Potentials Near a Curved Anode Edge in a PEM Fuel Cell: Analytical Solution for Placing a Reference Electrode.

We consider a PEM fuel cell with concentric circular electrodes: the small anode and the large cathode. A model for in-plane distributions of the cathode overpotential ɳ_c and the membrane potential Φ in the anode-free region of the cell is developed. Mathematically, the problem reduces to the axially symmetric Poisson-Boltzmann equation for ɳ_c. An approximate analytical solution shows that ǀɳ_cǀ exhibits rapid decay to zero with the radius, while ǀΦǀ grows to the value of ǀɳ⁰_cǀ the cathode overpotential in the working domain of the cell. For typical ɳ⁰_c, the radial shape of qc far from the anode edge only weakly depends on ɳ⁰_c; this effect is analogous to Debye screening in plasmas. The smaller the anode radius, the faster Φ approaches ɳ⁰_c with the distance from the anode. It follows, that a reference electrode for measuring the cathode overpotential in the working area can be placed at a small distance from the curved anode edge. [ABSTRACT FROM AUTHOR]