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Note on a sphere theorem for the axisymmetric stokes flow of a viscous fluid

Published online by Cambridge University Press:  26 February 2010

W. D. Collins
W. D. Collins
Affiliation:
King' College, Newcastle upon Tyne.
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Extract

An expression for the Stokes's stream-function for a slow steady axisymmetrical motion of viscous fluid due to a hydrodynamical distribution in the presence of a sphere has been given by the author [1] in terms of the stream-function for the motion due to the same distribution in unbounded fluid, this latter motion being assumed irrotational. The author has since been able to obtain a more general expression for the stream-function by not assuming the motion in unbounded fluid to be irrotational, this result being given in his Ph.D. dissertation [2]. Hasimoto [3] has since given these results, the second in a different form from that of the author. Since the general expression derived by the author is considerably simpler than that found by Hasimoto, it is given in this note. A corresponding result for the motion in a region bounded by a plane is also given.

Type
Research Article
Information
Mathematika , Volume 5 , Issue 2 , December 1958 , pp. 118 - 121
Copyright
Copyright © University College London 1958

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References

1.Collins, W. D., Mathematika, 1 (1954), 125–130.CrossRefGoogle Scholar
2.Collins, W. D., Ph.D. dissertation (London, 1956).Google Scholar
3.Hasimoto, H., J. Phys. Soc. Japan, 11 (1956), 793–797.CrossRefGoogle Scholar
4.Butler, S. F. J., Proc. Cambridge Phil. Soc., 49 (1953), 169–174.CrossRefGoogle Scholar