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Separation from the surface of two equal spheres in Stokes flow

Published online by Cambridge University Press:  11 April 2006

A. M. J. Davis ,
M. E. O'Neill ,
J. M. Dorrepaal  and
K. B. Ranger
A. M. J. Davis
Affiliation:
Department of Mathematics, University College London, Cower Street, London WC1E 6BT, England
M. E. O'Neill
Affiliation:
Department of Mathematics, University College London, Cower Street, London WC1E 6BT, England
J. M. Dorrepaal
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1W5 Present address: Department of Mathematical and Computing Science, Old Dominion University, Norfolk, Virgina, 23508, U.S.A.
K. B. Ranger
Affiliation:
Department of Mathematics, University of Toronto, Toronto. Canada. M5S 1Al
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Abstract

In this paper, it is shown that if two spheres of equal radii are placed axisymmetrically in a steady Stokes stream, separation of the flow from the spheres occurs if the distance between their centres is less than approximately 3-67 times the sphere radius. For spheres whose spacing is less than this value, wakes form on both spheres and the fluid within the wakes moves in closed eddy type motion. When the distance between the centres of the spheres is less than approximately 3.22 times the sphere radius, a cylinder of fluid links both spheres, and within this cylinder the fluid rotates in one or more ring vortices, the number of vortices increasing as the distance between the spheres is decreased. When the spheres are in contact, the fluid rotates in an infinite set of nested ring vortices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 77 , Issue 4 , 22 October 1976 , pp. 625 - 644
Copyright
© 1976 Cambridge University Press

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