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anywhere other than on the bottom for that matter), gravitational convection will occur [77]. In essence, gravitational convection is a strong function of cell design and configuration and can therefore either be avoided or used to one’s advantage. Electroconvection, on the other hand, is due to an electrical force, directed normally to the membrane, acting on the space charge region, in which it creates an excess pressure and therefore displaces the liquid from the space charge region to regions of lower pressures. This phenomenon causes the creation of vortices (electro-osmotic instability), which mix the fluid and help transport ions to the membrane and there- fore contribute to overlimiting current [87]. This kind of mechanism of mixing goes along with the formation of an extended space charge region that is roughly as large as the vortices [15]. The electro-osmotic instability usually consists of many vortices along the membrane; however, in a confined geometry, this phenomenon may be dra- matically reduced or even suppressed, which was shown in experiment by Yossifon et al [118] and Nam et al [70] in microchannels and in theory by Dydek et al [25] via calculations on a microchannel capped with a membrane. For example, in Yossifon’s experiment [118], the height of the microchannel interfacing with the nanochannel was varied from 2 microns to 122 microns. When the channel was 122 microns high, Yossifon was clearly able to see vortices form; however, when the channel height was decreased to 2 microns, the vortices were no longer present. Nam’s experiments [70] also showed that we can observe counter-rotating twin vortices at intermediate mi- crochannel heights (tens of microns). This observation was theoretically explained by Dydek et al [25]. In fact, they also identified the three different regimes, namely electro-osmotic instability, electro-osmotic flow (EOF), and surface conduction (SC). For very wide channels, the electro-osmotic instability was still predicted, just like in Rubinstein’s paper [87]. However, when the microchannel height is decreased to tens of microns, it will enter the electro-osmotic flow regime. This regime is characterized by two counter-rotating vortices in which fluid flows to the membrane on the walls (EO flow) and flows back in the middle (pressure-driven), which creates the type of flow field that Yaroshchuck and Zholkovskiy used to predict some concentration polarization dynamics [115]. In contrast, the surface conduction regime occurs when 32PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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