UNSTEADY MOTION OF A SPHERE IN A NEWTONIAN FLUID: I. VELOCITY BOUNDARY CONDITIONS

Abstract

Using linear operator techniques a general framework is developed in order determine the time dependent velocity and pressure fields of an incompressible Newtonian fluid in the creeping flow limit, when the velocity and/or pressure fields are specified on the boundary. For spherical boundaries detailed eigenfunction expansions are determined for several flow situations, including the motion of a spherical particle in an arbitrary, time dependent velocity field. When the sphere's motion is rectilinear and the external velocity field is uniform, the traditional solution due to Basset (1888) is recovered.

KEYWORDS:

• Newtonian fluid
• Sphere
• Particulate
• Linear operator
• Continuous spectra

Additional information

Notes on contributors

J.M. CARUTHERS

To whom correspondence should be addressed.