FUNDAMENTALS
Mass Transfer
PUBLICTIOX
has been active in the fundamental aspects of mass transfer during 1958. Of particular interest are a number of articles which clearly point out new areas in the field where further knowledge is needed. Among these are the general subject of longitudinal dispersion and particularly its influence in packed bed operations; and the distribution of turbulence scales and its importance in mixing and homogeneous reactions. The potential utility of boundary layer methods in the fluid mechanical analysis of mass transfer phenomena is gaining increasing recognition. A number of studies have pointed up the important role of interfacial phenomena and particularly the fluid motion induced by surface tension forces.
Increasing emphasis has been placed on mathematical analysis and experiments directed toward the gaining of a fundamental understanding of mass transfer mechanisms.
C. R. WlLKE received a B.S. in 1940 from the University of Dayton, M.S.
of Rochester. His Ph.D. was obtained from Princeton University, where he served as instructor for two years. Prausnitz's main interests are in phase equilibria and in rate processes in chemical reactors. He i s a member of the AIChE.
in 1942 from State College of Washington, and Ph.D. (1944) from the University of Wisconsin. Since 1946 he has been at the University of California where he is professor of chemical engineering and chairman of the department of chemical engineering. He i s a member of the AIChE, ACS, Electrochemical Society, and ASEE. Wilke received the junior reward of the AlChE in 195 1 and was institute lecturer in 1957.
JOHN M, PRAUSNITZ, assistant professor of chemical engineering at the University of California (Berkeley), attended Cornell and the University
466
Molecular Diffusion a n d Separation Processes
The subject of molecular diffusion coefficients is treated in detail in this review on Transport Properties. Only those articles which have particular bearing on mass transfer applications are discussed in this section. An excellent critical revieiv of available methods for estimating diffusion coefficients in gases and liquids is presented by Reid and Sherwood (76.4).
ANDREAS ACRIVOS, assistant professor of chemical engineering at the University of California (Berkeley), received his early education in Greece. He earned the 6.5 degree at Syracuse University in 1950 and the Ph.D. at the University of Minnesota in 1954. Acrivos' main interests are in applied mathematics in chemical engineering.
INDUSTRIAL AND ENGINEERING CHEMISTRY
LVestenberg and LValker (20.4) have developed a technique of measuring diffusion coefficients of gases from the spreading of a tracer gas injected from a point source into a laminar carrier gas stream of uniform velocity. The method offers the advantages of speed and ease of measurement at high temperatures. The corresponding states correlation of Slattery for diffusion in dense gases reported in last year's review has been published in more readily available form (78A). Keyes and Pigford (77A) measured separation factors for hydrogen-nitrogen diffusing simultaneously near atmospheric pressure in the presence of methanol and of cyclohexane vapors. The gases were allowed to diffuse through 4 feet of 1 inch copper tubing packed with glass wool. Situations were studied in which the vapors were stagnant and in which they were made to flow counter to the direction of hydrogen-nitrogen diffusion. I t is of considerable theoretical interest that the separation factors were within experimental error of those calculated by solutions of the MaxwellStefan equations for three-component diffusion. Application of the theory to separation of isotopes is discussed. Some interesting data for diffusion in nonideal liquid systems are reported by Anderson, Hall, and Babb (7-4). Measurements were made for methanolbenzene, ethanol-benzene, acetone-water, acetone-carbon tetrachloride, acetonechloroform, and acetone-benzene in the temperature range from 25" to 40' C. Inadequacy of the usual thermodynamic correction to the mutual diffusion co-
Role of surface forces may be key to further progress in two-phase mass transfer
efficients is demonstrated strikingly in this work. For the acetone-water system Figure 1 illustrates the rather extreme departure of Dq* (diffusion coefficient X viscosity-corrected for activity) from the linear relationship suggested by the Eyring theory. Details of the MachZehnder interferometer and diffusion cell assembly developed for this work are presented by Caldwell, Hall, and Babb (5A). Effect of temperature on self-diffusion in water, heptane, and tin is commented upon by Innes and Albright (7OA). The Stokes-Einstein relation, D,lT = constant (D = diffusion coefficient, 7,i = viscosity, T = temperature)? gave good agreement for Lvater over the range from 273.2 to j 7 3 . 2 O K. Errors of as much as 30% resulted from predicting the temperature dependence by this method for heptane and tin over more extensive temperature ranges although most of the errors \cere less than 10%. The authors obtained a better representation of the temperature dependence u i t h a three-constant Arrhenius equation. Effect of solute volume on diffusion coefficients in dilute aqueous solutions a t constant temperature is also discussed, and special equations are given for alcohols, amino acids, and sugars. Whitaker and Pigford (27-4) have proposed a theoretical model for thermal diffusion in liquids \vhich permits numerical solution of the equation of Drickamer and associates which relates the thermal diffusion constant to the net heats of transport. Enthalpies for flow activation and hole formation are related to the net heat of transport within the limits of certain assumed mixing rules. Agreement between the theory and experimental data of the authors and other investigators was found, particularly \vith respect to the effect of concentration on the thermal diffusion constants. For multicomponent liquid mixtures Baranoivski and Fulinski (2.4) have derived general formulas for the partial Soret coefficients and stationary thermal diffusion potentials. Separations in a batch column for benzeneheptane were reduced by imposing a pulsing floiv on the system by De Maria and Benenati (7.4): who attributed the effect to increased longitudinal mixing. The effect of pressure up to 1000 a m . on the thermal diffusion ratio was observed by Il’alther and Drickamer for several binary gas systems (79,4). A very sharp minimum in the ratio was found at densities near the critical density of the mixture in most cases. Neither the kinetic theory nor the thermodynamics of irreversible processes
gives a satisfactory explanation of the behavior. Liu (74A) discusses the effect of pressure-diffusion flux on the concentration distribution of gas mixtures in flow fields. A unique separating device combining ordinary gaseous diffusion through a porous carbon membrane and thermal diffusion between the hot inner surface of a carbon cylinder and a cooled outer wall is described by Shirotsuka and associates (77A). Separation of carbon dioxide and hydrogen was measured for various operating conditions. A thermal diffusion plant producing 2 cc. of He3 at standard conditions per week from atmospheric helium has been operated by the Atomic Energy Research Establishment at Harwell (4A). With two columns of the coaxial-tube type and a third hot-wire type column concentrations up to 10% He3 in helium have been obtained. Forster (&4) presents a valuable analytical technique for solving a class of diffusion problems lvith a moving boundary. This procedure however appears to be useful only when the corresponding problem with fixed boundaries can readily be solved. Even so: the final form of the solution, although of considerable theoretical value, involves repeated integrations, so that outright finite-difference numerical procedure might be preferable when an actual problem is attacked. By obtaining numerical solutions of the one-dimensional diffusion equation for simple geometries, Crank ( 6 A ) has studied theoretically a process where a limited number of diffusing molecules are rapidly and permanently prevented from diffusing further so that, mathematically, this also turns out to be a diffusion problem \vith a moving boundary. A method for separating isotopes by fractional crystallization is described by Kuhn and Thurkauf (73,4) who observed a n enrichment of H D O and H2O18 in the solid phase in the fractional crystallization of water. The authors discuss the possibility of applying a cyclic counterflow process analogous to a rectification column to enhance the separation. Such a process, however, due to diffusional resistance, appears promising only when the crystals of ice can be limited to a linear dimension of 10-4 cm. or less. Selective absorption of certain solvents from solvent mixtures by polymeric materials of limited s\vellability has been utilized to effect a novel separation procedure. Hwa: Meitzner, and hfcBurney
M
0
I
I
I
05 Mole Fraction Acefone
IO
Figure 1. Diffusion coefficients in the acetone-water system as a function of concentration ( 7 A )
( 9 A ) separated a toluene-iso-octane mixture by passage through a bed of cross-linked poly-n-butyl acrylate followed by desorbent; repeated cycles of sorption and desorption may be devised to operate the process in semicontinuous fashion. Data for a variety of polymeric materials indicate that polymeric absorbents may be tailor-made to effect desired specificity for certain solvent mixtures. Separation of stereoisomers by countercurrent distribution is described by Kortum and Bittel (72%) \Tho separated substituted cyclohexanes in a Scheibel column. The method is based on the fact that the configuration of the substituents is of critical significance in determining the separation factor. Kinetic data on the rate of desorption of noble gases arid light hydrocarbons from charcoal are given by Peters and Proksch (75A). These authors studied desorption in the vicinity of the gas critical temperature where the adsorption isotherms are strong functions of temperature. By adsorbing a gas mixture a t very low temperature and then desorbing at variable temperature it is possible to effect good separations of light gas mixtures. Becker and coworkers (3A) have continued their experiments with the separation nozzle and have used this device to study some of tht: variables Jvhich influence the separation of a natural A36-A40 mixture. In addition. the authors have proposed a theory of combined pressure and ordinary diffusion
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FUNDAMENTALS to explain their results and have also shown that by using a cascade of such nozzles it is feasible to separate uranium isotopes in the form of their hexafluorides.
Turbulent Diffusion and Mixing Processes Several studies on longitudinal diffusion appeared last year. Tichacek, Barkelew, and Baron (27B) extended G. I. Taylor’s treatment for longitudinal diffusion in pipe flow to lower Reynolds numbers and also included the effect of molecular diffusion. Because axial mixing is due to the relative axial motion of fluid elements a t different radial positions the authors conclude that the ratio of apparent axial eddy diffusivity to average velocity increases rapidly as the flow approaches the laminar region. The effect of true axial eddy diffusion is shown to be negligible compared to the apparent diffusion caused by a nonflat velocity profile. A diffusion model for longitudinal mixing was discussed by Levenspiel and Smith (72B) and a tabulation of available mixing data in pipes was also presented ( 7 7B). T h e central concept of Taylor’s treatment is that velocity gradients are responsible for axial mixing; this concept was also applied by Prausnitz (77B) to longitudinal diffusion in packed beds in a n attempt to provide a more realistic alternate to the mixing cell models proposed earlier and more recently by Carberry (223). New data on axial mixing for liquids in packed beds are given by Ebach and White (9B), Strang and Geankoplis (ZOB), and Carberry and Bretton (3B). All of these authors found that the Peclet group in the laminar region is considerably less than that in the turbulent region and the last named authors report a transition occurring a t the same Reynolds number where the friction factor curve changes. These results are different from those previously found by McHenry and Wilhelm for gas systems where the Peclet group was essentially constant for the Reynolds number range from 10 to 1000. Csanady (6B) discusses the application of concepts such as streamlines and equipotential lines to turbulent diffusion. These concepts are then applied to atmospheric diffusion from a point source into a steady wind. Phenomena involving the interaction between fluids and clouds of suspended particles such as the burning of pulverized solid fuel and of liquid fuel sprays, and the absorption of a gas component by a solvent spray, are studied theoretically by Spalding (79B).
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Exact solutions are given for a few simple geometries and numerical methods are indicated for more complex systems. However, the discussion is limited to very small particles only, for a basic assumption in the theory is that, in a turbulent flow field, the particles take part in the mixing process just as though they were molecules. Mixing characteristics of irrigated packed towers were investigated by Otake and Kunugita (76B) and the theoretical effect of axial mixing on extraction was reported by Nagata and Eguchi ( 75B). Beerbower and others (7B) describe the use of radioactive iodine as a tracer studying the mixing efficiency of processing equipment. The tracer is injected a t a point of the apparatus to be investigated and samples taken a t various times thereafter give a measure of the mixing efficiency. This technique is useful for studying the mixing of process streams under actual plant operating conditions because the decay product (xenon) will not contaminate the material being processed. Radioactive iodine is now readily available from the Brookhaven National Laboratory. Last year saw the publication of papers from the First European Symposium on Chemical Engineering devoted to chemical reaction engineering ( 4 B ) . This symposium considered the interaction between chemical kinetics and heat, mass and momentum transfer. Of special interest with respect to mass transfer is a n article by Danckwerts who considers the effect of mixing. on a homogeneous second-order reaction. T o be effective in a reaction such mixing must be on a molecular scale and in a preliminary article Danckwerts defines “molecular-scale mixing” with statistical concepts and shows how it can be measured. Further ideas on this complicated subject are given in two later articles (7B, 78B). New data on mass and momentum transfer in a wetted-wall duct are reported by Dhanak (8B) who took special care to avoid rippling on the liquid film. The results, which indicate a n almost linear relationship of eddy diffusivity in the center of the duct with Reynolds number, are somewhat lower than those reported in the classic study of Shenvood and Woertz. In agreement with previous workers Dhanak finds that mass flux is transferred about 60% faster than momentum flux. I n the field of isotropic turbulence, Corrsin (5B) has begun the development of a statistical theory for chemical reaction and has obtained solutions for the decay rates of mean concentration and fluctuations in some limiting cases and under simplifying assumptions.
INDUSTRIAL AND ENGINEERING CHEMISTRY
A symposium on engineering aspects of polymer processes included three contributions on mixing. Lee, Finch, and Wooledge (7OB) supply data on mixing polystyrene solutions in agitated tanks and thereby extend the power number-Reynolds number correlation to high-viscosity materials. Power consumption was little affected by baffling but shrouded impellers required u p to 50% more power than unshrouded ones a t the same Reynolds number. Mixing times were studied by a tracer-injection technique; over the Reynolds number range from 5 to 100 the mixing time for unshrouded impellers falls from 100 minutes to about 10 seconds. Mohr, Saxton, and Jepson (73B) give a theoretical treatment of mixing in laminar flow systems which is based on the concept that goodness of mixing depends on the generation of new interfacial area by shear. For a mixture of black cubes in white fluid an expression is derived for the striation thickness in terms of the shear supplied and the relative fluidity. This approach permits the calculation of energy requirements needed to attain a given uniformity of composition from the properties of the feed materials and the flow patterns of the mixing device. These ideas are then used by the same authors in a separate article (74B) to compute the mixing performance of a single-screw extruder.
Mass Transfer by Diffusion and Convection Mass Transfer from Surfaces. A valuable study on mass transfer from a soluble solid sphere was recently completed by Garner and Suckling ( 7 3 C ) . This work contains both experimental measurements of local mass transfer coefficients for 100< NRe< 700 and 1000 < N,, < 2000 as well as some theoretical calculations for the region past the separation point. T h e experimental method for making the measurements, although admittedly in need of some improvements, is particularly interesting and novel. Another important contribution to this general subject is the work by Thoenes and Kramers (342) who studied the over-all rate of mass transfer from a single sphere, located in a regular arrangement of similar but inactive spheres. It appears from the results reported in this article that for all practical purposes the rate of mass transfer from a single sphere in a packed bed is the same whether the surrounding spheres are activated or not. In addition, Sogin (33C) has verified the analogy between heat and mass transfer by measuring experimentally the rate
MASS TRANSFER
_______.____________
of sublimation from disks to air streams flowing normal to their surface and then showing that, by using the Colburn analogy, his results coincided with the data for heat transfer by convection in a n identical configuration. Mass transfer rates from a disk rotating a t various speeds in a n infinite environment in laminar and turbulent flows were reported by Kreith, Taylor, and Chong (25C). This is indeed a very positive contribution toward understanding mass and heat transfer phenomena from rotating surfaces. The results compare favorably with the exact solution of the laminar boundary layer equations, as well as Lvith a semiempirical formula for turbulent flows derived by the authors. Laminar boundary layer theory was used by Friedlander and Litt (70C) to study theoretically how the rate of mass transfer of a substance from a surface to a moving fluid would be affected by a very rapid irreversible chemical reaction. T h e flow past a flat plate was analyzed in detail by a n exact solution of the boundary layer equations, and it was shown how the expression for the Sherwood number as a function of the dimensionless parameters of the system must be modified to include the effects of the reaction. O n the same general subject, a short note by Denison and Dooley (7C) dealt with the problem of infinitely rapid combustion in the laminar boundary laver of chemically active sublimating surfaces for compressible supersonic flows. Also, another article dealing with the influence of a chemical reaction on the rate of mass transfer from a surface to a moving fluid in laminar boundary layer flow is by ChambrC and Young (4C). The analysis is concerned with first-order chemical reactions, under isothermal conditions. for flows past a wedge, and numerical results are reported for the flow past a flat plate. A theoretical study of mass transfer cooling with combustion in a laminar boundary layer has recently been completed (76C). This is an important contribution to the general area of mass transfer cooling since it determines, for certain simple cases, how the effectiveness of this method for protecting surfaces is influenced by chemical reactions which may occur in the boundary layer or on the surface. In another study of surface cooling (8C), analytical predictions were made from the laminar boundary layer theory, for developing the velocity, temperature, and concentration fields in the highspeed dissipation flow over a porous flat plate, the surface of which is cooled by hydrogen injection. The rate of evaporation a t very low
pressures is discussed by Burrows (3C) who is concerned with the result that experimental rates are often significantly lower than those calculated by kinetic theory. Burrows explains the discrepancy by pointing out that even when the characteristic geometric dimension is of the same order of magnitude as the mean free-path there is a significant number of collisions which cause evaporating molecules to be reflected and to be reabsorbed. By taking these collisions into account the appropriate theoretical expressions can be modified to give much better agreement with experimental results. In a comprehensive study of mass transfer in falling films by Brauer (2C) it is shown that the main resistance lies in that part of the film which is adjacent to the wall rather than in the part adjacent to the gas-liquid interface as postulated in the WhitmanLewis two-film theory and in the HigbieDanckwerts penetration theory. Owing, to wave formation there is convective transport a t the gas-liquid interface which however is not present in the liquid immediately adjacent to the pipe wall where molecular diffusion is the only mechanism for mass transfer. Hence the effective film thickness is less than the average film thickness which explains why observed mass transfer coefficients are considerably higher than those computed by previously published theories. Using experimental shear stress data Brauer computes a n effective film thickness which when applied to mass transfer gives good predictions of previously reported data on absorption, desorption, and dissolution of soiids in falling films. Brauer’s results, however, are open to question as he bases his calculations on a momentum transfermass transfer analogy which is not strictly valid. Garner (72C) has published a fine review of the relationship between hydrodynamics and mass transfer from solid spheres, bubbles, and drops to a flowing fluid. Of particular interest in this review is a discussion of various useful experimental techniques including methods suitable for visual observations of flow patterns and internal circulation. Krischer and Loos (26C) published a very comprehensive review of heat and mass transfer for water films evaporating into air from a variety of solid shapes and present new data and flow-pattern photographs for such irregular bodies as cylinders with rilled surfaces and star-shaped prisms. The results are correlated by standard dimensionless groups. In an interesting theoretical contribution to the theory of mass transfer between two immiscible fluids, Potter (29C) has obtained a n approximate
Pohlhausen-type solution to the boundary layer equations for mass transfer across the plane interface between two cocurrent parallel fluid streams. The introduction of boundary layer methods to a field which in the past has been analyzed almost exclusively by either the stagnant film theory or the penetration theory is most welcome. For example. Searle and Gordon (37C) found the two-film theory to be inadequate in explaining their experimental results on mass transfer between two liquids with chemical reaction. In a very coniprehensive review article, Rosner (3OC) discusses the recent advances in convective heat and mass transfer with dissociation and atom recombination whether on a surface or in the boundary layer, a field which is receiving considerable attention at present because of its great importance in problems of high speed flow. Thus, a theoretical study on mixing and chemical reaction in the laminar wake of a flat plate is reported by Cheng and Kovitz (5C). This work has applications in many combustion problems and is, in some respects, rather similar to the classical study by Marble and Adamson but differs in one important aspect: T h e velocity distribution in the two reaction streams is no longer uniform, which, as the authors point out, introduces appreciable differences in the distribution of temperature and concentration in the neighborhood of the trailing edge. Gas Absorption by Liquids. Kishinevskir (ZOC, 22C. 24C) has reexamined the physical formulation of the mass transfer process and has postulated a surface renewal theory very similar to that of Danckwerts. However, Kishinevskir does not concur with the latter’s concept of a n age distribution of the surface elements. Rather, it is assumed that each eddy, originating in the bulk, will remain on the surface for an average of T seconds. During this time, it is exposed to the gas phase, and absorbs the transferring solute by a process of unsteady state turbulent absorption. T h e absorption rate is derived as :
where A‘\. is the absorption rate, in moles per second per square centimeter, and D the molecular diffusion coefficient of the solute gas in the liquid. E is the eddy diffusivity in the surface layer which is considered to be in turbulent motion, rather than stagnant, as Danckwerts had assumed. C, and C t are the
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FUNDAMENTALS ---.-.....__.___________________________..........-..__. ----------------------....~~~~~~.~~....~...~~~~~. interfacial and bulk concentration of the solute, respectively, and AT is the period of time which the eddy is exposed to the gas phase. While Danckwerts' theory predicts a one-half power dependence of the mass transfer coefficient on the diffusion constant, this concept suggests that the coefficient be proportional to the molecular diffusivity to any power between zero and l/z, depending upon the relative magnitudes of D and E. Based on the same model of eddy behavior Kishinevskii has derived a rate expression for absorption accompanied by a n irreversible second order reaction of any speed (79C). A special form of the expression was applied to the absorption of carbon dioxide by sodium carbonate solutions in a tower packed with glass rings (27C, 23C). However, the validity of the fluid mechanical model and general application of this theory for both physical and chemical absorption remain to be determined by further experimental studies. Danckwerts and Kennedy ( 6 C ) measured the rate of absorption of carbon dioxide into neutral and alkaline solutions. These authors were not able to come to definite conclusions concerning the complex mechanism of absorption with chemical reaction. A study of the absorption of chlorine into acidic ferrous chloride solutions is reported by Gilliland, Baddour, and Brian (75C). Packed Beds and Slurries. Individual phase heights of transfer units (H.T.U.) were determined by Smith and Beckmann (32C) for two binary systems of differing physical properties for liquidliquid extraction in a 4 inch diameter column. T h e column was operated as a spray tower and with 1/2-inch Raschig ring packing for methyl isobutyl carbinol-water and methyl ethyl ketone-water systems. Continuous phase H.T.U.'s were proportional to ( V J Vd)"(V,,Vd = continuous and dispersed phase velocities, n = a n exponent ranging from 0.63 to 0.78 for the two systems). S o definitive correlations for the effect of physical properties were proposed, although some relationships are indicated. Empirical constants relating H.T.U.'s to flow rates for several systems and column packings including earlier data from the literature are summarized. Despite considerable scatter in the tentative correlations this work should be useful in predicting packed column operation. A limitation on developing of correlations of this kind may be in failure to account for longitudinal mixing effects as pointed out by Miyauchi (27C) and Jacques and Vermeulen (77C), or interfacial turbulence. An interesting study of the effect of packing configuration on gas phase
470
mass transfer in beds of stacked spheres is reported by Galloway, Komarnicky, and Epstein ( 7 7C). Experimental measurements were made by surface evaporation of water into air from two orthorhombic and two simple cubic assemblages of uniform Celite spheres. Markedly different slopes. n, in the plots of l o g j us. log R e ( j = Chilton-Colburn 3 factor, R e = Reynolds number) were observed which ranged from zero slope for rhombohedral packings to -0.638 for cubic arrangement. Designated as the index of turbulence inhibition. R could be correlated as a function of the fractional free area open to flow in the packings. Although the data show considerable experimental scatter, conventional methods for correlation in randomly packed beds lvere found to be inadequate ; the mass transfermomentum transfer analogy of Ergun diverged especially greatly from the experimental results. Effect of longitudinal mixing on the usual assumption of a log mean mass transfer driving potential is discussed in a theoretical equation by Epstein (QC) and the results suggest that a correction of about 15% would be applicable for the author's beds which were packed to a depth of 8-particle diameters. More shallow beds would be subject to greater correction. Effective wetted surface in packed columns relative to a column packed with glass beads was measured by Yoshida and Koyanagi (35C) for absorption of carbon dioxide into water and into methanol. Use of a glass bead column is suggested as a basis for scale-up in column design. Rates of absorption of carbon dioxide by buffered sodium carbonate and potassium carbonate solutions in a wetted wall column for laminar liquid flow agree with the penetration theory, according to studies by Nysing and Kramers (2%). The reaction in these solutions is pseudo first order. From plots of the amount of gas dissolved as a function of contact time the reaction rate constant and carbon dioxide solubility were evaluated and found to be reasonably consistent with results of other investigations. Plate Efficiency. Results of a 5-year study of bubble tray efficiencies conducted under the auspices of the American Institute of Chemical Engineers at the Universities of Delaware and Michigan and North Carolina State College, have been summarized in a design manual (7C). A comprehensive experimental program augmented by data on industrial columns served as a basis for theoretical interpretations. The various definitions of plate efficiency are summarized and related to mass transfer variables through the two-resistance theory. Correlations applicable to both
INDUSTRIAL AND ENGINEERING CHEMISTRY
bubble cap and sieve tral s are developed for: rates of mass transfer in the gas and liquid phases; degree of liquid mixing and its effect on plate efficiency; and magnitude of the liquid entrainment between trays. This work constitutes a very significant advance in the field of distillation, and these investigators are to be commended for their excellent handling of a rather unique effort in cooperative research on a most difficult problem. Details of the studies conducted a t the University of Delaware have been released in a companion report by Gerster and associates (74'2). For gas-liquid contacting on a perforated plate mixing by splashing of liquid through the gas is suggested by Johnson and iMarangozis (78C) as a mechanism alternative to eddy diffusion in the liquid 'to account for the effect of back-mixing on plate efficiency. Empirical correlations of a splash mixing factor are presented for experiments on ammonia desorption from water and backward distribution of sodium chloride.
Interfacial Phenomena The role of interfacial turbulence in mass transfer received a n increasing amount of attention last year. In the 1957 review attention was called to the work of Sigwart and Sassenstein who observed violent motions in drops of carbon tetrachloride when acetic acid was transferred to Jvater; similar observations recorded photographically were reported by Kroepelin and Neumann ( 5 D ) and by Japanese workers (40). Boye-Christensen and Terjesen ( 2 0 ) studied the effect of adding a surface active agent to the transfer of o-nitrophenol from water to falling drops of carbon tetrachloride and observed a sharp decrease in the rate of mass transfer. This decrease is undoubtedly due to the inhibition of interfacial turbulence by adding the surface-active agent. Lewis (6D)studied the mechanism of the transfer of uranyl nitrate and nitric acid between water and three solvents and found that mass transfer coefficients greater than predicted were found in a few cases where interfacial turbulence was observed. Interfacial effects in absorption are discussed by Bond and Donald (ID) who are concerned with the previously observed change in wetted area of packing when the gas absorbed has a high heat of solution. Gsing a wetted wall column for absorbing ammonia from a gas stream the authors determined the minimum water rate which will just maintain a continuous film; below this rate the film breaks down and
MASS TRANSFER there is a considerable reduction in the area exposed for absorption. T h e results are expressed as a difference in surface tension a t the point where t h e film breaks. between the main bulk of the liquid and the film of liquid which has become in equilibrium with the gas stream. Haydon (30) studied droplet oscillation during mass transfer and, like previous authors, concludes that the observed hydrodynamic effects are caused by a local lowering of interfacial tension by the solute. Data are reported for transfer of various solutes from drops of acetone. acetic acid, and eth>l alcohol into petroleum ether and equations of motion are derived 1% hich predict the frequency of drop oscillation. I n another article Pearson ( 7 0 ) discusses the effect of surface tension on natural convection and in a mathematical analysis similar to that first used by Ravleigh shows that the cellular convective motion of the type observed by Benard can be induced by surface tension forces. Pearson concludes that surface tension forces are responsible for cellular motion in many cases where the usual criteria given in terms of buoyancy forces would not indicate any instability. Further progress in mass transfer between fluid phases is strongly dependent on increasing our understanding of interfacial turbulence a n d it is to be hoped that research in this area will continue a t a n increasing rate.
Acknowledgment T h e assistance of Donald R. Olander in reviewing the Russian literature on gas absorption is gratefully acknoxvledged.
(11A) Keyes, J. J., Jr., Pigford, R. L., Chem. Eng. Scz. 6, 215 (1957). (12‘4) Kortiim, G., Bittel, .4.,Chem. Ingr. Tech. 30, 95 (1958). (13A) Kuhn, W., Thurkauf, M., Helv. Chzm. Acta 41, 938 (1958). (14A) Liu, V. C., J . Ah$. Phys. 29, 1188 (1958). (15A) Peters, K., Proksch, E., Z. Elektrochem. 61, 1241 (1957). (16A) Reid, R. C., Sherwood, T. K., “The Properties of Gases and Liquids,” chap. 8, McGraw-Hill, New York, 1958. 117A) Shirotsuka, T., Honda, N., others, Kagaku Kogaku 22, 29 (1958). (18A) Slattery, J. C., BZd, R. B., A.I.Ch.E. Journal 4, 137 (1958). (19.4) Walther, J. E., Drickamer, H . G., J . Phys. Chem. 62, 421 (1958). (20A) Westenberg, A. A., Walker, R. E., J . Chem. Phys. 26, 1753 (1957). (21A) Whitaker, S., Pigford, R . L., IND. ENG.CHEhf. 50, 1026 (1958). Turbulent Diffusion a n d Mixing Processes (IB) Berrbower, .k, Forster, E. O., others, IND.ENG.CHEM.49, 1075 (1957). (2B) Carberrv, J. J.. A.I.Ch.E. Journal 4, 13M (1958). (3% Carberrv. J. J.. Bretton. R. H.. Zbid.. 4,367 (1958j. ’ (4B) Chern. Eng. Sci.8, Nos. 1/2 (1958). (5B) Corrsin, S., Phys. of Fluids 1, 42 11 9i8’1 \ - - - - I .
(6B) Csanady, G. T., IND. EXG. CHEM. 49, 1453 (1957). (7B) Danckwerts. P. V.. Chem. E m . Sci. 9; 78 11958). ’ (8Bj Dhanakj A. M., A.I.Ch.E. Journal 4, 190 (1958). (9B) Ebach, E. A , White, R. R., Ibid., 4, 161 (1958). (10B) Lee, R. E., Finch, C. R., Wooledge, J. D.. IND.ENG.CHEM.49. 1849 11957). (11B) Levenspiel, O., Ibid., 50, 343 (1958). (12B) Levenspiel, O., Smith, W. K., Chem. Eng. Sci. 6 , 227 (1957). (13B) Mohr, W. D., Saxton, R. L., Jepson, C . H., IND. ENG. CHEM. 49, 1855 (1957). (14B) Ibid., p. 1857. (15B) Nagata, S., Eguchi, W.,Kagaku Kogaku 22.218 119581. (‘$B),
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