Secondary flow in an elastico-viscous fluid caused by rotational oscillations of a sphere. Part 1

Abstract

When the angular amplitude of oscillation of a sphere in an infinite mass of elastico-viscous fluid is fairly small, so that velocity and stress components may be expanded as power series in this amplitude, the purely periodic primary motion has associated with it a secondary flow which has a steady component as well as a component of double the primary frequency. An expression for the stream function of the steady secondary flow is obtained for all possible frequencies and the results are illustrated by considering in detail a particular fluid. It is shown that the streamline projections on a plane containing the axis of rotation are strongly dependent on the parameters measuring the elasticity of the fluid and on the frequency. The circulatory secondary flow can be in the opposite sense to that in a Newtonian fluid, in either the whole or part of the elastico-viscous fluid.