Bubbles in the anode channel and performance of a DMFC: Asymptotic solutions

Our recent 1D + 1D model of DMFC, which takes into account gaseous bubbles in the anode channel is analyzed. In this work, we derive asymptotic solution to model equations for the case of small rate of bubbles formation. The formula for the change in the mean current density of the cell due to bubbles is obtained and the effect of bubbles on the limiting current density is rationalized. Physically, the bubbles (i) decrease time-average methanol concentration in the anode channel, which reduces cell performance and (ii) decrease methanol crossover, which improves it. The resulting effect is controlled by parameter γ, which is proportional to the ratio of inlet oxygen and methanol concentrations. If oxygen is in excess, the bubbles strongly decrease cell performance close to the limiting current and have marginal positive effect at small and medium currents. Under lack of oxygen the bubbles almost always dramatically improve performance. Furthermore, in that case there exists optimal stoichiometry of the flows, which provides maximal performance. The origin of these effects is discussed.