Stokes flow between two confocal rotating spheroids with slip

Abstract

The steady axisymmetric flow problem of a viscous fluid confined between two confocal spheroids that are rotating about their axis of revolution with different angular velocities is considered. A linear slip, of Basset type, boundary condition on both surfaces of the spheroidal particle and the container is used. Under the Stokesian assumption, a general solution is constructed from the superposition of basic solutions in prolate and oblate spheroidal coordinates. The boundary conditions on the particle’s surface and spheroidal container are satisfied by a collocation technique. The torque exerted on the spheroidal particle by the fluid is evaluated with good convergence for various values of the slip parameters, the relative angular velocity and aspect ratios of the spheroids. The limiting case of no-slip is in good agreement with the available values in the literature.