1070) (1450) (700) (700,1320)
(650,7090) (770) t550) (480) (7690) (30,1270) (1480) (1080) (1210)
in packed beds and theoretical model studies were reported. Balla and Weber (2B)and Urban and Gomezplata (42B)report new data on axial dispersion of gases. Bischoff (4B)notes a theoretical basis for the maximum value of Peclet number reported by recent studies. Levenspiel and Dayan (29B)report on the complications introduced by packed beds of porous absorbing solids. Buffham and Gibilard (8B)give an analytical solution to the "Deans-Levich Model" for dispersion in porous media. Schertz and Bischoff (37B)report on a study on radial and axial components of effective thermal conductivity and mass-dispersion coefficient. Both isothermal and nonisothermal data are reported and significant differences were found between the two cases. Pstergaard and Michelsen (3323)discuss problems connected with the imperfect pulse method of analysis for the determination of axial mixing and holdup in two phase flow. Gill (21B)presented a theory for heat and mass transfer with time variable flow in multiphase systems. Clements (13B) gives a least-squares method for determination of the parameters of the dispersion model from experimental data. Cassell and Perona (71B)report on axial dispersion through 90 degree elbows and report increases that depend on the direction of flow.
Subject
Tor E
Bubble size distribution Fluidized beds Fluid mechanical description (S-L) Incipient fluidization velocity Cross-flow coefficients from RTD Bubbling bed model Adsorption of steam Two-phase theory Uniformity Bubble velocity and bed expansion Expansion of screen-packed beds Mass transfer driving forces Spray columns Crystallization in spray droplets Drop size spectrum Retention, axial and radial electrical conductance Extraction during drop accumulation Design methods Review Pipeline flows Particle dynamics (S-G) Single density model (S-L) Local and average void fraction (G-L) Improved contacting with screens (G-L) Other Method to predict packed bed behavior Two-phase reactor design Water droplets with two-phase nozzles Particle coagulation and interaction in dilute and settling suspensions Novel type of countercurrent fluid-solids contactor
T
Reference
(600)
T,E (20) T,E (110, 740, 1050)
T (760) T,E (820,830) E T,E
T T,E
(420) (470,7530) (1610) (430-460) (880,1250)
E E
(190) (1670)
E E
(500) (340)
E
(1060)
E
(7350) (50,6 0 ) (940)
E E
(7260) (1400)
E,T (120,780,490) E
(1630)
T,E
(150) (2601
E
(250)
E
(1030, 7040)
E
(1410)
Boundary conditions for dispersion models are still receiving considerable attention. The thermodynamic significance of the Danckwerts boundary conditions is discussed by Standart (47B). Wissler (45B)considered the relationship of the Taylor-Aris model and the diffusion model. Bischoff (3B)presents calculations on the accuracy of the axial dispersion model with chemical reaction. Burghardt and Zaleski (QB)considered the solution to the dispersion model for general kinetics a t small and large Peclet numbers. Drott and Aris (15B)present a parametric study of firstorder, irreversible exothermic reaction in a flat slab of catalyst, Leung and Chang (28B)discuss the optimal design of a tubular reactor with Taylor diffusion. General Mixing Processes in Flow Systems
T h e many papers on the analysis and measurement of residence time distributions (RTD) are summarized i n Table IC. Included are studies by Van Swaaij, Charpentier, and Villermaux (34C,35C) on the R T D of the liquid i n packed columns under trickle-flow conditions. Results indicate that two mechanisms contribute to the spread in residence time-an eddy diffusion process and mass exchange with stagnant areas. They present VOL. 6 2
NO.
2
FEBRUARY 1970
45
~
TABLE I-F.
INTERFACIAL PHENOMENA
Subject
Solid-liquid
TABLE I-E.
SIMULTANEOUS MASS AND HEAT TRANSFER
Subject
Parametric pumping Transpiration and changing diameter of rigid spheres Vertical plane Porous membranes Porous media Porous catalyst particle Extended surface fin Smooth-walled duct Turbulent pipe flow of dilute polymers
a n analytical expression for the R T D in a semi-infinite reactor with axially dispersed piston flow with stagnant zones. Krambeck, Katz, and Shinnar (77C)report on the interpretation of tracer experiments in systems with fluctuating throughput which leads to different types of sojourn time distribution of material in the system. Stochastic transfer functions are discussed by King (7") for continuous flow systems. The estimation of parameters for commonly used stochastic models is considered by Sweet and Bogdanoff (32C). Methods of measurements for evaluation of the stochastic model parameters are described by VBclavek (33C) for the case of nonideally mixed flow vessels. Buffham and Gibilaro (5C) suggest a generalization of the tankin-series model to include a nonintegral number of reactors. Buffham ( 4 C ) also gives analytical solutions of the stirred-tankbackflow model for infinite and semi-infinite number of stages. Fan and coworkers (7C)consider varying stage size with the inclusion of a parameter to account for backmixing. The RTD's can be derived from these solutions. Corrigan and Beavers (6C) present a model of a continuous stirred tank reactor which includes a dead space and active volumes. Oldshue's annual mixing review (25C) is an excellent reference. Kunii and Levenspiel's bubbling fluidized model (7013) can be expected to receive attention in the future because of its considerable improvement over presently available models. In a series of papers, Mecklenburgh and Hartland (ZUC, 27C) explain design methods for extraction and distillation. These include manual calculation methods which account for backmixing between stages. Interphase Mass Transfer
Tables I-D through IV-D condense the large numbers of refer ences in this section into smaller groups. We have included selected references in related areas that are necessary for the accurate estimation of transport rates. These extra references will be helpful to workers in the field. I n the area of general interphase mass transfer, Davies and Warner (300)found that the rate of COz absorption into water was increased by a factor of 3.5 by providing large-scale roughness on the surface. Several studies (240,540) report on the characteristics of turbulent contactors. Motion of the loose packing in these liquid-gas countercurrent contactors is responsible for the vigorous action reported. Sharma and Gehlawat (1330)used jet and stirred tank apparatus to perform a kinetic study coupled with absorption. Their complete results include data needed to design industrial absorbers. Treybal ( 15gD) presents design methods for adiabatic packed gas absorbers which include mass and heat transfer resistances of the liquid phase.
46
Solid-gas Liquid-gas
Reference
( I E , 2E, l l E , 12E, 14E, 15E)
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
~~
Liquid-liquid Diffusion in monolayers Diffusion in polymers Contributions of waves to mass transfer in liquid films Effect of surfactants on flow characteristics of falling liquid films Structure of dissolving thin liquid films Mass transfer in ion-exchange resin bed Effect of diffusion on thermal decomposition rate of solids Intraparticle diffusion in adsorption Vaporization and gas phase-controlled desorption in a wetted wall column Mass transfer in thin liquid films in upward flow Diffusion in porous solids Diffusion and relaxation phenomena in ice Self-diffusion of chloride ions in rubidium chloride Self-diffusion of 0 2 in magnetite Effect of pulsations in the flow field on interphase mass transfer
Reference
(14F, 77F, ZIF, 26F, 31F, 34F, 35F,37F) ( 78F)
(QF--l lF,15F, 39F,40F) (ZF,13F) (3F,5F, 29F) ( I F , 6F, 7F,23F, 30F)
(72F) (76F,27F, 28F)
Multiplicity of steady states is considered by Lindberg and Schmitz (850)for boundary layer problems with surface reaction, and by Luss (90D)for distributed parameter systems with chemical reaction and heat and mass diffusion. The voluminous literature on mass transfer to and from single particle continues. Gal-or and coworkers (370)present a good review on the subject. Garbarini and Tien ( 4 1 0 ) compare experimental methods for mass transfer in gas-liquid systems. Mensing and Schugerl (7OOO) describe a new experimental setup to suspend single particles and to measure instantaneous mass transfer rates. The important area of the effect of impurities on mass transfer has received attention (52D,62D, 1240, 1660,
1700). Transfer between a continuous phase and a discontinuous phase can best be summarized by Table IV-D which gives individual references for agitated tanks, stage-contactors, bubble columns, fluidized beds, spray columns, and pipe line contactors. Some items of interest will be presented here. Gal-or and coworkers (380,390, 7200, 1510, 165D) have done a creditable job on the theoretical prediction of the hydrodynamics of swarms of particles. Discrepancies in the experimentally reported exponent of the Reynolds and Schmidt numbers can now be explained from theoretical considerations. For mass transfer from suspended solid particles in stirred tanks, Hughmark (630)proposes an interesting correlation based on mean particle slip velocities that are back-calculated from best fit equation for single particle mass transfer. Two other correlations for stirred tanks worthy of note are by Nienow (7730)and Brian, Hales, and Sherwood (170). The distribution of gas flow in a fluidized bed is still in dispute (440,470,880,1530)as well as the two-phase theory of fluidiza-
TABLE I-G.
PORE DIFFUSION
Subject
TorE
Effect of different structure on gaseous diffusion in the transition region Effect of boundary condition on drying granular solids Effusion from Knudsen cells Gaseous diffusion in zeolites and related solids Combined gradients of concentration and pressure in porous materials Evaporation of volatile liquids from porous systems Effective diffusivities in catalyst pellets
Reference
E
T T
Simultaneous Heat and Mars Transfer
E
E
T
TABLE Il-G. PORE DIFFUSION EFFECTS ON CHEMICAL REACTION System
Effectiveness factors
tion. A model for gas fluidized beds based on transport considerations of single bubbles and the cloud surrounding them is presented in Kunii and Levenspiel’s book (IOH). Many studies of the characteristics of these single bubbles are reported (30,110, 4 6 0 , 760,820, 830, 1 5 4 0 ) and will be of considerable help in supplying and testing new models for a fluidized bed.
T or E Reference T,E (8G,IIG, 13G15G, 19G, 22G, 23G,
Sweed and Wilhelm (15E)presented a computational investigation of separation by direct thermal mode in liquid phase parametric pumping. The calculations were performed with the new STOP-GO Algorithm. They investigated system parameters for the toluene-heptane-silica gel system and simulated experimental separations. A computational model, based on intraparticle profiles was presented by Rolke and Wilhelm (12E) for a recuperative parametric pumping column. A theory of separation by parametric pumping based on the assumption of local equilibrium between solid and fluid phases was presented by Pigford et al. ( I IE)and generalized by Aris (7E). A discussion of the difficulties of applying parametric pumping as a possible model for active biological transport is given by Booij (ZE).
TABLE I-H.
30G, 33G) Poisoning in a single pellet Oxidation of ethylene on cuprous oxide-aluminum trioxide Simple expression for the rate of formation of ammonia Modeling of zero-order reaction within a catalyst Influence of mass transfer within the porous structure Effective diffusivity Integral equation method for reaction rates in catalysts Interaction of heat and mass transfer Intraparticle diffusion effects Kolbe-Schmitt carbonation of 2-naphthol Hydrogenation of alpha-methylstyrene in a trickle-bed reactor Change in pore size distribution from surface reaction Analysis of combined film and pore diffusion with rapid reaction in a fixed-bed reactor Knudsen flow and chemical reaction in a porous catalyst Diffusion-controlled rate mechanisms in gas-solid reaction systems Diffusion kinetics and catalyst attrition in cyclic processes
T,E ( I G ) E
(2G)
T
(6G)
T
(9G)
E (10G) T,E (IZG, 28G, 29G)
T E E,T
(16G)
(18G) (ZOG, 27G)
E
(21G)
E
(24G)
E,T
(25G)
E,T (26G)
T
(31G)
T
(35G)
T,E
(38G)
MASS TRANSFER I N BOUNDARY LAYER FLOW Subject
TorE
Heat and mass transfer form vertical plate Perturbation solutions of diffusion-controlled moving boundary problems Radial mass and momentum in a n axial fluid stream between coaxial rotating cylinders Solution to boundary layer equations for moving flat surfaces with suction and injection Transfer from pipe surface in streamline flow Diffusion from defined shapes into laminar flowing liquid Heat and mass transfer to continuous fiber Unsteady mass transfer with irreversible first-order reaction in laminar boundary layer Film thickness for two immiscible falling films
E
TABLE 11-H.
E,T
Reference
(2H)
(4H, 5 H )
T
(16H)
T
(17H)
BOOKS AND REVIEWS RELATED TO MASS TRANSFER Subject
Reference
Nonlinear equations of transport processes Fluid dynamics review Heat and mass transfer in process metallurgy (book) Fluidization engineering (book) Mixing review Gas absorption review Cocurrent gas-liquid flows (book) Mass transfer operations (book) Complex heterogeneous chemical reaction system
VOL. 6.2 NO. 2
(IH)
(7H) (9H) (IOH) ( 72H) ( 73H) (7 4 ~ ) (78W (19H)
FEBRUARY 1970
47
Findley et al. (5E)studied the coupled system of water evaporation through a water-repellent porous membrane. The mass transfer is a result of the vapor pressure difference and, hence, temperature difference across the membrane. lnlerfacial Phenomena
Sutey and Knudsen (34F) utilized a diffusion controlled electrochemical reaction to measure mass transfer coefficients a t the solid-liquid interface in upward gas-liquid climbing film flow in a vertical annular duct. These measurements were used for predictions of incipient downflow of the film, shear stress a t the inner wall, and interfacial shear stress. The results were in good agreement with theoretical predictions based on simplified momentum balance concepts. Experimental evidence is presented by Berg and Morig ( Z F ) showing that density gradients developed during solute transfer across a liquid-liquid interface exerts a strong influence on convection generated by interfacial tension variations. New correlations were developed on an individual polymer basis by Durrill and Griskey ( 7 F ) for the solubilities and diffusivities of various gases on molten or thermally softened polymers. Correlations for Henry’s law constants in solid polymer systems were inapplicable. Vivian and Schoenberg (38F)point out that the agreement they found between various systems in gas-phase controlled desorption in a wetted-wall column seems to indicate that discrepancies observed in packed tower data arc? the results of liquid phase resistance due to wide distribution of lifetimes of liquid surface elements. Pore Diffusion in Solids
Cunningham and Geankoplis (3G) studied the effects of dif ferent structures of porous solids on diffusion of gases in the transition region. Keeping the micropore radius approximately constant and varying the macropore radius and bulk density, they found that the random pore model gave good agreement with experimental data. Diffusion studies in zeolites and related solids were carried out by Eberly (7G) employing gas chromatographic techniques. He found that the effect of molecular weight on diffusivity is more pronounced than expected for Kundsen diffusion and described a mathematical procedure to include the effects of adsorption on the diffusion constant.
TABLE I-J.
MEMBRANE TRANSPORT
Subject
Permeability measurement technique Time lag for diffusion of gas mixtures Concentration dependence of Nall transport in cellulose acetate Oxygenation of blood Elec tro-osmosis Aerosol filters Ionic transport across membranes Reverse osmosis Gaseous flow induced by volatile liquids Electrodialysis with ion-exchange membranes Convective diffusion across a porous diaphragm Liquid ion-exchange membranes Operational methods for a convective diffusion equation Membrane separation parameters (review) Temperature-separation factor in gaseous diffusion across a membrane Water transport through cellophane membranes Drying of cellulose acetate membranes Convective diffusion in rotating disk with imperfect semipermeable interface
48
INDUSTRIAL AND ENGINEERING C H E M I S T R Y
Aris et al. (ZZG, 23G) discussed the effect of shape on the effectiveness factor and how to simulate the shape effects. Weisz (38G) pointed out that the mechanical particle attrition rate in cyclic processes depends on the regeneration kinetics. He shows how the attrition rates in the commercial TCC process were markedly reduced by the development of bead catalyst, having nearly doubled diffusivity without changing the chemical composition. Membrane Transport
The problem of gas-exchange in whole blood through a silicone rubber membrane was studied by several investigators (4J, 6 J , QJ, 305). Aiba and Huang ( I J ) presented a simple electrode method of determining the oxygen permeability and diffusivity in polymer membranes immersed in liquids. Sourirajan et al. (13J-75J, 7 8 J ) presented expressions for calculating local and average mass transfer coefficients, analyzed the solute transport parameter, and developed equations for stagewise reverse osmosis process design. Bennion and Rhee (35)presented a very comprehensive study of NaCI transport in cellulose acetate. Coupling fluxes were significant in some instances. They tested methods for determining the six independent transport parameters and showed a dependence on concentration for the three most used parameters. REFERENCES Molecular Diffusion (1A) Albery, W. J., Ryan, C and Totterdel, D. S “Diffusion in a Three Ion System,” Trflns. Forad~ySoc.:’65, 1530-1536 (1969):’ (2A) Albright, J. G., “Two Semiempirical Equations Which Relate Viscosity and the Intradiffusion Coefficients for Multicomponent Systems,’’ J. Phys. Chem., 73, 1280-1286 (1969). (3A) Bartelt, J. L., and Horne, F. H., “Proof of a Theorem on the Determinancy of Phenomenological Coefficients for Dependent Fluxes,” J. Chem. Phys,, 51, 210 (1969). (4A) Beg, S. A., Bombrowski, N., and Cornish, A. R. H. “Measuremcnts of Local Rates of Mass Transfer from Solid Bodies of Revolution,” Chem. Enp. Sci., 23, 1157-11 58 (1968). (SA) Beyerlein A . and Bearman R. J., “Thermogravitational Thermal Diffusion V. Temperktde Difference Ekects. Thermal Diffusion Factors for the System Carbon Tetrachloride-Cyclohexane and Carbon Tetrachloride-Ethyl Alcohol,” J. Chem. Phys., 49, 5022 (1968). (6A) Boerboom, A. J. H., and Kleyn, G., “Diffusion Coefficients of Noble Gases in Water,” ibid., 50, 1086-1088 (1969). (7.4) Bresler, E. H., and Wendt, R . D., “Onsager’s Reciprocal Relation. An Examination of Its Application to a Simple Membrane Transport Process,” J.Phys. Chem., 73, 264-266 (1969). (8A) Brokaw, R. S., “Predicting Transport Properties of Dilute Gases,” I m . END. 8 , 240-253 (1969). CHEM.,PROOESS DES.DEVELOP., (9A) Carman, P. C., “Transport in Concentrated Solurions of 1 : 1 Electrolytes,” J . Phys. Chem., 73, 1095-1105 (1969). (10A) Cukrowski, A. S., “The Diaphragm Cell Method for the Investigation of Thermal and Self Diffusion in Liquid Electrolyte Solutions,” ibid., pp 6-14. (11A) DeLancey, G. B., “Analysis of hlulticomponent Diaphragm Cell Data,” ibzd., pp 1591-1593. (12A) Devyatykh, G. G., Vlasov, S. M., and Tsinovoi Yu. N. “Determination of the Thermal Diffusion Constant and the Force Condtants of ;he (12-6) LennardJones Potential for Binary Hydride-Hydrogen and Hydride-Hydride Mixtures,” Russian-J. Phyr. Chem., 42, 1460-1463 (1968). (134) Duda, J. L., Sigelko, W.,,L., and Vrentus, J. S., “Binary Diffusion Studies with a Wedge Interferometer, J.Phys. Chem., 73, 141-149 (1969). (14A) Eriksen, T. E. “Diffusion Studies in Aqueous Solutions of Sulfur Dioxide,” Chem. Eng. Sci., 24,’273-278 (1969). (15A) Gary-Bobo, C. M., and Weber H. W. “Diffusion of Alcohols and Amides in Water from 4 to 37O,” J. Phys. Ciern., 73,’1155-1156 (1969). (16A) Hershey, D., and Karhan, T., “Diffusion Coefficients for Oxygen Transport in Whole Blood,” A.I.Ch.E. J., 14, 969-972 (1968). (17A) Hoshino, S., and Sato, K., “The Diffusion of a Small Molecule in a Polymer Solution,” Kagaku K q o k u , 31, 961-966 (1967). (18A) Huang, A. L., Desai, S. V., and Wellek, R. M., “Diffusion Coefficients of D-Glucose in Aqueous Carboxymethylcellulose and Carboxypolymethylene Solutions,’’ J. Chem. Eng. Data, 14, 356 (1969). (19A) Kataoka, T., Maeda, N., Sato, M . , and Ueyama, K., “Ion Exchange Kinetics on Liquid Phase Diffusion-Exchange of Ion with Equal Valence,” Kagnkcr Kogaku, 31, 491-497 (1967). (20A) Kesti2, J., and Yata, J., “Viscosity and Diffusion Coefficient of Six Binary Mixtures, J. Chem. Phyr., 49, 4780-4791 (1968). (21.4) Ketelaar, I. A. A , , and Kwak, J. C. Th., “Ionic Mobilities and Diffusion Coefficients in the NaNOa CsNOa System at 450°C,” Trans. Faraday Soc., 6 5 , 139 (1969). (22A) Kett, T. K., and Anderson, D. K., “Multicomponent Diffusion io Nonassociating Non-electrolyte Solutions,” J . Chem. Phys., 73, 1262-1267 (1 969). (23A) Kett, T. K., and Anderson, D . K., “Ternary Isothermal Diffusion and the Validity of the Onsager Reciprocal Relations in Yon-associating Systems,” J . Phys. Chem., 73, 1268-1274 (1769). (24.4) Kett, T. K., Kelly, C. M.,,ancl,Anderson, C. K., “Diffusion in the Solvents Hexane and Carbon Tetrachloride, J . Chem. E n g . Data, 14, 342 (1969). (25A) Kim, H., “Combined Use of Various Experimsntal Techniques for the Determination of Nine Diffusion Coefficients in Four-Component Systems,” J. Phys. Chem., 73, 1716-1722 (1969). (26A) Loflin, T., and McLaughlin, E., “Diffusion in Binary Liquid Mixtures,” ibid., pp 186-190. (27A) Malinauskas, A. P., and Silverman, M. D., “Gaseous Diffusion in NeonNoble Gas Systems,” J. Chem. Phys., 5 0 , 3263-3270 (1969). (28.4) McLaughlin, E., “Diffusion in a Mixed Dense Fluid,” ibid., p 1254.
+
(29A) Merliss, F. E., and Colver, C;,P., “Molecular Diffusion Coefficients for the Triethylene Glycol-Water System, J . Chem. Eng. Data, 14, 149 (1969). (30A) O’Conell, J. P., Gillespie, M . D., Krostek W D . and Prausnitz J M “Diffusivities of Water in Nonpolar Gases,” J . P i y ~C. h e i . , 73, 2000-2004 (i969j: (31A) Othmer H G and Scriven L. E. “Interactions of Reaction and Diffusion in Open ~ys;ems,”’iND. ENO.cA, F ~ N D A M . , 8, 302-313 (1969). (32A) Perkins, L. R., and Geankoplis, C . J., “Molecular Diffusion in a Ternary Liquid System with the Diffusing Component Dilute,” Chem. Eng. Sci., 24, 1035 (1969). (33A) Raman, S., Mathor, B. P., Howard, A. J., Champlin, J. W., and Watson W. W., “Thermal Diffusion in Polyatomic Gases: Isotopic 16Nr14N2, J . Chem: Phys., 49, 4877 (1968). (34A) Rastogi, R. P., Singh, K., and Srivastava, M. L., “Cross-Phenomenological Coefficients. X I . Nonlinear Transport Equation,” J . Phys. Chem., 73, 46 (1969). (35A) StFneider P. and Smith J. M., “Chromatographic Study of Surface Diffusion, A.Z.Ci.E.>., 14, 886-b95 (1968). (36A) Schonert, H., “ O n the Concentration Dependence of Transport Coefficients in Multicomponent Mixtures,” J . Phys. Chem., 73, 62-70 (1969). (37A) Shair, F. H., and Cohen, D. S., “Transient Ordinary and Forced Diffusion in a Tube Connecting Stirred-Tank End Bulbs of Finite Size,” Chem. Eng. Sci., 24, 39-48 (1969). (38A) Shi$ J. J., “Thermal Diffusion and Segmental Motion in Binary n-Alkane Systems, J . Phys. Chem., 73, 1508-1513 (1969). (39A) Simmons, P. J., and Spinner, I. H., “Cyclic Steady State Diffusion,” A.Z.Ch.E. J . , 15, 489-494 (1969). (40A) Standart, G., “The Second Law of Thermodynamics for Heterogeneous Effect of a Linear Dependence Among the Driving Forces Flow Systems-IV. on the Independence of the Fluxes,” Chem. Eng. Sci.,24, 241-266 (1969). (41A) Story, M . J., and Turner, J. C. R., “Flow-Cell Studies of Thermal Diffusion Benzene and Cyclohexane f Benzene Systems,’’ in Liquids. Part 4-CC14 Trans. Faradav SOL..65. 349-354 (1969). (42A) Stor M J and Turner J. C. R. “Flow-cell Studies of Thermal Diffusion in L i q u i z . Par; 5-Binary Mixtures l f C H I O H with CCh, Benzene and Cyclohexane a t 25OC,” nbtd., pp 1523-1529. (43A) Story, M. J., and Turner, J. C. R., “Thermal Diffusion of Diphenyl in Benzene and of Urea in Water,” ibid., p p 1610-1811. (44A) Suzuki Y Noda I and Nagasawa M., “The Diffusion of Polyelectrolyte in the Prese)nck’of Add)ed’kalt,” J . Phys. &hem., 73,797-803 (1969). (45A) Taylor, W. L., Weissman, S . , Haubach W. J and Pickett P. T. “ThermalDiffusion Factors for the Neon-Xenon System,” Chem. Phyi., 50, 4886 (1969). (46A) Tham, M. J., and Gobbins, K . E. “Free Volume Theory for Self-Diffusivity of Simple Nonpolar Liquids,” A.Z.Ch.2.. J., 15, 306 (1969). (47A) Toei R. Okazaki M Uragami, A,, and Takaki Y “Mass Transfer Through ’Rarefied Gas ’Bet$een Concentric Spheres,” J.’Cilrn. Eng. Japan, 1, 125-131 (1968). (48A) Turner, J. C. R., and Snowdow C . B. “Liquid-Side Mass Transfer Coefficients in Ion Exchange-H+/Cu++-& Systdm,” Chem. Eng. Sci.,23, 1099 (1968). (49A) Vitagliano, V., Laurentino, R., Costantino L. “Diffusion in a Ternary System with Strong Interacting Flows,” J . Phys. ?he;., 73, 2456-2457 (1969). (50A) Wise, D. L., and Hou hton, G., “Effect of 5: Impermeable Wall on Bubble Collapse in Diffusion Coetfcient Measurements, Chem. Eng. Sci., 23, 1501-1503 11968). (51A) Witherspoon P. A and Bonoli L. “Correlation of Diffusion Coefficients for Paraffin, Arokatic,‘gnd Cyclo a‘raffin Hydrcarbons in Water,” IND. END. CHEM.,FUNDAM., 8,588-591 (19697.
+
.;
Turbulent Diffusion and Dispersion (1B) Arai, K., Saito, S., znd Maeda, S., “On the Dispersion Mechanism in Laminar Flow Through Tubes, Kagaku Kogaku, 31, 25-31 (1967). (2B) Balla, L. Z., and Weber, T. W., “Axial Dispersion of Gases in Packed Beds,” A.Z.Ch.E. J . , 15, 146-149 (1969). (3B) Bischoff, K. B., “Accuracy of the Axial Dispersion Model for Chemical Reactors,” ibid., 14, 820-821 (1968). (4B) Bischoff, K., “A Note on Gas Dispersion in Packed Beds,” Chem. Eng. Sci.,24, 607 (1969). (5B) Berman, N. S., and Santos, V. A,, “Laminar Velocity Profiles in Developing Flows Using a Laser Doppler Technique,” A.Z.Ch.E. J., 15, 323-327 (1969). (6B) Briller, R., and Robinson, M., “A Me$md for Measuring Particle Diffusivity in Two-phase Flow in the Core of a Duct, A.Z.Ch.E. J., 15, 733-735 (1969). (7B) Brinkworth B. J. and Smith P. C. “Velocity Distribution in the Core of Turbulent Pip; Flow:” Chem. En;. Sci.,i4, 787-791 (1969). (8B) Ruffham, B. A , , and Gibilard, L. G “The Analytical Solution of the DeansLevich Model for Dispersion in Poroud’Media,” Chem. Eng. Sci., 23, 1399-1401 (1968). (9B) Bur hardt, A., and Zaleski, T., “Longitudinal Dis ersion a t Small and Large Peclet &umbers in Chemical Flow Reactors,” ibid., 5?5-591 (1968). (10B) Bush, S. F., “The Design and Operation of Single-phase Jet-Stirred Reactors for Chemical Kinetic Studies,” Trans. Znst. Chem. Eng., 47, T59-72 (1969). (11B) Cassell R E. Jr. and Perona J. J “Axial Dispersion in Turbulent Flow Through S h d a r d 90 beg. Elbows,’: A.Z.ch.E. J., 15, 81-85 (1969). (12B) Chung, S . F., and Wen, C. Y . “Longitudinal Dis ersion of Liquid Flowing Through Fixed and Fluidized Beds:” ibid., 14, 857-86f!(1968). (13B) Clements, W. C., Jr., “A Note on Determination of the Parameters of the Longitudinal Dispersion Model from Experimental Data,” Chem. Eng. Sci., 24, 957-963 (1969). (14B) Dicke B. R and Durbin L. D. “Continuous and Discrete Time Response Analysis opthe Ba)ckHow Cell Model h t h Linear Interphase Mass Transfer on a Distillation Plate,” Can. J . Chem. Eng., 46, 369-379 (1968). (15B) Drott, D. W., and Ark, R., “Communication of the Theory of Diffusion and Reaction-I. A Complete Parametric Study of the First-Order, Irreversible Exothermic Reaction in a Flat Slab of Catalyst,” Chem. Eng. Sci., 24, 541-551 (1969). (16B) Dutkai E and Ruckenstein E. “Liquid Distribution in Packed Columns,” Chem. Eng. kct.‘,’ 23, 1365-1373 (lb695. (17B) Fenn, R. W I11 and Middleman S., “Newtonian Jet Stability: T h e Role of Air Resistancd:” A:Z.Ch.E. J . , 15, 339-383 (1969). (18B) Flint L. F., and Eisenklam P., “Longitudinal Gas-Dispersion in Transitional i n d Turbulent Flow Thrbugh a Straight Tube,” Can. J . Chem. Eng., 47, 101-106 (1969). (19B) Fluendy M. A D and Horne D S., “Investigation of Diffusion Through Packed Beds’by a MonTe Carlo Me;hod,” Separation Sci., 3, 203-209 (1968).
@OB) Frantisak, F., Palade de Iribarne, A., Smith, J. W., and Hummel, R. L. “Experimental Technique, Nondisturbing Tracer Techniques for Q u a n t i t a t i d Measurements in Turbulent Flow,” IND.END. CHEM., Fundnm., 8 , 160-1G7 (1969). (21B) Gill,,,W. N., “Axial Dispersion with Time Variable Flow i n Multiphase Systems, A.Z.Ch.E. J..15. 745 (1969). (22B) Gill W N Ananthakrishnan V. and Nunge, R. J., “Dispersion in Developing Veldcit; F&ds,” ibid., 14, 936-94k (1968). (23B) Goldschmidt V. W and Householder M . K. “Comments on an Article on Longitudinal Disbersion”for Turbulent FIdw in Pipes and a Reply,” IND. END. CHEM., FUNDAM., 8, 172-174 (1969). (24B) Gomezplata A. and Brown R. W. “Axial Dispersion Measurement in TwoPhase Flow,” A . i . C h . J., 14, i57-658’(1968). (25B) Jefferson, C. P., “A Further Note on Dynamics of Packed Bed with Intraphase Heat and Mass Transfer,” Chem. Eng. Sci., 24, 613-614 (1969). (26B) Sirkar K. K and Hanratty T J “Limiting Behavior of the Transverse Turbulent’Velocii; Fluctuations dlosd to”a Wall,” TND. ENC. CHEM.,FUNDAM., 8, 189-192 (1969). (27B) Kroesser, F. W., and Middleman, S., “Viscoelastic Jet Stability,” A.Z.Ch.E. J.,15, 383-386 (1969). (28B) Leung, V. P., and Chan , K. S., “Optimal Design of Jacketed Turbular Reactor with Taylor Diffusion,” A.Z.Ch.E. J., 15, 782-784 (1969). (29B) Levenspiel 0 and Dayan J., “Longitudinal Dispersion in Packed Beds of Porous Absorbing Solids,” C h d . Eng. Sci., 23, 1327-1334 (1969). (30B) Meister, B. J., and Scheele, G . F., “Prediction of Jet Length in Immiscible Liquid Systems,” A.Z.Ch.E. J., 15, 689-699 (1969). (31B) Men’schchikov V. A. and Aerov M. E. “Axial Mixing of Gas in Gas-liquid Reactors,” Tear. Oinouy d i m . Tekh., 891-195 (1967). (32B) Otake T . , and Komasawa I., “Longitudinal Dispersion Characteristics of Liquid in )Perforated-Plate Colimns with Reciprocated Flow,” Kagaku Kogaku, 32, 583-588 (1968). (33B) Pstergaard K and Michelsen M L., “ O n the Use of the Imperfect Tracer Pulse Method {or getermination o? Hold-up and Axial Mixing,” Can. J. Chem. Eng., 47, 107-112 (1969). (35B) Rodriguez, J..M., and Patterson, G . K “Comparison of Logran ian T i m e Correlations Obtained from Dispersion Expiriments and from Space-’hme Correlation Function,” A.I.Ch.E. J., 15, 790-792 (1969). (36B) Saito, S., and Maeda S “ O n the Dispersion Mechanism in Laminar Flow Accompanying a First Ordk’r Chemical Reaction,” Kagaku Kogaku, 31, 1137 (1967). (37B) Schertz, W. W., and Bischoff, K. B “Thermal and Material Transport in Nonisothermal Packed Beds,” A.Z.Ch.E. 15, 597 (1969). (38B) Seyer F. A and Metzner A B. “Turbulence Phenomena in Drag Reducing Systems,”)A.Z.Ci.E. J.,15,42&4;4 (1969). (39B) Sherwood T. K Smith K. A. and Fowles P. E., “The Velocity and E d d y Viscosity Dist;ibutioz in the’Wall Region of Tdrbulent Pipe Flow,” Chem. Eng. Sci., 23,1225-1236 (1968). (40B) Siftel, C. N., J?, Threadgill, W. D., and Schnelle, K . B., Jr., “Comments on a n Article on Longitudinal Dispersion for Turbulent Flow in Pipes and Reply,” IND. ENO.CHEM.,FUNDAM., 8,172-174 (1969). (41B) Standart, G . , “The Thermodynamic Significance of the Danckwerts’ Boundary Conditions,” Chem. Eng. Sci., 23,645-655 (1968). (42B) Urban J C and Gomezplata A., “Axial Dispersion Coefficients in Packed Bedsat LoGReyr;bldsNumber,”Cah J . Chem. Eng., 47,353-359 (1969). (4?B), Vasil’iev, A. S., “Measurement of Local Concentrations for Gas Jet Impingingintoliquid,” Teor.Osnouy Khim. Tekh, 1,349-353 (1967). (44B) Wissler, E. H., “On the Asymptotic Behavior of a Tubular Reactor in the LimitofSmall AxialDiffusivity,” Ckem. Eng.Sci. 24,829-832 (1969). (45B) Wissler, E. H., “ O n the Applicability of the Taylor-Aris Axial Diffusion Model to Tubular Reactor Calculations,” ibid., p p 527-539. (46B) Wood, T., “Mixing Characteristics of a Bounded Turbulent Jet,” ibid., 23, 783-789 (1968).
i,
3.,
Oeneral Mixing Processes in Flow Systems (1C) Anderssen, A. S., and White, E. T., “The Anal sis of Residence Time Distribution Measurements Using Laguerre Functions,” 6 a n . J . Chem. Eng.,47, 288-295 (1969). (2C) Asbjgrnsen, 0. A., and Klovning, M., “The Mixing of Large Gas Streams, An Experimental Study with Reference to the Cold Shot Reactor,” Chem. Eng Sci..23.1053-1065 (1968). (3C) Boerma, H., and Lankester, J. H., “The Occurrence of Minimum Stirring Rates in Gas-Liquid Reactors,” ibid., pp 799-801. (4C) Buffham, B. A., “Impulse Res onse of Infinite and Semi-infinite Sequences of Identical Stirred Tanks with Bacfflow,” IND.ENO.CHEM.,FUNDAX8, 428-430 (1969). (5C) Buffham, B. A., and Gibilaro, L. G., “A Generalization of the Tank-in-Series Mixing Model,” A.Z.Ch.E. J., 14,805-806 (1968). (6C), Corrigan, T. E., an,$ Beavers W 0 “Dead S ace Interactions in Continuous Stirred Tank Reactors, Chem. Eng. .&i.;’23, 1003-7006 (1968). (7C) Fan, L. T., Chen, S. K., Ahn, Y . K., and Wen, C . Y., “Mixing Models with Varying Stage Size,” Can. J.Chem. Eng., 47,141-148 (1969). (8C) Fort, I., Podivinskl, J., and Baloun, R., “Studies of Mixing. XXII. T h e Study of Convective Flow in a System with a Rotary Mixer and Barnes,’’ Collect. Czech. Chem. Commun., 34,959-974 (1969). (9C) Gluz, M. D., and Pavlushenko I. S. “Time of Homogenisation in Mixing ofNon-Newtonian Fluids,” Z h . Priki. Khi;., 39,2419 (1966). (1OC) Gwyn, J. E “Digital Resolution of Residence Time Distribution from Pulse ResponseData,’;h.Z.Ch.E. J.,15,126-127 (1969). (11C) Harada, M., Tanaka, K., Eguchi, W., and Nagata, S., “The Effect of MicroMixing on the Homogeneous Polymerization of Styrene in a Continuous Flow Reactor,” J . Chcm. Eng., Japan, 1,148-152 (1968). (12C) Hopkins, M. J Sheppard, A. J., and Eisenklam, P., “The Use of Transfer Functions in Evalua’ling Residence Time Distribution Curves,” Chem. Eng. Sci. 24, 1131-1 137 (1969). (13C) Inoue, I., and Unno, Ha., “On Liquid Mixing on Perforated Tray-An Application ofTurbulent DiffusionTheory,” Kagaku Kagaku, 32,480-485 (1968). (14C) Miller K. J. and Edwards R. M., “Gas-Solids Mixing and Heat Transfer Studies in incipiently Fluidized ’Beds of Nonuniform Cross-Sectional Area,” IND. ENQ.CHEM.,PROCESS DES.DEVELOP.,8,232-240 (1969). (15C) Kato K. Imafuku K. and Kubota H. “Fluid Behaviour in Packed-FluidizedBed,’: Kakaku KogaLu, S i , 967-973 (1467): I
,
VOL. 6 2
NO,
2
FEBRUARY 1970
49
(16C) King, R . P “Continuous Flow System with Stochastic Transfer Functions,” Chem.Eng.Sci., i$,1035-1044 (1968). (17C) Krambeck, F. J., Katz, S., and Shinnar, R., “Interpretation of Tracer Experiments in Systems with Fluctuating Throughput,” IND.ENG.CHEM.,FUKDAM., 8,431-441 (1969). (18C) Letan, R., and Kehat, E. “Residence Time Distribution of the Dispersed PhaseinaSprayColumn.,”A.I.’Ch.E. J., 15,4-10 (1969). (19C) McSwain, C. V., and Durbin, L. D., “Frrquency Response of the Back-flow Cell Model of Mass-transfer Processes: Packed Column Characteristics for Tracer-Gas Absorotion.” SebaratzonSca.. 4.24-50 (1969). (20C) Mecklenburgh J. C. and Hartland, S., “Design Methods for Countercurrent Flow with Ea’ckmixjng-I. Distillation with Constant Molar Enthalpy,” Chem.EEng.Sci., 24, 899-907 (1969). (21C) Mecklenburgh, J . C., and Hartland S “Two-phase Countercurrent Extraction High Backmixing,” Chem. Eng. Sci.,i3,?421-1430 (1968). ( Z Z C ) Nauman, E. B., and Collinge, C. N., “The Theory of Contact Time Distrihution in Gas Fluidized Beds,” ibid., pp, 1309-1316. (23C) Nauman, E . B., and Collinge, C. N., “Measurement of Contact Time Distributions in Gas Fluidized Beds,” ibid., pp 1317- 1326. (24C) Oigenblik, A. A,, et al., “Influence of Gas-distributing Screen on Heat Transfer and Mixing of Solid Phase in Fluidized Bed,” Khim. Prom., 44, 615-617 (1968). (25C) Oldshue, J. Y . ,“Mixing,” I m . END.CHEM., 60, No. 11, 25-35 (1968). (26C) Park, W. H., Kang, W. K., Capes, C. E., and Osberg, G. L., “The Properties of Bubbles in Fluidized Beds of Conducting Particles as Measured by a n Electroresistivity Probe,” Chem. Ene. Sci., 24,851-865 (1969). (27C) Petha A. “Notes on the Drtermination of the Residence Time Distribution in Contin;ous-’flow Systems,” ibid., 23, 807-810 (1968). (28C) Ruckenstein, E., and Tzechulescu-Fili escu, “Hydrodynamics of Fluidized Beds with Incipient Nonhomogeneities,” ibiu?, pp 1121-1125. (29C) Sato, K., “Mixing Process in a Jet Mixing Vessel,” Kagaku Kogaku, 32, 588594 (1968). (30C) Shirotsuka T., and Murakami, A “Mixing Characteristics of Continuous Phase on Perforated Plate in Liquid Extrlction Column,” ibid., 31, 497-504 (1967). (31C) Snider, D., and Corri an, T. E., “Measurement of Thoroughness of Mixing,” A.I.Ch.E. J . , 14,813 (19687. (32C) Sweet, A. L., and Bogdanoff, J L. “The Estimation of Parameters for a Commonly Used Stochastic Model,” ibid.,’15, 100-110 (1969). (33C) Vdclavek “Stochastic Model of a Non-ideally Mixed Flow-vessel,” Collect Czech,, Chem. dommun., 33,3646-3662 (1967). (34C) Van Swaaij W P M . Charpentier J. C and Villermaux, J., “Residence Time Distrihutidn in’thk Li(uid Phase of Trick1k)Flow in Packed Beds,“ Chem Eng. Sci... 24.. 1083-1095 (1969). (35C) Villermaux, J.? and Van Swaaij, 74’. P. M., “Mode’le Representatif De La Distribution Des Temps De Se’jour Dans U n R,eacteur Semi-infini A Dispersion Axiale Avec Zones Stagnantes. Application .A L’Ecoulement Ruisselant Dans Des Colonnes D ‘Anneaux Rachig,” ibid., pp 1097-1 111. (36C) Yoshida, J. and Kunii, D. “Axial Dispersion of Gas in Bubbling Fluidized Beds,” IND.EXG.CHEhx., F U N D A8,402-406 ~, (1969). I
I
,
General Interphase Mass Transfer (1D) Anderson, R. B., Hamielec A. E and Stifel, G. R. “Diffusion-controlled AdsorptionProcesses,”Can. J . dhem. E&., 46,419-423 (196h). (2D) Anderson, T. B., and Jackson, R., “A Fluid Mechanical Description of Fluidized Beds. Comparison of Theory and Experiment,” 1x0. ENG.CHEM.,FUNDAY. 8, 137-144 (1969). (3D) Aoyama, Y . , Ogushi, K.,,, Koide, K and Kubota, H., “Liquid Mixing in Concurrent Bubble Columns, J . Chem. Eng. Japan, 1,158-163 (1968). (4D) Aylor D. and Bradfield W. S., “Effects of Electrostatic Force, Relative Humidit;, Hdating Surface ?em erature, and Size and Shape on Droplet Evap~ U N D A Y . ,8, 8-16 (1969). oration Rate,” IND.ENG.CHEM., (5D) Baltas, I,;, and Gauvin, W. H., “Performance Predictions for a Cocurrent Spray Dryer, A.I.Ch.E. J . , 15,764-771 (1969). (6D) Baltas, L., and Gauvin, W. H., “Transport Characteristics of a Cocurrent Spray Dryer,” ibid., pp 772-779. (7D) Baltas, L. and Gauvin W. H., “Some Observations of Crystallization in SprayDrople&,” Can. J . Chem. Eng., 47,204-205 (1969). (8D) Bayens, C . A and Laurence R. L., “A Model for Mass Transfer in a Coalescing Dispersion,” ?KD, ENG.CHE;.: FLIND.AM. 8,71-77 (1969). (9D) Beg, S. A Dombrowski N., and Cornish, A. R. H., “Measurement of Local Rates of Mass’hansfer fromkolid Bodies of Revolution,” Chem. Eng. Sci., 23, 11571158 (1968). (10D) Bell, R. L., and Babb, A. L., “Holdup and Axial Distribution of Holdup in a END.CHEM., PROCESS DES. Pulsed Sieve-Plate Solvent Extraction Column,” IND. DEVELOP., 8,392-400 (1969). (11D) Ben‘a J. Havalada, I., Bafrnec, M., and Ilavskd J., “The Velocities a t Incipient ’ Fldidization of Polydisperse Materials, I. Theoretical,” Collect. Czech. Chem. Commun., 33, 2620-2635 (1968). (12D) Bhatia, V. K., “Gas Holdu of a Bubble Swarm in Two Phase Vertical Flow,” A.I.Ch.E. J., 15,466-467 (19695. (13D) Boulos, J. I., and David, C. T., “Simultaneous Heat and Mass Transfer from a Single Sphere to a Turbulent Air Stream,” Can. J . Chem. Eng., 46,30-34 (1969). (14D) Bourgeois P. and Grenier P., “The Rate of Terminal Velocity to Minimum Fluidization Vklodity for Spherjcal Partical Particles,” ibid., pp 325-328. (15D) Bow.en, J . H. and Lacey D. T. “A Single Pellet Prediction of Fixed Bed Behaviour,” Chern.’Eng. Sci., 22, 965-9’73 (1969). (16D) Boyadzhiev, L., Elenkov, D., and Kyuchukov, G., “ O n Liquid-liquid Mass Transfer Inside Drops in a Turbulent Flow Field,” Can. J . Chem. Eng. 47, 42-44 (1969). (17D) Brian, P. L. T Hales, H . B., and Sherwood, T. K., “Transport of Heat and Mass Between Liquyds and Spherical Particles in an Agitated Tank,” A.I.Ch.E.J., 15,727-753 (1969). (18D) Brown F. C and Kranich, W. L.,“A Model for the Prediction of Velocity and Void F;actiozProfiles inTwo-Phase Flow,” A.I.Ch.E. J . , 14,750 (1968). (19D) Capes, C. E., and McIlhinney “The Pseudo articulate Expansion of Screen-Packed Gas-Fluidized Beds,” ibh., pp 917-922 (f968). (20D) Carberry, J. J., “Chemical Reactions Engineering,” IND.ENG. CHEM.,61 (2), 51-53 (1969). (21D) Carberry, J. J., and White, D., “ O n the Role of Transport Phenomena in Catalytic Reactor Behavior,” ibid., 7,27-35 (1969). (22D) Carre B and Bu are1 R. “Determination Experimentale De L’Accroissement De
