Journal of Fluid Mechanics

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

S. H.  Lee a1, R. S.  Chadwick a1p1 and L. G.  Leal a1
a1 Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125

Article author query
lee sh   [Google Scholar] 
chadwick rs   [Google Scholar] 
leal lg   [Google Scholar] 


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.