A new derivation and numerical analysis of current–voltage characteristics for an ion-exchange membrane under limiting current density

Based on the Nernst–Planck equations of ion flow, a simple model was proposed for the current–voltage characteristics of an ion-exchange membrane under limiting current density. The numerical analysis depicts the influence of parameters such as solution concentration, diffusion boundary layer thickness, diffusion coefficient and transport number in solution and in membranes on current–voltage curves, as well as the profiles of the concentration and potential in membrane phase and in diffusion boundary layers. Limiting current density is discussed with the parameters and is consistent with the well known expressions. This work can be regarded as a supplement of the previous studies by Spiegler [Desalination, 9 (1971) 367] and Mafé [Journal of Membrane Science, 61 (1991) 177].

The new model depicts numerically the current–voltage curves as well as the concentration and potential profiles. Moreover, the limiting current density calculated is consistent with classical expression. It is expected that the system modeled here may be of some interest in studying polarization and ion transport through ion-exchange membranes used in electrodialysis.