Effective transport coefficients in PEM fuel cell catalyst and gas diffusion layers: Beyond Bruggeman approximation

The Bruggeman approximation has widely been used for estimating the effective conductivity and diffusivity of both the catalyst and gas diffusion layers of polymer electrolyte membrane (PEM) fuel cells. This approximation is based on the Bruggeman’s Effective Medium Theory [Bruggeman D. Berechnung verschiedener physikalischer konstanten von heterogenen substanzen. Ann Phys (Leipzig) 1935;24:636–79], which provides empirical correlation for the effective properties of a composite system. Since it is an empirical correlation, a unique correlation based on the Bruggeman approximation does not always hold for the PEM fuel cell effective properties. Rather, the Bruggeman correlation is a cell specific and experiment dependent correlation that depends on structure, phase composition, water saturation, experimental parameters, etc. Further, this correlation needs to be combined with other correlations to estimate the effective diffusivities. In this article, a set of mathematical formulations has been proposed for the effective transport properties in both the catalyst and gas diffusion layers of a PEM fuel cell. The effective conductivity and diffusivity expressions are derived from the mathematical formulations of the Hashin Coated Sphere model [Hashin Z. The elastic moduli of heterogeneous materials. J Appl Mech 1962;29:143–50], which provides an identical mathematical foundation for each of these effective properties rather than an empirical correlation and avoid to use of multiple correlations together. The present model formulations agree well with the results available in literature for the limiting case. Hence, the proposed formulations for the effective transport properties will be a useful estimating tool in the numerical modeling of PEM fuel cells.