Stokes flow between eccentric rotating spheres with slip regime

Abstract

The steady axisymmetric flow problem of a viscous fluid contained between two eccentric spheres that rotate about an axis joining their centers with different angular velocities is considered. A linear slip of Basset-type boundary condition at both surfaces of the spherical particle and the container is used. Under the Stokesian assumption, a general solution is constructed from the superposition of basic solutions in the spherical coordinate systems based on the inner solid particle and the spherical container. The boundary conditions on the particle’s surface and spherical container are satisfied by a collocation technique. Numerical results for the coupling coefficient acting on the particle are obtained with good convergence for various values of the ratio of particle-to-container radii, the relative distance between the centers of the particle and container, the slip coefficients and the relative angular velocity. In the limiting cases, the numerical values of the coupling coefficient for the solid sphere in concentric position with the container and when the particle is near the inner surface of the container are obtained, and the results are in good agreement with the available values in the literature. The variation of the coupling coefficient with respect the parameters considered are tabulated and displayed graphically.