Fractal model for predicting the effective binary oxygen diffusivity of the gas diffusion layer in proton exchange membrane fuel cells

We propose an analytical model to predict the effective binary oxygen diffusivity of the porous gas diffusion layer (GDL) in proton exchange membrane fuel cells (PEMFCs). In this study, we consider the fractal characteristics of the porous GDL as well as its general microstructure, and we adopt the Bosanquet equation to derive effective diffusivity. The fractal characterization of GDL enables us to model effective diffusivity in a continuous manner while taking into account the effect of pore size distribution. Comparison to two other theoretical models that are generally accepted in the simulation of PEMFCs shows similar trends in all three models, indicating that our proposed model is well founded. Furthermore, the predicted effective binary oxygen diffusivities of two samples show that after treatment with polytetrafluoroethylene (PTFE), the effective binary diffusivity of the GDL decreases. Based on the parametric effect analysis, we conclude that effective binary diffusivity is negatively correlated with tortuosity fractal dimension but positively correlated with the fractal dimension of pore area, porosity, or mean pore diameter. The proposed model facilitates fast prediction of effective diffusivity as well as multi-scale modeling of PEMFCs and thus facilitates the design of the GDLs and of PEMFCs.