Effects of reactant crossover and electrode dimensions on the performance of a microfluidic based laminar flow fuel cell

A mathematical model is developed to simulate the performance of a laminar flow fuel cell with reactant crossover using the Poisson-Nernst-Plank (PNP) equations. The model includes a more general treatment of reactant (fuel or oxidant) crossover than the common method where it is assumed that the crossover flux is fully utilized as crossover current. This new model allows for the analysis of very narrow channels and estimation of parasitic crossover current at both the anode and the cathode. It also allows for the consideration of a laminar flow fuel cell with a significant amount of reactant crossover where the crossover species are not fully consumed by the crossover current. Moreover, the combination of the PNP equations and the general reactant crossover treatment reveal the two-dimensional developing region for electrode mixed potentials which is a novel result. The parameters considered in this study are electrode length and separation (channel height). Numerical results show that the reactant crossover, transport limitations, and Ohmic losses are the primary performance limitation factors. The current distributions along the anode and cathode are presented as well as the reactant concentrations at the anode as evidence of these performance limitations. It is also shown that the fluid velocity field, as it changes with channel height, plays a small role in the development of the depletion boundary layer.