Improvement of Mathematical Model for Sedimentation Process
In this article, the fractional-order differential equation of particle sedimentation was obtained. It considers the Basset force’s fractional origin and contains the Riemann–Liouville fractional integral rewritten as a Grunwald–Letnikov derivative. As a result, the general solution of the proposed...
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MDPI AG
2021-07-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/14/15/4561 |
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| author | Ivan Pavlenko Marek Ochowiak Praveen Agarwal Radosław Olszewski Bernard Michałek Andżelika Krupińska |
| author_facet | Ivan Pavlenko Marek Ochowiak Praveen Agarwal Radosław Olszewski Bernard Michałek Andżelika Krupińska |
| author_sort | Ivan Pavlenko |
| collection | DOAJ |
| description | In this article, the fractional-order differential equation of particle sedimentation was obtained. It considers the Basset force’s fractional origin and contains the Riemann–Liouville fractional integral rewritten as a Grunwald–Letnikov derivative. As a result, the general solution of the proposed fractional-order differential equation was found analytically. The belonging of this solution to the real range of values was strictly theoretically proven. The obtained solution was validated on a particular analytical case study. In addition, it was proven numerically with the approach based on the S-approximation method using the block-pulse operational matrix. The proposed mathematical model can be applied for modeling the processes of fine particles sedimentation in liquids, aerosol deposition in gas flows, and particle deposition in gas-dispersed systems. |
| first_indexed | 2024-03-10T09:16:02Z |
| format | Article |
| id | doaj.art-8c3f6109ffa740c488b52cada7f0857f |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T09:16:02Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-8c3f6109ffa740c488b52cada7f0857f2023-11-22T05:34:42ZengMDPI AGEnergies1996-10732021-07-011415456110.3390/en14154561Improvement of Mathematical Model for Sedimentation ProcessIvan Pavlenko0Marek Ochowiak1Praveen Agarwal2Radosław Olszewski3Bernard Michałek4Andżelika Krupińska5Department of Computational Mechanics Named after V. Martsynkovskyy, Sumy State University, 2, Rymskogo-Korsakova Str., 40007 Sumy, UkraineDepartment of Chemical Engineering and Equipment, Poznan University of Technology, 5, M. Skłodowskiej-Curie Sq., 60-965 Poznan, PolandDepartment of Mathematics, Anand International College of Engineering, D-40, Shanti Path, Jawahar Nagar, Jaipur 303012, IndiaFaculty of Chemistry, Adam Mickiewicz University, 1, Wieniawskiego Str., 61-614 Poznan, PolandFaculty of Chemistry, Adam Mickiewicz University, 1, Wieniawskiego Str., 61-614 Poznan, PolandDepartment of Chemical Engineering and Equipment, Poznan University of Technology, 5, M. Skłodowskiej-Curie Sq., 60-965 Poznan, PolandIn this article, the fractional-order differential equation of particle sedimentation was obtained. It considers the Basset force’s fractional origin and contains the Riemann–Liouville fractional integral rewritten as a Grunwald–Letnikov derivative. As a result, the general solution of the proposed fractional-order differential equation was found analytically. The belonging of this solution to the real range of values was strictly theoretically proven. The obtained solution was validated on a particular analytical case study. In addition, it was proven numerically with the approach based on the S-approximation method using the block-pulse operational matrix. The proposed mathematical model can be applied for modeling the processes of fine particles sedimentation in liquids, aerosol deposition in gas flows, and particle deposition in gas-dispersed systems.https://www.mdpi.com/1996-1073/14/15/4561particle sedimentationresistance forcefractional-order integro-differential equationlaplace transformMittag–Leffler functionblock-pulse operational matrix |
| spellingShingle | Ivan Pavlenko Marek Ochowiak Praveen Agarwal Radosław Olszewski Bernard Michałek Andżelika Krupińska Improvement of Mathematical Model for Sedimentation Process Energies particle sedimentation resistance force fractional-order integro-differential equation laplace transform Mittag–Leffler function block-pulse operational matrix |
| title | Improvement of Mathematical Model for Sedimentation Process |
| title_full | Improvement of Mathematical Model for Sedimentation Process |
| title_fullStr | Improvement of Mathematical Model for Sedimentation Process |
| title_full_unstemmed | Improvement of Mathematical Model for Sedimentation Process |
| title_short | Improvement of Mathematical Model for Sedimentation Process |
| title_sort | improvement of mathematical model for sedimentation process |
| topic | particle sedimentation resistance force fractional-order integro-differential equation laplace transform Mittag–Leffler function block-pulse operational matrix |
| url | https://www.mdpi.com/1996-1073/14/15/4561 |
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