Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-28T04:56:20.356Z Has data issue: false hasContentIssue false

A model for velocity fluctuations in sedimentation

Published online by Cambridge University Press:  23 February 2004

PETER J. MUCHA
Affiliation:
School of Mathematics and Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332-0160, USAmucha@math.gatech.edu
SHANG-YOU TEE
Affiliation:
Department of Physics, Harvard University, Cambridge, MA 02138, USA
DAVID A. WEITZ
Affiliation:
Department of Physics, Harvard University, Cambridge, MA 02138, USA Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
BORIS I. SHRAIMAN
Affiliation:
Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA
MICHAEL P. BRENNER
Affiliation:
Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA

Abstract

We present a model for velocity fluctuations of dilute sedimenting spheres at low Reynolds number. The central idea is that a vertical stratification causes the fluctuations to decrease below those of an independent uniform distribution of particles, such a stratification naturally occurring from the broadening of the sedimentation front. We use numerical simulations, scaling arguments, structure factor calculations, and experiments to show that there is a critical stratification above which the characteristics of the density and velocity fluctuations change significantly. For thin cells, the broadening of the sediment front (and the resulting stratification) is small, so the velocity fluctuations are predicted by independent-Poisson-distribution estimates. In very thick cells, the stratification is significant, leading to persistent decay of the velocity fluctuations for the duration of the experiment. Estimated stratifications quantitatively agree with the simulations, and indicate the likelihood that previous experimental measurements were also affected by stratification. The velocity fluctuations in sedimentation are therefore not universal but instead depend on both the cell shape and developing stratification.

Type
Papers
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)