Motion of a spheroidal particle in a micropolar fluid contained in a spherical envelope

Abstract

This paper investigates first the Stokes’ axisymmetrical translational motion of a spheroid particle, whose shape differs slightly from that of a sphere, in an unbounded micropolar fluid. A linear slip, Basset-type, boundary condition has been used. The drag acting on the spheroid is evaluated and discussed for the various parameters of the problem. Also, the terminal velocity is evaluated and tabulated for the slip, deformity, and micropolarity parameters. Secondly, the motion of a spheroidal particle at the instant it passes the centre of a spherical envelope filled with a micropolar fluid is investigated using the slip condition at the surface of the particle. The analytical expressions for the stream function and microrotation component are obtained to first order in the small parameter characterizing the deformation. As an application, we consider an oblate spheroidal particle and the drag acting on the body is evaluated. Its variation with respect to the diameter ratio, deformity, micropolarity, and slip parameters is tabulated and displayed graphically. Well-known cases are deduced, the wall effect is then examined and comparisons are attempted between the classical fluid and micropolar fluid.PACS Nos.: 47.45.Gx, 47.15.Gf, 47.50.–d