  In this work, analytical solutions were derived (for any methanol oxidation
reaction order) for the profiles of methanol concentration and proton current
density by assuming diffusion mass transport mechanism, Tafel kinetics, and
fast proton transport in the anodic catalyst layer of a direct methanol fuel
cell. An expression for the Thiele modulus that allows to express the anodic
overpotential as a function of the cell current, and kinetic and mass transfer
parameters was obtained. For high cell current densities, it was found that the
Thiele modulus ($\phi^2$) varies quadratically with cell current density;
yielding a simple correlation between anodic overpotential and cell current
density. Analytical solutions were derived for the profiles of both local
methanol concentration in the catalyst layer and local anodic current density
in the catalyst layer. Under the assumptions of the model presented here, in
general, the local methanol concentration in the catalyst layer cannot be
expressed as an explicit function of the position in the layer. In spite of
this, the equations presented here for the anodic overpotential allow the
derivation of new semi-empirical equations.

Chemical Physics;Materials Science