Steady-state Ion Transport through a Three-Layered Membrane System: A Mathematical Model Allowing for Violation of the Electroneutrality Condition

A relatively simple mathematical model based on the Poisson equation is considered. The model is intended for modeling transport through multilayered ion-exchange membranes operating at overlimiting currents. The boundary-value problem is solved by a numerical method of parallel shooting and by an approximate method based on the assumption that the charge density is distributed quasi-uniformly. Concentration profiles in diffusion layers and membranes, current–voltage curves, and dependences of effective transport numbers on the current density are examined.