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Membranes 2020, 10, 221 10 of 72 3.2.2. Concentration Polarization Concentration gradients formed on both sides of the membrane result in an accumulation of positive charges on one side and negative charges on the other. This phenomenon is called concentration polarization (CP). The visualization of CP and consequently formation and development of diffusion layers during ED in a wide range of current densities was demonstrated by Vasil’eva et al. [20] (Figure 6). Figure 6. Interferograms of a 1.0 × 10−2 mol/L sodium chloride solution in the diluate compartment of an ED cell at different current densities (a) 0 A/m2, (b) 18.5 A/m2, (c) 59.7 A/m2 and (d) 126.0 A/m2. Experimental conditions: flow rate of 1.26 × 10−3 m/s, intermembrane distance of 1.5 × 10−3 m, coordinate in the direction of solution feed 1.1 × 10−2 m (with permission from Vasil’eva et al. [20]). AEM: Anion-exchange membrane; CEM: Cation-exchange membrane. The polarization effect forces a limiting current density that should not be exceeded. Effectively, if the current is still increased, the limiting concentration of CMemb ≈ 0 in the CEM-diluate DBL is then i reached. At this moment, the resistance of the CEM-diluate DBL highly increases and the current density reaches a limiting value (Figure 5b) [22]. In these conditions, the flux of ions by diffusion reaches a maximum and is given by the following equation: JDiff = DiC (14) max δ when the flux of ions by electrotransport (JMigr) is equal to the flux of ions by maximal diffusion (JDiff ), i max the ED process is carried out at its optimal mass transfer. 3.3. Limiting Current Density (LCD) 3.3.1. Limiting Current Density and Water Dissociation A subsequent increase in the voltage difference, at the electrodes of the ED stack, will raise the current density but not the mass transfer. The main part of this additional current will not be used for the mass transfer of the ions in the dilute solution toward the concentrate solution but for the dissociation of water molecules [23,24]. Then, water dissociation generates H+ and OH− ions, which are immediately taken up by the ion transport (Figure 5c). Generation of H+ and OH− ions at the surface of IEMs was first noted by Kressman and Tye [25] and at the surface of bipolar membranes by Frilette [26]. The generation of H+ and OH− ions occurs when the electrolyte concentration near thePDF Image | Electrodialytic Processes
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