Wall effects of an eccentric fluid sphere: Happel's and Kuwabara's models

Abstract In the limit of very low Reynolds numbers, the steady translation of a fluid sphere situated at a non‐concentric position in a second immiscible fluid bounded by spherical cavity is investigated using boundary collocation technique. The flow inside and outside the fluid sphere is governed by Stokes equations. Boundary conditions at the fluid sphere are continuity of velocity and shear stress. Zero shear stress and zero vorticity are used on spherical cavity. By using superposition principle, a general solution is constructed from the basic solutions in the two spherical coordinate systems based on both the fluid sphere and spherical cavity. The normalized drag force exerted on the fluid sphere contained in a cavity is depended on the ratio of fluid sphere and cavity radii, viscosity ratio of fluid sphere and cavity, relative distance between the centers of fluid sphere and cavity. The results are in good agreement with previously published work in the limiting cases. The numerical results of the drag force are good agreement with the solutions of the translation of the fluid sphere in a concentric cavity and the translation of a solid sphere in a non‐concentric cavity. The drag force is increasing function of the viscosity ratio, volume fraction, and the relative distance. This work is extension of the previous work of Keh and Lee for the fluid sphere using Happel's and Kuwabara's models.