An analysis on ion transport process in electrodialysis desalination

• A parabolic set of Nernst–Planck equations is proposed for electrodialysis.
• All governing equations are combined into ordinary differential equations.
• One can easily estimate salt concentration of the concentrate and its flow rate in an electrodialysis stack.
• The present analysis agrees well with available experimental data.
• The model can be used to estimate limiting current density in an electrodialysis stack.

An analysis based on the Nernst–Planck equation has been carried out on the transport process of salt ions in the ion-exchange membrane electrodialysis technology. The individual transport equations for both diluate phase and concentrate phase are considered to investigate the conservation of mass and salt ions driven by convection, molecular diffusion and electrophoresis. For the first time, the ion transport flow across the membranes driven by the osmotic pressure has been accounted for the overflow type of electrodialysis with the concentrate compartments sealed at the bottom end. The equations are integrated across the desalination channel and the concentrate reservoir to form one dimensional set of the transport equations with respect to the bulk velocities and concentrations of the diluate and concentrate phases. Subsequently, the equations are solved by the Runge–Kutta–Gill method, and the results are found to agree well with available experimental data. An analytic expression has been obtained for estimating a limiting current density.