Secondary flow of elastico-viscous fluid between two concentric spheres oscillating about a fixed diameter

Abstract

The paper investigates the secondary flow induced in an Oldroyd fluid, contained between two concentric spheres due to the rotational oscillations of the spheres about a fixed axis. The secondary motion consists of a steady velocity distribution as well as a periodic motion with twice the frequency of the primary. The steady part of this flow is studied in detail for three cases, namely (i) the outer sphere at rest and the inner oscillating, (ii) the two spheres oscillating with the same angular amplitude in the same sense and (iii) the two spheres oscillating with the same angular amplitude but in opposite senses. We notice that the secondary flow is strongly dependent on the frequency of oscillation and also on the rotational nature of the motion of the spheres.