Computer simulations of electrodiffusion problems based on Nernst–Planck and Poisson equations

Abstract

A numerical procedure based on the method of lines for time-dependent electrodiffusion transport has been developed. Two types of boundary conditions (Neumann and Dirichlet) are considered. Finite difference space discretization with suitably selected weights based on a non-uniform grid is applied. Consistency of this method and the method put forward by Brumleve and Buck are analysed and compared. The resulting stiff system of ordinary differential equations is effectively solved using the RADAU5, RODAS and SEULEX integrators. The applications to selected electrochemical systems: liquid junction, bi-ionic case, ion selective electrodes and electrochemical impedance spectroscopy have been demonstrated. In the paper we promote the use of the full form of the Nernst–Planck and Poisson (NPP) equations, that is including explicitly the electric field as an unknown variable with no simplifications like electroneutrality or constant field assumptions. An effective method of the numerical solution of the NPP problem for arbitrary number of ionic species and valence numbers either for a steady state or a transient state is shown. The presented formulae – numerical solutions to the NPP problem – are ready to be implemented by anyone. Moreover, we make the resulting software freely available to anybody interested in using it.