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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 de- rived, from which we provide a rigorous 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 group- ings 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 and asymptotic solutions shows very good agreement. Implications of the results are discussed and future work is outlined.

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