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
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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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doaj-8c3f6109ffa740c488b52cada7f0857f2021-08-06T15:21:56ZengMDPI AGEnergies1996-10732021-07-01144561456110.3390/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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ivan Pavlenko Marek Ochowiak Praveen Agarwal Radosław Olszewski Bernard Michałek Andżelika Krupińska |
| 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 |
| author_facet |
Ivan Pavlenko Marek Ochowiak Praveen Agarwal Radosław Olszewski Bernard Michałek Andżelika Krupińska |
| author_sort |
Ivan Pavlenko |
| title |
Improvement of Mathematical Model for Sedimentation Process |
| title_short |
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_sort |
improvement of mathematical model for sedimentation process |
| publisher |
MDPI AG |
| series |
Energies |
| issn |
1996-1073 |
| publishDate |
2021-07-01 |
| 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. |
| 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 |
| work_keys_str_mv |
AT ivanpavlenko improvementofmathematicalmodelforsedimentationprocess AT marekochowiak improvementofmathematicalmodelforsedimentationprocess AT praveenagarwal improvementofmathematicalmodelforsedimentationprocess AT radosławolszewski improvementofmathematicalmodelforsedimentationprocess AT bernardmichałek improvementofmathematicalmodelforsedimentationprocess AT andzelikakrupinska improvementofmathematicalmodelforsedimentationprocess |
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1721218611114147840 |