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The motion of a small sphere in fluid near a circular hole in a plane wall

Published online by Cambridge University Press:  20 April 2006

Takeshi Miyazaki  and
Hidenori Hasimoto
Takeshi Miyazaki
Affiliation:
Division of Atmospheric Environment, The National Institute for Environmental Studies, Tsukuba, Ibaraki, Japan
Hidenori Hasimoto
Affiliation:
Department of Physics, University of Tokyo, Japan
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Abstract

The Stokes flow due to the motion of a small particle in arbitrary directions is investigated in the presence of a circular hole in an infinite thin plane wall separating a quiescent viscous fluid.

The solutions of the boundary-value problem are obtained in closed forms to the point-force approximation in toroidal coordinates, by the use of the Green and Neumann functions supplemented by the edge function to remove the singularity at the rim of the hole. The volume flux through the hole and the force and torque experienced by the small spherical particle are determined on the basis of this solution. The case of linear motion parallel to the plane of the wall is discussed in detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 201 - 221
Copyright
© 1984 Cambridge University Press

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