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In this work, analytical solutions were derived (for any methanol oxidationreaction order) for the profiles of methanol concentration and proton currentdensity by assuming diffusion mass transport mechanism, Tafel kinetics, andfast proton transport in the anodic catalyst layer of a direct methanol fuelcell. An expression for the Thiele modulus that allows to express the anodicoverpotential as a function of the cell current, and kinetic and mass transferparameters was obtained. For high cell current densities, it was found that theThiele modulus ($\phi^2$) varies quadratically with cell current density;yielding a simple correlation between anodic overpotential and cell currentdensity. Analytical solutions were derived for the profiles of both localmethanol concentration in the catalyst layer and local anodic current densityin the catalyst layer. Under the assumptions of the model presented here, ingeneral, the local methanol concentration in the catalyst layer cannot beexpressed as an explicit function of the position in the layer. In spite ofthis, the equations presented here for the anodic overpotential allow thederivation of new semi-empirical equations.

Modeling of the anode side of a direct methanol fuel cell with analytical solutions