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On the motion of small spheroidal particles in a viscous liquid

Published online by Cambridge University Press:  28 March 2006

P. G. Saffman
P. G. Saffman
Affiliation:
Trinity College, Cambridge
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Abstract

Small spheroidal particles suspended in a sheared viscous liquid are sometimes observed to take up slowly preferred orientations, relative to the motion of the undisturbed liquid, which are independent of the initial conditions of release. These obsevations cannot be accounted for by the solution, obtained by Jeffery (1922), of the linearized Navier-Stokes equations. It is shown in this paper that the effect of the inertia of the liquid is to alter slowly the orbit of the particle in accordance with Jeffery's hypothesis that the particle ultimately moves in such a way that the dissipation of energy is a minimum, but that this effect is orders of magnitude too small to account for any of the experimental observations.

It is suggested that non-Newtonian properties of the liquid account for the observations. It is shown that the rate of orientation of a particle would then be independent of its size, and this prediction is verified experimentally. Other experimental evidence in support of this suggestion is also described.

Some remarks are also made about the possible effect of collisions between the particles when more than one particle is present.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 1 , Issue 5 , November 1956 , pp. 540 - 553
Copyright
© 1956 Cambridge University Press

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References

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