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The instability of a dispersion of sedimenting spheroids

Published online by Cambridge University Press:  26 April 2006

Donald L. Koch  and
Eric S. G. Shaqfeh
Donald L. Koch
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
Eric S. G. Shaqfeh
Affiliation:
AT & T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974, USA
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Abstract

It is shown that hydrodynamic interactions between non-Brownian, non-spherical, sedimenting particles give rise to an increase in the number of neighbouring particles in the vicinity of any given particle. This result suggests that the suspension is unstable to particle density fluctuations even in the absence of inertia; a linear stability analysis confirms this inference. It is argued that the instability will lead to convection on a lengthscale (nl)−½, where l is a characteristic particle length and n is the particle number density. Sedimenting suspensions of spherical particles are shown to be stable in the absence of inertial effects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 521 - 542
Copyright
© 1989 Cambridge University Press

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