A new two-dimensional model of a direct methanol fuel cell ͑DMFC͒ has been developed and numerically tested. In complement to the existing developments, this model regards the diffusion layers as water-gas systems in the pore space with saturation and permeability varying according to capillary effects. The presence of hydrophilic and hydrophobic pores has been taken into account by introducing a new parametrization of the relationship between capillary pressure and saturation. Thus, mass transport occurs in parallel in the two phases, gas and liquid. The exchange between these phases is due to condensation and evaporation with rates given by the available exchange surface and the temperature. The gas transport is governed by the Stefan-Maxwell equations incorporated into the two-phase flow modeling approach. Instead of the often used Tafel and Butler-Volmer equations which are insufficient in the case of catalytic methanol oxidation and oxygen reduction, according to recent investigations, the electrochemical reactions are split up into reaction chains involving the covering of the catalysts with the various intermediate species. The main advantage of this approach is that it incorporates the effects of the limitation of the reaction rates due to the limited number of catalyst sites in a natural manner. The resulting system of transport and reaction equations is discretized in time by the backward Euler method and in space by a finite volume technique with proper upwinding.
Basic EquationsGases flow.-Our model of gas flow is based on the following assumptions. (i) the electrode is isothermal, (ii) there is no pressure gradient, and (iii) the membrane is impermeable to gases. Under these assumptions, the diffusion flux of the kth component in a multicomponent mixture of gases in a free space is defined by the Stefan-Maxwell relation
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