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Published November 1958 | Published
Journal Article Open

Ion exchange kinetics. A nonlinear diffusion problem. II. Particle diffusion controlled exchange of univalent and bivalent ions


The differential equation derived previously which describes the particle diffusion controlled ion exchange between spherical beads of uniform size and a well-stirred solution is solved numerically for the exchange of monovalent ions for bivalent ions, and of bivalent ions for monovalent ions. The approach is based on the Nernst-Planck equations of ionic motion. Numerical results for six different mobility ratios are presented and discussed. They were obtained by use of a digital computer. An explicit equation approximating the numerical data is given.

Additional Information

© 1958 American Institute of Physics. Received July 7, 1958. This investigation was supported in part by the Office of Naval Research. We wish to express our gratitude to Mr. K.J. Hebert for his valuable assistance in the numerical integration and to Miss Z. Lindberg for computing the explicit approximation. Contribution No. 2374 from the Gates and Crellin Laboratories of Chemistry.

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