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Published August 1979 | Published
Journal Article Open

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.

Additional Information

© 1979 Cambridge University Press. Received 19 October 1978 and in revised form 22 February 1979. Published Online April 19 2006. This work was supported by a grant, ENG78-10317, from the National Science Foundation. The authors also wish to thank Professor Howard Brenner for many helpful discussions during the initial stages of this work.

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August 19, 2023
October 18, 2023