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Improvement of Mathematical Model for Sedimentation Process

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ivan Pavlenko & Marek Ochowiak & Praveen Agarwal & Radosław Olszewski & Bernard Michałek & Andżelika Krupińska, 2021. "Improvement of Mathematical Model for Sedimentation Process," Energies, MDPI, vol. 14(15), pages 1-12, July.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:15:p:4561-:d:603196
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    References listed on IDEAS

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    1. Liu, Lu & Xue, Dingyu & Zhang, Shuo, 2019. "Closed-loop time response analysis of irrational fractional-order systems with numerical Laplace transform technique," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 133-152.
    2. Du, Feifei & Jia, Baoguo, 2020. "Finite time stability of fractional delay difference systems: A discrete delayed Mittag-Leffler matrix function approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Lin Su & Guangxu Zhou & Dairong Hu & Yuan Liu & Yunhai Zhu, 2021. "Research on the State of Charge of Lithium-Ion Battery Based on the Fractional Order Model," Energies, MDPI, vol. 14(19), pages 1-23, October.

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