Mathematical Modeling of the Phenomenon of Space-Charge Breakdown in the Galvanostatic Mode in the Section of the Electromembrane Desalination Channel

Abstract

One of the ways to increase the efficiency of the desalination process in membrane systems is to use intensive current modes. Recently, the phenomenon of space-charge breakdown was theoretically described for desalination under intensive current modes. The space-charge breakdown is a decrease in the magnitude and size of the extended space charge regions (SCRs) of opposite signs, formed at the cation- and anion-exchange membranes in the desalination channel, when they approach each other. Therefore, this phenomenon negatively affects the intensity of electroconvection and the efficiency of mass transfer in membrane systems. We report the results of the first theoretical analysis of the space-charge breakdown in the galvanostatic electric mode, which is generally used in the research and operation of membrane systems. For this purpose, a one-dimensional model of the ion transfer of the electrolyte solution in the section of the desalination channel at the direct current is developed. The regularities of changes in the extended SCRs in the galvanostatic mode are determined. A relation is obtained for the onset time of the space-charge breakdown, which makes it possible to determine the parameters of the effective operation of the membrane system.

Keywords

• ion-exchange membrane
• space charge
• galvanostatic mode
• desalination
• mathematical modeling
• Nernst–Planck–Poisson equations