Comparison and numerical treatment of generalised NernstPlanck models
In its most widespread, classical formulation, the NernstPlanckPoisson system for ion transport in electrolytes fails to take into account finite ion sizes. As a consequence, it predicts unphysically high ion concentrations near electrode surfaces. Historical and recent approaches to an appropriate modification of the model are able to fix this problem. Several appropriate formulations are compared in this paper. The resulting equations are reformulated using absolute activities as basic variables describing the species amounts. This reformulation allows to introduce a straightforward generalisation of the ScharfetterGummel finite volume discretisation scheme for driftdiffusion equations. It is shown that it is thermodynamically consistent in the sense that the solution of the corresponding discretised generalised PoissonBoltzmann system describing the thermodynamical equilibrium is a stationary state of the discretised time-dependent generalised NernstPlanck system. Numerical examples demonstrate the improved physical correctness of the generalised models and the feasibility of the numerical approach.
electrolytes nernstplanck equations bikermanfreise model finite volume methods