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Membranes 2020, 10, 221 15 of 72 3.4.2. Current-induced convection The most powerful mechanism leading to the essential exceeding of the current above its limiting value is current-induced convection [8,9,21,30,55–57]. Two current-induced convection mechanisms, causing the mixing of the depletion region with well conductive bulk, are recognized, namely gravitational convection (minor effect) and electroconvection (major effect). Gravitational Convection Gravitational convection is caused by natural convection that occurs due to a difference in concentration and/or temperature (larger heat dissipation in the depletion layer) gradient within the same solution. Indeed, the gradients created by these differences generate density gradients. For example, at the membrane surface, the very low conductivity of the extended SCR causes high electrical resistance and promotes a rise in temperature by the Joule effect [57]: the conductivity in this location is 100 to 1000 times lower than in membranes and in the solution at the center of the compartment [58]. In the case of vertically placed membranes, when a density gradient appears due to this temperature rise, the solution at the membrane interface, less dense, tends to go up while under the effect of the earth’s gravitational force, the raw solution, in the center of the compartment, more dense, move towards the zone of the least dense solution and goes down, thus creating a convection. This type of convection can be diminished by positioning the membrane horizontally [59]. This convection event remains negligible for infinitely diluted solutions, since the density differences are almost zero [21]. It has been found that gravitational convection occurs when the Rayleigh number (NRa), product of Grashof and Schmidt numbers, was around 1700 [60]. In addition, experimental data and modeling calculations demonstrate that gravitational convection can have a significant contribution on mass transfer only when the concentration of the solution is relatively high (>0.05 M) and that the velocity of the solution is low (<0.4 cm/s) [61–63]. Electroconvection The other type of convection, referred as electroconvection, originates from the interaction of an electric field and a spatial charge. Electroconvection is the major phenomena responsible for ion transport when the system operates in overlimiting current regime, since it allows a better availability of ions at the membrane interface by supplying fresh solution to the membrane surface and by removing the depleted solution [64–66]. Electroconvection can occur in the volume (volumetric electroconvection) and near the membrane surface (electro-osmotic motion). However, due to the close values of diffusion coefficients of cations and anions, volumetric electroconvection does not play noticeable role in the mass transfer [67,68]. Hence, electroconvection near the membrane interface is conventionally considered as the main electroconvection phenomenon contributing to the mass transfer improvement. It is considered as an electro-osmotic motion and may be distinguished into two principal kinds [21,57,69]. Electro-osmosis of the first kind arises under the limiting current region due to the action of tangential electric field upon the quasi-equilibrium diffusion part of DBL (Figure 9), which has almost the same structure to that for zero current; it has insignificant increment in the mass transfer [21]. Electroconvection is mainly caused by electroosmosis of the second kind. Electro-osmosis of the second kind occurs in overlimiting condition, due to the action of the electrical force upon the non-equilibrium space charge region. Indeed, when a high electric field is applied perpendicularly on the SCR near the membrane interface, an excess pressure arises within the SCR (Figure 10a, step 1). This excess pressure (secondary effect from the electric field) displaces the liquid out from the SCR in tangential direction towards zones with lower pressure, corresponding to zones having lower space charge (Figure 10a, step 2). When moving along the membrane interface, this displaced fluid collides with inertial non-slipped liquid layers (Figure 10a, step 3). The resulting difference in inertia redirects the movement of the fluid towards the depletion solution or solution bulk [21]. This results in the occurrence of two electroconvective vortices rotating in opposite senses and having a major role inPDF Image | Electrodialytic Processes
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