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ftuhnecgtilonbaolfrtehseisvtaonltcaegoefatphepleieledc.trIondtihailsysriesgsioynst,etmhe(Rsy)sitsefmairfloyllcoownsttahnet.Ohm’s law (U = RI) and the global resistance of the electrodialysis system (R) is fairly constant. 2. A «plateau» region (II), named limiting region, where the current remains relatively constant 2. Aw«hpilleatehaeuv»orletaggioenin(IcIr)e,ansaems. eTdhilsimpiatirntigcurleagriovna,luwehrerfertshetocuthrerelnimt rietimngaicnusrrelnatidvenlysictyonwsthaincth wcohrirlestphoenvdosltaogteheinmcraexaismesa.l Tcuhrisrepnatrvtiaclulear(Ilvima)lufreomrefwerhsictoh wthaetelirmdiitsisnogcicautirorennbtedgeins.ity which Membranes 2020, 10, 221 12 of 72 cAorrtehsiprdonrdesgitonth(eIImI),axniammaeldcuorrvenrtlivmailtuineg(Ilrime)gfioronm, wheircehtwhaetecrudrriessnotcinatciroenasbeesgiwnsh.en voltage Aaptphliired risegfiuornth(eIrIIi)n,cnreaamsed. Tovheisrlrimegiitoingcorrergeisopno, nwdhs etroeatnheovceurrpraesnstinigncorfeathsesliwmhiteingvcoultraregnet a d p e p n l s i e i t d y i d s u f u r i r n t g h e w r h i n i c c h r e t a h s e e d e l . e T c t h r i i s c a r l e g e n i o e n r g c y o r i s r e u s s p e o d n t d o s d t o i s s a o n c i o a v t e e r wp a a s t e s r i n mg o o l f e c t h u e l e l s i mw i i t t i h n o g u c t u t a r r k e i n n t g during which the electrical energy is used to dissociate water molecules without taking part d p e a n r s t i t i n y d s o u l r u i t n e g s w s e h p i a c r h a t t i h o e n e . l T e h c t i r s i c r a e l g e i m n e e r g i s y a i l s s o u s c e h d a r t a o c d t e i r s i s z o e c d i a b t e y w t h a e t e o r c mc u o r l r e e c n u c l e e s o f w e i x t h a o l t u a t t i t o a n k i a n n g d in solutes separation. This regime is also characterized by the occurrence of exaltation and pcaurrtrients-oinludtuescesdepcaornavtieocnti.oTnhpishreengoimenias a(slesoe Schecatriaocnte3r.i4z)e. d by the occurrence of exaltation and current-induced convection phenomena (see Section 3.4). current-induced convection phenomena (see Section 3.4). Figure 7. Typical current-voltage curve for an ion-exchange membrane and value of the limiting Figure 7. Typical current-voltage curve for an ion-exchange membrane and value of the limiting current Fciugrurreent7(.aTdyapitceadl fcruormreBnat-zvionlettaagnedcuCravsetafiogrnean[11io])n.-exchange membrane and value of the limiting (adapted from Bazinet and Castaigne [11]). current (adapted from Bazinet and Castaigne [11]). grapAhnofththeer mreesitshtoadncies (fUre/qI)uiesnptllyotutesdedastoadfeutnecrmtioineoef xtpherrimeceipnrtaolclayl tchuerrleimntitvinagluceu(r1r/eIn) t(Fviagluree. A8). A graph of the resistance (U/I) is plotted as a function of the reciprocal current value (1/I) (Figure 8). gTrhape hreocfiptrhoecarel slismtaitninceg (cUu/rIr)einst pvlaoltutedisatsheanfuant cthtieoninotefrtsheectiroencipofrothcaeltcwuorrleinet sv[a4l1u]e. (1/I) (Figure 8). The reciprocal limiting current value is then at the intersection of the two lines [41]. The reciprocal limiting current value is then at the intersection of the two lines [41]. Figure 8. Determination of the reciprocal limiting current value by the method of Cowan and Brown [41]. 3.3.3. Calculation of the Limiting Current Density The limiting current density (in A/m2 of electrode) can be approximated by the Lévêque equation [48]: dIlim =1.47 Memb Sol LD (15) Nbti −Nbti h i where F is the Faraday constant, Di the salt diffusion coefficient, Cinlet the inlet concentration (in eq./m3), h the distance between the membranes (in m), v the average linear solution velocity (in m/s), NbtMemb i and NbtSol the salt counterion effective transport number in the membrane and solution, respectively, i and L the length of the membrane active area (in m). 3. 3. Another method is frequently used to determine experimentally the limiting current value. A Another method is frequently used to determine experimentally the limiting current value. 1 FDiCinlet h2v3PDF Image | Electrodialytic Processes
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