Mathematical modelling of transport of single and double charged ions through layered ion exchange membranes

Abstract

Monovalent selectivity of ion exchange membranes is important for such areas as hardness removal, stabilization of mining waters and fining of foods. The modern approach to the creation of monovalent selective ion exchange membranes is layer-by-layer adsorption of polyelectrolytes onto a membrane surface, which showed significant improvement in comparison with previously used approaches, most notably in comparison with the creation of a single thick layer of polyelectrolyte. Despite the practical importance, the mechanism of improvement in selectivity is unknown. Knowledge of the distribution of ions within the membrane and adjacent layers of solution would answer the question of the mechanism, but such information is unobtainable through the experiment. Hence we develop the 1D mathematical model based on Nernst-Planck-Poisson equations to describe the fluxes and the concentrations of single and double charged ions, as well as potential drop / current density through the ion exchange membrane. In this paper we formulate the problem and list experimentally determined parameters. Results of calculations will be compared with experimentally recorded I-V and V-t curves.