Improvement of Mathematical Model for Sedimentation Process

被引：7

作者：

Pavlenko, Ivan ^{[1
]}

Ochowiak, Marek ^{[2
]}

Agarwal, Praveen ^{[3
]}

Olszewski, Radoslaw ^{[4
]}

Michalek, Bernard ^{[4
]}

Krupinska, Andzelika ^{[2
]}

机构：

[1] Sumy State Univ, Dept Computat Mech, 2 Rymskogo Korsakova Str, UA-40007 Sumy, Ukraine

[2] Poznan Univ Tech, Dept Chem Engn & Equipment, 5 M Sklodowskiej Curie Sq, PL-60965 Poznan, Poland

[3] Anand Int Coll Engn, Dept Math, D-40, Jaipur 303012, Rajasthan, India

[4] Adam Mickiewicz Univ, Fac Chem, 1 Wieniawskiego Str, PL-61614 Poznan, Poland

来源：

ENERGIES | 2021年 / 14卷 / 15期

关键词：

particle sedimentation; resistance force; fractional-order integro-differential equation; laplace transform; Mittag-Leffler function; block-pulse operational matrix; RESPONSE ANALYSIS; BASSET FORCE; PARTICLE; MOTION; SYSTEM; FLUID;

D O I：

10.3390/en14154561

中图分类号：

TE [石油、天然气工业]; TK [能源与动力工程];

学科分类号：

0807 ; 0820 ;

摘要：

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.

引用

页数：12

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