A Cell Model of an Ion-Exchange Membrane. Hydrodynamic Permeability
A cell model formulated in terms of the thermodynamics of nonequilibrium processes has been proposed for an ion-exchange membrane. The membrane is assumed to consist of an ordered set of porous charged spherical particles placed into spherical shells filled with a binary electrolyte solution. The pr...
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| Veröffentlicht in: | Colloid journal of the Russian Academy of Sciences Jg. 80; H. 6; S. 716 - 727 |
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| Sprache: | Englisch |
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Moscow
Pleiades Publishing
01.11.2018
Springer Nature B.V |
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| Abstract | A cell model formulated in terms of the thermodynamics of nonequilibrium processes has been proposed for an ion-exchange membrane. The membrane is assumed to consist of an ordered set of porous charged spherical particles placed into spherical shells filled with a binary electrolyte solution. The problem of determining all the kinetic coefficients in the Onsager matrix has been set and the general solution of the boundary value problem has been obtained for the cell. The consideration has been realized within the framework of small deviations of system parameters from their equilibrium values upon imposition of external fields. The boundary value problem has been analytically solved for determining the hydrodynamic permeability of the membrane under the Kuwabara boundary condition imposed on the cell surface. It has been found that, when the volume charge disappears, the equation for the permeability is transformed into the equation derived previously for an uncharged membrane. It has been shown that the hydrodynamic permeability (direct kinetic coefficient) of a cation-exchange membrane grows, tending to its limiting value, with increasing electrolyte concentration and decreases with a rise in the exchange capacity of ion exchanger grains. |
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| AbstractList | A cell model formulated in terms of the thermodynamics of nonequilibrium processes has been proposed for an ion-exchange membrane. The membrane is assumed to consist of an ordered set of porous charged spherical particles placed into spherical shells filled with a binary electrolyte solution. The problem of determining all the kinetic coefficients in the Onsager matrix has been set and the general solution of the boundary value problem has been obtained for the cell. The consideration has been realized within the framework of small deviations of system parameters from their equilibrium values upon imposition of external fields. The boundary value problem has been analytically solved for determining the hydrodynamic permeability of the membrane under the Kuwabara boundary condition imposed on the cell surface. It has been found that, when the volume charge disappears, the equation for the permeability is transformed into the equation derived previously for an uncharged membrane. It has been shown that the hydrodynamic permeability (direct kinetic coefficient) of a cation-exchange membrane grows, tending to its limiting value, with increasing electrolyte concentration and decreases with a rise in the exchange capacity of ion exchanger grains. |
| Author | Filippov, A. N. |
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| Cites_doi | 10.1016/0001-8686(93)80016-5 10.1134/S1061933X09010049 10.1016/j.colsurfa.2012.11.047 10.1016/j.cis.2008.01.005 10.1002/sapm197150293 10.1134/S1061933X18020060 10.3390/polym10040366 10.1002/cjce.5450850517 |
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| References | Filippov, A. and Philippova, T., Abstracts of Papers, Conf. on Ion Transport in Organic and Inorganic Membranes, Sochi, 2017, p. 129. Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics, Leyden: Noordhoff, 1965, 1973. FilippovA.PetrovaD.FalinaI.KononenkoN.IvanovE.LvovY.VinokurovV.Polymers20181036610.3390/polym100403661:CAS:528:DC%2BC1cXps1ymsr4%3D6415090 Moelwyn-HughesE.A.Physical Chemistry1961LondonPergamon RoldughinV.I.FilippovA.N.KharitonovaT.V.Colloid J.20188018910.1134/S1061933X180200601:CAS:528:DC%2BC1cXmt1agt7w%3D StarovV.M.ChuraevN.V.Adv. Colloid Interface Sci.19934314510.1016/0001-8686(93)80016-51:CAS:528:DyaK3sXksFKkurk%3D8318168 ZholkovskiyE.K.ShilovV.N.MasliyahJ.H.BondarenkoM.P.Can. J. Chem. Eng.20078570110.1002/cjce.54508505171:CAS:528:DC%2BD2sXht1ynsr7M ShilovV.N.ZharkikhN.I.BorkovskayaYu.B.Kolloidn. Zh.1981435401:CAS:528:DyaL3MXksFSjsrk%3D SaffmanP.G.Stud. Appl. Math.1971509310.1002/sapm197150293 TongK.ZhangY.ChuP.K.Colloids Surf. A20134194610.1016/j.colsurfa.2012.11.0471:CAS:528:DC%2BC3sXptlGrsA%3D%3D Filippov, A.N. and Shkirskaya, S.A., Membr. Membr. Tekhnol., 2018, vol. 8, p. 254. PerepelkinP.V.StarovV.M.FilippovA.N.Kolloidn. Zh.1992541391:CAS:528:DyaK38XltlyntLc%3D VasinS.I.FilippovA.N.StarovV.M.Adv. Colloid Interface Sci.20081398310.1016/j.cis.2008.01.0051:CAS:528:DC%2BD1cXls1Kru7s%3D18328455 VasinS.I.FilippovA.N.Colloid J.2009713110.1134/S1061933X090100491:CAS:528:DC%2BD1MXjs1Wkt7o%3D BrinkmanH.C.Appl. Sci. Res.1947A1271:CAS:528:DyaH1cXjsl2msg%3D%3D 8015_CR3 8015_CR4 E.K. Zholkovskiy (8015_CR11) 2007; 85 P.G. Saffman (8015_CR6) 1971; 50 V.M. Starov (8015_CR8) 1993; 43 K. Tong (8015_CR15) 2013; 419 P.V. Perepelkin (8015_CR9) 1992; 54 E.A. Moelwyn-Hughes (8015_CR14) 1961 S.I. Vasin (8015_CR10) 2008; 139 S.I. Vasin (8015_CR12) 2009; 71 V.N. Shilov (8015_CR2) 1981; 43 H.C. Brinkman (8015_CR5) 1947; A1 V.I. Roldughin (8015_CR7) 2018; 80 8015_CR1 A. Filippov (8015_CR13) 2018; 10 |
| References_xml | – reference: SaffmanP.G.Stud. Appl. Math.1971509310.1002/sapm197150293 – reference: PerepelkinP.V.StarovV.M.FilippovA.N.Kolloidn. Zh.1992541391:CAS:528:DyaK38XltlyntLc%3D – reference: Filippov, A. and Philippova, T., Abstracts of Papers, Conf. on Ion Transport in Organic and Inorganic Membranes, Sochi, 2017, p. 129. – reference: StarovV.M.ChuraevN.V.Adv. Colloid Interface Sci.19934314510.1016/0001-8686(93)80016-51:CAS:528:DyaK3sXksFKkurk%3D8318168 – reference: FilippovA.PetrovaD.FalinaI.KononenkoN.IvanovE.LvovY.VinokurovV.Polymers20181036610.3390/polym100403661:CAS:528:DC%2BC1cXps1ymsr4%3D6415090 – reference: RoldughinV.I.FilippovA.N.KharitonovaT.V.Colloid J.20188018910.1134/S1061933X180200601:CAS:528:DC%2BC1cXmt1agt7w%3D – reference: VasinS.I.FilippovA.N.Colloid J.2009713110.1134/S1061933X090100491:CAS:528:DC%2BD1MXjs1Wkt7o%3D – reference: TongK.ZhangY.ChuP.K.Colloids Surf. A20134194610.1016/j.colsurfa.2012.11.0471:CAS:528:DC%2BC3sXptlGrsA%3D%3D – reference: Moelwyn-HughesE.A.Physical Chemistry1961LondonPergamon – reference: BrinkmanH.C.Appl. Sci. Res.1947A1271:CAS:528:DyaH1cXjsl2msg%3D%3D – reference: ZholkovskiyE.K.ShilovV.N.MasliyahJ.H.BondarenkoM.P.Can. J. Chem. Eng.20078570110.1002/cjce.54508505171:CAS:528:DC%2BD2sXht1ynsr7M – reference: Filippov, A.N. and Shkirskaya, S.A., Membr. Membr. Tekhnol., 2018, vol. 8, p. 254. – reference: ShilovV.N.ZharkikhN.I.BorkovskayaYu.B.Kolloidn. Zh.1981435401:CAS:528:DyaL3MXksFSjsrk%3D – reference: Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics, Leyden: Noordhoff, 1965, 1973. – reference: VasinS.I.FilippovA.N.StarovV.M.Adv. Colloid Interface Sci.20081398310.1016/j.cis.2008.01.0051:CAS:528:DC%2BD1cXls1Kru7s%3D18328455 – volume: 43 start-page: 145 year: 1993 ident: 8015_CR8 publication-title: Adv. Colloid Interface Sci. doi: 10.1016/0001-8686(93)80016-5 – ident: 8015_CR3 – ident: 8015_CR1 – volume: A1 start-page: 27 year: 1947 ident: 8015_CR5 publication-title: Appl. Sci. Res. – volume: 71 start-page: 31 year: 2009 ident: 8015_CR12 publication-title: Colloid J. doi: 10.1134/S1061933X09010049 – ident: 8015_CR4 – volume: 54 start-page: 139 year: 1992 ident: 8015_CR9 publication-title: Kolloidn. Zh. – volume: 419 start-page: 46 year: 2013 ident: 8015_CR15 publication-title: Colloids Surf. A doi: 10.1016/j.colsurfa.2012.11.047 – volume: 43 start-page: 540 year: 1981 ident: 8015_CR2 publication-title: Kolloidn. Zh. – volume-title: Physical Chemistry year: 1961 ident: 8015_CR14 – volume: 139 start-page: 83 year: 2008 ident: 8015_CR10 publication-title: Adv. Colloid Interface Sci. doi: 10.1016/j.cis.2008.01.005 – volume: 50 start-page: 93 year: 1971 ident: 8015_CR6 publication-title: Stud. Appl. Math. doi: 10.1002/sapm197150293 – volume: 80 start-page: 189 year: 2018 ident: 8015_CR7 publication-title: Colloid J. doi: 10.1134/S1061933X18020060 – volume: 10 start-page: 366 year: 2018 ident: 8015_CR13 publication-title: Polymers doi: 10.3390/polym10040366 – volume: 85 start-page: 701 year: 2007 ident: 8015_CR11 publication-title: Can. J. Chem. Eng. doi: 10.1002/cjce.5450850517 |
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| SubjectTerms | Boundary conditions Boundary value problems Cation exchanging Charged particles Chemistry Chemistry and Materials Science Electrolytes Ion exchange Ion exchangers Kinetic coefficients Permeability Polymer Sciences Spherical shells Surfaces and Interfaces Thin Films |
| Title | A Cell Model of an Ion-Exchange Membrane. Hydrodynamic Permeability |
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