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Hydromechanics of low-Reynolds-number flow. Part 4. Translation of spheroids

Published online by Cambridge University Press:  29 March 2006

Allen T. Chwang  and
Theodore Y. Wu
Allen T. Chwang
Affiliation:
Engineering Science Department, California Institute of Technology, Pasadena
Theodore Y. Wu
Affiliation:
Engineering Science Department, California Institute of Technology, Pasadena
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Abstract

The problem of a uniform transverse flow past a prolate spheroid of arbitrary aspect ratio at low Reynolds numbers has been analysed by the method of matched asymptotic expansions. The solution is found to depend on two Reynolds numbers, one based on the semi-minor axis b, Rb = Ub/v, and the other on the semi-major axis a, Ra = Ua/v (U being the free-stream velocity at infinity, which is perpendicular to the major axis of the spheroid, and v the kinematic viscosity of the fluid). A drag formula is obtained for small values of Rb and arbitrary values of Ra. When Ra is also small, the present drag formula reduces to the Oberbeck (1876) result for Stokes flow past a spheroid, and it gives the Oseen (1910) drag for an infinitely long cylinder when Ra tends to infinity. This result thus provides a clear physical picture and explanation of the ‘Stokes paradox’ known in viscous flow theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 75 , Issue 4 , 25 June 1976 , pp. 677 - 689
Copyright
© 1976 Cambridge University Press

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