Activity based finite volume methods for generalised nernst-planck-poisson systems

Abstract

The paper shortly introduces models which improve the Nernst-Planck- Poisson system to obtain more realistic ion concentrations near electrode surfaces in comparison to classical models. The resulting equations are reformulated using activities as basic variables describing the species amounts. This reformulation allows to introduce a straightforward generalisation of the Scharfetter-Gummel scheme for drift-diffusion equations. Numerical examples demonstrate the improved physical correctness of the generalised model, the thermodynamic consistency in the sense of the decay of the free energy, and the usefulness in nanofluidic problems.