@article{25102,
  author = {Charles Delacourt and John S Newman},
  title = {Mathematical Modeling of a Cation-Exchange Membrane Containing Two Cations},
  abstract = {<p><br />Transport phenomena in an ion-exchange membrane containing both H<sup>+</sup> and K<sup>+</sup> 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, D<sub>ij</sub>, used in the multicomponent transport equations. As experimental data for only four transport properties are available in the literature, the six D<sub>ij</sub> values cannot be determined in an unequivocal manner. It is in harmony with the data that D<sub>H+,K+</sub> is large, and linear variations of ln(D<sub>ij</sub>) with y<sub>HM</sub> are assumed for the other D<sub>ij</sub> 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<sup>+</sup> and K<sup>+</sup> are presented, and the model is used with particular boundary conditions to describe the behavior of a membrane used in a CO<sub>2</sub>–H<sub>2</sub>O electrolyzer. This provides some insights on macroscopic quantities such as the ohmic drop and water transport that are relevant for cell operation.</p>},
  year = {2008},
  journal = {Electrochemical Society},
  volume = {155},
  pages = {B1210-B2328},
  month = {09/2008},
  doi = {10.1149/1.2977960},
  language = {eng},
}