The paper is concerned with convection at an ion exchange electrodialysis membrane induced by nonequilibrium electro-osmosis in the course of concentration polarization under the passage of electric current through the membrane. Derivation of nonequilibrium electro-osmotic slip condition is recapitulated along with the linear stability analysis of quiescent electrodiffusion through a flat ion exchange membrane. Results of numerical calculation for nonlinear steady state convection, developing from the respective instability, are reported along with those for a slightly wavy membrane. Besides these results, we report those of time dependent calculations for periodic and chaotic oscillations, resulting from instability of the respective steady state flows, and also the results of recent experiments with modified membranes. These latter rule in favor of electro-osmotic versus bulk electroconvective origin of overlimiting conductance through ion exchange membranes.

Electric conduction from an electrolyte solution into a charge selective solid, such as ion exchange membrane or electrode, becomes unstable when the electrolyte concentration near the interface approaches zero owing to diffusion limitation. The sequence of events leading to instability is as follows: upon the decrease of the interface concentration, the electric double layer at the interface transforms from its common quasi-equilibrium structure to a different, non-equilibrium one. The key feature of this new structure is an extended space charge added to the usual one of the quasi-equilibrium electric double layer. The non-equilibrium electro-osmotic slip related to this extended space charge renders the quiescent conductance unstable. A unified asymptotic picture of the electric double-layer undercurrent, encompassing all regimes from quasi-equilibrium to the extreme non-equilibrium one, is developed and employed for derivation of a universal electro-osmotic slip formula. This formula is used for a linear stability study of quiescent electric conduction, yielding the precise parameter range of instability, compared with that in the full electroconvective formulation. The physical mechanism of instability is traced both kinematically, in terms of non-equilibrium electro-osmotic slip, and dynamically, in terms of forces acting in the electric double layer.

We revisit the classical problem of diffusion-limited ion transport to a membrane (or electrode) by considering the effects of charged side walls. Using simple mathematical models and numerical simulations, we identify three basic mechanisms for over-limiting current in a microchannel: (i) surface conduction carried by excess counterions, which dominates for very thin channels, (ii) convection by electro-osmotic flow on the side walls, which dominates for thicker channels and transitions to (iii) electro-osmotic instability on the membrane end in very thick channels. These intriguing electrokinetic phenomena may find applications in biological separations, water desalination, and electrochemical energy storage.

We present a visualization of the predicted instability in ionic conduction from a binary electrolyte into a charge selective solid. This instability develops when a voltage greater than critical is applied to a thin layer of copper sulfate flanked by a copper anode and a cation selective membrane. The current-voltage dependence exhibits a saturation at the limiting current. With a further increase of voltage, the current increases, marking the transition to the overlimiting conductance. This transition is mediated by the appearing vortical flow that increases with the applied voltage. DOI: 10.1103/PhysRevLett.101.236101 PACS numbers: 82.45.Gj, 47.20.Ma, 82.40.Ck Microscale fluid flows commonly arise when a dc current passes through the diffusion layers (DL) of binary ionic solutions adjacent to charge selective solids, such as electrodes [1], ion exchange granules [2] or membranes [3], and arrays of nanochannels [4]. Under conditions of extreme diffusion limitation (concentration polarization (CP) near the limiting current [5]), these flows provide an additional ionic transport mechanism. This mechanism is essential for the operation of nanofluidic preconcentrators [4] and overlimiting electrodialysis [6,7]. On short length scales and in the absence of free interfaces, these flows are not driven by gravity or surface tension. Instead, they are driven by the electric force acting upon the space charge of the nanometers-thick interfacial electric double layer (EDL). Slip-like fluid flow induced by this force is known as electro-osmosis (EO).There are two regimes of EO that correspond to the different states of the EDL and are controlled by the nonequilibrium voltage drop (overvoltage) across it [8]. These are the quasiequilibrium regime [9,10] and the nonequilibrium EO [2,8,11]. While both regimes result from the action of a tangential electric field upon the space charge of the EDL, the first relates to the charge of quasiequilibrium EDL, whereas the second relates to the extended space charge of nonequilibrium EDL. The nonequilibrium EDL develops in the course of CP near the limiting current.According to a recent theory [8], a novel critical instability of quiescent ionic conduction related to the extended charge EO stands behind the overlimiting conductance through a planar ion exchange membrane. During 1D conduction through a planar layer, an electrolyte concentration gradient forms. The related electric force does not impair the mechanical equilibrium in the system, which remains stable as long as the EDL retains its quasiequilibrium structure. As voltage increases, the system moves away from quasiequilibrium, and an extended space charge develops in the EDL. EO slip related to this extended space charge renders the quiescent conduction unstable [8]. This instability of 1D ionic conduction is reminiscent of instabilities in 1D thermal conduction, such as the RayleighBenard and Marangoni instabilities. While reports of the underlying extended space charge EO [2] and possibly its related flow patterns [1] ...