Modeling Donnan dialysis separation for carboxylic anion recovery

A dynamic model for transport of multiple ions through an anion exchange membrane is derived based on an irreversible thermodynamics approach. This model accounts for the convective transport of the dissociated and undissociated species in the channels with diffusion and migration across the boundary layers and membranes. Donnan equilibrium, flux continuity of the transported ions, the electroneutrality condition and Faraday’s law are employed to describe the electrical potential and concentration discontinuities at the interfaces. The Nernst–Planck equation is used to model the ion transport though boundary layers and membranes. The model consists of a system of partial differential equations that are solved numerically. The aim of this paper is to corroborate this general model for several monoprotic carboxylic acids reported in the literature. The model reproduces satisfactorily experimental fluxes for monoprotic ions. Additionally, previously qualitatively estimated concentration profiles within the boundary layers and membranes are predicted.