We present a systematic, multiscale, fully detailed numerical modeling for dynamics of fluid flow and ion transport covering Ohmic, limiting, and overlimiting current regimes in conductance of ion-selective membrane. By numerically solving the Poisson-Nernst-Planck-Navier-Stokes equations, it is demonstrated that the electroconvective instability, arising from the electric field acting upon the extended space charge layer, and the induced strong vortical fluid flow are the dominant factors of the overlimiting current in the planar membrane system. More importantly, at the transition between the limiting and the overlimiting current regimes, hysteresis of electric current is identified. The hysteresis demonstrates the important role of the electroconvective flow in enhancing of current in electrolyte systems with ion-selective membrane.

We consider electroconvective fluid flows initiated by ion concentration polarization (ICP) under pressure-driven shear flow, a scenario often found in many electrochemical devices and systems. Combining scaling analysis, experiment, and numerical modeling, we reveal unique behaviors of ICP under shear flow: a unidirectional vortex structure, its height selection, and vortex advection. Determined by both the external pressure gradient and the electric body force, the dimensionless height of the sheared electroconvective vortex is shown to scale as (ϕ(2)/U(HP))(1/3), which is a clear departure from the previous diffusion-drift model prediction. To the best of our knowledge, this is the first microscopic characterization of ion concentration polarization under shear flow, and it firmly establishes electroconvection as the mechanism for an overlimiting current in realistic, large-area ion exchange membrane systems such as electrodialysis. The new scaling law has significant implications on the optimization of electrodialysis and other electrochemical systems.

There is an increasing need for the desalination of high concentration brine (>TDS 35,000 ppm) efficiently and economically, either for the treatment of produced water from shale gas/oil development, or minimizing the environmental impact of brine from existing desalination plants. Yet, reverse osmosis (RO), which is the most widely used for desalination currently, is not practical for brine desalination. This paper demonstrates technical and economic feasibility of ICP (Ion Concentration Polarization) electrical desalination for the high saline water treatment, by adopting multi-stage operation with better energy efficiency. Optimized multi-staging configurations, dependent on the brine salinity values, can be designed based on experimental and numerical analysis. Such an optimization aims at achieving not just the energy efficiency but also (membrane) area efficiency, lowering the true cost of brine treatment. ICP electrical desalination is shown here to treat brine salinity up to 100,000 ppm of Total Dissolved Solids (TDS) with flexible salt rejection rate up to 70% which is promising in a various application treating brine waste. We also demonstrate that ICP desalination has advantage of removing both salts and diverse suspended solids simultaneously, and less susceptibility to membrane fouling/scaling, which is a significant challenge in the membrane processes.