Hydrodynamic diffusion of a sphere sedimenting through a dilute suspension of neutrally buoyant spheres

Davis, R.H. and Hill, N.A. (1992) Hydrodynamic diffusion of a sphere sedimenting through a dilute suspension of neutrally buoyant spheres. Journal of Fluid Mechanics, 236, pp. 513-533. (doi: 10.1017/S0022112092001514)

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Publisher's URL: http://dx.doi.org/10.1017/S0022112092001514


The motion of a heavy sphere sedimenting through a dilute background suspension of neutrally buoyant spheres is analysed for small Reynolds number and large Péclet number. For this particular problem, it is possible not only to calculate the mean velocity of the heavy particle, but also the variance of the velocity and the coefficient of hydrodynamic diffusivity. Pairwise, hydrodynamic interactions between the heavy sphere and the background sphere are considered exactly using volume integrals and a trajectory analysis. Explicit formulae are given for the two limiting cases when the radius of the heavy sphere is much greater and much less than that of the background spheres, and numerical results are given for moderate size ratios. The mean velocity is relatively insensitive to the ratio of the radius of the background spheres to that of the heavy sphere, unless this ratio is very large, whereas the hydrodynamic diffusivity increases rapidly as the radius ratio is increased. The predictions are in reasonable agreement with the results of falling-ball rheometry experiments.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Hill, Professor Nicholas
Authors: Davis, R.H., and Hill, N.A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Fluid Mechanics
Journal Abbr.:J. Fluid Mech.
Publisher:Cambridge University Press
ISSN (Online):1469-7645
Copyright Holders:Copyright © 1992 Cambridge University Press
First Published:First published in Journal of Fluid Mechanics 236:513-533
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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