Phenomenological Theory of Electro‐osmotic Effect and Water Management in Polymer Electrolyte Proton‐Conducting Membranes

Partial dehydration of the proton‐conducting membrane under working conditions is one of the major problems in low‐temperature fuel cell technology. In this paper a model, which accounts for the electro‐osmotically induced drag of water from anode to cathode and the counterflow in a hydraulic pressure gradient is proposed. A balance of these flows determines a gradient of water content across the membrane, which causes a decline of the current‐voltage performance. Phenomenological transport equations coupled with the capillary pressure isotherm are used, involving the conductivity, permeability, and electro‐osmotic drag coefficients dependent on the local water content. The effects of membrane parameters on current‐voltage performance are investigated. A universal feature of the obtained current‐voltage plots is the existence of a critical current at which the potential drop across the membrane increases dramatically due to the dehydration of membrane layers close to the anode. For a membrane with zero residual conductivity in its dry parts, the critical current is a limiting current. Well below the critical current the effect of dehydration is negligible and the current‐voltage plot obeys Ohm's law. The shape of the capillary pressure isotherm determines the nonohmic corrections. A comparison of the results of this study to those of the pertinent diffusion‐type models reveals qualitatively different features, the convection model is found to be closer to experimental observations.