Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: Effect of local saturation and application to macroscopic continuum models

Macroscopic continuum models are an essential tool to understand the complex transport phenomena that take place in gas diffusion layers (GDLs) used in polymer electrolyte fuel cells (PEFCs). Previous work has shown that macroscopic models require effective properties obtained under uniform saturation conditions to get a consistent physical formulation. This issue, mostly unappreciated in the open literature, is addressed in detail in this work. To this end, lattice Boltzmann simulations were performed on tomographic images of dry and water-invaded carbon-paper GDL subsamples with nearly uniform porosity and saturation distributions. The computed effective diffusivity shows an anisotropic dependence on local porosity similar to that reported for morphologically analogous GDLs. In contrast, the dependence on local saturation is rather isotropic, following a nearly quadratic power law. The capability of the local correlations to recover the layer-scale properties obtained from inhomogeneous GDLs is checked by global averaging. Good agreement is found between the upscaled results and the diffusivity data of the GDL from which the present subsamples were taken, as well as other global data presented in the literature. A higher blockage effect of local saturation is, however, expected for the under-the-rib region in operating PEFCs.