Oscillatory flow of a micropolar fluid generated by the rotary oscillations of two concentric spheres

Abstract

In this paper we examine the flow of an incompressible micropolar fluid between two concentric spheres, generated by their rotary oscillations about a common diameter. The spheres are assumed to be oscillating with the same amplitude but with different angular speeds. The speeds of oscillation are assumed to be small so that the nonlinear terms in the equations of motion can be neglected under the usual Stokesian assumption. The analytical expressions for velocity and microrotation components are determined in terms of modified Bessel functions of first and second kind. The couples experienced by the inner and outer spheres are calculated and are expressed in terms of two real parameters K and K ′ whose variation is studied numerically. The variations of K and K ′ with respect to micropolarity parameter and frequency parameter are displayed graphically.