Slow Steady Rotation of an Approximate Sphere in an Approximate Spherical Container with Slip Surfaces

Abstract

The slow steady rotation of an approximate sphere (whose shape deviates slightly from that of a sphere) in a concentric approximate spherical container is studied analytically. The slip boundary condition is applied at the particle and container surfaces. An exact solution is obtained to the first order in the small parameter characterizing the deformation. The hydrodynamic couple and coupling coefficient exerted on the particle in presence of the cavity is calculated. As an application, the case of flow past spheroid in a spheroidal container is considered and the couple experienced by spheroid is evaluated. In the limiting cases, the hydrodynamic couple acting on the sphere in an unbounded medium is obtained in case of no slip condition. It is noticed that under the Stokesian assumption, the deformation in the body has significant influence on the couple experienced.