Improvement of Mathematical Model for Sedimentation Process

Ivan Pavlenko, Marek Ochowiak, Praveen Agarwal, Radosław Olszewski, Bernard Michałek and Andżelika Krupińska
Additional contact information
Ivan Pavlenko: Department of Computational Mechanics Named after V. Martsynkovskyy, Sumy State University, 2, Rymskogo-Korsakova Str., 40007 Sumy, Ukraine
Marek Ochowiak: Department of Chemical Engineering and Equipment, Poznan University of Technology, 5, M. Skłodowskiej-Curie Sq., 60-965 Poznan, Poland
Praveen Agarwal: Department of Mathematics, Anand International College of Engineering, D-40, Shanti Path, Jawahar Nagar, Jaipur 303012, India
Radosław Olszewski: Faculty of Chemistry, Adam Mickiewicz University, 1, Wieniawskiego Str., 61-614 Poznan, Poland
Bernard Michałek: Faculty of Chemistry, Adam Mickiewicz University, 1, Wieniawskiego Str., 61-614 Poznan, Poland
Andżelika Krupińska: Department of Chemical Engineering and Equipment, Poznan University of Technology, 5, M. Skłodowskiej-Curie Sq., 60-965 Poznan, Poland

Energies, 2021, vol. 14, issue 15, 1-12

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.

Keywords: particle sedimentation; resistance force; fractional-order integro-differential equation; laplace transform; Mittag–Leffler function; block-pulse operational matrix (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/1996-1073/14/15/4561/pdf (application/pdf)
https://www.mdpi.com/1996-1073/14/15/4561/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:14:y:2021:i:15:p:4561-:d:603196

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().