Boris Zaltzman

Experimental verification of the electroosmotic mechanism of overlimiting conductance through a cation exchange electrodialysis membrane

The paper is concerned with convection at an ion-exchange electrodialysis membrane induced by nonequilibrium electroosmosis as a source of overlimiting conductance current through the membrane. Derivation of nonequilibrium electroosmotic slip condition is recapitulated along with the results of linear stability analysis of quiescent electrodiffusion through a flat ion-exchange membrane. Results of numerical calculation pertaining to nonlinear convection, developing from the respective instability, are reported along with those of recent experiments with modified membranes. These latter rule in favor of electroosmotic versus bulk electroconvective origin of overlimiting conductance through ion-exchange membranes.

Overlimiting current and shock electrodialysis in porous media.

Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electroosmotic flow also contribute to ionic flux. In this article, we report experimental evidence for surface-driven overlimiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with a 500 nm mean pore size) in an aqueous electrolyte (CuSO4 or AgNO3) passing ionic current from a reservoir to a cation-selective membrane (Nafion). The current-voltage relation of the whole system is consistent with a proposed theory based on the electroosmotic flow mechanism over a broad range of reservoir salt concentrations (0.1 mM to 1.0 M) after accounting for (Cu) electrode polarization and pH-regulated silica charge. Above the limiting current, deionized water (≈10 μM) can be continuously extracted from the frit, which implies the existence of a stable shock propagating against the flow, bordering a depleted region that extends more than 0.5 mm across the outlet. The results suggest the feasibility of shock electrodialysis as a new approach to water desalination and other electrochemical separations.

Equilibrium electroconvective instability.

Since its prediction 15 years ago, hydrodynamic instability in concentration polarization at a charge-selective interface has been attributed to nonequilibrium electro-osmosis related to the extended space charge which develops at the limiting current. This attribution had a double basis. On the one hand, it has been recognized that neither equilibrium electro-osmosis nor bulk electroconvection can yield instability for a perfectly charge-selective solid. On the other hand, it has been shown that nonequilibrium electro-osmosis can. The first theoretical studies in which electro-osmotic instability was predicted and analyzed employed the assumption of perfect charge selectivity for the sake of simplicity and so did the subsequent studies of various time-dependent and nonlinear features of electro-osmotic instability. In this Letter, we show that relaxing the assumption of perfect charge selectivity (tantamount to fixing the electrochemical potential of counterions in the solid) allows for the equilibrium electroconvective instability. In addition, we suggest a simple experimental test for determining the true, either equilibrium or nonequilibrium, origin of instability in concentration polarization.

Extended space charge in concentration polarization.

This paper is concerned with ionic currents from an electrolyte solution into a charge-selective solid, such as, an electrode, an ion-exchange membrane or an array of nano-channels in a micro-fluidic system, and the related viscous fluid flows on the length scales varying from nanometers to millimeters. All systems of this kind have characteristic voltage-current curves with segments in which current nearly saturates at some plateau values due to concentration polarization--formation of solute concentration gradients under the passage of a DC current. A number of seemingly different phenomena occurring in that range, such as anomalous rectification in cathodic copper deposition from a copper sulfate solution, super-fast vortexes near an ion-exchange granule, overlimiting conductance in electrodialysis and the recently observed non-equilibrium electroosmotic instability, result from the formation of an additional extended space charge layer next to that of a classical electrical double layer at the solid/liquid interface. In this paper we review the peculiar features of the non-equilibrium electric double layer and extended space charge and the possibility of their direct probing by harmonic voltage/current perturbations through a linear and non-linear systems response, by the methods of electrical impedance spectroscopy and via the anomalous rectification effect. On the relevant microscopic scales the ionic transport in the direction normal to the interface is dominated by drift-diffusion; hence, the extended space charge related viscous flows remain beyond the scope of this paper.

Two-phase Stefan problem with supercooling

Both one-dimensional two-phase Stefan problems with the thermodynamic equilibrium condition

Two continuous models for the dynamics of sandpile surfaces.

\theta (R(t),t) = 0

Driving factors of electro-convective instability in concentration polarization

, and with the kinetic rule

Modified Heterogeneous Anion-Exchange Membranes for Desalination of Brackish and Recycled Water

\theta (R(t),t) = - \varepsilon \dot R(t)

INTERFACIAL KINETICS EFFECT IN PLANAR SOLIDIFICATION PROBLEMS WITHOUT INITIAL UNDERCOOLING

at the moving boundary

Equilibrium electro-convective instability in concentration polarization: The effect of non-equal ionic diffusivities and longitudinal flow

x = R(t)