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A simplified model for water management in a polymer electrolyte membrane ͑PEM͒ fuel cell operating under prescribed current with iso-potential plates is presented. The consumption of gases in the flow field channels, coupled to the electric potential and water content in the polymer membrane, is modeled in a two-dimensional slice from inlet to outlet and through the membrane. Both co-and counter-flowing air and fuel streams are considered, with attention paid to sensitivity of along-the-channel current density to inlet humidities, gas stream composition, and fuel and oxygen stoichiometries. The parameters describing the nonequilibrium kinetics of the membrane/catalyst interface are found to be fundamental to accurate fuel cell modeling. A new parameter which models nonequilibrium membrane water uptake rates is introduced. Four parameters, the exchange current, a membrane water transfer coefficient, an effective oxygen diffusivity, and an average membrane resistance, are fit to a subset of data and then held constant in subsequent runs which compare polarization curves, current density and membrane hydration distributions, water transfer, and stoichiometric sensitivity to the balance of the experimental data.

In response to mechanical stimulation of a single cell, airway epithelial cells in culture exhibit a wave of increased intracellular free Ca2+ concentration that spreads from cell to cell over a limited distance through the culture. We present a detailed analysis of the intercellular wave in a two-dimensional sheet of cells. The model is based on the hypothesis that the wave is the result of diffusion of inositol trisphosphate (IP3) from the stimulated cell. The two-dimensional model agrees well with experimental data and makes the following quantitative predictions: as the distance from the stimulated cells increases, 1) the intercellular delay increases exponentially, 2) the intracellular wave speed decreases exponentially, and 3) the arrival time increases exponentially. Furthermore, 4) a proportion of the cells at the periphery of the response will exhibit waves of decreased amplitude, 5) the intercellular membrane permeability to IP3 must be approximately 2 microns/s or greater, and 6) the ratio of the maximum concentration of IP3 in the stimulated cell to the Km of the IP3 receptor (with respect to IP3) must be approximately 300 or greater. These predictions constitute a rigorous test of the hypothesis that the intercellular Ca2+ waves are mediated by IP3 diffusion.

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