Boundary effects of slow flow past a fluid coated sphere

The problem of steady translation of a fluid coated sphere (solid sphere covered with a fluid coating) situated at an eccentric position in a second immiscible fluid bounded by a spherical cell is investigated using a boundary collocation technique. The fluid inside the coating and outside the fluid coated sphere are governed by Stokes equations. The inertia effect is negligible for flows both inside the coating and within the virtual cell. At the solid–fluid interface, no-slip boundary condition is employed. On the fluid–fluid interface, continuity of velocity and shear stress are employed. Zero shear stress and zero vorticity are used on virtual cell. By using superposition principle, a general solution is constructed from the basic solutions in the two spherical coordinate systems based on both the fluid coated sphere and spherical cavity. Numerical solutions of the normalized drag force exerted on the fluid coated sphere in the presence of the cell are obtained for different cases on the ratio of fluid coated sphere and cell radii, viscosity ratio of fluid coated sphere and cavity, relative distance between the centers of fluid coated sphere and cavity, separation parameter between the solid sphere and fluid coated sphere. 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 coated sphere in a concentric cavity. The drag force is an increasing function of the viscosity ratio, the separation parameter, and the relative distance.