FUNDAMENTALS REVIEW
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II Mass Transfer I
R E S E A R C H and publication activities have continued at a rather moderate level during the past year. Although important progress has been made in some directions, no radically new concepts appear to have been added to our understanding of the field. The interrelation of fluid mechanics and molecular properties with mass transfer behavior is becoming increasingly quantitative, as additional information on thermodynamic and transport properties of fluids is made available. Further research on these properties appears to be essential for maximum progress. During the past year significant progress has been made in the measurement and interpretation of molecular diffusion in gases and liquids. Thermal diffusion is receiving greater emphasis as a tool for effecting special separations on a small scale and as an aid to the theoretical interpretation of fluidphase properties. Several very excellent books give general coverage of the mass transfer field. A very readable and fundamental treatment of the unit operations involving mass transfer is given in the new undergraduate text by McCabe and Smith ( 7 4 . A more advanced and comprehensive presentation is offered in “Mass Transfer Operations” by Treybal (ZA). Valuable information on separation and purification procedures has been brought together by Weksberger and associates ( 3 4 . The treatments of thermal diffusion by Jones, barrier separations by Kammermeyer, dialysis and electrodialysis by Stauffer, and zone electrophoresis by McWilliam are of particular interest, as these subjects have received relatively little attention in standard reference works and textbooks in chemical engineering.
Molecular Diffusion in Gases and liquids Attention in this section is directed primarily toward diffusion processes, mathematical solutions of the diffusion equations, and general correlations of diffusion data. Papers dealing mainly with the molecular theory of diffusion and specific data on diffusion coefficients are covered more appropriately in the review on transport properties. Caldwell and Babb (3B) measured mutual diffwion constants for three
nearly ideal binary liquid systems over the entire range of mole fraction and at several temperature levels. A sign%cant result of the study is the agreement obtained with the relation proposed by Roseveare, Powell, and Eyring that the group D?/T should be linear with mole fraction for ideal binary solutions, where D = diffusion coefficient, 9 = viscosity of the.solution, and T = absolute temperature. This result gives added support for the commonly recommended procedure of estimating diffusion constants in concentrated solutions from values in dilute solution on the basis of this linear relation with mole fraction and appropriate activity co&cient corrections. The complexity of the liquid diffusion process in nonideal solutions is illustrated in a study by the same authors (4B) on the methanol-benzene systems. A plot of activation energy for diffusion as a function of methanol concentration shows a sharp maximum a t about 0.08 mole fraction methanol. Definite changes in the alcohol aggregates with concentration are indicated by this behavior. A comprehensive review of liquid diffusion is given by Johnson and Babb (9B). The extensive tables of diffusion data for nonelectrolytes should be especially useful. Fair and Lerner (7B)present methods for calculation of gas diffusion co&cients based on the equations of Hirschfelder, Bird, and Spotz. A method of es-
timation is proposed using the concept of “barrier gas ratio,” which is the ratio of the critical coefficient of a gas A in gas B to the critical coefficient of A in air. A correlation of the barrier gas ratio with the molecular properties of gas B is suggerted. Although this represents a new concept in the correlation of diffusion coefficients, which is always welcome, a more thorough evaluation of the method with respect to accuracy and limitations seems desirable. A significant series of papers relative to multicomponent diffusion was published by Gosting and others (7B,6B, 88). Interacting flows among various components are interpreted on the basis of the phenomenological equations of Onsager, and solutions to these equations are developed for three component systems. Extension of this approach to the interpretation of mass transfer problems from an engineering viewpoint might offer interesting possibilities. An approximate solution to the Maxwell equations for free diffusion of two gases in the presence of a fixed concentration of a third is given by Senett, Gollob, and Taylor (73B). The specific mathematical solutions and experimental method involve diffusive mixing between two interconnected bulbs in the unnteady state. Sage and others (7OB-72B)present solution1 to the diffusion equations for unsteady state absorption of a gas into a liquid phase of semiinfinite extent.
C. R. WllKE received a B.S. in 1940 from the University of Dayton, M.S. in 1942 from State College of Washington, and Ph.D. (1 944) 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 division of chemical engineering. He is a member of the AIChE, whose junior award he received in 195 1, the ACS, Electrechemical Society, and ASEE.
JOHN M. PRAUSNITZ, assistant professor of chemical engineering at the University of California (Berkeley), attended Cornell and the University of Rochester. His Ph.D. was obtained from Princeton University, where he served as instructor for two years. Prausnitr’s main interests ate in rate processes in chemical reactors. He is a membw of the American Institute of Chemical Engineers. VOL. 49, NO. I , PART II
MARCH 1957
577
General correlations for quantitative estimation of plate efficiencies in fractionating towers can b e anticipated soon. Terms for a n interfacial resistance are included in the theory. Results in hydrocarbon measurements indicate marked variations of the diffusion coefficient with conditions of temperature. pressure, and liquid composition, which might be typical of those encountered in hydrocarbon absorption rowers. A comprehensive reference book devoted to the mathematics of diffusion has been prepared by Crank ( 5 4 . The differential equations are solved for a wide variety of boundary conditions and physical situations. Also included are a chapter on finite difference methods and useful tables of mathematical functions. This work is a particularly welcome addition to the diffusion literature. A valuable theoretical review, prepared by Bird (ZB), summarizes many solutions to the diffusion equations of interest to chemical engineering problems and presents methods of estimating diffusion coefficients and other transport properties. Of particular interest is the presentation of a new chart (Figure 1) prepared by Slattery (74B) showing the effect of pressure on the coefficient of self-diffusion for dense gases. Application of the chart to binary gases is suggested through the use of pseudo-reduced temperature and pressure.
et
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Turbulent Diffusion
A comprehensive review of our present understanding of turbulent diffusion is presented by Batchelor and Townsend ( I C ) in a special volume commemorating the seventieth birthday of G. I. Taylor. T h e authors point out that the problem of turbulent diffusion in shear flow is not one problem but rather the sum of many hydrodynamic problems which may exhibit different features in different applications. T h e most fruitful task a t present, it appears, is to classify the various kinds of effects and situations which may arise and to perceive basic features which are common to them. One badly neglected complication of the theory of turbulent diffusion is the fact that it is often not possible to ignore the effects of molecular diffusion, since the interaction of molecular and turbulent diffusion is frequently important. T h e simple procedure of adding molecular and turbulent diffusivities to describe the diffusion process is not valid, as was also recently shown by Stirba and Hurt (77C). One of the unsolved problems in turbulence theory is the relationship between the Eulerian correlation coefficient which can be measured by hot-wire
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Figure 1 . Generalized chart for calculation of coefficient of self-diffusion of gases at high densities ( 7 46) ( p D ) / ( p D ) ’ . Generalized function of reduced temperature and pressure, where pD is actual product of pressure and diffusion coefficient and (pD)’ is product calculated on assumption of ideal gas behavior
578
INDUSTRIAL AND ENGINEERING CHEMISTRY
anemometry, and the Lagrangian currclation coefficient which Cannot be measured directly but is the moyt important parameter in the theory of turbulent diffusion. An experimental study of this relationship in homogeneous isotropic turbulence was made by hlickelson ( 7 3 C ) !\vho round that the Eulerian and Lagrangian correlation coefficients have similar shapes. The linear relationship between the shapes of the Lagrangian and Eulerian correlation coefficients provides a means for the quantitative solution of mixing problems from hot-wire anemometry data. In two pioneering theoretical papers on the role of eddy diffusivity in turbulent transport, Hanratty (6C, 7C) has effectively shown the applicability of Taylor‘s theory of turbulence to mass transfer in turbulent flow. The heart of the first paper lies in the recognition that because of the large scale of the motion responsible for mixing in turbulent flow the accompanying turbulent transport process differs significantly from the analogous molecular process. This important difference is due to the fact that in turbulent flow the mixing depends not only on the conditions a t the point of interest but also on the previous history of the diffusing material. The concept of “scaling up” molecular diffusion by merely replacing the molecular diffusivity with an eddy diffusivity is therefore shown to be valid only in some limiting cases. T h e case of heat transfer through an isotropic turbulent fluid is examined in some detail and the results are in good agreement with the temperature profiles of Sage and coworkers ( 75C). In his second paper Hanratty critically discusses the Higbie-Danckwerts theory of mass transfer and shows that it is consistent with Fage and Townsend’s descriptive studies (5C) of pipe flow in the vicinity of the wall. He proposes a “discontinuous film” model for mass transfer between a solid and a flowing fluid; concentration profiles are computed in terms of a single parameter which characterizes the distribution of eddy ages. The profile is remarkably insensitive to this distribution but in good agreement with the mass transfer data of Lin, Moulton, and Putnam (77C). T o show that the discontinuous film theory is not inconsistent with momentum transfer data, Hanratty computes the velocity profile in the vicinity of the wall and shows that it agrees well with the experimental results of Deissler (42). Mass transfer in turbulent pipe flow was studied by Schwarz and Hoelscher (76C) who measured concentration profiles of water vapor in a wetted-wall
MASS TRANSFER column. Eddy diffusivities for mass and momentum transfer were computed. The authors also computed the mass and momentum transfer correlations u,h and u,u,, where h is humidity, u is velocity, and the subscripts 7 and z refer, respectively, to the radial and axial directions. These computations involve graphical differentiations and are therefore probably not very accurate. The results, however, are of the same order of magnitude as those of an analogous heat transfer study by Isakoff and Drew (9C). A somewhat more novel approach to the study of mass transfer in turbulent flow was described by Keyes (70C), who used the dynamic response method a t considerably higher Reynolds numbers than had been used in a previous application of this method to packed beds by Deisler and Wilhelm (3C). Keyes’ results, which are expressed in the form of a n effective film thickness, agree with the semitheorktical equation of Martinelli (72C) as applied to mass transfer. Turbulent diffusion in a bed of particulately fluidized solids was investigated by Hanratty, Latinen, and Wilhelm (K), who measured the spreading of dye from a point source in a tube where glass spheres were fluidized with water. Eddy diffusivities were calculated on the assumption of isotropic turbulence; as expected from Taylor’s theory of turbulence, the eddy diffusivity is not a true constant but approaches a constant value as the distance from the point source becomes large. The Peclet number is a strong function of the fraction voids; while progressing from the packed bed to the empty tube the Peclet group goes through a minimum (eddy diffusivity is a maximum) a t the fluidized state corresponding to a fraction void of about 0.65 as shown in Figure 2. This study of mixing in ideally fluidized beds together with previous mixing studies by Wilhelm and coworkers provides a good frame of reference for consideration of mixing characteristics in the more complex geometries which are of interest to chemical engineers. Mixing of particles in a fluidized bed is analogous to the motion of molecules in a gas. Brotz (2C) found that a t fluid velocities about twice those required for fluidization the diffusivity of solid particles is of the same order of magnitude as that for common gases a t room temperature. Larger particles appear to have a larger diffusivity. The role of turbulence in thermal and material transport is discussed by Opfell and Sage (142) in a fine review article. The authors briefly summarize the essential ideas in turbulence theory, the analogies in mass, heat, and momentum transfer, and the definition and use of effective eddy conductivities.
-
Figure 2.
Effect of expansion on turbulent diffusivity bed
40
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FRACTION S O L I D S ( 1 - C )
Diffusion and Convection Within a Single Phase A useful mathematical technique known as the method of characteristics has been applied to heat and mass transfer problems by Acrivos (70). Problems involving transfer from a solid to a moving fluid, such as occur in adsorbers, ion exchangers, catalytic reactors, etc., can be treated by this method; the solutions must be found numerically. The method, however, is restricted to processes which can be described by differential equations having only first-order derivatives. Because of its simplicity and accuracy, this mathematical technique may become a useful tool for many chemical engineering calculations as high-speed computing machines become more generally available to design engineers. A fundamental paper by Furber (40) presents heat and mass transfer data on humid air flowing over a plane containing a n isolated cooled region. The influence on both heat and mass transfer of a nontransferring section upstream from the transferring region is shown to be very important; the mean coefficient may be as much as 86% greater than the corresponding mean coefficient for a region where transfer begins a t the leading edge of the plane. T h e very close agreement between the results for heat and mass transfer once again confirms the validity of the heatmass transfer analogy, a t least for flat plates. Another study of mass transfer from a solid to a turbulent fluid was reported by who measured Johnson and Huang (60), the rates of dissolution of several organic solids in various solvents in a n agitated vessel. Their results show that the mass transfer coefficient is proportional to the v
one-half power of the molecular diffusivity, which is in agreement with the Higbie-Danckwerts theory, although it does not preclude other theoretical interpretations. Heat and mass transfer in spray drying was reviewed by Marshall ( 8 0 ) , who presents equations for evaporation from pure liquid drops and from drops with solids present in quiescent and in moving air. The problem of the evaporation of a drop of volatile liquid in high-temperzture surroundings was analyzed by Ranz (9D)in terms of the rate of heat transfer. Ranz emphasizes the interesting fact that the flow of cold vapor to the surroundings during evaporation requires that a considerable amount of heat conducted inward be used to heat u p vapor moving outward. This waylaying of heat energy results in a significant decrease in the apparent rate of heat tranrfer as measured by the rate of evaporation. Two additional papers on the simul: taneous transfer of heat and mass should be mentioned. Cairns and Roper ( 2 0 ) present a mass transfer correlation for both humidification and dehumidification in a wetted-wall tower for cases where the partial pressure of water is high. The well-known equations of Chilton and Colburn were modified to account for the effect of mass transfer on heat transfer. The second paper, by Heyser ( 5 0 ) , also considers heat and mass transfer with large partial pressures of the diffusing component. Heyser’s experiments consisted of partial condensation of water vapor from air and of benzene vapor from air; this experimental technique is subject to serious difficulties, one of which is the loss of condensate due to fog formation. T h e paper is obscurely written and the conclusions are not en-
VOL. 49, NO.
a,
PART II
MARCH 1957
579
FUNDAMENTALS REVIEW
d
A. Flow pattern with tetrachloride
170acetic
acid in carbon
C. Flow pattern with 10% acetic acid in carbon tetrachloride. Drop deformed following a violent eruption
B . Flow pattern with 4% acetic acid in carbon tetrachloride
D. Undisturbed diffusion boundary with 34/, acetic acid in carbon tetrachloride. Small quantity o f surface-active agent a d d e d to water
Figure 3. Transfer of acetic acid from a drop of carbon tetrachloride into water
(4E) a.
End of capillary
b.
Drop
c.
tirely clear. It appears. h o ~ v e v e r .that the .-lckermann correction is too large and that results in a5reement \\-it11 Heyser's experiments may be obtained if the effect of mass transfer on heat transfer is neglected and if transfer rates are coniputed on the basis of an effecrive film thickness as predicted by the analogy of heat and mass transfer. Heyser's treatment of this problem is a considerable simplification. His esperiinental results. hoivevcr, appear to be in conflict \vith previous studies. including those citcd above. .An important theoretical and exprrimental study of fractionation during condensation of vapor mixtures l\,as reported by Kent and PiTford ( 7 0 ) . T h e rransfer unit concept is applied to Ixirtial condensation and ne\v equations arc derived relating the number of transfer units to liquid- and qas-phase resistances. surface area, and amount of condensation. T-his paper thus sholvs clearly the engineer's need for basic data on thermodynamic and transport properties of mixtures. The use of partial condensers for effecting a separation appears to be most attractive for vapor products having a low dew point. The first extensi\'e data on mass transfer in liquid metals \- several investigators this ).ear. Garner and Skelland ( / E % 2 E ) found that small concentrations of surfxe-active a q r n t s decrease the internal circulation ivith drops fallin.. tlirouqti a liquid immiscible ivith the drops and thereby decrease the mass transfer coefficient. A similar effect \\-as observed by Lindland and Terjrsen (.?E), ivho studied the extraction of iodine from aqueous solution Tvith carbon tetrachloride drops. These authors reported that as loiv a concentration as 6 X 10-5 gram of sodium oleoyl-p-anisidine sulfonate per 100 ml. of aqueous solution reduced the mass transfer coefficient by 67%. T h e mrchanism of transfer across a liquid-liquid interface !vas observed by Siqvart and Sassenstein ( /Ej
INDUSTRIAL AND ENGINEERING CHEMISTRY
using a Schlieren optical technique bvhich sho\ved some interesting effects o f surface active agents. Drops of carbon tetrachloride containing sinall amounts of acetic acid ~ v e r ebrought in contact \vith lvatcr. 'I'he c.ruptions a t the drop's surfacr can be scen in the photographs reproduced in l'igure 3 ; as the concrntration of acid in the organic phase is increased, thc eruptions become mwr violent. 'I'he last photograph shoivs the almnce of atirface eruptions when a sinall amount o f a surfaceactivt: alkyl sulfonate \vas added to the tvater. Sipvdrt and Sassenstein explain these surface eruptions on the basis of heterogeneity in the surfry comprehensive and sumiiiarizes plate efficiency d a m as a function of operating variables and i~hysical properties of thc gas and licluid for ii large n u m b e r o f systcms. Particular progress appears to have. been made in correlating tht, eitect c ~ fqas-phase p r u p erties arid the iinportant IWIY uf' coniact time on efficiency. ' l h c detailed t r a y design \\ ithin ctartain limits aplicars to have c:omparatively little c.tt;.ct. By mc'aris of rc.1tLrenc.e citr\'es dc individual gas arid licliiid transfrr coc.ficienrs. and [ I J r contact tiine a n d other pt,l-forlnancr d a t a 011 s e \ ~ ' r a l coliiinns. it iippcat's possilJI(. t o combine the gas and liquid-lJli. makc useful estirnatrs of plattx c,tticiencii,s for c.oniiiicrciai clistilla~ion columns. E i 1 r u i . r ] ) h i i s for iinl)r(iveiiicnt of the cot relations are outlined. as t h e 1)t'oyrain i.: a con ti nil in^ joint t . f f o r t oC thr uniwrsity groups. .I study directed specifically lolvard liquid-!ilm rfficiencics in I)erirJrdted [)late columns !vas publishrd b y 1,'oss and (;elster '?/;), Oxygen desorption from \\'ater ti!- air in 18-inch and .?()-inch trays \vith perforations inch in diarnctcr \\-asmeasured ovei a range ol gas and liquid rates. 'TIic most important factors Lvere found to bc intrrfacial arra ivitliin the frcith and the time of contact
MASS TRANSFER between liquid and gas. Efficiency goes through a maximum with gas rate due to competing effects of increase in interfacial area and decrease in contact time as gas flow increases, since the number of liquid film transfer units is proportional to both variables. Tray performance is related to total gas flow in the column rather than to velocity through the individual perforations. Gas phase transfer with perforated plates was studied by Kamei and associates (6F)by the adiabatic, humidification of air. I n agreement with the data on liquid films cited above, efficiency increased with foam height. The problem of mass transfer in ionic systems such as occurs in chemical absorption is discussed by Sherwood and Wei (7F) in the light of the theory of diffusion in mixed electrolytes as formulated by Vinograd and McBain (8F). I n a mixed electrolyte diffusion of individual ions may be accelerated or hindered, depending upon the concentration and type of other ions which are present. For example, in the barium chloridehydrogen chloride system in water at 25 "C. the effective diffusion constant for hydrogen ion ,is increased from 4.2 to 10.6 sq. cm. per day as the ratio of hydrogen to barium ion is decreased from 1.3 to 0. By extension of these effects into the theoretical framework of the Hatta theory for rapid irreversible chemical absorption, the relative effects of mixed electrolyte diffusion on the mass transfer coefficients can be illustrated. Hence, the work represents a distinct contribution to present concepts of such problems. A critical review of existing theories for gas absorption with chemical reaction is made by Danckwerts ( I F ) . The speculative discussion involving limitations of the film and penetration theories and other unsolved problems should be valuable to those engaged in research in this field. A number of amine absorbents are described by Goodridge ( 4 F ) . For transfer into freely falling drops of absorbent solutions the initial rates of absorption were directly proportional to partial pressure of carbon dioxide and absorbent concentration. Effect of physical properties of liquid on wetted areas of packings was measured by Hikita and Kataoka ( 5 F ) , employing the method of Mayo, Hunter, and Nash. Surface tension appeared to have a pronomced effect, while viscosity had no observable effect over a somewhat limited range of 0.9 to 3.8 centipoises. Mass Transfer to and Within Porous Solids One German review paper on mass transfer in ion exchange (7G)and four
Russian papers on the theory of ionic exchange dynamics (9G72G) appeared during the year. The German article provides a useful summary of our present understanding of rate processes in column performance. The Russian papers discuss cases which have all been previously treated, without adding any essentially new information. The additivity of mass transfer resistances in ion exchangers was discussed by Hiester, Radding, Nelson, and Vermeulen (3G). These authors propose a method of adding resistances which assumes equilibrium a t the interface but omits the usual assumption of a linear equilibrium relationship. This method is not limited to ion exchangers but should be applicable to other cases where mass transfer resistances occur in series. T o determine the effect of the nature of the ionogenic group in resins, Nair, Govindan, and Bafna (8G) measured the self-diffusion rates of rubidium ion in and through two resins, one containing an ionogenic group of the sulfonic acid type and the other containing an ionogenic group of the carboxylic acid type. These experiments indicate that the nature of the ionogenic group does not materially affect the self-diffusion rates of cations. Three papers on cation exchange membranes (42, 6G, -7G) indicate increasing interest in this separation process. Of these three, the most complete discussion is that by Mackie and Meares (6G). These authors derive an equation for the flux of electrolyte through a waterswollen cation exchange resin membrane separating two solutions of the same electrolyte at different concentrations. The equation was tested for the diffusion of five salts a t three temperatures through a Zeo-Karb disk. The good agreement obtained supports the prediction of the theory that transport of ions in the resin takes place in a n internal aqueous phase. Some error in the theory is due to the neglect of the electrophoretic effect (which is important a t high concentration) and of counterion binding (which is important at low concentration). Various studies of diffusion in solids were published during the year; of these only three are mentioned here. Data on the diffusion of uranium through graphite in the temperature range 3000' to 4350' F, were reported by Loch, Gambino, and Duckworth (5G), who noticed two distinct types of uranium transport which could be associated, respectively, with volume diffusion and with migration along pores. Pore migration, which is strongly temperature dependent, resulted in uranium penetration far beyond that arising from volume diffusion a t equivalent tempera-
tures and diffusion times. An investigation of effective diffusion coefficients in extruded carbon rods by Walker, Rusinko, and Raats (73G) showed strong anisotropy; the diffusion coefficients parallel were about 1.5 times larger than those perpendicular to the direction of extrusion. Diffusivities of hydrogen and deuterium in high purity zirconium were measured by Gulbransen and Andrew (ZG), who studied the reaction kinetics of zirconium with these gases in the temperature range 60" to 250" C. T h e ratio of the diffusivity of hydrogen to that of deuterium is 1.5.
Diffusive Separation Processes Separation of gases by thermal diffusion in annular columns was investigated in two pilot plants by Thomas and Watkins (4H).Existing theories were found applicabli to total reflux, but not for continuous flow operation. Large effects of concentration and temperature on the thermal diffusion constant, complex effects of convective turbulence, and dependence of transport coefficients on withdrawal rates were regarded as causes for failure of theoretical interpretations. It was concluded that pilot plant data are essential for the design of columns for gas separations. Corbett and Watson (7H) studied the separation of argon isotopes in a hot-wire batch thermal diffusion column. Excellent agreement with the Furry-Jones theory was observed a t ratios of Tz/ TIc 2 (where T I = cold wall temperature and Tt = hot wire temperature a t T I = 280" C.) without use of a parasitic remixing factor. Discrepancies between theory a n d , experiment a t higher temperature ratios were attributed possibly to non-Maxwellian character of the gas and temperature dependence of the thermal diffusion constant. A unique thermal diffusion apparatus for gases, called the "separation swing," is described by Clusius and Huber (ZH). A number of vertical tubes heated at one end and cooled a t the other are connected in series by a capillary leading from the bottom of one tube to the top of the next tube in the line. By means of a reciprocating piston operation in a cylinder connected to the bottom of the last tube and the top of the first tube the gas is pumped back and forth at suitable intervals. Repetition of the process serves to concentrate the components going to the hot wall in the first tube and the other component in the last tube. The separation is thus magnified over that obtainable with one tube alone, and leads to a more precise experimental measurement of the thermal diffusion factor a t small temperature differences.
VOL. 49, NO. 3, PART II
MARCH 1957
581
FUNDAMENTALS REVIEW Considerable progress in the theoretical prediction of thermal diffusion ratios for binary liquids was made by Drickamer and associates (5H).I n a refinement of earlier developments reported last year in this review based upon the thermodynamics of irreversible processes, equations are derived which give encouraging results for solutions including one o r more associated compounds. Although the magnitudes of calculated ratios were often found to be incorrect, the concentration dependmce, including a sign change, 1vas predicted very well for a variety of systems. .A continuous method for the separation of dissolved substances by countercurrent diffusion was described by Riehl a n d Wirths (3H). A porous solid or membrane contains a solution of two solutes. O n one side of the membrane solvent is evaporated and fresh solvent is added to the other side; a solute concentration gradient is thus created and the t\so solutes diffuse in a direction opposite to that of the solvent flow. If the diffusion coefficients of the t\so solutes are significantly different from each other, a separation may be achieved. This method is, in effect, a modified form of dialysis which may find application in the separation of small quantities of complex organic mixtures. Acknowledgment T h e authors are grateful to Theodore Vermeulen for advice on the literature concerned bvith ion exchange.
13B) Johnson, P. A , Babb, A. L., Chem. Rers. 56, 387 (1956). (!OB) Reamer, H. H., Duffy, C. H., Saqe, B. H., IND.ENG.CHEM.48. 282
(1956). (11R) Zbid., p. 285. (12B) Reamer, H. H., Opfell, J. E.. Sage. B. H., Ibid., 48, 27.5 ( 1 9 5 6 ) . (13B) Senett. It‘. P., Gollob. Fred. Taylor: T. I., J . Chem. P/!J.s. 23, 1679 (1955). (14B) Slattery, J. C . ? “Diffusion Coefficients and the Principle of Corresponding States,” Xl. S. thesis, University of Wisconsin, 1955.
LITERATURE CITED
(1‘4) McCabe, LV. L.. Smith, J. C., “Unit Operations of Chemical Engineerinp.” XfcGraLv-Hili, New York, 1956:’ ( 2 A ) Treybal, R. E.. “Mass Transfer Operations,” McGraw-Hill, Ne\v York, 1356. (3.4) LVeissberger, Arnold, “Technique of Organic Chemistry, vol. 111, Part I. Separation and Purification,” Interscience, New York, 1956. Molecular Diffusion (1B) Baldwin, R. L., Dunlop, P. J., Gosting, I,. J., J . A m . Chenz. Soc. 77, 5235 (1955). (2B) Bird, R. B..: “.Advances in Chemical Engineering,” pp. 155-239, .\cademic Press, New York. 1956. (3B) Caldwell, C. S., Babb, .4. L., J . Phys. Chem. 59, 1113 (1955). ( 4 R ) Zbid., 60, 51 (1956). (5B) Crank, J., “The hiathematics of Diffusion,” Oxford University Press, London, 1956. (6B) Dunlop, P. J., Gostine;, L. J., J . Am. Chem. Soc. 77, 5238 (1955). (7B) Fair, J. R., Lerner, B. J., A.Z.Ch.E. Journal 2, 13 (1956). (8B) Fujita, H., Gosting, L. J., J . .4m. Chem. Soc. 78, 1099 (1956).
582
Interfacial Resistance ( I n ) Garner: F. H., Skclland. A , H. P., C‘iiem. Enng. .Sei. 4, 140 (1955 I. (21:) Garner, I. H., Skelland. :\. €1. P., IND.ENG.C ~ E M 48, . 51 (t956). (3E) Lindland. K. P.. ‘I’crjesrn. S. G.. Chem. Eny. Sci. 5, 1 (1956). ( 4 E ) Sit.\vart. K., Nasscnstein. H.. T Z T . rirzrt. Ins. %. 98, 453 ( 1 9 5 6 1. Transfer Between Two Liquid Phases
Turbulent Diffusion (1C ) Batchelor. G. K.: Townsend, .I. A , , ”Surveys in hlechanics.” Cambridye L ni\wsity Press. London, 19.56. ~.
(11;) I)anckwcrts, P. V., .t,I.C/!,E. .lournnl 1, 456 (13.55 I. (2F) Foss, .\. S., Gcrster, .I. .\.. Chrm. I:‘ni.. I’rugr. 52, 285 (19.56~. ( 3 F ) Gerstcr. .I. :I., LVilliainq, Brymri..
X l . . 1:iiit.d Annual Prog-ress Kcport. lirse;irrh Corninittrr. .\In. Inst. Chcin. K n q r r . . .Tune 30. 1955. ’icliornborn. 1;.
Brotr. IValter. C / ! r l ~ i , - I ~ l ~ , -28, ~.l’~~!, 165 (1956). (4F) Goodridqc. F., Y . T ~ I > /. ; i r a t i q Deider, P. K., IVilhelrn, K. H., 51, 1-03 (1955’1. JSD. CNG. CHEM. 45, 1219 11953). (.5F) Hikita, H., Kotaoka. Deissler, R. G., Natl. AdtGory ( J a p m l 20, 528 (1956 I . Comm. .Aeronautics, Tech. Notes (61;) Kamt-i. S.,Takatnatsu. ‘1’ .. Snkazal,.i. 3145(May1954). S . , Zbid., 20, 71 ( 1 9 S f ~ ) . Fage. .4.,Townsend. H. C. H . . (7F) Shcrwood, T. Ii., !Vri. .1. (:., .1.1.Proc. Roy. Soc. London 135A, 656 C1i.E. Journal 1 , 5 2 2 (1955 I. (1932 ). (81’)Vinoqrad. ~ J . K.. LlcHain. .J. I\-.. Hanrattv, T. J.: A.Z.Ch.E. Journal J . A m . Chem. S o r . 63, 2008 ! 1 ‘I41 1. 2 , 42 (1956). Ibid., p. 359. Hanratty, T. J., Latinen, G., Solids LVilhelin, R. H., Zbid., 2, 372 (1956). (1G) Bccker-Boost, F,. H.. (.%em.-/nc..Isakoff, S. E., Drew, T. B., Tech. 28, 41 1 ( 1 956 I . Proc. General Discussion on (2G’l Gnlbransen, E. A , , .\ndre\.r. K. F . . Heat Transfer. Inst. of hlechaniJ . Electrochem. .Cor. 101, .5(1’) cal Engineers. London,1951. ( 1 954). (1OC) Keyes, J. J., Jr., .4.Z.Ch.E. Journal ( 3 G ) Hirster, S . K . > R a t i t h i . , I
