{"title":"Transference Numbers of Counterions in the Cell Model of a Charged Membrane","authors":"A. N. Filippov","doi":"10.1134/S2517751623050037","DOIUrl":null,"url":null,"abstract":"<p>The paper suggests exact formulae for calculating the electromigration, diffusion, and convective transference numbers of counterions in the cell model of a charged membrane depending on the physicochemical parameters and equilibrium concentration of the electrolyte. The cell model was previously developed to calculate all the kinetic coefficients of the Onsager matrix, and the asymmetry of the cross coefficients was established. A limiting case of an ideally selective membrane is studied in detail, for which approximate formulae for transference numbers are obtained. The obtained dependences are illustrated by graphs by way of example of an MK-40 cation-exchange membrane after conditioning at room temperature. The proposed calculation procedure for transference numbers is applicable to any single-layer membranes in solutions of a binary electrolyte.</p>","PeriodicalId":700,"journal":{"name":"Membranes and Membrane Technologies","volume":"5 5","pages":"344 - 351"},"PeriodicalIF":2.0000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Membranes and Membrane Technologies","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S2517751623050037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The paper suggests exact formulae for calculating the electromigration, diffusion, and convective transference numbers of counterions in the cell model of a charged membrane depending on the physicochemical parameters and equilibrium concentration of the electrolyte. The cell model was previously developed to calculate all the kinetic coefficients of the Onsager matrix, and the asymmetry of the cross coefficients was established. A limiting case of an ideally selective membrane is studied in detail, for which approximate formulae for transference numbers are obtained. The obtained dependences are illustrated by graphs by way of example of an MK-40 cation-exchange membrane after conditioning at room temperature. The proposed calculation procedure for transference numbers is applicable to any single-layer membranes in solutions of a binary electrolyte.
期刊介绍：
The journal Membranes and Membrane Technologies publishes original research articles and reviews devoted to scientific research and technological advancements in the field of membranes and membrane technologies, including the following main topics:novel membrane materials and creation of highly efficient polymeric and inorganic membranes;hybrid membranes, nanocomposites, and nanostructured membranes;aqueous and nonaqueous filtration processes (micro-, ultra-, and nanofiltration; reverse osmosis);gas separation;electromembrane processes and fuel cells;membrane pervaporation and membrane distillation;membrane catalysis and membrane reactors;water desalination and wastewater treatment;hybrid membrane processes;membrane sensors;membrane extraction and membrane emulsification;mathematical simulation of porous structures and membrane separation processes;membrane characterization;membrane technologies in industry (energy, mineral extraction, pharmaceutics and medicine, chemistry and petroleum chemistry, food industry, and others);membranes and protection of environment (“green chemistry”).The journal has been published in Russian already for several years, English translations of the content used to be integrated in the journal Petroleum Chemistry. This journal is a split off with additional topics.
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