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On converging solid spheres in a highly viscous fluid
Author(s) -
Hansford Robert E.
Publication year - 1970
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300002928
Subject(s) - spheres , mathematics , limiting , limit (mathematics) , reynolds number , zero (linguistics) , mathematical analysis , exact solutions in general relativity , mechanics , classical mechanics , physics , astronomy , mechanical engineering , turbulence , linguistics , philosophy , engineering
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.