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New bounds on the sedimentation velocity for hard, charged and adhesive hard-sphere colloids

Published online by Cambridge University Press:  14 January 2011

W. TODD GILLELAND ,
SALVATORE TORQUATO  and
WILLIAM B. RUSSEL
W. TODD GILLELAND
Affiliation:
Department of Chemical Engineering, Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
SALVATORE TORQUATO
Affiliation:
Department of Physics, Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA
WILLIAM B. RUSSEL*
Affiliation:
Department of Chemical Engineering, Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: wbrussel@princeton.edu
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Abstract

The sedimentation velocity of colloidal dispersions is known from experiment and theory at dilute concentrations to be quite sensitive to the interparticle potential with attractions/repulsions increasing/decreasing the rate significantly at intermediate volume fractions. Since the differences necessarily disappear at close packing, this implies a substantial maximum in the rate for attractions. This paper describes the derivation of a robust upper bound on the velocity that reflects these trends quantitatively and motivates wider application of a simple theory formulated for hard spheres. The treatment pertains to sedimentation velocities slow enough that Brownian motion sustains an equilibrium microstructure without large-scale inhomogeneities in density.

JFM classification

Complex Fluids: Colloids Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 667 , 25 January 2011 , pp. 403 - 425
Copyright
Copyright © Cambridge University Press 2011

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