Ion and Solvent Transport in Ion‐Exchange Membranes: I . A Macrohomogeneous Mathematical Model

A mathematical model for the simulation of ion and solvent transport within an ion‐exchange membrane is developed and analyzed. A Nernst‐Planck equation is employed for the description of ion transport by diffusion, migration, and convection. Solvent transport driven by pressure and electric‐potential gradients is described by an equation of motion. The physicochemical parameters used in this analysis are experimentally easy to obtain. The set of equations used in the simulation are presented in a dimensionless form so that important dimensionless parameters can be evaluated. In particular, an electrokinetic Peclet number is identified; large values of this dimensionless quantity, for example, would indicate that convection is the dominant mode of mass transport.