A Comparison of Fick and Maxwell-Stefan Diffusion Formulations in PEMFC Cathode Gas Diffusion Layers

TL;DR

This paper compares Fick and Maxwell-Stefan diffusion models in PEMFC cathode layers, showing their predictions are similar and providing insights into their differences and applications in fuel cell modeling.

Contribution

It offers a computational comparison of Fick and Maxwell-Stefan diffusion formulations in a simplified PEMFC cathode setting, highlighting their similarities and differences.

Findings

Predictions of Fick and Maxwell-Stefan are very similar in the studied setting.

Diffusion laws are small perturbations from bulk flow for both models.

Analytic insights explain the similarity of the formulations.

Abstract

This paper explores the mathematical formulations of Fick and Maxwell-Stefan diffusion in the context of polymer electrolyte membrane fuel cell cathode gas diffusion layers. Formulations of diffusion combined with mass-averaged Darcy flow are considered for three component gases. Fick formulations can be considered as approximations of Maxwell-Stefan in a certain sense. For this application, the formulations can be compared computationally in a simple, one dimensional setting. We observe that the predictions of the formulations are very similar, despite their seemingly different structure. Analytic insight is given to the result. In addition, it is seen that for both formulations, diffusion laws are small perturbations from bulk flow. The work is also intended as a reference to multi-component gas diffusion formulations in the fuel cell setting.