Simple mathematical model for water diffusion in Nafion® membranes

Abstract

A simple mathematical model for water diffusion in Nafion® membranes was derived assuming that membrane properties are independent of membrane water content (water diffusion coefficient, membrane thickness), an equilibrium exists at the interface between channel and membrane, and the relationship between membrane water content and channel water concentration is linear. General analytical expressions were obtained as well as approximations. Comparison with experimental data showed good agreement with an error generally smaller than 20 %. Membrane properties derived from curve fitting the model general relative humidity equation to experimental data do not agree with independently obtained values. As a result, model calibration is required for predictive purposes.