Effective macroscopic equations for species transport and reactions in porous catalyst layers

A macroscopic model for a porous catalyst layer is derived from a microscopic description that includes the reduction of oxygen in periodically distributed pores filled with liquid water. While specific transport equations are established for a cathode catalyst layer in a PEM fuel cell, the same multi-scale approach would yield governing equations for other types of electrodes which are mathematically analogous. Macroscopic transport characteristics such as porous media (corrector) tensors, Darcy’s law and an effective Butler-Volmer equation, are inherently linked to the dynamics at the microscale and can be computed in a fairly straightforward manner under the assumption of local thermodynamic equilibrium. In the case of periodic and strongly convective flows, we also obtain so-called diffusion-dispersion relations, e.g. Taylor-Aris dispersion.