Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T18:37:27.913Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramovitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.Google Scholar
Bourot, J. M. 1975 Comptes Rendus Acad. Sci. Paris, A 281, 178–182.Google Scholar
Bucewald, V. T. 1964 Proc. Roy. Soc. A 277, 385–400.Google Scholar
Cooley, M. D. A. & O'neill, M. E. 1969 Proc. Camb. Phil. Soc. 66, 407–415.Google Scholar
Dean, W. R. & Montagnon, P. E. 1949 Proc. Camb. Phil. Soc., 45, 389–394.Google Scholar
Dorrepaal, J. M., Majumdar, S. R., O'neill, M. E. & Ranger, K. B. 1976a Quart. J. Mech. Appl. Math. (in press)Google Scholar
Dorrepaal, J. M., O'neill, M. E. & Ranger, K. B. 1976b J. Fluid Mech. 75, 273–286.Google Scholar
Finn, R. & Noll, W. 1957 Arch. Rat. Mech. Anal. 1, 97–106.Google Scholar
Gradseteyn, I. S. & Ryzkie, I. M. 1965 Tables of Integrals, Series and Prodmts. Academic.Google Scholar
Jeffery, G. B. 1922 Proc. Roy. Soc. A 101, 169–174.Google Scholar
Moffatt, H. K. 1964 J. Fluid Mech. 18, 1–18.Google Scholar
Sceubert, G. 1967 J. Fluid Mech. 27, 647–656.Google Scholar
Stimson, M. & Jeffery, G. B. 1926 Proc. Roy. Soc. A 111, 110.Google Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Stanford: Parabolic Press.Google Scholar
Wakna, S. 1975 J. Phys. Soc. Japan, 39, 1113.Google Scholar
Wannier, G. H. 1950 Quart. Appl. Math. 8, 7–22.Google Scholar