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C C =−CZ,i=1,2,3,4 Membranes 2021, 11, 697 edge are 2,1 = 0.375 mM, 5,1 i i , where NaCl enters the chamber from the lower boundary as a supplement buffer to maintain electrical neutrality. In the ideal simplified model of the ion-selective membrane, the results of fixed voltage and fixed counter ion concentration are accurate in most cases, especially in the case of high voltage and/or high charge density [36]. At the membrane boundary, the voltage V is from 7 of 13 V = 0 to V = 30VT, with the thermal voltage VT equal to 25.8 mV [31]. The assumption of charge selectivity is a fixed counterion boundary. We set the fixed concentration of Cl− at Cm = 10C5,0 [37]. As for other parameters, we set P1 = 100 Pa, T = 300 K, ρ = 1000 kg/m3, V = 0 to V = 30VT, with the thermal voltage VT equal to 25.8 mV [31]. The assumption of and η = 0.001 Pa⋅s, respectively. − charge selectivity is a fixed counterion boundary. We set the fixed concentration of Cl at The concentration of Na+ is not an essential research item. Although the content of 3 Cm =10C5,0 [37].Asforotherparameters,wesetP1 =100Pa,T=300K,ρ=1000kg/m , this ion in the brine is high, the Li+ can be collected in the subsequent steps [31]. Therefore, and η = 0.001 Pa·s, respectively. ++ it is easTyhtoe csoepnacerantteraLtioinonosf Nfroamisit.nIontsatenaeds,swenetihaalvresteoafrocchuisteomn.thAeltehxoturagchtitohneqcuoanntetintyt of + 2+ + + of tLhiisioionns,ienstphecibarlilnyethisehMiggh, /tLhie Lfliuxcraantiboeicnotlhlecmtedicrinocthaensnueblsaenqdueunstesthepissp[3a1ra].mTehtereafosre, + a sietpisareatseyitnodsiecaptaorra.teStLeiadiyo-nsstaftreomsoliut.tIinosntseadre, wuseehdatvoe sttoufdoycutsheonpethrfeoerxmtrancctieoonfqtuhaenstyitsy- of + 2++ temL.i Tihoengs,oevseprenciinagllyEtqhueaMtiogns /(1L)i–(5fl)uaxrerastoiolviendthweimthicthroecahbaonvnelbaonudndusaerythciosnpdairtaiomneste(6r)a–s a (10s)e.parate indicator. Steady-state solutions are used to study the performance of the system. ThWegeosvimerunilnatgeEthqeuastieoandsy(-1s)t–a(t5e)baerheasvoilovredofwthitihstshyestaebmovaetbVo=un3d0VarTy,acnodndthiteioPnDs(F6)c–o(n1-0). We simulate the steady-state behavior of this system at V = 30V , and the PDF strains the fluid velocity uout = 0.5 mm/s in the x-direction, and the velocityT rate of y-di- constrains the fluid velocity uout = 0.5 mm/s in the x-direction, and the velocity rate of rection is u = 0.63 mm/s and u = 1 mm/s. y-directionisu =0.63mm/sandu =1mm/s. 1122 CoCmopmarpianrginthgethtwetowpoicptuicrteusre(Fsi(gFuigreu2rea,2ba),bw),ewceancafninfidntdhathtaintitnhethbelabclkacdkadshaeshdebdobxox ++ ranrganeg(1e8(1μ8mμ≤my≤ 3y1≤.5 μ31m.5),μthme)L, tihieoLnis cioncsencotrnacteionntrwataiosnmwuachs mhiughcherhtihgahnerththeafenetdh.eWfeed. puWt tehpeuctoltlheectcoorlltehcetroertohegrettaohgiegtha-rheisgohlu-rteiosonlusetipoanrasteipoanraeftfioecnt.eTffhecetb. oTxheinbdoixcaitnedsitchaetelsot-he catliocnatoifonthoefctohlelecotollre.ctor. Figure 2. (a) The concentration distribution of Li+ in the chamber (b) The concentration distribution of Mg2+ in the chamber. Values of other parameters: V = 30VT, uout = 0.5 mm/s, u1 = 0.63 mm/s, and u2 = 1 mm/s. Since the initial concentrations were different, we paid more attention to the flux of the two ions. Most Li+ flow through the upper right of the chamber where the collector box is located (Figure 3). The flux of Mg2+ at the right outlet of the chamber is much lower than the feed (Figure 4). These two figures demonstrated that the proposed system could continuously extract Li+ ions with a concentration of 1.28 times in the raw brine while simultaneously removing Mg2+ ions.PDF Image | Brines Based on Free Flow Ion Concentration Polarization
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