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

A film-model approximation is developed to predict multicomponent ion exchange in spherical particles. Mass transfer is represented by pseudosteady-state diffusion through a stagnant film of thickness equal to one-fifth of the particle radius. An exact analytic solution is found for the case of homovalent exchange and an approximate solution for the case of heterovalent exchange. Results obtained from the exact solution of the Nernst-Planck model are compared to those obtained using the film-model approximation for the case of ternary exchange in infinite-batch and fixed-bed systems. The predictions based on the film-model approximation are in good agreement with the exact solution for both homovalent and heterovalent ion exchange, indicating that the film-model approximation can be used effectively in numerical simulations of complex ion-exchange systems.