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 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.

Flow-through electrodialysis membrane cells are widely used in water purification and the processing of agricultural products (milk, wine, etc.). In the research and operating practice of such systems, a significant place is occupied by a galvanodynamic (or galvanostatic) mode. 2D mathematical modelling of ion transfer in the galvanodynamic mode requires solving the problem of setting the average current density equal to a certain value, while the current density distribution in the system is uneven. This article develops a 2D mathematical model of the overlimiting transfer enhanced by electroconvection in a flow-through electrodialysis cell in the galvanodynamic mode. The model is based on the system of Navier–Stokes, Nernst–Planck, Poisson equations and equations for the electric current stream function. To set the electric mode we use a boundary condition, relating the electric field strength and current density. This approach allows us to describe the formation of the extended space charge region and development of electroconvection at overlimiting currents. For the first time, chronopotentiograms and current–voltage characteristics of the membrane systems are calculated for the galvanodynamic mode taking into account the forced flow and development of electroconvection. The behaviors of the calculated chronopotentiograms and current–voltage characteristic coincide qualitatively with experimental data. The effects of the electrolyte concentration, forced flow velocity and channel size on the mass transfer at overlimiting currents are estimated.