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On the slow motion of two spheres in contact along their line of centres through a viscous fluid

Published online by Cambridge University Press:  24 October 2008

M. B. A. Cooley  and
M. E. O'Neill
M. B. A. Cooley
Affiliation:
C.E.G.B., Computing Division, London
M. E. O'Neill
Affiliation:
Department of Mathematics, University College London
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Extract

An exact solution in terms of analytic functions is given for the Stokes stream function and forces acting on two spheres in contact when the spheres move uniformly with the same velocity along their line of centres. For the case of equal sized spheres, the values of the forces agree with the Faxén limit of the Stimson–Jeffery forces for separated spheres when the minimum clearance between the spheres tends to zero. Numerical values of the forces for arbitrary sized spheres are tabulated and compared with corresponding values when the spheres are separated over a range of values of the minimum clearance. Comparison of the theoretical results with those obtained experimentally for the case of equal sized spheres is also given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 407 - 415
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Stimson, M. and Jeffery, G. B.Proc. Roy. Soc. Ser. A 111 (1926), 110.Google Scholar
(2)Faxén, H.Z. Angew. Math. Mech. 7 (1927), 79.Google Scholar
(3)Bart, E., M.Ch.E. Thesis, New York University, 1959.Google Scholar
(4)Eveson, G. F., Hall, E. W. and Ward, S. G.Brit. J. Appl. Phys. 10 (1959), 43.CrossRefGoogle Scholar
(5)Happel, J. and Brener, H.Low Reynolds Number Hydrodynamics (Prentice-Hall, 1965).Google Scholar