A vanadium redox flow battery model incorporating the effect of ion concentrations on ion mobility

Previous vanadium redox flow battery models (VRFB) use the ion mobility deduced from the ion diffusivity measured at low ion concentrations, resulting in an overestimation of the ionic conductivity in VRFBs that virtually operate at much higher ion concentrations. To address this issue, we propose to use the Stokes–Einstein relationship to determine an ion concentration-dependent ion mobility. A two-dimensional, transient model that incorporates the effect of ion concentrations on ion mobility is developed for VRFBs. It is shown that the present model results in: (i) a more accurate estimation of ionic conductivity, (ii) a more accurate prediction of cell voltage particularly at high current densities, and (iii) a more realistic simulation of the concentration distributions and local current density distributions in the electrodes. Finally, the model is applied to the study of the effects of important electrode design parameters and operating conditions on cell performance. It is found that the local current density, being distributed across the electrode in a manner opposite to that predicted by previous models, is much lower at the current collector side than that at the membrane side. This fact suggests that the region away from the membrane is not well utilized in conventional electrodes, thus a thinner electrode is preferred.