A Generalized Phenomenological Model and Database for the Transport of Water and Current in Polymer Electrolyte Membranes

The semiempirical model developed by Springer et al. [J. Electrochem. Soc., 138, 2334 (1991)] continues to be popular for water transport in polymer membranes. The implementation of this model into a computational fluid dynamic (CFD) code poses some problems. First, the dependent variable in the membrane is the water content, ג , while that in the diffusion layers and channels is the species mass fractions. Thus, the membrane has to be designated a separate domain, wherein a transport equation for ג is solved and iteratively coupled to the mass fractions. This is computationally expensive and sometimes unstable. The second problem is associated with the notion that because the membrane is "thin" it is sufficient to have a few computational nodes across its thickness. A model that extends Springer's model to include convective transport is presented. It is found that accurate calculation of water transport through the membrane requires few hundred nodes. A database that provides water flux and average membrane electrical conductivity for relevant mass-transport Peclet numbers and interfacial conditions is created. When used with CFD calculations, the database will allow accurate and efficient calculation of water and current transport in the membrane without solution of the transport equation for ג