Isaak Rubinstein

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.

Driving factors of electro-convective instability in concentration polarization

Ionic current through a charge-selective interface in a binary electrolyte is a basic element of many electrochemical engineering and microfluidic processes. Such current passage is diffusion-limited: it induces a decrease of electrolyte concentration towards the interface (concentration polarization, CP), expressed in the saturation of current upon increasing voltage at some value (limiting current, LC). With further increase of voltage, this saturation breaks down (overlimiting conductance, OLC). In open systems OLC is mediated by a microscale vortical flow which develops as a result of electroconvective instability (ECI) of quiescent CP near LC. Electroconvection (EC) is a flow driven by the electric force acting either upon the space charge of the interfacial EDL (electroosmosis, EO) or the residual space charge of the quasielectroneutral bulk (bulk EC). There are two types of EO, the equilibrium and the nonequilibrium one. The former relates to the action of the tangential electric field upon the space charge of the EDL, and the latter pertains to the similar action upon the extended space charge, forming next to the EDL near LC. For a perfectly charge-selective interface, CP is stable under the equilibrium EO or bulk EC, but nonequilibrium EO may cause ECI. For this reason until recently, ECI in CP was attributed to this latter mechanism. Lately, it was shown that imperfect charge-selectivity of the interface makes equilibrium ECI possible, driven by either equilibrium EO or bulk EC, or both. Here we identify and analyze the major surface and bulk factors affecting the ECI. These factors (diffusioosmosis, EO, bulk EC, and some newly identified ones) are manifestations of the electric force and pressure gradient, balanced by the viscous force acting in various locations in solution. The contribution of these factors to ECI in CP is analyzed for a varying interface permselectivity.

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

In the desalination of recycled water, the triple demand for a high recovery ratio, low energy consumption, and fouling resistance can be met by electrodialysis (ED) under certain conditions: high recovery is an inherent property of the process, while low energy consumption and fouling resistance can be obtained by the use of modified heterogeneous membranes. To this end, heterogeneous polyethylene-based anionexchange membranes were modified by a hydrophilic anion-exchange coating, having an ion-exchange capacity of 2.2 to 2.9 mEq/g (dry weight) and a specific conductance of 70 to 110 mS/cm. The coating was found to be stable in continuous ED operation (66 days). The modification suppressed water splitting and brought the performance of the coated heterogeneous membranes into line with that of homogeneous commercial anion-exchange membranes. Direct measurement of the polarization at the coated membranes indicated that this phenomenon decreased as a result of the coating. Mathematical modeling showed that ...

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

For a long time, based on the analysis pertaining to a perfectly charge selective interface, electro-convective instability in concentration polarization was attributed to a nonequilibrium mechanism related to the extended space charge which forms next to that of the electric double layer near the limiting current. More recently, it was shown that imperfect charge selectivity of the interface makes equilibrium instability possible, driven by either equilibrium electro-osmosis or bulk electro-convection, or both. In that study, addressing stability of a quiescent binary electrolyte, equal ionic diffusivities were assumed. Here we study the effect of non-equal ionic diffusivities and imposed longitudinal flow upon the onset and further nonlinear development of the equilibrium electro-convective instability at a non-perfectly permselective interface. It is observed through a suitable analytical and numerical study that the imposed flow along the perm-selective interface does not affect fundamentally the equilibrium electro-convective instability in concentration polarization either in terms of the temporal instability threshold or the resulting nonlinear flow. For the former, the critical voltage is practically identical with that in quiescent concentration polarization. For the latter, with non-slip interface conditions, the resulting nonlinear flow, with high accuracy, may be represented as a superposition of the imposed Poiseuille flow and the vortices of the quiescent instability. Differing ionic diffusivities may have a considerable effect upon the onset of the electro-convective instability. In particular, co-ionic diffusivity appreciably lower than the counter-ionic one may yield an appreciable increase of the critical voltage. This is explained by the stabilizing effect of the diffusion potential’s contribution to the electric potential fluctuations.

COMPLEXITY AND HIERARCHICAL MAJORITY RULE

Hierarchical structure is an essential part of complexity, an important notion relevant for a wide range of applications ranging from biological population dynamics through robotics to social sciences. In this paper we propose a simple cellular-automata tool for study of hierarchical population dynamics.