A boundary layer analysis for determination of the limiting current density in an electrodialysis desalination

A general ion-transport equation has been derived eliminating the electrophoresis term from the set of Nernst-Planck equations for cations and anions, under the local electro-neutrality assumption. Boundary layer solutions were obtained for the two asymptotic cases of sufficiently short and long channels, respectively, when the electric current is applied uniformly across the channels. A local volume averaging theory for porous media was also introduced to describe the cases of electrodialysis stacks with spacers. The results obtained for both with and without spacers are compared against available experimental data. The predicted limiting current density and stack voltage based on the asymptotic solutions for sufficiently short channels agree well with those of measurements for both cases with and without spacers, revealing the validity of the present analysis based on the local electro-neutrality assumption. It has been clearly shown that the spacers work to delay possible depletion of the ions on the dilute side of the membrane, thus increasing the limiting current density.