Mathematical Modeling of a Cation-Exchange Membrane Containing Two Cations
Transport phenomena in an ion-exchange membrane containing both H+ and K+ are described using the multicomponent diffusion (extended Stefan–Maxwell) equations. Expressions for macroscopic transport parameters, i.e., conductivity, proton transference number, water electro-osmotic coefficient, and transport parameters characterizing diffusion at zero current, are derived as a function of the binary interaction parameters, Dij, used in the multicomponent transport equations. As experimental data for only four transport properties are available in the literature, the six Dij values cannot be determined in an unequivocal manner. It is in harmony with the data that DH+,K+ is large, and linear variations of ln(Dij) with yHM are assumed for the other Dij coefficients. Values for the slopes of those linear variations are refined by nonlinear least-square regression on the four experimental transport properties. General governing equations to describe complete transport in the membrane with H+ and K+ are presented, and the model is used with particular boundary conditions to describe the behavior of a membrane used in a CO2–H2O electrolyzer. This provides some insights on macroscopic quantities such as the ohmic drop and water transport that are relevant for cell operation.