A model of transport across the ion-exchange membrane in all-vanadium redox flow batteries has been proposed based on concentrated solution theory for species with high concentration. The model is based upon the Stefan-Maxwell multicomponent diffusion equation where the fluxes of the species including protons (H~+), bisulfate (HSO_4~-), water (H_2O) and the sulfonate functional groups (-SO_3~-) are fully coupled. The driving force for species transport has been modeled in terms of concentration and electrostatic potential gradients. The ionic transference numbers as well as water electro-osmosis drag coefficient has been calculated for different acid concentrations.
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