Numerical modeling of non-steady-state ion transfer in electrochemical systems with allowance for migration

Numerical methods that are used for modeling non-steady-state ion transfer in electrochemical systems and account for the diffusion, migration, convection, and homogeneous chemical reactions are analyzed. It is shown that the violation of the electroneutrality condition (ENC) in the process of numerical solution is due to the difference equations being inconsistent with the initial differential equations. Difference schemes for numerical calculation of transfer processes, which make it possible to split a set of coupled equations, are designed and conditions for their stability are determined. The explicit difference scheme is self-consistent, i.e. it ensures that ENC is rigorously met. In the implicit difference scheme, ENC is probably violated when splitting the set of equations. To restore electroneutrality of the medium, it is proposed to use a physically substantiated analytical relation for the space charge relaxation under the action of a strong electric field.