Mathematical modeling of electrodialysis of a dilute solution with accounting for water dissociation-recombination reactions

Abstract

The paper explores the limitations of electrodialysis (ED) in the range of very dilute feed solutions. The results of first principles modeling of this process are presented, taking into account water dissociation-recombination reactions (without catalytic effects). A 1D and a 2D model are formulated and applied. Both models use the equation for the rate of chemical reactions, the Nernst-Planck and Poisson equations; additionally, the Navier-Stokes equation is used in the 2D model. We show that the dissociation-recombination reactions can cause the appearance of a space charge region (SCR) in the central part of the desalination chamber (DC). In electrochemistry and colloidal science, the formation of a SCR is associated with the formation of an electrical double layer (EDL) at a charged solid surface. Our modeling predicts that in conditions where the concentrations of H+/OH− ions and salt ions in solution are comparable, a SCR can appear in the bulk solution due to the recombination of H+ and OH− ions. The latter are generated at the membrane forming the DC (water splitting). Water splitting makes impossible total desalting of aqueous solutions by conventional ED. An inversion of the salt concentration profiles is observed: the salt ions are accumulated near the membranes; a depletion region occurs in the center of the DC. Interplay between the chemical reactions and space charge is discussed.