Mathematical modeling of the effect of spacers on mass transfer in electromembrane systems
The transfer of ions near ion-exchange membranes causes concentration polarization, which significantly complicates mass transfer in electromembrane systems. Spacers are used to neutralize the effect of concentration polarization and increase mass transfer. Spacers reduce the thickness of the bounda...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2022-09-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/109482/pdf_1 |
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| author | Anna V. Kovalenko Aminat M. Uzdenova Anna Ovsyannikova Makhamet Kh. Urtenov Ramazan A. Bostanov |
| author_facet | Anna V. Kovalenko Aminat M. Uzdenova Anna Ovsyannikova Makhamet Kh. Urtenov Ramazan A. Bostanov |
| author_sort | Anna V. Kovalenko |
| collection | DOAJ |
| description | The transfer of ions near ion-exchange membranes causes concentration polarization, which significantly complicates mass transfer in electromembrane systems. Spacers are used to neutralize the effect of concentration polarization and increase mass transfer. Spacers reduce the thickness of the boundary layer by increasing the mixing depth of the solution and creating a normal component of convective transport; ions can reach membranes faster, and the current increases, from a hydrodynamic point of view. However, spacers significantly increase the hydrodynamic resistance and consequently the cost of pumping the solution.
For the first time, the main regularities of the transfer of salt ions in the desalination channel of an electrodialysis apparatus with spacers of various shapes and arrangements are determined, taking into account electroconvection, in overlimiting current modes. Namely, it is shown, using the current-voltage characteristic, that spacers of different shapes and locations are optimal at different stages of the desalination process.
The paper presents the results of mathematical and simulation modeling of the salt ion transport process in electromembrane systems with spacers in overlimiting current modes. 2D direct numerical simulation was carried out for the coupled system of the NernstPlanckPoisson and NavierStokes equations without fitting parameters. The finite element method was used in combination with the method of successive approximations and segregation to solve boundary value problems for systems of nonlinear differential equations with partial derivatives. The novelty of the method lies in the fact that after discretization in time, the problem on each time layer is split into hydrodynamic and electrochemical problems, each of which is solved by the method of successive approximations until a complete mutual agreement. |
| first_indexed | 2024-04-10T16:03:20Z |
| format | Article |
| id | doaj.art-1fe4f3fea5644dc4a4e0944137121a8d |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-10T16:03:20Z |
| publishDate | 2022-09-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-1fe4f3fea5644dc4a4e0944137121a8d2023-02-10T08:13:30ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812022-09-0126352054310.14498/vsgtu194477841Mathematical modeling of the effect of spacers on mass transfer in electromembrane systemsAnna V. Kovalenko0https://orcid.org/0000-0002-3991-3953Aminat M. Uzdenova1https://orcid.org/0000-0001-5951-9876Anna Ovsyannikova2https://orcid.org/0000-0002-1716-3100Makhamet Kh. Urtenov3https://orcid.org/0000-0002-0252-6247Ramazan A. Bostanov4https://orcid.org/0000-0002-8502-7653Kuban State UniversityUmar Aliev Karachay–Cherkess State UniversityFinancial University under the Government of the Russian FederationKuban State UniversityUmar Aliev Karachay–Cherkess State UniversityThe transfer of ions near ion-exchange membranes causes concentration polarization, which significantly complicates mass transfer in electromembrane systems. Spacers are used to neutralize the effect of concentration polarization and increase mass transfer. Spacers reduce the thickness of the boundary layer by increasing the mixing depth of the solution and creating a normal component of convective transport; ions can reach membranes faster, and the current increases, from a hydrodynamic point of view. However, spacers significantly increase the hydrodynamic resistance and consequently the cost of pumping the solution. For the first time, the main regularities of the transfer of salt ions in the desalination channel of an electrodialysis apparatus with spacers of various shapes and arrangements are determined, taking into account electroconvection, in overlimiting current modes. Namely, it is shown, using the current-voltage characteristic, that spacers of different shapes and locations are optimal at different stages of the desalination process. The paper presents the results of mathematical and simulation modeling of the salt ion transport process in electromembrane systems with spacers in overlimiting current modes. 2D direct numerical simulation was carried out for the coupled system of the NernstPlanckPoisson and NavierStokes equations without fitting parameters. The finite element method was used in combination with the method of successive approximations and segregation to solve boundary value problems for systems of nonlinear differential equations with partial derivatives. The novelty of the method lies in the fact that after discretization in time, the problem on each time layer is split into hydrodynamic and electrochemical problems, each of which is solved by the method of successive approximations until a complete mutual agreement.https://journals.eco-vector.com/1991-8615/article/viewFile/109482/pdf_1electromembrane systemspacersmass transferion transfermathematical model |
| spellingShingle | Anna V. Kovalenko Aminat M. Uzdenova Anna Ovsyannikova Makhamet Kh. Urtenov Ramazan A. Bostanov Mathematical modeling of the effect of spacers on mass transfer in electromembrane systems Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki electromembrane system spacers mass transfer ion transfer mathematical model |
| title | Mathematical modeling of the effect of spacers on mass transfer in electromembrane systems |
| title_full | Mathematical modeling of the effect of spacers on mass transfer in electromembrane systems |
| title_fullStr | Mathematical modeling of the effect of spacers on mass transfer in electromembrane systems |
| title_full_unstemmed | Mathematical modeling of the effect of spacers on mass transfer in electromembrane systems |
| title_short | Mathematical modeling of the effect of spacers on mass transfer in electromembrane systems |
| title_sort | mathematical modeling of the effect of spacers on mass transfer in electromembrane systems |
| topic | electromembrane system spacers mass transfer ion transfer mathematical model |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/109482/pdf_1 |
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