Bi-modal water transport behavior across a simple Nafion membrane

The development of predictive mathematical models for water management in polymer electrolyte membrane fuel cells requires detailed understanding of water distribution and water transport across the Nafion layer. The anisotropic microstructure of Nafion suggests the measurement of water content and mass transport should be along the fuel cell functional direction, i.e. across the membrane. Non-invasive, high resolution, microscopy measurements of this type are very challenging.We report here the calibration of a minimal mathematical model for diffusive water transport in Nafion against data from high-resolution water content maps determined with a new magnetic resonance imaging methodology developed for this purpose. A mock fuel cell was designed to permit well-controlled wetting and drying boundary conditions. With no chemical potential driving force involved, we assume the water transport behavior will be dominated by diffusion. Moreover we show that, in this context, our model is mathematically equivalent to the traditional permeation models based upon saturation dependent pressure gradients via a capillary pressure ansatz.The non-linear equilibrium water distribution across the Nafion membrane measured in this work suggests a bi-modal diffusivity. The model constructed associates distinct transport behaviors to water contents above and below a critical threshold, consistent with a rearrangement of a micro-structural pore network. The experimental observation and the model prediction agree with the primary features of Weber's model of Nafion, which predicts distinct modes of transport for hydration fronts traversing the through-plane direction of the membrane.