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The effect of Brownian motion on the stability of sedimenting suspensions of polarizable rods in an electric field

Published online by Cambridge University Press:  10 April 2009

BRENDAN D. HOFFMAN  and
ERIC S. G. SHAQFEH
BRENDAN D. HOFFMAN
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305-5025, USA
ERIC S. G. SHAQFEH*
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305-5025, USA Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-3030, USA
*
†Email address for correspondence: esgs@stanford.edu
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Abstract

We examine the collective dynamics of polarizable, Brownian, sedimenting rods of high aspect ratio. Previous work of Koch and Shaqfeh (J. Fluids Mech., vol. 209, 1989 pp. 521–542) has shown that in the absence of Brownian motion, sedimenting suspensions of rods are unstable to concentration fluctuations and form dense streamers via interparticle hydrodynamic interactions. Recently, Saintillan, Shaqfeh & Darve (Phys. Fluids, vol. 18 (121701), 2006b p. 1) demonstrated that electric fields can act to stabilize these non-Brownian suspensions of polarizable rods through induced-charge electrokinetic rotation, which forces particle alignment. In this paper, we employ a mean-field linear stability analysis as well as Brownian dynamics simulations to study the effect of thermal motion on the onset of instability. We find that in the absence of electric fields, Brownian motion consistently suppresses instability formation through randomization of particle orientation. However, when electric fields are applied, thermal motion can act to induce instability by counteracting the stabilizing effect of induced-charge orientation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 624 , 10 April 2009 , pp. 361 - 388
Copyright
Copyright © Cambridge University Press 2009

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