Electroneutrality and ionic interactions in the modeling of mass transport in dilute electrochemical systems

We propose a simple, but novel mathematical and numerical approach to describe mass transport in dilute solutions, taking into consideration ionic interactions. Our proposed approach treats fluxes due to ionic interactions as additional unknowns in the transport equation. Through variational arguments, we derive a simple expression for these ionic fluxes in terms of the electroneutrality condition, which allows for a straightforward treatment of the new unknowns. Furthermore, a finite element formulation based on our mathematical model is presented. Finally, using the distribution of the interionic flux density and an energy dissipation function, we show that besides properly capturing flow due to ionic interactions, our model can also describe independent ionic flow as predicted by the conventional Nernst-Planck equation in regions where ionic interactions are weak. (C) 2011 Elsevier Ltd. All rights reserved.