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Slow motion of an incompressible viscous liquid generated by the rotation of two spheres in contact

Published online by Cambridge University Press:  26 February 2010

S. R. Majumdar
S. R. Majumdar
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona, U.S.A.
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Extract

1. G. B. Jeffery [1] investigated the axisymmetrical flow of an incompressible viscous fluid caused by two spheres rotating slowly and steadily in the liquid about their line of centres. The numerical results he gave were for spheres of equal radii.

The present problem is to investigate what happens when the spheres touch each other either externally or internally and when they are unequal in size. This problem could be approached by taking a limit of Jeffery's solution, but in fact it will be more convenient to use a co-ordinate system different from Jeffery's and, of course, his results would not yield information about unequal spheres.

Type
Research Article
Information
Mathematika , Volume 14 , Issue 1 , June 1967 , pp. 43 - 46
Copyright
Copyright © University College London 1967

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References

1.Jeffery, G. B., Proc. London Math. Soc. (2), 14 (1915), 327–338.Google Scholar
2.Sneddon, I. N., Special functions of mathematical physics and chemistry (Oliver & Boyd, 1960).Google Scholar
3.Lamé, , “Coordonnees Curvilignes”, p. 284.Google Scholar