Motion of a sphere in the presence of a plane interface. Part 1. An approximate solution by generalization of the method of Lorentz
The motion of a sphere in the presence of a fluid-fluid interface is studied. First, a solution is derived for a point force near a plane interface. Then the solution is extended to include the higher-order terms which are required to describe the motion of a solid sphere. Singularities of higher orders at the centre of the sphere are obtained by using the method of reflexions. For a fluid–fluid interface with an arbitrary viscosity ratio, the drag force and the hydrodynamic torque are calculated for the special cases of motion of a sphere perpendicular and parallel to the interface. In addition, the rotational motion of a sphere is also investigated.(Published Online April 19 2006)
(Received October 19 1978)
(Revised February 22 1979)
p1 Present address: Department of Mechanics and Structures, UCLA.