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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.
Appears in Collections: Наукові видання (ТеСЕТ)

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