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Membranes 2021, 11, x FOR PEER REVIEW 4 of 13 Membranes 2021, 11, 697 On the other hand, if FD,y is smaller than FD,y, the ion moves downward. If the y-com- 4 of 13 ponents of two forces are equal, the ion will be balanced in that location. Because of the ICP effect, the electric field at the boundary of IDZ is significantly higher than in the other regions. These uneven distributions of electric force define different equilibrium positions the other regions. These uneven distributions of electric force define differ+ent equilibrium in y-direction for different cation species. As shown in Figure 1a, as Li ion enters the positions in y-direction for different cation species. As shown in Figure 1a, as Li+ ion chamber at the center of the inlet, it is subject to a larger FD,y than FE,y (because the down- enters the chamber at the center of the inlet, it is subject to a larger F than F (because D,y E,y ward electric field there is low). Hence, it will move upward as it is moving with fluid in the downward electric field there is low). Hence, it will move upward as it is moving the right direction. When it is closer to the IDZ region, the electric field will become with fluid in the right direction. When it is closer to the IDZ region, the electric field stronger, and the electric force will increase. This upward motion will stop when the two will become stronger, and the electric force will increase. This upward motion will stop forces (FD,y and FE,y) are equal. It will move rightward and run out through microchannels when the two forces (F and F ) are equal. It will move rightward and run out through D,y E,y 2+ at the right side of the chamber. In the meantime, Mg is subject to a 2-times higher electric microchannels at the right side of the chamber. In the meantime, Mg2+ is subject to a field and a 1.46-times (calculated from the diffusion coefficients shown in Table 1) higher 2-times higher electric field and a 1.46-times (calculated from the diffusion coefficients fluid drag force as compared to those of Li+, the balance position for Mg2+ will be lower shown in Table 1) higher fluid drag force as compared to those of Li+, the balance position than that of Li+. If we optimize the fluid flow speeds and the electric field such that the for Mg2+ will be lower than that of Li+. If we optimize the fluid flow speeds and the electric focused peaks of Li+ and Mg2+ run out of the system through a different group of micro- field such that the focused peaks of Li+ and Mg2+ run out of the system through a different channels, these two ion species are separated. Index i group of microchannels, these two ion species are separated. Figure 1. (a) Schematic of FF-ICP system for ion concentration and separation. (b) The simulation model. Figure 1. (a) Schematic of FF-ICP system for ion concentration and separation. (b) The simulation mTaobdlel1..Thetransportparametersoftheionsintherawbrine[35]. Species Diffusion Coefficient D (×10−9 m2/s) Electrophoretic Mobility μ (×10−8 m2/V·s) Table 1. The transport parameters oi f the ions in the raw brine [35]. i Index i 1 2 3 4 5 Species Li+ Diffusion Coefficient Di (×10−9 m2/s) Electrophoretic Mobility μi (×10−8 m2/V⋅s) 3.98 5.152 1 2 3 4 5 Li+ 1.029 3.98 5.4577.853 7.853 Na Mg2+ K+ Cl− Na+ Mg2+ K+ 1.029 1.334 0.706 1.957 2.032 1.334 0.706 1.957 2.032 7.563 + 5.152 7.5635.457 Cl− 2.2. Simulation Model We use a simplified model for our simulation study, as shown in Figure 1b. In this model, the chamber is of length L and width H. At the left and right sides of the chambers, there are a number of microchannels of length Lc and width Hc. On the upper and lowerPDF Image | Brines Based on Free Flow Ion Concentration Polarization
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