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On the motion of small spheroidal particles in a viscous liquid

Saffman, P. G. (1956) On the motion of small spheroidal particles in a viscous liquid. Journal of Fluid Mechanics, 1 (5). pp. 540-553. ISSN 0022-1120. doi:10.1017/s0022112056000354.

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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.

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Additional Information:© 1956 Cambridge University Press. (Received 22 May 1956) I wish to thank Sir Geoffrey Taylor for suggesting this problem to me, and I am grateful to both him and Dr G. K. Batchelor for the kind interest that they have shown in this work. I also wish to thank Dr K. Weissenberg for the supply of some ammonium polymethyl acrilate.
Issue or Number:5
Record Number:CaltechAUTHORS:20181119-161052574
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Official Citation:Saffman, P. (1956). On the motion of small spheroidal particles in a viscous liquid. Journal of Fluid Mechanics, 1(5), 540-553. doi:10.1017/S0022112056000354
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91045
Deposited By: George Porter
Deposited On:20 Nov 2018 21:24
Last Modified:16 Nov 2021 03:38

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