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On converging solid spheres in a highly viscous fluid

Published online by Cambridge University Press:  26 February 2010

Robert E. Hansford
Robert E. Hansford
Affiliation:
Westland Helicopters Ltd.
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Abstract

A method of “inner and outer expansions” employed by Cox and Brenner (1967) is used to calculate the hydrodynamic force experienced by either of two identical small solid spheres, approaching each other, at low Reynolds number, with the same velocity along their line of centres, for the limiting case when the gap width between them tends to zero. Numerical results are compared with those furnished by the exact solution and an improved expression is then obtained for a similar problem arising from the motion of a small sphere towards an identical stationary sphere, in the limit of small gap widths.

Type
Research Article
Information
Mathematika , Volume 17 , Issue 2 , December 1970 , pp. 250 - 254
Copyright
Copyright © University College London 1970

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References

Brenner, H., Chem. Engng. Sci., 16 (1961), 242.CrossRefGoogle Scholar
Cooley, M. D. A. and O'Neill, M. E., Mathematika, 16 (1969), 37.CrossRefGoogle Scholar
Cox, R. G. and Brenner, H., Chem. Engng. Sci., 22 (1967), 1753.CrossRefGoogle Scholar
Faxén, H., Z. angew. Math. Mech., 7 (1927), 79.Google Scholar
Stimson, M. and Jeffery, G. B., Proc. Royal Soc., A, 111 (1926), 110.Google Scholar