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Rods falling near a vertical wall

Published online by Cambridge University Press:  12 April 2006

W. B. Russel ,
E. J. Hinch ,
L. G. Leal  and
G. Tieffenbruck
W. B. Russel
Affiliation:
Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08540
E. J. Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
L. G. Leal
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena
G. Tieffenbruck
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena
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Abstract

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 2 , 22 November 1977 , pp. 273 - 287
Copyright
© 1977 Cambridge University Press

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References

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Leal, L. G. 1975 J. Fluid Mech. 69, 305.
Mestre, N. J. De & Russel, W. B. 1975 J. Engng Math. 9, 81.
Taylor, G. I. 1969 In Problems of Hydrodynamics and Continuum Mechanics, p. 718. SIAM Publ.
Tuck, E. O. 1964 J. Fluid Mech. 18, 619.
Youngren, G. K. & Acrivos, A. 1975 J. Fluid Mech. 69, 377.