Improvement of Mathematical Model for Sedimentation Process

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.

Automated summary

This article obtained the fractional-order differential equation of particle sedimentation, which considers the fractional origin of the Basset force and includes the Riemann-Liouville fractional integral rewritten as a Grunwald-Letnikov derivative. The general solution of the proposed equation was found analytically and validated theoretically and numerically, showing its applicability in modeling various sedimentation processes.