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.

Reexamination of electrodiffusion time scales.

The characteristic time scales in ac ionic conduction near equilibrium are reassessed via consideration of a selection of one-dimensional model problems. It is observed that, in addition to the two basic electrodiffusion time scales, those of diffusion relaxation in the macroscopic- and Debye-scale domains, T and t{D} (the latter identical with the bulk charge relaxation time), some intermediate time scales are present in each system. It is concluded that, due to insensitivity of the electric double layers to harmonic voltage disturbances, the short-time response on the t{D} scale is determined by the quasielectroneutral bulk.

Direct observation of a nonequilibrium electro-osmotic instability.

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.

Two continuous models for the dynamics of sandpile surfaces.

We consider a modified Bouchaud-Cates-Ravi Prakash-Edwards model for pile surface dynamics, and show that in the long-scale limit this model converges to a quasistationary model of pile growth in the form of an evolutionary variational inequality.

Electro-osmotically induced convection at a permselective membrane

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.

Diffusional mechanism of strong selection in ostwald ripening

The purpose of this paper is to show through a systematic asymptotic analysis that fluctuations, accounted for as a diffusional perturbation in the Lifshitz-Slyozov-Wagner (LSW) model of Ostwald ripening, provides, as conjectured previously by Meerson [Phys. Rev. E 60, 3072 (1999)], a "strong" selection of the limiting solution, out of a one-parameter family of similarity solutions with a finite support, as the sole attractor of time evolution. Throughout the latter, the previously described weak selection of other similarity solutions of that family, by the initial conditions with finite supports, occurs as intermediate time asymptotics. The respective mechanism is traced first for a simple instance of the LSW model with linear characteristic equations (integer power in the particle growth rate law equals -1), beginning with the analysis of steady states in the perturbed problem in similarity variables and weak selection in the unperturbed problem, followed by a detailed asymptotic analysis of the time-dependent perturbed problem, and generalized next for an arbitrary integer power in the range [-1,2]. The approximate asymptotic solutions obtained are compared with the exact numerical ones.