An analytical study of the transient motion of a dense rigid sphere in an incompressible Newtonian fluid

Abstract

A theoretical study of the transient sphere motion (under the influence of gravity) through an incompressible Newtonian fluid subject to an Oseen-type drag relationship has been carried out. Exact closed form expressions for the instantaneous position, velocity and acceleration of the sphere are presented. An analytical expression developed herein also enables the delineation of the "best" sphere-fluid combination for the experimental observations of transient effects and these provide useful guidelines for designing laboratory experiments. However, this study is restricted to dense spheres falling in light liquids when the additional effects arising from the added mass and the Basset forces are negligible. Also, the boundary effects are altogether neglected.