Analytical modeling of gas diffusivity in PEM fuel cell gas diffusion layer substrates under dry and partially saturated conditions

The diffusivity of a GDL can be determined if its tortuosity is known. However, most tortuosity correlations in the literature were developed for packed beds with various particle shapes, making them unsuitable for GDLs. The few correlations developed for fibrous porous structures, which resemble the GDL microstructure, were typically based solely on porosity. However, porosity alone does not fully capture the microstructure of a GDL, leading to inaccuracies in diffusivity predictions when using existing tortuosity correlations. In this study, a new analytical model is developed to calculate the tortuosity of a GDL by incorporating both porosity and pore size distribution under dry and partially saturated conditions. The inclusion of pore size distribution enables a more accurate estimation of tortuosity, thereby improving the diffusivity predictions. To validate the model, the diffusivity of several GDL samples was measured using a symmetrical modified Loschmidt cell and compared with the model predictions. The results showed good agreement, with a maximum relative difference of 12%. To analyze the water saturation effect on gas diffusivity of GDLs, a new analytical capillary model is also developed. This model calculates the entry pressure for each pore based on its size and geometry, allowing determination of whether a pore is invaded by water. This information is integrated into the diffusivity model to account for the saturation effect. While the model performs well for materials with relatively uniform pore structures, discrepancies at low saturation levels highlight limitations in capturing pore connectivity effects, particularly for GDLs with broad pore size distributions. • Anew analytical model predicts GDL diffusivity using porosity and PSD. • Experimental validation with SMLC shows ≤12% relative difference across GDL types. • An analytical capillary model estimates water invasion and diffusivity impact. • First analytical model to capture gas transport under partial saturation.