Geometry-Dependent Oxygen Diffusion Flux and Limiting Current Density of the Cathode in a Cathode-Supported Solid Oxide Fuel Cell

An analysis is performed on the diffusion of oxygen through tubular porous cathode substrates having several different geometries. It is shown that the flux of oxygen as it diffuses through these different substrate geometries can be explicitly expressed by a general analytical form with a unique geometric factor for each type of substrate geometry. Experimental measurements of the geometry-independent term, oxygen diffusivity, were conducted for two representative geometries: cylindrical and triangular tubes. These measurements show good agreement between samples with similar porosities and thus favorably support the oxygen flux equations presented. Formulations for the limiting current density were also derived directly from the oxygen flux equations. These are similarly expressed by a general analytical form with the same unique geometric factor depending on the particular substrate. Finally, three representative geometries, cylindrical, triangular, and square tubes, are used to illustrate the influence of the various dimensional parameters on the limiting current density