Space-Charge breakdown phenomenon and spatio-temporal ion concentration and fluid flow patterns in overlimiting current electrodialysis

Abstract

Overlimiting current regimes are of practical interest for electrodialysis with ion-exchange membranes (IEMs) operating at current densities significantly higher than the limiting current density. Such high ion currents across the membranes allows reducing the investments into expensive IEMs and stacks. Electroconvection (EC) is the major contributor to the overlimiting current and concepts to utilize EC are highly desired. Most of the known theoretical works describing EC in electrodialysis channels are performed when only a single cation exchange membrane is considered. The presence of a neighboring anion-exchange membrane has not been considered so far.We report the results of direct numerical simulations of ion and water transport involving EC in an electrodialysis channel formed by a cation- and an anion-exchange membrane. A 2D “basic” model involving the Nernst-Planck-Poisson-Navier-Stokes equations is introduced. Details of spatio-temporal changes in the distribution of concentrations and space charge patterns as well as the interactions of EC vortices are analyzed.The presence of the anion-exchange membrane in the transition to a close-to-chaotic regime at high potential difference is examined. For the first time, we discover the phenomenon of space-charge breakdown where the space charges of opposite sign formed at the two membranes are short-circuited throughout the desalination channel. The details of the mechanism of this phenomenon are analyzed using the 2D model and a simplified 1D model. Simulations show that the space-charge breakdown leads to a decrease in the size and number of EC vortices in the region of breakdown, which results in a reduction of the local current density. This phenomenon, apparently, determines the upper limit of the possible increase in the mass transfer rate by electroconvection.