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Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches
For a theoretical analysis of mass transfer processes in electromembrane systems, the Nernst–Planck and Poisson equations (NPP) are generally used. In the case of 1D direct-current-mode modelling, a fixed potential (for example, zero) is set on one of the boundaries of the considered region, and on...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2023
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10146742/ https://www.ncbi.nlm.nih.gov/pubmed/37103848 http://dx.doi.org/10.3390/membranes13040421 |
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author | Uzdenova, Aminat |
author_facet | Uzdenova, Aminat |
author_sort | Uzdenova, Aminat |
collection | PubMed |
description | For a theoretical analysis of mass transfer processes in electromembrane systems, the Nernst–Planck and Poisson equations (NPP) are generally used. In the case of 1D direct-current-mode modelling, a fixed potential (for example, zero) is set on one of the boundaries of the considered region, and on the other—a condition connecting the spatial derivative of the potential and the given current density. Therefore, in the approach based on the system of NPP equations, the accuracy of the solution is significantly affected by the accuracy of calculating the concentration and potential fields at this boundary. This article proposes a new approach to the description of the direct current mode in electromembrane systems, which does not require boundary conditions on the derivative of the potential. The essence of the approach is to replace the Poisson equation in the NPP system with the equation for the displacement current (NPD). Based on the system of NPD equations, the concentration profiles and the electric field were calculated in the depleted diffusion layer near the ion-exchange membrane, as well as in the cross section of the desalination channel under the direct current passage. The NPD system, as well as NPP, allows one to describe the formation of an extended space charge region near the surface of the ion-exchange membrane, which is important for describing overlimiting current modes. Comparison of the direct-current-mode modelling approaches based on NPP and NPD showed that the calculation time is less for the NPP approach, but the calculation accuracy is higher for the NPD approach. |
format | Online Article Text |
id | pubmed-10146742 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-101467422023-04-29 Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches Uzdenova, Aminat Membranes (Basel) Article For a theoretical analysis of mass transfer processes in electromembrane systems, the Nernst–Planck and Poisson equations (NPP) are generally used. In the case of 1D direct-current-mode modelling, a fixed potential (for example, zero) is set on one of the boundaries of the considered region, and on the other—a condition connecting the spatial derivative of the potential and the given current density. Therefore, in the approach based on the system of NPP equations, the accuracy of the solution is significantly affected by the accuracy of calculating the concentration and potential fields at this boundary. This article proposes a new approach to the description of the direct current mode in electromembrane systems, which does not require boundary conditions on the derivative of the potential. The essence of the approach is to replace the Poisson equation in the NPP system with the equation for the displacement current (NPD). Based on the system of NPD equations, the concentration profiles and the electric field were calculated in the depleted diffusion layer near the ion-exchange membrane, as well as in the cross section of the desalination channel under the direct current passage. The NPD system, as well as NPP, allows one to describe the formation of an extended space charge region near the surface of the ion-exchange membrane, which is important for describing overlimiting current modes. Comparison of the direct-current-mode modelling approaches based on NPP and NPD showed that the calculation time is less for the NPP approach, but the calculation accuracy is higher for the NPD approach. MDPI 2023-04-08 /pmc/articles/PMC10146742/ /pubmed/37103848 http://dx.doi.org/10.3390/membranes13040421 Text en © 2023 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Uzdenova, Aminat Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches |
title | Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches |
title_full | Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches |
title_fullStr | Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches |
title_full_unstemmed | Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches |
title_short | Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches |
title_sort | ion transport in electromembrane systems under the passage of direct current: 1d modelling approaches |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10146742/ https://www.ncbi.nlm.nih.gov/pubmed/37103848 http://dx.doi.org/10.3390/membranes13040421 |
work_keys_str_mv | AT uzdenovaaminat iontransportinelectromembranesystemsunderthepassageofdirectcurrent1dmodellingapproaches |