Separations
Ion-exchange kinetics: Heterogeneous resin-phase model
Abul Hasnat,
Vinay A. Juvekar,
Abul Hasnat
Dept. of Chemical Engineering, Indian Institute of Technology, Bombay 400076, India
Search for more papers by this authorCorresponding Author
Vinay A. Juvekar
Dept. of Chemical Engineering, Indian Institute of Technology, Bombay 400076, India
Dept. of Chemical Engineering, Indian Institute of Technology, Bombay 400076, IndiaSearch for more papers by this authorAbul Hasnat,
Vinay A. Juvekar,
Abul Hasnat
Dept. of Chemical Engineering, Indian Institute of Technology, Bombay 400076, India
Search for more papers by this authorCorresponding Author
Vinay A. Juvekar
Dept. of Chemical Engineering, Indian Institute of Technology, Bombay 400076, India
Dept. of Chemical Engineering, Indian Institute of Technology, Bombay 400076, IndiaSearch for more papers by this authorAbstract
A new approach to cation-exchange kinetics views ion-exchange resin as an aggregate of uniform cylindrical pores. Ion exchange occurs at the pore surface. The counterions dissociate only partially from the fixed sites, and the charge created on the pore surface is balanced by the counterions in the electrical double layer. Thus, any cross section of a pore consists of an annular double-layer region and a central core region. Electroneutrality prevails in the core region through an influx of coions. Diffusion of ions through both regions is considered. The complete model incorporating these ideas for kinetics of monovalent cation exchange was tested with our experimental data as well as with the reported data. The pore diffusion coefficients used in the model are free ionic diffusion coefficients corrected for the tortuosity factor of the pores. Unknown parameters of the model are the degree of dissociation of counterions from the fixed sites of the pore (fσ), and the film thickness (δ). Both parameters are insensitive to the type of counterions, solution concentration, and the direction of exchange. Further, fσ appears to be a characteristic property of resin alone. Superiority of the developed model over the previous models is established.
Literature Cited
- Anderson, R. E., “ Ion-Exchange Separations,” Handbook of Separation Techniques for Chemical Engineers, 2nd ed., P. A. Schweitzer, eds., McGraw-Hill, New York (1988).
- Bajpai, R. K., A. K. Gupta and M. Gopala Rao, “Single Particle Studies of Binary and Ternary Ion Exchange Kinetics,” AIChE J., 20 (5), 989 (1974).
- Bhandari, V. M., V. A. Juvekar, and S. R. Patwardhan, “Sorption Studies on Ion Exchange Resin. 1. Sorption of Strong Acids in Weak Base Resins,” Ind. Eng. Chem. Res., 31, 1060 (1992).
- Bockris, J. O. M. and A. K. N. Reddy, Modern Electrochemistry, Vol. 2, Plenum Press, New York, p. 747 (1970).
- Boyd, G. E. and K. Bunzl, “The Donnan Equilibrium in Cross-Linked Polystyrene Cation and Anion Exchangers,” J. Amer. Chem. Soc., 89 (8), 1776 (1967).
- Boyd, G. E. and B. A. Soldano, “Self-Diffusion of Cations in and Through Sulphonated Polystyrene Cation Exchange Polymers,” J. Amer. Chem. Soc., 75 (24), 6091 (1954).
- Boyd, G. E., A. W. Adamson and L. S. Myers, Jr., “The Exchange Adsorption of Ions from Aqueous Solutions by Organic Zeolites: II. Kinetics,” J. Amer. Chem. Soc., 60, 836 (1947).
- Brown, C. J. and C. J. Fletcher, “ Water Deionization by Recoflo Short Bed Ion Exchange” Proc. Int. Water Con., Pittsburgh (Oct. 27–29, 1986).
- Costa, E., A. deLucas, and M. E. Gonzalez, “Ion Exchange: Determination of Interdiffusion Coefficients,” Ind. Eng. Chem. Fund., 23, 400 (1984).
- Glaski, F. A. and J. S. Dranoff, “Ion Exchange Kinetics: A Comparison of Models,” AIChE J., 9 (3), 427 (1963).
- Rao, M. Gopala, and M. M. David, “Single-Particle Studies of Ion Exchange in Packed Beds: Cupric Ion-Sodium Ion System,” AIChE J., 10 (2), 213 (1964).
- Graham, E. E., “ Application of Stefan-Maxwell Equation to Multicomponent Ion Exchange,” Fundamentals and Applications of Ion Exchange, L. Liberty and J. R. Miller, eds., NATO, ASI Series, Martinus Nijhoff Publishers, The Netherlands (1985).
- Graham, E. E. and J. S. Dranoff, “Application of Stefan-Maxwell Equations to Diffusion in Ion Exchangers: 1. Theory,” Ind. Eng. Chem. Fund., 21, 360 (1982).
- Graham, E. E. and J. S. Dranoff, “Application of Stefan-Maxwell Equations to Diffusion in Ion Exchangers: 2. Experimental Results,” Ind. Eng. Chem. Fund., 21, 365 (1982).
- Helfferich, F., “ Ion Exchange Kinetics,” in Ion Exchange, Chap. 2, J. A. Marinsky, eds., Marcel Dekker, New York (1966).
- Helfferich, F. “Ion Exchange Kinetics. Vs. Ion Exchange Accompanied by Chemical Reactions,” J. Phys. Chem., 69 (4), 1178 (1965).
- Helfferich, F., Ion Exchange, McGraw-Hill, New York (1962a).
- Helfferich, F. “Ion Exchange Kinetics: III. Experimental Test of the Theory of Particle Diffusion Controlled Ion Exchange,” J. Phys. Chem., 66 (1), 39 (1962b).
- Helfferich, F. and M. S. Plesset, “Ion Exchange Kinetics: A Nonlinear Diffusion Problem,” J. Chem. Phys., 28 (3), 418 (1958a).
- Hering, B. and H. Bliss, “Diffusion in Ion Exchange Resins,” AIChE J., 9 (4), 495 (1963).
- Kataoka, T., H. Yoshida, and H. Sanda, “Estimation of the Resin Phase Diffusivity in Isotopic Ion Exchange,” J. Chem. Eng. Japan, 7 (2), 105 (1974).
- Kraaijeveld, G. and J. A. Wesselingh, “The Kinetics of Film Diffusion-Limited Ion Exchange,” Chem. Eng. Sci., 48 (3), 467 (1993).
- Krishna, R. “Diffusion in Multicomponent Electrolyte Systems,” Chem. Eng. J., 35, 19 (1987).
- Kuo, J. C. W. and M. M. David, “Single Particle Studies of Cation Exchange Rates in Packed Beds: Barium Ion-Sodium Ion Systems,” AIChE J., 9 (3), 365 (1963).
- Liberti, L. and R. Passino, “ Ion Exchange Kinetics in Selective Systems,” Ion Exchange and Solvent Extraction, Chap. 3, J. A. Marinsky and Y. Marcus, eds., Marcel Dekker, New York (1985).
- Miller, J. R., D. G. Smith, W. E. Marr, and T. R. E. Kressmann, “Solvent-Modified Polymer Networks: I. The Preparation and Characterization of Expanded Network and Macroporous Styrene Divinyl Benzene Copolymers and Their Sulphonates,” J. Chem. Soc., 218 (1963).
- Morig, C. R. and M. Gopala Rao, “Diffusion in Ion Exchange Resins: Sodium Ion-Strontium Ion System,” Chem. Eng. Sci., 20, 889 (1965).
- Morrison, Jr., F. A. and J. F. Osterle, “Electrokinetic Energy Conversion in Ultrafine Capillaries,” J. Chem. Phys., 43 (6), 2111 (1965).
- Neale, G. H. and W. K. Nader, “Porous Media: Diffusive Flow Processes within an Homogeneous Swarm of Spherical Particles,” AIChE J., 19 (1), 112 (1973).
- Pinto, N. G. and E. E. Graham, “Characterization of Resin Phase Diffusivities in Ion Exchange Resins,” Ind. Eng. Chem. Fundam., 26, 2331 (1987).
- Plesset, M. S., F. Helfferich, and J. N. Franklin, “Ion Exchange Kinetics: A Nonlinear Diffusion Problem: II. Particle Diffusion Control Exchange of Univalent and Bivalent Ions,” J. Chem. Phys., 29 (5), 1064 (1958b).
- Reichenberg, D. “Properties of Ion-Exchange Resins in Relation to Their Structure. III Kinetics of Exchange,” J. Amer. Chem. Soc., 75, 589 (1953).
- Robinson, R. A. and R. M. Stokes, Electrolyte Solutions, Butterworths Scientific Publications, London (1959).
- Schlögl, R., and F. Helfferich, “Comment on the Significance of Diffusion Potentials in Ion Exchange Kinetics,” J. Chem. Phys., 26, 5 (1957).
- Smith, T. G. and J. S. Dranoff, “Film Diffusion-Controlled Kinetics in Binary Ion Exchange,” Ind. Eng. Chem. Fund., 3 (3), 195 (1964).
- Tetenbaum, M., and H. P. Gregor, “Self-Diffusion of Cations, Non-ExchangeAnions and Solvent in a Cation Exchange Resin System,” J. Phys. Chem., 58, 1156 (1954).
- Turner, J. C. R., “ Nernst-Planck or No,” Fundamentals and Applications of Ion Exchange, L. Liberty and J. R. Miller, eds., NATO, ASI series, Martinus Nijhoff Publishers, The Netherlands (1985).
- Turner, J. C. R. and C. B. Snowdon, “Liquid-Side Mass-Transfer Coefficients in Ion Exchange: An Examination of the Nernst-Planck Model,” Chem. Eng. Sci., 23, 321 (1968).
- Turner, J. C. R., M. R. Church, A. S. W. Johnson, and C. B. Snowdon, “An Experimental Verification of the Nerst-Planck Model for Diffusion in an Ion Exchange Resin,” Chem. Eng. Sci., 21, 317 (1966).
- Vermeulen, T., M. D. LeVan, N. K. Hiester, and G. Klein, “Adsorption and Ion Exchange,” in Perry's Chemical Engineering Handbook, 6th ed., R. H. Perry, D. W. Green, and J. O. Maloney, eds., p. 16–1.
- Villadsen, J. and M. L. Michaelsen, Solution of Differential Equation Models by Polynomial Approximation, Prentice-Hall, Englewood Cliffs, NJ (1978).
- Weatherley, L. R. and J. C. R. Turner, “Ion Exchange Kinetics—Comparison between a Macroporous and a Gel Resin,” Trans. Inst. Chem. Eng., 54, 89 (1976).
- Yoshida, H. and T. Kataoka, “Intraparticle Mass Transfer in Bidispersed Porous Ion Exchangers Part II. Mutual Ion Exchange,” Can. J. Chem. Eng., 63, 430 (1985).
