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

Highlights: → A simple ionic transport model including Coulombic interactions is proposed. → A connection between electroneutrality and Onsager's cross-flux terms is established. → Interionic flux densities are obtained from a constrained variational statement. → The numerical stiffness of the classical P-N-P system is bypassed using our proposed approach. - Abstract: 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.