Mathematical Sciences - Colloquium

The gas diffusion electrode is a critical component of the proton exchange membrane fuel cell.  Electrodes are composed of a highly porous material that serves to distribute reactant gases uniformly to the active catalyst sites.  We develop a mathematical model for flow of a binary gas mixture in a porous medium which consists of a coupled system of nonlinear parabolic differential equations: a porous medium equation for the evolution of the gas mixture; and a singularly perturbed convection-diffusion equation for interspecies mass transfer within the mixture.  The two equations are supplemented by a set of nonlinear boundary conditions that describe consumption of reactants and generation of end products at the catalyst layer.

Using a multi-scale asymptotic expansion, we obtain a reduced system of equations that captures the slow, diffusively-driven, adiabatic relaxation to the steady state at each electrode.  The asymptotic results are compared with computations of the full system.  We also present numerical simulations that show how fuel cell performance can be optimized by varying electrode geometry and material parameters.
 
 

Spring 2000 Colloquium Schedule | Mathematical Sciences home | The University of Montana home