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The motion of rigid particles in a shear flow at low Reynolds number

Published online by Cambridge University Press:  28 March 2006

F. P. Bretherton
F. P. Bretherton
Affiliation:
Trinity College, Cambridge
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Abstract

According to Jeffery (1923) the axis of an isolated rigid neutrally buoyant ellipsoid of revolution in a uniform simple shear at low Reynolds number moves in one of a family of closed periodic orbits, the centre of the particle moving with the velocity of the undisturbed fluid at that point. The present work is a theoretical investigation of how far the orbit of a particle of more general shape in a non-uniform shear in the presence of rigid boundaries may be expected to be qualitatively similar. Inertial and non-Newtonian effects are entirely neglected.

The orientation of the axis of almost any body of revolution is a periodic function of time in any unidirectional flow, and also in a Couette viscometer. This is also true if there is a gravitational force on the particle in the direction of the streamlines. There is no lateral drift. On the other hand, certain extreme shapes, including some bodies of revolution, will assume one of two orientations and migrate to the bounding surfaces or to the centre of the flow. In any constant slightly three-dimensional uniform shear any body of revolution will ultimately assume a preferred orientation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 14 , Issue 2 , October 1962 , pp. 284 - 304
Copyright
© 1962 Cambridge University Press

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References

Bretherton, F. P. & Rothschild, Lord 1961 Proc. Roy. Soc. B, 153, 490.
Christopherson, D. G. & Dowson, D. 1959 Proc. Roy. Soc. A, 251, 550.
Goldsmith, H. L. & Mason, S. G. 1961a Nature, Land., 190, 1095.
Goldsmith, H. L. & Mason, S. G. 1961b Private communication.
Hancock, G. J. 1953 Proc. Roy. Soc. A, 217, 96.
Jeffery, G. B. 1923 Proc. Roy. Soc. A, 102, 161.
Lamb, H. 1932 Hydrodynamics, Sixth ed. Cambridge University Press.
Mason, S. G. & Manley, R. St J. 1956 Proc. Roy. Soc. A, 238, 117.
Saffman, P. G. 1956 J. Fluid Mech. 1, 540.
Scott-Blair, G. W. 1958 Rheol. Acta, 1, 123.
Segré, G. & Silberberg, A. 1961 Nature, Lond., 189, 209.
Segré, G. & Silberberg, A. 1962 J. Fluid Mech. 14, 115, 136.
Starkey, T. V. 1956 Brit. J. Appl. Phys. 7, 52.
Taylor, G. I. 1923 Proc. Roy. Soc. A, 103, 58.
Trevelyan, B. J. & Mason, S. G. 1951 J. Colloid. Sci. 6, 354.