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A note on the Jeffery paradox

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

S. H. Smith
S. H. Smith
Affiliation:
Department of Mathematics, University of Toronto, Toronto M5S 1A1, Ontario, Canada.
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Abstract

When a weak rotlet and a circular cylinder rotate together in a viscous fluid at low Reynolds number R, the Stokes' flow solution indicates a uniform stream as the radial distance r tends to infinity. It is shown here, when R is distinctly non-zero, that the flow is modified to form a spiral motion in the domain where R In r = O(l), but is not damped until the more distant domain R2 In r = O(l).

MSC classification

Secondary: 76D05: Navier-Stokes equations
Type
Research Article
Information
Mathematika , Volume 34 , Issue 2 , December 1987 , pp. 178 - 186
Copyright
Copyright © University College London 1987

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References

1.Jeffery, G. B.. The rotation of two circular cylinders in a viscous fluid. Proc. Roy. Soc. A, 101 (1922), 169.Google Scholar
2.Dorrepaal, J. M.O'Neill, M. E. and Ranger, K. B.. Two-dimensional Stokes flows with cylinders and line singularities. Mathematika, 31 (1984), 65.CrossRefGoogle Scholar
3.Proudman, I. and Pearson, J. R. A.. Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech., 2 (1957), 237.CrossRefGoogle Scholar