A transient electrochemical model incorporating the Donnan effect for all-vanadium redox flow batteries

In a typical all-vanadium redox flow battery (VRFB), the ion exchange membrane is directly exposed in the bulk electrolyte. Consequently, the Donnan effect occurs at the membrane/electrolyte (M/E) interfaces, which is critical for modeling of ion transport through the membrane and the prediction of cell performance. However, unrealistic assumptions in previous VRFB models, such as electroneutrality and discontinuities of ionic potential and ion concentrations at the M/E interfaces, lead to simulated results inconsistent with the theoretical analysis of ion adsorption in the membrane. To address this issue, this work proposes a continuous-Donnan effect-model using the Poisson equation coupled with the Nernst-Planck equation to describe variable distributions at the M/E interfaces. A one-dimensional transient VRFB model incorporating the Donnan effect is developed. It is demonstrated that the present model enables (i) a more realistic simulation of continuous distributions of ion concentrations and ionic potential throughout the membrane and (ii) a more comprehensive estimation for the effect of the fixed charge concentration on species crossover across the membrane and cell performance.