A transient, one-dimensional, model of the membrane of a proton exchange membrane fuel cell is presented. The role of the membrane is to transport protons from the anode to cathode of the fuel cell while preventing the transport of other reactants. The membrane is modeled assuming mono-phase, multi-species flow. For water transport, the principle driving forces modeled are a convective force, an osmotic force (i.e. diffusion), and an electric force. The first of these results from a pressure gradient, the second from a concentration gradient, and the third from the migration of protons from anode to cathode and their effect (drag) on the dipole water molecules. Equations are developed for the conservation of protons and water, the conservation of thermal energy, and the variation of proton potential within the membrane.
The model is solved using a fully implicit finite difference approach. Results showing the effects of current density, pressure gradients, water and heat fluxes, and fuel cell start-up on water concentration, temperature, and proton potential across the membrane are presented.