BRIEFS Summary of papers published in this month's research quarterly, I@EC Fundamentals RECYCLE IN LIQUID EXTRACTION
BOUNDARY-LAYER EFFECTS IN REVERSE OSMOSIS
I n mixer-settler liquid extractors, the effect on stage efficiency of recycling the settled liquids back to the mixer was studied mathematically. Recycling that liquid favored by solute distribution increases the stage efficiency, whereas recycling the other, or recycling both, reduces it. When solute distribution favors the dispersed phase and stage efficiency is low without recycle, a minimum of cascade volume may result. These effects are in addition to any benefit which may result from better settling or inversion of the dispersion. Robert E. Treybal, New Xork University, New Xork 53, N . Y . IND. ENG.CHEM.FUNDAMENTALS 3, 185-188 (1964)
Boundary-layer effects on membrane permeation in a reverse osmosis system have been studied experimentally. Two distinct effects of boundary-layer conditions on permeation rate werc observed. The first occurred with a highly soluble salt (NaCl) in the system, and was attributed to changes in interface salt concentration and hence in effective osmotic pressure as the boundarylayer conditions were varied. The second occurred with a relatively insoluble salt ( C a S 0 4 ) in the system, and was attributed to precipitation a t the interface under certain flow conditions. Ulrich Merten, H. K. Lonsdale, and R. L. Riley, General Dynamics Corp., San Diego, Calif. IND. END.CHEM.FUNDAMENTALS 3, 210-213 (1964)
MATHEMATICAL DETERMINATION OF CONCENTRATION PROFILES IN TWO-PHASE CONTINUOUS COUNTERCURRENT EXTRACTORS
The differential equations describing the mass transfer process are derived for a two-phase countercurrent extractor in which the volumetric fraction, e t , of the phases is not constant. These equations are solved for the special case where the axial boundaries of the extractor do not correspond to the feed stream inlet points, but are located above and below these points. The results obtained are compared to those obtained by Miyauchi for the cases where they do correspond. N . P. Wilburn, Hanford Laboratories, Richland, Wash. IND.ENG.CHEM.FUNDAMENTALS 3,189-195 (1964) FILM DIFFUSION-CONTROLLED KINETICS IN BINARY ION EXCHANGE
The rate of exchange of H + and N a + ions with Dowex 50 resin was studied in dilute solutions. A batch reactor with a built-in electrical conductivity cell was used to obtain data in the region of external film diffusion control. The experimental data were compared with predictions based on the use of the Nernst-Planck equations to describe the diffusional process. The results indicate the general validity of the approach, but additional work will be required before truly quantitative agreement of theory and experiment is possible.
T . G. Smith and J . S. Dranoff, Northwestern University, Evanston, Ill. IND.ENG.CHEM.FUNDAMENTALS 3, 195-200 (1964) SIMPLIFIED DESIGN MODEL FOR A N ION EXCLUSION COLUMN
A simplified design model for a chromatographic ion exclusion column is developed, in which the fixed bed of resin is divided into a number of perfectly mixed equilibrium stages and the liquid flow rate is constant. The model is represented by the following dimensionless differential equation, which results from the combination of a material balance about the 7th stage and a second-degree phase equilibrium relationship : (1/h)($., - $?- 1) K (d$,/d7) M$, (d$,/dr) = 0, where K and M are dimensionless groups while 1/ h is the number of equilibrium stages. and 7 are dimensionless concentration and time, respectively. The numerical solutions of this equation for single, square wave inputs are presented for different values of the dimensionless groups, feed volumes, and number of stages. The resulting calculated elution curves and experimentally determined curves are compared. Design applications are discussed. H. A . Johnson and T. D . Wheelock, Iowa State Uniuersity of Science and Technology, Ames, Iowa IND.ENC.CHEM.FUNDAMENTALS -,201-206 (1964)
+
+
SEPARATION OF SOME INORGANIC SALTS IN AQUEOUS SOLUTION BY FLOW, UNDER PRESSURE, THROUGH POROUS CELLULOSE ACETATE MEMBRANES
The experimental results illustrate the general applicability of this separation technique for aqueous inorganic solutions, the possible predictability of the separation and flow characteristics of porous cellulose acetate membranes, and the concept that separations arc similar for ions of the same valency. S. Sourirajan, Notional Research Coumil, Ottawa, Canada IND.ENC.CHEM.FUNDAMENTALS 3,206-210 (1964).
PECLET NUMBERS AND RETARDATION FACTORS FOR ION-EXCHANGE COLUMNS
A solution for the problem of miscible displacement, or for the chromatographic problem involving a linear isotherm and dispersion, is given and adapted to a least squares calculation. The procedure enables utilization of all the data from column breakthrough experiments. The method is illustrated by a study of the velocity dependence of the dispersion coefficient. When applied to data not fulfilling the theoretical postulates, the method produces empirical descriptions of column behavior, a representation of column performance in terms of equivalent column volume, and a single additional parameter. The theory gives excellent, and undoubtedly fortuitous, agreement for a case of slow.isotopic exchange. Isao Hashimoto, K. B. Derhpande, and Henry C. Thomas, University o j North Carolina, Chapel Hill, N . C. IND.ENC.CHEM. FUNDAMENTALS 3,213-218 (1964)
TRANSITIONAL BEHAVIOR FOR THE SIMULTANEOUS MASS AND HEAT TRANSFER OF GASES FLOWING THROUGH PACKED AND DISTENDED BEDS OF SPHERES
Simultaneous mass and heat transfer associated with the evaporation of water from the surfaces of Celite spheres have been experimentally studied at high Reynolds numbers ranging from N R = ~ 1935 to Nxe = 10,300. The resulting q'h and q'd values decreased with increasing Reynolds numbers for NRe < 4000 and N R > ~ 5000. In the interval 4000 < N R < ~ 5000, the €]fh vs. NEe and cjd us. N R relationships ~ exhibited a double reversal of slopes with a maximum value of q' occurring at NR@~ 5 4800. . This unexpected transitional behavior presents a novel feature that has not been encountered previously in similar studies. Ashis Sen Gupta and George Thodos, Northwestern University, Evanstnn , Ill. I N D . E N D . CHEM. FUNDAMENTALS 3, 218-220 (1964)
CORRELATION OF SOME GAS ADSORPTION DATA EXTENDING TO LOW PRESSURES AND SUPERCRITICAL TEMPERATURES
Adsorption isotherms of nitrogen, methane, argon, hydrogen, and neon in the -195.8' to -78" C . temperature range have been determined on two activated carbons and a silica gel. Thc resulting data and published data have been correlated by a modified Polanyi-type correlation. No difficulty was found in correlating data a t low pressures (to torr) or a t supercritical temperatures. Moreover, the method correlated data from each of two published articles in which correlation difficulties were reported. The modified Polanyi-type correlation appears to be widely applicable and is suggested for the preliminary design of adsorption systems in the absence of direct data. R. J . Grant and Milton Manrs, Pittsburgh Chemical Co., Pittsburgh 25, Pa. IND.ENG.CHEM.FUNDAMENTALS 3, 221-224 (1964) (Continued on page 8 7) VOL. 5 6
NO. a A U G U S T 1 9 6 4
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INDUSTRIAL AND ENGINEERING
CHEMISTRY
BRIEFS
MATRIX CALCULATION OF MULTICOMPONENT MASS TRANSFER IN ISOTHERMAL SYSTEMS
Matrix methods are developed for solving multicomponent diffusion problems in terms of related binary problems. The diffusion coefficients of the binary problems are determined by the eigenvalues of a multicomponent diffusivity matrix, and are shown to be real and positive. When the diffusivity matrix is known, multicomponent concentration profiles and mass transfer rates can be calculated for systems of any geometry for which the corresponding binary functions are available. The treatment holds for nonideal mixtures in laminar or turbulent isothermal flow with moderate concentration differences and no homogeneous chemical reactions. The theory is tested by comparison with exact boundary-layer calculations for mass transfer between a flat plate and a three-component gas stream. Warren E. Stewart and Richard Prober, University of Wisconsin, Madison, Wis. IND.ENC.CHEM.FUNDAMENTALS 3,224-235 (1964).
tive agreement with the predicted behavior and confirm that the flux plot is effectively doubly concave. A rising concentration gradient immediately above the fixed bed was observed for initially uniform slurries of intermediate concentrations. The intersection of this gradient with the fluid-slurry interface accounts for the nonlinearity of settling curves when the initial volume fraction of solids is between 0.15 and 0.45. P. T. Shannon, R. D . DeHaas, and E. P. Stroupe, Purdue University, Lafayette, Ind., and E. M . Tory, McMaster Univerisity, Hamilton, Ohio IND.ENG.CHEM.FUNDAMENTALS 3, 250-260 (1964) HOMOGENEOUS FLUIDIZATION
The solute redistribution resulting from progressive freezing or zone melting of a simple eutectic-forming mixture has been solved analytically for pure diffusional mass transfer. Comparison with experimental results shows that constitutional subcooling usually occurs and produces considerable trapping of impurity. W. R. Wilcox, Aerospace Corp., E l Segundo, Calif. IND. END.CHEM.FUNDAMENTALS 3,235-239 (1964)
A physical model is proposed for a homogeneous fluidized bed. An equation of motion is established for one of an ensemble of particles in interaction with a fluid. By means of this equation an expression is established for the variance, u2, of the void fraction, a quantity connected with the mixing process taking place in the fluidizing agent. An expression for the axial diffusion coefficient is established starting frem the model suggested here and using the equation derived for ue. This equation is in satisfactory agreement with experimental results obtained by Kramers. E. Ruckenstein, Polytechnical Institute, Bucharest, Romania IND.ENG.CHEM.FUNDAMENTALS 3,260-268 (1964)
KINETICS OF ABSORPTION OF CARBON DIOXIDE IN MONOETHANOLAMINE SOLUTIONS AT SHORT CONTACT TIMES
COMMUNICATION. ALGEBRAIC REPRESENTATION OF EQUILIBRIUM PROCESSES IN MULTICOMPONENT SYSTEMS
Work was carried out to measure the absorption rate of a gas, at short contact times, with a fast chemical reaction taking place simultaneously, and to test the relation between the absorption rates observed and the diffusion coefficient, the physical solubility of the gas, and the kinetic rate constant for the homogeneous liquid phase reaction. Measurements are reported of rates of absorption of carbon dioxide in laminar jets of aqueous monoethanolamine solutions at contact times of 3 to 20 msec. and gas pressures of 1 and 0.1 atm. Rates of gas take-up observed a t the lower pressure are in agreement with the “penetration” theory for pseudo-first-order reactions developed by Danckwerts. Absorption at atmospheric pressure corresponds to a less amenable kinetic condition, since the concentration of unreacted monoethanolamine at the interface becomes seriously depleted during even the shortest attainable contact time of gas and liquid, and heat of reaction appears to influence the observed rates of absorption. J. K . A . Clarke, Defiartment of Scient& and Industrial Research, Stevenage, Hertfordshire, England IND.ENC. CHEM.FUNDAMENTALS 3, 239-245 (1964)
Reacting chemical systems in which the total number of compounds exceeds that possible in a single equilibrium are called multisystems by Korzhinskil. By algebraically specifying the number of molecules of each compound and the composition of each compound by element, an exact statement of possible phase composition can be made. D. R. Suayze, 47 Savre St., Elizabeth, .Y. .I. IsD. E N G . CHEhf. FUNDAMESTALS 3, 269-270 (1964)
FRACTIONAL SOLIDIFICATION OF EUTECTIC-FORMING MIXTURES
COMMUNICATION. SYMMETRICAL FORM OF THE FOUR-SUFFIX MARGULES EQUATIONS FOR QUATERNARY SYSTEMS
The asymmetrical form of the four-suffix Margules equations for quaternary systems derived by Marek is transformed into a symmetrical form. The new form of the equations not only avoids ambiguity with the definition of the systems, but also permits easier evaluation of the activity coefficients, especially when a digital computer is used. C.-H. Lu and Y.-L. Wang, Burroughs Cor@.,Pasadena, C a y . IND.ENG.CHEM.FUNDAMENTALS 3,271-272 (1964)
VELOCITY, TEMPERATURE, AND CONCENTRATION DISTRIBUTIONS DURING FIBER SPINNING
The velocity distribution was experimentally measured and the temperature and concentration profiles were theoretically calculated for the region surrounding a fiber during wet spinning of a single filament. The transition from laminar to turbulent flow was correlated with process conditions and found to occur near values typical of commercial spinning. Multifilament flow was simulated and a possible correlation of the data discussed. Finally, elastic forces within the spinnerette were found responsible for most of the tension needed in spinning the polyacrylonitrile fiber used in this work. R. M . Gri$ith, American Cyanamid Co., Stamford, Conn. IND.ENG.CHEM.FUNDAMENTALS 3, 245-250 (1964) BATCH AND CONTINUOUS THICKENING. PREDICTION OF BATCH SETTLING BEHAVIOR FROM INITIAL RATE DATA WITH RESULTS FOR RIGID SPHERES
A general method is presented for predicting batch settling for slurries of initially uniform concentration from the solids flux plot based on initial rate data. It is assumed that settling velocity is a function of local solids concentration only. Experimental batch settling curves for rigid glass spheres in water are presented. The experimental results are in complete qualitative and close quantita-
CORRESPONDENCE
Comments on an article by C. M. Sliepcevich and Don Finn, [IND.ENC.CHEM.FUNDAMENTALS 2, 249 (1963)] on a macroscopic approach to irreversible thermodynamics (rebuttal by the authors). J . L. Duda and J . S. Vrentas, The Daw Chemical Co., Midland, Mich. I?. C. Andrews, University of Wisconsin, Madison, Wis. C. M . Sliepcevich, Don Finn, Hadi Hashemi, and Michael Heymann, University of Oklahoma, Norman, Okla. IND. ENG.CHEM.FUNDAMENTALS 3,272-277‘( 1964). CORRESPONDENCE
Comments on some previously published data concerned with correlations for the coefficients of gaseous diffusion and two replies. D. S. Scott, Dejartment of Chemical Engineering, Cambridge University, Cambridge, England N . H. Chen and D . F. Othmer, Defiartment of Chemical Engineering, Polytechnic Institute of Brooklyn, Brooklyn, N . Y . T. K. Sherwood, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. IND.ENO.CHEM.FUNDAMENTALS 3,278-280 (1964)
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