A. V. Kovalenko

Competition between diffusion and electroconvection at an ion-selective surface in intensive current regimes.

Considering diffusion near a solid surface and simplifying the shape of concentration profile in diffusion-dominated layer allowed Nernst and Brunner to propose their famous equation for calculating the solute diffusion flux. Intensive (overlimiting) currents generate electroconvection (EC), which is a recently discovered interfacial phenomenon produced by the action of an external electric field on the electric space charge formed near an ion-selective interface. EC microscale vortices effectively mix the depleted solution layer that allows the reduction of diffusion transport limitations. Enhancement of ion transport by EC is important in membrane separation, nano-microfluidics, analytical chemistry, electrode kinetics and some other fields. This paper presents a review of the actual understanding of the transport mechanisms in intensive current regimes, where the role of diffusion declines in the profit of EC. We analyse recent publications devoted to explore the properties of different zones of the diffusion layer. Visualization of concentration profile and fluid current lines are considered as well as mathematical modelling of the overlimiting transfer.

Effect of electroconvection and its use in intensifying the mass transfer in electrodialysis (Review)

The modern concepts on the origin of electroconvection (EC) are surveyed briefly and the known mechanisms of this phenomenon are classified. Factors that influence the EC character and intensity at the surface of ion-exchange membranes are analyzed, such as electrical and geometrical heterogeneity of the membrane surface, its degree of hydrophobicity, and the surface charge. The EC mechanism is shown also to depend on the applied potential difference and the rate of solution flow between membranes. The mechanism of the EC-induced gain in the mass transfer is elucidated, the possible gain in the mass transfer is estimated, and the prospects for using the EC for reducing the membrane fouling caused by sedimentation and formation of organic deposits are assessed.

Model and experimental studies of gravitational convection in an electromembrane cell

The model and experimental studies of the effect of gravitational convection on transport processes in an electromembrane cell are carried out. A model of an unsteady process of binary electrolyte transfer in moderately dilute solutions in an electromembrane cell for underlimiting current modes with allowance made for the natural and forced convection is built in the form of a system of two-dimensional equations of Navier-Stokes, Nernst-Planck, thermal conductivity, and electric current continuity. The dynamics of the appearance and development of vortex structures that arise in response to operation of gravitational archimedian forces is considered as well as their effect on the transfer of salt ions. Chronoampero- and chronopotentiograms obtained in an experimental study of desalination channels in electromembrane systems are interpreted.

Theoretical Analysis of the Effect of Ion Concentration in Solution Bulk and at Membrane Surface on the Mass Transfer at Overlimiting Currents

Overlimiting current modes are of considerable interest for the practice of electrodialysis (ED). However, the economical expedience of such ED modes is evident only for desalination of dilute solutions. Here, we show the theoretical analysis of the effect of concentration on the behavior of an ED cell with homogeneous ion-exchange membranes. The study is based on numerical solution of the two-dimensional system of coupled equations of Nernst–Planck–Poisson–Navier–Stokes. It is shown that as the electrolyte concentration in solution that enters the ED desalination chamber increases, the intensity of electroconvection decreases, which induces a decrease in the relative mass-transfer rate (the decrease in the ratio of current density to its limiting value). This effect is stronger in the region of high potential differences where the electroconvective instability of Rubinstein–Zaltzman is realized under the conditions of a nonuniform concentration field caused by solution desalination. In contrast, the increase in the counterion concentration at the membrane surface (associated with the increase in the surface charge) intensifies the electroconvection.

Inclusion of the concentration dependence of the diffusion coefficient in the sand equation

The applications of the Sand equation in potentiometry of electrode and membrane systems for precise measurements of the transition time (τ) have been determined. An approach was suggested for choosing the diffusion coefficient of electrolyte (D) in the case when the concentration changes from its value in the agitated solution (where D = Db) to the nearly zero value at the surface (D = D0 corresponds to an infinitely dilute solution), Db and D0 being substantially different. The Nernst–Planck–Poisson nonstationary equations were numerically solved in a one-dimensional system including an ion-exchange membrane and two adjacent diffusion layers (for the electrode–solution system, the result is a particular case). An effective value Def was found, whose substitution in the Sand equation gave τ identical to that obtained by numerical solution. The neglect of the concentration dependence D(с) can lead to a nonadequate determination of the ion transport numbers in the membrane.

Mathematical Modeling of Ion Transport and Water Dissociation at the Ion-Exchange Membrane/Solution Interface in Intense Current Regimes

At current densities exceeding the limiting current density, H+ and OH− ions are generated at the interface of the ion-exchange membrane with a depleted solution as a result of the dissociation of water molecules. At present, it is generally accepted that water splitting occurs in a thin (a few nanometers) layer inside the membrane, this reaction being catalytic in nature. The mathematical model of ion transport in the diffusion layer near the membrane surface has been constructed and numerically studied under conditions when dissociation and recombination processes involving water molecules and H+ and OH− ions occur simultaneously. It has been shown that in overlimiting current regimes under very high voltages, intense noncatalytic dissociation of water molecules in the extended space charge region of the depleted solution can occur irrespective of the catalytic splitting of water. Since this region has macroscopic dimensions, the rate of noncatalytic water dissociation is comparable with the rate of the corresponding catalytic process. The obtained results significantly supplement modern concepts of the mechanism of generation of H+ and OH− ions in membrane systems, showing that this process can proceed not only in accordance with the conventional mechanism with the catalytic participation of functional groups and/or other compounds, but also via the noncatalytic mechanism that has not been taken into account to the present.

1D Mathematical Modelling of Non-Stationary Ion Transfer in the Diffusion Layer Adjacent to an Ion-Exchange Membrane in Galvanostatic Mode

The use of the Nernst–Planck and Poisson (NPP) equations allows computation of the space charge density near solution/electrode or solution/ion-exchange membrane interface. This is important in modelling ion transfer, especially when taking into account electroconvective transport. The most solutions in literature use the condition setting a potential difference in the system (potentiostatic or potentiodynamic mode). However, very often in practice and experiment (such as chronopotentiometry and voltammetry), the galvanostatic/galvanodynamic mode is applied. In this study, a depleted stagnant diffusion layer adjacent to an ion-exchange membrane is considered. In this article, a new boundary condition is proposed, which sets a total current density, i, via an equation expressing the potential gradient as an explicit function of i. The numerical solution of the problem is compared with an approximate solution, which is obtained by a combination of numerical solution in one part of the diffusion layer (including the electroneutral region and the extended space charge region, zone (I) with an analytical solution in the other part (the quasi-equilibrium electric double layer (EDL), zone (II). It is shown that this approach (called the “zonal” model) allows reducing the computational complexity of the problem tens of times without significant loss of accuracy. An additional simplification is introduced by neglecting the thickness of the quasi-equilibrium EDL in comparison to the diffusion layer thickness (the “simplified” model). For the first time, the distributions of concentrations, space charge density and current density along the distance to an ion-exchange membrane surface are computed as functions of time in galvanostatic mode. The calculation of the transition time, τ, for an ion-exchange membrane agree with an experiment from literature. It is suggested that rapid changes of space charge density, and current density with time and distance, could lead to lateral electroosmotic flows delaying depletion of near-surface solution and increasing τ.

Asymptotic solutions of boundary value problems of two-dimensional transport models for a ternary electrolyte

This paper is a continuation of [1, 2]. An asymptotic method for solving boundary value problems of two-dimensional mathematical transport models for a ternary electrolyte is proposed.