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Effect of finite boundaries on the Stokes resistance of an arbitrary particle Part 3. Translation and rotation

Published online by Cambridge University Press:  28 March 2006

R. G. Cox  and
H. Brenner
R. G. Cox
Affiliation:
Present address: Pulp and Paper Research Institute of Canada, Montreal, Canada. Department of Chemical Engineering, New York University
H. Brenner
Affiliation:
Present address: Department of Chemical Engineering, Carnegie Institute of Technology, Pittsburgh, Pennsylvania. Department of Chemical Engineering, New York University
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Abstract

A general theory is given for the effect of solid walls on a translating and rotating particle in the limiting case of zero Reynolds number. Both the force and couple on the body are found as an expansion in terms of a parameter k = a/d, assumed small, where a is a characteristic particle size and d a characteristic distance of the particle from walls. It is shown how such expansions may be used in specific examples. The theory is then extended to include the general motion of a small particle in an arbitrary Stokes flow field in which solid or other boundaries are present. Finally the motion of two small bodies of arbitrary shape in an arbitrary Stokes flow field is considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 2 , 8 May 1967 , pp. 391 - 411
Copyright
© 1967 Cambridge University Press

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