Shah, A., Kim, G.S. and Promislow, K.
Mathematical modelling of the catalyst layer of a
polymer-electrolyte fuel cell.
IMA Journal of Applied Mathematics, 72, (3), .
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.
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