On the gravitational fall of a non-spherical particle in a quiescent fluid medium

Abstract

Closed-form analytical solutions have been derived for the gravitational fall of a non-spherical particle in a quiescent fluid. The Boussinesq-Basset-Oseen equation accounting for history force and particle slip effects was applied to derive the particle motion equation, using a sphericity-dependent drag law for transitional flow in the range 0.001<Re≤100000 and valid for sphericities >0.50. The derived closed-form solutions were validated with published experimental data and the accuracy was verified using published approximate analytical solutions and numerical results. The closed-form solutions were found to agree with experiments and produced more accurate results than other published approximate analytical solutions. Also, the effects of sphericity, Basset force and particle slip on the particle motion were investigated and discussed. The present analytical solutions are applicable to zero and non-zero initial velocity, steady and unsteady motion, and the corresponding displacements and accelerations. Additionally, new settling velocity formula valid for non-spherical particles was derived.