Limiting current density in the electrodialysis of multi-ionic solutions

The aim of this work was the development of an explicit model to estimate the limiting current density in the electrodialysis of dilute multi-ionic solutions. The model assumes that the ionic transport occurs in a film layer adjacent to an ion exchange membrane and it is quantified by a linearized form of the Nernst–Planck (NP) equations together with the electroneutrality requirement at the solution/ion exchange membrane interface. An explicit expression for the limiting current density of a dilute multi-ionic solution was derived, involving a mass-transfer coefficient based on an effective diffusivity of the multi-ionic solution. The model further assumes that the steric exclusion of the ions by the membrane is negligible, and thereby the limiting current density is attained when the concentration of each and every ion is null at the solution/membrane interface. The model predictions for the limiting current density were compared with experimental data of single salt solutions (MgCl2) and multi-ionic solutions (MgSO4 + MgCl2) in a bench-scale electrodialysis unit (EUR2C-7P18, Eurodia, France) for various Reynolds numbers and salts concentrations. The average relative deviations between the model predictions and the experimental data were lower than 13% for MgCl2 solutions (10, 20 equiv./m3) and solutions of MgSO4 + MgCl2 (5 + 5, 10 + 10 equiv./m3). The dimensionless limiting current density and the counterions transport numbers predicted by the linearized and non-linear Nernst–Planck equations were also compared for a broad range of dimensionless operating parameters and a fair to good agreement was observed between the two approaches.