Stability analysis for liquid water accumulation in low temperature fuel cells

In this paper we analyze the stability and two-phase dynamics of the equilibrium water distributions inside the porous media of a polymer electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL), which is described with first and second-order parabolic partial differential equations (PDE). A Lyapunov function-based stability criterion is implemented for the liquid mass continuity PDE, while physics and math-based arguments are used to demonstrate a key range of liquid distribution that cannot attain equilibrium. The quantity of water within the fuel cell directly affects performance, efficiency, and durability. High membrane humidity is desirable for proton conductivity, yet excess liquid water in the anode has been experimentally shown to be a cause of output voltage degradation. We identify the unstable state(s) representing unbounded growth of liquid water and show that stabilization of channel water mass is sufficient for a stable liquid distribution.