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IMA Journal of Applied Mathematics Advance Access originally published online on March 22, 2007
IMA Journal of Applied Mathematics 2007 72(3):302-330; doi:10.1093/imamat/hxm005
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Mathematical modelling of the catalyst layer of a polymer electrolyte fuel cell

A. A. Shah**,1, Gwang-Soo Kim2 and K. Promislow3

1 Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6, 2 Ballard Power Systems, 4343 North Fraser Way, Burnaby, British Columbia, Canada V5J 5J9, 3 Department of Mathematics, Michigan State University, East Lansing MI 48824, USA

** Present address: School of Engineering, University of Southampton, SO17 1BJ Southampton, UK. Email: ashah{at}pims.math.ca, a.shah{at}soton.ac.uk


  Abstract

In this paper, we derive a mathematical model for the cathode catalyst layer of a polymer electrolyte fuel cell. The model explicitly incorporates the restriction placed on oxygen in reaching the reaction sites, capturing the experimentally observed fall in the current density to a limiting value at low cell voltages. Temperature variations and interfacial transfer of O2 between the dissolved and gas phases are also included. Bounds on the solutions are derived from which we provide a rigourous proof that the model admits a solution. Of particular interest are the maximum and minimum attainable values. We perform an asymptotic analysis in several limits inherent in the problem by identifying important groupings of parameters. This analysis reveals a number of key relationships between the solutions, including the current density, and the composition of the layer. A comparison of numerically computed solutions and asymptotic solutions shows very good agreement. Implications of the results are discussed and future work is outlined.

Keywords: fuel cell; catalyst layer; oxygen diffusion; temperature variations; bounds; asymptotic analysis.

Received on 5 December 2005. Accepted on 19 November 2006.


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