An 1-D model for species crossover through the membrane in all-vanadium redox flow batteries

Membrane, as a key component in all-vanadium redox flow batteries, plays the role of conducting the current and isolating the solutions between the anode and cathode electrodes. Both functional groups and charge numbers of membranes influence the performance of the battery. However, in simulating the species crossover through the membrane conventional models take account of mass transfer with the effect of functional groups in the membrane on crossover neglected. In this work, we propose an 1-D model for the membrane region of all-vanadium redox flow battery with the effect of functional groups considered. The model is formulated based on the conservation equations for charge and mass. Donnan potentials at the interfacial regions between membrane and electrodes are modeled, where the conditions are non-electrically neutral. The effects of various factors, including the state of charge, the number of functional groups and the applied current on species crossover are studied. It is shown that there exists a significant jump in electric potential and ion concentrations at the interfacial regions between membrane and electrodes. For a cation membrane, the concentrations of cations at the membrane side in the interfacial region are higher than those at the electrode side, while those of anions opposite. With more charges in the cation exchange membrane, the fluxes of vanadium ions crossover through the membrane are larger, leading to a lower efficiency. The model not only helps shed light into the mechanism of species crossover through the membrane, but also provides a tool to optimize the membrane design for all-vanadium flow batteries.