1D + 1D model of a DMFC: localized solutions and mixedpotential

Our 1D + 1D model of DMFC reveals a new effect. At infinitely small total current in the cell, near the channel inlet forms a “bridge”, a narrow region with finite local current density. The bridge short-circuits the electrodes, thus reducing cell open-circuit voltage. In our previous work the effect is described for the case of equal methanol λ^a and oxygen λ^c stoichiometries. In this Letter, we analyze the general case of arbitrary λ^a and λ^c. In the case of λ^a > λ^c current may occupy finite domain of the cell surface. Asymptotic solution for the case of λ^a  λ^c shows, that the size of this domain is proportional to oxygen stoichiometry. In the opposite limit of λ^a  λ^c local current exponentially decreases with the distance along the channel. Asymptotic solutions suggest that the bridge forms regardless of the relationship between λ^a and λ^c. In all cases local current density in the bridge increases with the rate of methanol crossover and decreases with the growth of the “rate-determining” stoichiometry. The expression for voltage loss at open-circuit is derived.