A model for a crack or a delaminated region in a PEM fuel cell anode: analytical solutions

We develop a model for the potential and current density distributions in and around a long, straight and inactive (“dead”) gap inside a PEM fuel cell anode. Physically speaking, such gaps represent cracked or delaminated domains in an anode catalyst layer. The dead region is modeled as a step function for the anode exchange current density. An analytical solution to the model equations is derived; the solution exhibits a large peak of the anode current density japeak just outside the gap. For a typical cell current density of 1 A cm−2, a gap with a width of 400 μm induces japeak of about 4 A cm−2. For smaller gap widths on the order of 10 μm, which is typical for cracks, the effect is marginal. Variations in membrane thickness have a minor effect on japeak.