An effective gravitational temperature for sedimentation

P. N. Segrè, F. Liu, Paul Umbanhowar, D. A. Weitz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

136 Scopus citations

Abstract

The slow sedimentation of suspensions of solid particles in a fluid results in complex phenomena that are poorly understood. For a low volume fraction (φ) of particles, long-range hydrodynamic interactions result in surprising spatial correlations1 in the velocity fluctuations; these are reminiscent of turbulence, even though the Reynolds number is very low2-4. At higher values of φ, the behaviour of sedimentation remains unclear; the upward backflow of fluid becomes increasingly important, while collisions and crowding further complicate inter-particle interactions5-8. Concepts from equilibrium statistical mechanics could in principle be used to describe the fluctuations and thereby provide a unified picture of sedimentation, but one essential ingredient - an effective temperature that provides a mechanism for thermalization - is missing. Here we show that the gravitational energy of fluctuations in particle number can act as an effective temperature. Moreover, we demonstrate that the high-φ behaviour is in fact identical to that at low φ, provided that the suspension viscosity and sedimentation velocity are scaled appropriately, and that the effects of particle packing are included.

Original languageEnglish (US)
Pages (from-to)594-597
Number of pages4
JournalNature
Volume409
Issue number6820
DOIs
StatePublished - Feb 1 2001

ASJC Scopus subject areas

  • General

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