Modeling of ion transport in a three-layer system with an ion-exchange membrane based on the Nernst-Planck and displacement current equations

Abstract

Modeling of ion transport in a three-layer system containing an ion-exchange membrane and two adjacent diffusion layers makes it possible to describe the permselectivity of the membrane by determining its fixed charge density. For theoretical analysis of ion transport in such systems, the Nernst–Planck and Poisson equations are widely used. The article shows that in the galvanodynamic mode of operation of the membrane system, when the density of the flowing current is specified, the Poisson equation in the ion transport model can be replaced by the equation for the displacement current. A new model was constructed in the form of a boundary value problem for the system of the Nernst–Planck and displacement current equations. Based on this model, ion concentrations, electric field strength, space charge density and chronopotentiogram of the ion-exchange membrane and adjacent diffusion layers in direct current mode were numerically calculated. The calculation results of the proposed model are in good agreement with the modeling results based on the previously described approach using the Nernst–Planck and Poisson equations, as well as with the analytical assessment of the transition time. It is shown that in the case of the three-layer geometry of the problem, the required accuracy of numerical calculation using the proposed model is achieved with a smaller number of computational mesh elements and takes less (about 26.7 times for the considered system parameters) processor time compared to the model based on the Nernst–Planck and Poisson equations.