Mathematical description of ion transport in membrane systems

A review of works resulting in development of a hierarchic system of mathematical models is presented. Different scales of ion transport are considered: 1) in the membrane, where. two approaches are used, the irreversible thermodynamics and modelling of the membrane material, the last permits to link physicochemical properties with structure-kinetic parameters of the membrane; 2) in a three-layer system composed of a membrane with two adjoining diffusion layers; and 3) in an electrodialysis 2D cell, where the differential equation of convective diffusion is used.