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A one-dimensional-isothermal model and an analytical solution for the mass transport (migration and diffusion) of protons in a single PEM fuel cell have been developed. Under a linear approximation between current density and electric potential (pseudo-primary current distribution) we have obtained the proton concentration profile along the cathodic and anodic gas diffusers as a function of the position. The graphical shape of the function allows us to discuss the effect of the physicochemical parameters in our model especially on the anodic side of the diffuser. From the dependence of the electric potential and current density with the position we have obtained a theoretical polarization curve. Under the pseudo-primary current distribution, the fitting of the first points yields a high Tafel slope for the cell operation performance. In spite of being a limited model for the cell performance, this is one of the least analytical and exact solved solutions obtained from mass balances in the course of the hydrogen electrooxidation and oxygen electroreduction. We consider that this situation would probably put some more knowledge in the understanding of the PEMFC functional description.

On the Mathematical Modelling of Diffusion-Migration Mass Transport of Protons