AN ANALYTICAL STUDY OF THE TRANSIENT MOTION OF A DENSE RIGID SPHERE IN AN INCOMPRESSIBLE NEWTONIAN FLUID

A theoretical study of the transient sphere motion (under the influenc e of gravity) through an incompressible Newtonian fluid subject to an Oseen-type drag relationship has been carried out. Exact closed form e xpressions for the instantaneous position, velocity and acceleration o f 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 provi de useful guidelines for designing laboratory experiments. However, th is study is restricted to dense spheres falling in light liquids when the additional effects arising from the added mass and the Basset forc es are negligible. Also, the boundary effects are altogether neglected .