With its long cycle life and scalable design, the vanadium redox flow battery (VRB) is a promising technology for grid energy storage. However, high materials costs have impeded its commercialization. An essential but costly component of the VRB is the ion-exchange membrane. The ideal VRB membrane provides a highly conductive path for protons, prevents crossover of reactive species, and is tolerant of the acidic and oxidizing chemical environment of the cell. In order to study membrane performance and optimize cell design, mathematical models of the separator membrane have been developed. Where previous VRB membrane models considered minimal details of membrane transport, generally focusing on conductivity or self-discharge at zero current, the model presented here considers coupled interactions between each of the major species by way of rigorous material balances and concentrated solution theory. The model describes uptake and transport of sulfuric acid, water, and vanadium ions in Nafion membranes, focusing on operation at high current density. Governing equations for membrane transport are solved in finite difference form using the Newton-Raphson method. Model capabilities were explored, leading to predictions of Ohmic losses, vanadium crossover, and electro-osmotic drag. Experimental methods were presented for validating the model and for further improving estimates of uptake parameters and transport coefficients. / text