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Motion of a sphere in the presence of a plane interface. Part 1. An approximate solution by generalization of the method of Lorentz

Published online by Cambridge University Press:  19 April 2006

S. H. Lee
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125
R. S. Chadwick
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125 Present address: Department of Mechanics and Structures, UCLA.
L. G. Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125

Abstract

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.

Type
Research Article
Copyright
© 1979 Cambridge University Press

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References

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Motion of a sphere in the presence of a plane interface. Part 1. An approximate solution by generalization of the method of Lorentz
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