Analytical solutions and dimensional analysis of pseudo 2D current density distribution model in PEM fuel cells

In this paper, a new dimensionless pseudo 2D steady state current density distribution model along the channel of a polymer electrolyte membrane (PEM) fuel cell is presented. This model includes four fundamental phenomena observed in PEM fuel cell cathode such as the air concentration depletion along the channel, the mass transport through the gas diffusion layer (GDL), the charge transport through the membrane and the electrochemical transfer in the catalyst layer (CL). A dimensional analysis is performed, and three dimensionless parameters are found to govern the current density distribution along the channel: a Peclet number at the channel/GDL interface, a Damkhöler number at the GDL/CL interface, and a Wagner number at the CL/PEM interface. Four regimes of operation are defined based on the values of these dimensionless numbers, and for each of them new analytical solutions are developed. A good agreement with the experimental measurements of current density distribution reported in literature is found, concluding that the macroscopic PEM fuel cell physic is well described by our model. The specific operating regime described with relatively simple equations of current density distributions paves the way for a better control of fuel cell operation and performance, and in situ characterisation of fuel cell material properties.