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

Published online by Cambridge University Press:  26 April 2006

Robert H. Davis  and
N. A. Hill
Robert H. Davis
Affiliation:
Department of Chemical Engineering, University of Colorado, Boulder, CO 80309-0424, USA
N. A. Hill
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, UK
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 236 , March 1992 , pp. 513 - 533
Copyright
© 1992 Cambridge University Press

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