Polymer electrolyte fuel cell transport mechanisms: a universal modelling framework from fundamental theory

A mathematical multi-species modelling framework for polymer electrolyte fuel cells (PEFCs) is presented on the basis of fundamental molecular theory. Characteristically, the resulting general transport equation describes transport in concentrated solutions and also explicitly accommodates for multi-species electro-osmotic drag. The multi-species nature of the general transport equation allows for cross-interactions to be considered, rather than relying upon the superimposition of Fick’s law to account for the transport of any secondary species in the membrane region such as hydrogen. The presented general transport equation is also used to derive the key transport equations used by the historically prominent PEFC models. Thus, this work bridges the gap that exists between the different modelling philosophies for membrane transport in the literature. The general transport equation is then used in the electrode and membrane regions of the PEFC with available membrane properties from the literature to compare simulated one-dimensional water content curves, which are compared with published data under isobaric and isothermal operating conditions. Previous work is used to determine the composition of the humidified air and fuel supply streams in the gas channels. Finally, the general transport equation is used to simulate the crossover of hydrogen across the membrane for different membrane thicknesses and current densities. The results show that at 353 K, 1 atm, and 1 A/cm2, the nominal membrane thickness for less than 5 mA/cm2 equivalent crossover current density is 30 mm. At 3 atm and 353 K, the nominal membrane thickness for the same equivalent crossover current density is about 150 mm and increases further to 175 mm at 383 K with the same pressure. Thin membranes exhibit consistently higher crossover at all practical current densities compared with thicker membranes. At least a 50 per cent decrease in crossover is achieved at all practical current densities, when the membrane thickness is doubled from 50 to 100 mm.