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Title | Improvement of Mathematical Model for Sedimentation Process |
Authors |
Pavlenko, Ivan Volodymyrovych
Ochowiak, M. Agarwal, P. Olszewski, R. Michałek, B. Krupińska, A. |
ORCID |
http://orcid.org/0000-0002-6136-1040 |
Keywords |
particle sedimentation resistance force fractional-order integro-differential equation laplace transform Mittag–Leffler function block-pulse operational matrix |
Type | Article |
Date of Issue | 2021 |
URI | https://essuir.sumdu.edu.ua/handle/123456789/85368 |
Publisher | MDPI |
License | Creative Commons Attribution 4.0 International License |
Citation | Pavlenko, I.; Ochowiak, M.; Agarwal, P.; Olszewski, R.; Michałek, B.; Krupi ´nska, A. Improvement of Mathematical Model for Sedimentation Process. Energies 2021, 14, 4561. https://doi.org/10.3390/en14154561 |
Abstract |
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. |
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File | Size | Format | Downloads |
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Pavlenko_et.al_Improvement_of_Mathematical_Model_2021.pdf | 609.44 kB | Adobe PDF | 114392216 |
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