Film model approximation for particle-diffusion-controlled binary ion exchange

A new rate expression for particle-diffusion-controlled ion exchange, based on an equivalent pseudosteady-state Nm resistance model, is developed. The rate expression approximates the electric field effects on intraparticle diffusion in spherical ion-exchangers. With regard to the prediction of batch exchange and column breakthrough curves for both irreversible and reversible processes, the model captures the essential traits of the coupled diffusion phenomenon described by the Nernst-Planck equation with results of accuracy comparable to that obtained when using the linear driving force approximation for systems with constant diffusivity. Numerical results for the exchange of two counterions of equal valence are presented as application examples for different mobility ratios and selectivity coefficients.