A Mathematical Model of the Solid‐Polymer‐Electrolyte Fuel Cell

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Abstract
We present a mathematical model of the solid‐polymer‐electrolyte fuel cell and apply it to (i) investigate factors that limit cell performance and (ii) elucidate the mechanism of species transport in the complex network of gas, liquid, and solid phases of the cell. Calculations of cell polarization behavior compare favorably with existing experimental data. For most practical electrode thicknesses, model results indicate that the volume fraction of the cathode available for gas transport must exceed 20% in order to avoid unacceptably low cell‐limiting current densities. It is shown that membrane dehydration can also pose limitations on operating current density; circumvention of this problem by appropriate membrane and electrode design and efficient water‐management schemes is discussed. Our model results indicate that for a broad range of practical current densities there are no external water requirements because the water produced at the cathode is enough to satisfy the water requirement of the membrane. Inefficiencies due to the transport of unreacted hydrogen or oxygen through the membrane are shown to be insignificant at practical operating current densities. The transport of gases dissolved in the membrane phase, however, limits the utilization of catalyst. Predictions of cell performance with different types of membranes are also examined, and the model results compare favorably with experimental data.

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