Analysis of Two-Phase Flow in the Gas Diffusion Layer of a Polymer Electrolyte Fuel Cell

The last decade has seen a proliferation of modelling activity on the polymer electrolyte fuel cell (PEFC); an important subset of this activity is the modelling of the two-phase (gas/liquid) flow that occurs in the porous gas diffusion layer (GDL) on the cathode (Djilali, Energy 32:269–280, 2007; Gurau and Mann, SIAM J. Appl. Maths 70:410–454, 2009). The prevailing approach employs a generalized form of Darcy’s law, which has been widely used over the last several decades to analyze the movement of oil and water in soils and porous rock (Bear, Dynamics of Fluids in Porous Media, American Elsevier, New York, 1972). Applied to water transport in fuel cells, the Darcy model characterizes the response of the porous material by the capillary pressure, the gas and liquid phase relative permeabilities, and the effective gas diffusion coefficient, all of which depend on the fraction of the local pore volume occupied by liquid water; an additional feature is that the porous medium can be either hydrophobic or hydrophilic. The majority of approaches have, however, been primarily numerical, which has obscured some of the properties of the model. Here, using asymptotic methods, we extend earlier work (Vynnycky, Appl. Math. Comp. 189:1560–1575, 2007) to demonstrate how the degree of water saturation depends on the liquid phase relative permeability, as well as how the model behaves when the GDL is only just hydrophilic.