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. The simple Fick law with a diagonal diffusion matrix is an approximation of Maxwell–Stefan. Formulations of diffusion combined with mass-averaged Darcy flow are considered for three component gases. For this application, the formulations can be compared computationally in a simple, one dimensional setting. Despite the models’ seemingly different structure, it is observed that the predictions of the formulations are very similar on the cathode when air is used as oxidant. The two formulations give quite different results when the Nitrogen in the air oxidant is replaced by helium (this is often done as a diagnostic for fuel cells designs). The two formulations also give quite different results for the anode with a dilute Hydrogen stream. These results give direction to when Maxwell–Stefan diffusion, which is more complicated to implement computationally in many codes, should be used in fuel cell simulations.
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The first author thanks NSERC for a graduate scholarship and the Automotive Fuel Cell Corporation (AFCC) and the MITACS Accelerate Internship programme for funding for this work. The second author acknowledges research funding support from an NSERC Canada grant. We would both like to thank the referee that suggested extending the air cathode results to the helox cathode and dilute hydrogen anode.
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Lindstrom, M., Wetton, B. A comparison of Fick and Maxwell–Stefan diffusion formulations in PEMFC gas diffusion layers. Heat Mass Transfer 53, 205–212 (2017). https://doi.org/10.1007/s00231-016-1812-7