Application of the Stefan-Maxwell Equations to Diffusion in Ion Exchangers. 1. Theory

Starting with the Stefan-Maxwell equations, general expressions for the ionic flux rates for binary exchange in ion-exchange resins have been developed. These equations have been shown to reduce to the Nernst-Planck equations exactly only as the concentration of either exchanging ion approaches unity. Furthermore, the single-ion diffusion coefficients used In the Nernst-Planck equations are shown to be certain combinations of the Stefan-Maxwell Interaction coefficients. Most importantly, these combinations of the Stefan-Maxwell interaction coefficients are shown to reduce to the tracer diffusion coefficient of each exchanging ion, measured in ion-exchange resin completely in the competing ion form. As these limiting tracer Ion diffusion coefficients may be very different from the usual pure self-diffusion coefficients, this result may explain existing anomalies resulting from the use of the Nernst-Planck equations to describe diffusion in ion-exchange resins and related ion-exchange systems.