Mathematical modelling of a membrane-less redox flow battery based on immiscible electrolytes

Abstract

We present a mathematical model to study the steady-state performance of a membrane-less reversible redox flow battery formed by two immiscible electrolytes that spontaneously form a liquid-liquid system separated by a well defined interface. The model assumes a two-dimensional battery with two coflowing electrolytes and flat electrodes at the channel walls. In this configuration, the analysis of the far downstream solution indicates that the interface remains stable in all the parameter range covered by this study. To simplify the description of the problem, we use the dilute solution theory to decouple the calculation of the velocity and species concentration fields. Once the velocity field is known, we obtain the distribution of the mobile ionic species along with the current and the electric potential field of the flowing electrolyte solution. The numerical integration of the problem provides the variation of the battery current density Iapp with the State of Charge (SoC) for different applied cell voltages Vcell. A detailed analysis of the concentration density plots indicates that the normal operation of the battery is interrupted when reactant depletion is achieved near the negative electrode both during charge and discharge. The effect of the electrolyte flow on the performance of the system is studied by varying the Reynolds, Re and Péclet, Pe, numbers. As expected, the flow velocity only affects the polarization curve in the concentration polarization region, when is well below the equilibrium potential, resulting in limiting current densities that grow with Re......