Transport in polymer-electrolyte membranes - II. Mathematical model

A mathematical model is developed that is based on our previous physical model. The governing equations are presented for both the vapor- and liquid-equilibrated transport modes as well as when they both occur. Thus, this model bridges the gap between the one-phase and two-phase macroscopic models currently used in the literature. In addition to being able to model such phenomena as Schroeder's paradox, the model incorporates other relatively novel features including the effect of temperature on water uptake by the membrane from water vapor, and its associated effects on transport properties. Just as in the physical model, the mathematical model uses the wealth of knowledge contained in the literature to examine and determine values for the relevant transport and membrane parameters. This also helps in corroborating the physical model. The mathematical model developed is further validated and its results examined in a subsequent paper where it is placed in a simple fuel-cell model. (C) 2004 The Electrochemical Society.