A fractal model for determining oxygen effective diffusivity of gas diffusion layer under the dry and wet conditions

In this paper, we propose a new fractal model to determine the oxygen effective diffusivity of the porous gas diffusion layer (GDL) in proton exchange membrane fuel cell for both the dry and wet conditions. The model considers the GDL structure in terms of tortuosity and area fractal dimensions and also takes the Knudsen effect into account, which has no empirical constant but parameters with physical meanings. The fractal model is verified by the fair agreement with the experimental data and the results obtained from existing models. It is revealed that the Knudsen effect is essential for the understanding of the oxygen transport through the GDL. Under the dry condition, the oxygen effective diffusivity increases with higher area fractal dimension and lower tortuosity fractal dimension. For the wet condition, the water condensation in the GDL of mixed wettability is considered; and it is found that the behavior of oxygen effective diffusivity with liquid saturation depends on the GDL wettability. It is further revealed that for a given liquid saturation, the oxygen effective diffusivity increases with greater area fractal dimension; with the decrease of tortuosity fractal dimension, it also increases, except for the hydrophilic case at high liquid saturation.