{"title":"Modeling of Ion Transport in a Three-Layer System with an Ion-Exchange Membrane Based on the Nernst–Planck and Displacement Current Equations","authors":"A. M. Uzdenova","doi":"10.1134/s2517751624010074","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Modeling of ion transport in a three-layer system containing an ion-exchange membrane and two adjacent diffusion layers makes it possible to describe the permselectivity of the membrane by determining its fixed charge density. For theoretical analysis of ion transport in such systems, the Nernst–Planck and Poisson equations are widely used. The article shows that, in the galvanodynamic mode of operation of the membrane system when the density of the flowing current is specified, the Poisson equation in the ion transport model can be replaced by the equation for the displacement current. A new model is constructed in the form of a boundary value problem for the system of the Nernst–Planck and displacement current equations, based on which the concentrations of ions, electric field strength, space charge density, and chronopotentiogram of the ion-exchange membrane and adjacent diffusion layers in a direct current mode are numerically calculated. The calculation results of the proposed model are in a good agreement with the results of the modeling based on the previously described approach using the Nernst–Planck and Poisson equations as well as with the analytical assessment of the transition time. It is shown that, in the case of the three-layer geometry of the problem, the required accuracy of the numerical calculation using the proposed model is achieved with a smaller number of computational mesh elements and takes less (about 26.7-fold for the system parameters under consideration) processor time in comparison with the model based on the Nernst–Planck and Poisson equations.</p>","PeriodicalId":700,"journal":{"name":"Membranes and Membrane Technologies","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-05-09","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://doi.org/10.1134/s2517751624010074","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
Modeling of ion transport in a three-layer system containing an ion-exchange membrane and two adjacent diffusion layers makes it possible to describe the permselectivity of the membrane by determining its fixed charge density. For theoretical analysis of ion transport in such systems, the Nernst–Planck and Poisson equations are widely used. The article shows that, in the galvanodynamic mode of operation of the membrane system when the density of the flowing current is specified, the Poisson equation in the ion transport model can be replaced by the equation for the displacement current. A new model is constructed in the form of a boundary value problem for the system of the Nernst–Planck and displacement current equations, based on which the concentrations of ions, electric field strength, space charge density, and chronopotentiogram of the ion-exchange membrane and adjacent diffusion layers in a direct current mode are numerically calculated. The calculation results of the proposed model are in a good agreement with the results of the modeling based on the previously described approach using the Nernst–Planck and Poisson equations as well as with the analytical assessment of the transition time. It is shown that, in the case of the three-layer geometry of the problem, the required accuracy of the numerical calculation using the proposed model is achieved with a smaller number of computational mesh elements and takes less (about 26.7-fold for the system parameters under consideration) processor time in comparison with the model based on the Nernst–Planck and Poisson equations.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
