Fractal-based theoretical model on saturation and relative permeability in the gas diffusion layer of polymer electrolyte membrane fuel cells

After polytetrafluoroethylene (PTFE) treatment, due to the coexistence of hydrophilic and hydrophobic pores, the gas diffusion layer (GDL) of a polymer electrolyte membrane fuel cell (PEMFC) shows a character of mixed wettability, which in turn affects liquid water and mass transfer. A series of fractal models are developed in this work to investigate the effect of GDL's wettability on liquid water and gas permeation in GDL. Compared to the widely-used empirical models, the proposed model of saturation versus capillary pressure in a good agreement with experimental data is more suitable for the GDL of mixed wettability. By using this model, liquid water saturation is found to be positively correlated with tortuosity and pore area fractal dimensions for a hydrophilic case and hydrophilic pore fraction, whereas to be negatively correlated with these fractal dimensions for a hydrophobic case. Furthermore, theoretical predictions on gas and water relative permeability are made via the proposed models. Water relative permeability increases with the increases in the fractal dimensions for a hydrophobic GDL and liquid water saturation, whereas it decreases with the increases in the fractal dimensions for a hydrophilic GDL and hydrophilic pore fraction. For gas phase, an opposite result is obtained.

► Fractal bundle-of-hydrophilic-and-hydrophobic-capillaries model is used.
► Theoretical model of saturation versus capillary pressure is established.
► Empirical models describing p–s curve are not suitable at the mixed wettability.
► Theoretical models of liquid water and gas relative permeability are derived.
► Relative permeability does not follow a power law of saturation at the mixed wettability.