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A note on Stokes flow due to a line rotlet

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, Canada.
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Summary

The results developed by Watson [1] are interpreted to indicate how the slow viscous flow due to the rotation of a small circular cylinder in the presence of a stationary cylinder can be calculated. It is shown how the stream function is given as a combination of the force-free representations corresponding to a line rotlet and a line stokeslet outside the stationary body, plus the streaming flow past the body. The coefficients which multiply these representations are calculated by techniques already described by Watson.

MSC classification

Secondary: 76D07: Stokes and related (Oseen, etc.) flows
Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995 , pp. 127 - 132
Copyright
Copyright © University College London 1995

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References

1.Watson, E. J.. The rotation of two circular cylinders in a viscous fluid. Mathematika, 42 (1995), 105–126.CrossRefGoogle Scholar
2.Jeffery, G. B.. The rotation of two circular cylinders in a viscous fluid. Proc. Roy. Soc. (A), 101 (1922), 169–174.Google Scholar
3.Smith, S. H.. The rotation of two circular cylinders in a viscous fluid. Mathematika, 38 (1991), 63–66.CrossRefGoogle Scholar
4.Dorrepaal, J. M., O'Neill, M. E. and Ranger, K. B.. Two-dimensional Stokes flows with cylinders and line singularities. Mathematika, 31 (1984), 65–75.CrossRefGoogle Scholar
5.Shail, R. and Onslow, S. H.. Some Stokes flows exterior to a spherical boundary. Mathematika, 35 (1988), 233–246.CrossRefGoogle Scholar
6.Smith, S. H.. The Jeffery paradox as the limit of a three-dimensional Stokes flow. Phys. Fluids A, 2 (1990), 661–665.CrossRefGoogle Scholar
7.Ranger, K. B.. The Stokes flow round a smooth body with an attached vortex. J. Eng. Math., 11 (1977), 81–88.CrossRefGoogle Scholar