Adiabatic relaxation of convective-diffusive gas transport in a porous fuel cell electrode

The gas diffusion layer in the electrode of a proton exchange membrane fuel cell is a highly porous material which acts to distribute reactant gases uniformly to the active catalyst sites. We develop a mathematical model for ow of a multicomponent mixture of ideal gases in a highly porous electrode. The model is comprised of a porous medium equation for the evolution of the gas mixture and a singularly perturbed convection-diffusion equation for the interspecies mass transfer within the mixture. The equations are coupled through nonlinear boundary conditions which describe consumption of reactants and generation of end products at the catalyst layer. Through a two-time-scale analysis, we derive a single reduced equation which captures the slow, diffusively driven, adiabatic relaxation to the steady state at each electrode. The asymptotic results are compared with one- and two-dimensional computations of the full system.