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A Slow motion of viscous liquid caused by a slowly moving solid sphere

Published online by Cambridge University Press:  26 February 2010

M. E. O'Neill
M. E. O'Neill
Affiliation:
University College, London, W.C.1.

Extract

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A slow steady motion of incompressible viscous liquid, bounded by an infinite rigid plane, which is generated when a rigid sphere of radius a moves steadily without rotation in a direction parallel to, and at a distance d from, the plane is considered. Use is made of bispherical coordinates, which were employed some years ago by G. B. Jeffery [1] and Stimson and Jeffery [2] in solving the axi-symmetrical problems in which the sphere is fixed and rotates about a diameter perpendicular to the plane, or when two spheres move without rotation along their line of centres in infinite liquid. The coordinate system has been used recently by Dean and O'Neill [3] in solving the problem in which the sphere is fixed and rotates about a diameter parallel to the plane.

Type
Research Article
Information
Mathematika , Volume 11 , Issue 1 , June 1964 , pp. 67 - 74
Copyright
Copyright © University College London 1964

References

1.Jeffery, G. B., Proc. London Math. Soc. (2), 14 (1915), 327–338.CrossRefGoogle Scholar
2.Stimson, M. and Jeffery, G. B., Proc. Roy. Soc. (A), 3 (1926), 110–116.Google Scholar
3.Dean, W. R. and O'Neill, M. E., Mathematika, 10 (1963), 13–24.CrossRefGoogle Scholar
4.Jeffery, G. B., Proc. Roy. Soc. (A), 87 (1912), 109–120.Google Scholar