A multi-scale approach to material modeling of fuel cell diffusion media

Effective diffusivity of porous media in fuel cells has been identified as a relevant material property in automotive applications. Pore-scale simulations utilizing imaging data sets of real materials or virtual model representations provide such diffusivity numbers. However, components like the microporous layer (MPL) or the gas diffusion electrode have not been covered adequately so far by efficient and practical modeling approaches due the small pore sizes and resulting Knudsen contribution to diffusion. In this publication we report the development of a numerical method which allows for the determination of binary diffusion coefficients for all Knudsen numbers and demonstrate the application to fuel cell diffusion media in a multi-scale modeling approach. For high Knudsen numbers effective diffusivity is determined by tracking a large number of individual molecules that collide with the pore walls. For low Knudsen numbers, effective diffusivity is determined by solving the Laplace equation on the pore space. Both contributions to the overall diffusivity are merged by applying Bosanquet's formula. The resulting diffusivity can be used as an effective number for a microporous layer coating of a spatially resolved fibrous diffusion medium. As this multi-scale method is also based on a 3D voxel grid, we could study any distribution of the MPL on and inside the gas diffusion layer (GDL) with this model, e.g. cracks, different penetration depths, etc.