Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus
A new 3D model of 1:1 salt ion transfer in the desalting channel of an electrodialysis apparatus is presented and investigated in this paper. For the first time a three-dimensional mathematical model of salt ion transfer in the desalting channel taking into account the electroconvection based on the...
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| Format: | Article |
| Language: | Belarusian |
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Belarusian State University
2022-08-01
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| Series: | Журнал Белорусского государственного университета: Математика, информатика |
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| Online Access: | https://journals.bsu.by/index.php/mathematics/article/view/4535 |
| _version_ | 1811183085504430080 |
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| author | Anna V. Kovalenko Anna V. Ovsyannikova |
| author_facet | Anna V. Kovalenko Anna V. Ovsyannikova |
| author_sort | Anna V. Kovalenko |
| collection | DOAJ |
| description | A new 3D model of 1:1 salt ion transfer in the desalting channel of an electrodialysis apparatus is presented and investigated in this paper. For the first time a three-dimensional mathematical model of salt ion transfer in the desalting channel taking into account the electroconvection based on the system of Nernst – Planck, Poisson and Navier – Stokes equations with the electric force and the natural boundary conditions is proposed. To solve the boundary value problem, the finite element method is used in the cross-platform numerical analysis software COMSOL Multiphysics in combination with the method of successive approximations, when the electrochemical and hydrodynamic parts of the problem are solved one by one on the current layer. In turn, the electrochemical and hydrodynamic parts of the problem are solved by Newton’s method. As a result of numerical analysis, the fundamental regularities of salt ion transfer in a three-dimensional channel, the emergence and development of electroconvective vortices, including the discovery of new three-dimensional spiral forms of salt ions, are established for the first time. It is shown that electroconvective vortices exist in the form of clusters, within which vortex bifurcations can occur. Thus, the currently existing simplified view of the structure of electroconvective vortices is clarified and developed. |
| first_indexed | 2024-04-11T09:42:05Z |
| format | Article |
| id | doaj.art-66c9d07e8fc44c169db02440cbf46fe1 |
| institution | Directory Open Access Journal |
| issn | 2520-6508 2617-3956 |
| language | Belarusian |
| last_indexed | 2024-04-11T09:42:05Z |
| publishDate | 2022-08-01 |
| publisher | Belarusian State University |
| record_format | Article |
| series | Журнал Белорусского государственного университета: Математика, информатика |
| spelling | doaj.art-66c9d07e8fc44c169db02440cbf46fe12022-12-22T04:31:11ZbelBelarusian State UniversityЖурнал Белорусского государственного университета: Математика, информатика2520-65082617-39562022-08-012708110.33581/2520-6508-2022-2-70-814535Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatusAnna V. Kovalenko0Anna V. Ovsyannikova1Kuban State University, 149 Stavropol’skaya Street, Krasnodar 350040, RussiaFinancial University under the Government of the Russian Federation, 49/2 Leningradskii Avenue, Moscow 125167, RussiaA new 3D model of 1:1 salt ion transfer in the desalting channel of an electrodialysis apparatus is presented and investigated in this paper. For the first time a three-dimensional mathematical model of salt ion transfer in the desalting channel taking into account the electroconvection based on the system of Nernst – Planck, Poisson and Navier – Stokes equations with the electric force and the natural boundary conditions is proposed. To solve the boundary value problem, the finite element method is used in the cross-platform numerical analysis software COMSOL Multiphysics in combination with the method of successive approximations, when the electrochemical and hydrodynamic parts of the problem are solved one by one on the current layer. In turn, the electrochemical and hydrodynamic parts of the problem are solved by Newton’s method. As a result of numerical analysis, the fundamental regularities of salt ion transfer in a three-dimensional channel, the emergence and development of electroconvective vortices, including the discovery of new three-dimensional spiral forms of salt ions, are established for the first time. It is shown that electroconvective vortices exist in the form of clusters, within which vortex bifurcations can occur. Thus, the currently existing simplified view of the structure of electroconvective vortices is clarified and developed.https://journals.bsu.by/index.php/mathematics/article/view/45353d mathematical model of transport3d modelthree-dimensional modelmembrane systemsion exchange membranemathematical modellingelectroconvective vorticesdirect numerical simulation |
| spellingShingle | Anna V. Kovalenko Anna V. Ovsyannikova Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus Журнал Белорусского государственного университета: Математика, информатика 3d mathematical model of transport 3d model three-dimensional model membrane systems ion exchange membrane mathematical modelling electroconvective vortices direct numerical simulation |
| title | Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus |
| title_full | Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus |
| title_fullStr | Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus |
| title_full_unstemmed | Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus |
| title_short | Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus |
| title_sort | mathematical modelling of salt ion transfer in the three dimensional desalting channel of an electrodialysis apparatus |
| topic | 3d mathematical model of transport 3d model three-dimensional model membrane systems ion exchange membrane mathematical modelling electroconvective vortices direct numerical simulation |
| url | https://journals.bsu.by/index.php/mathematics/article/view/4535 |
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