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Far-field disturbance flow induced by a small non-neutrally buoyant sphere in a linear shear flow

Published online by Cambridge University Press:  15 January 2010

EVGENY S. ASMOLOV  and
FRANÇOIS FEUILLEBOIS
EVGENY S. ASMOLOV*
Affiliation:
Central Aero-Hydrodynamics Institute, 1 Zhukovsky str., Zhukovsky, Moscow region, 140180, Russia Institute of Mechanics, Lomonosov Moscow State University, 1 Michurinsky prosp., Moscow, 119192, Russia
FRANÇOIS FEUILLEBOIS
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), ESPCI, 10 rue Vauquelin, 75231 Paris cedex 05, France
*
†Email address for correspondence: [email protected]
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Abstract

The disturbance flow due to the motion of a small sphere parallel to the streamlines of an unbounded linear shear flow is evaluated at small Reynolds number using the method of matched expansions. Decaying laws are obtained for all velocity components in a far inviscid region and viscous wakes. The z component (in the direction of the shear-rate gradient) of the disturbance velocity is cylindrically symmetric in the inviscid region. It decays with the distance r from the sphere like r−5/3, while the y component (in the direction of vorticity) decays like r−4/3. The widths of two viscous wakes, located upstream and downstream of the sphere, grow with the longitudinal coordinate x as yw ~ zw ~ |x|1/3. The maximum x and z components of the velocity are located in the wake cores; they scale like |x|−2/3 and |x|−1 respectively. For two particles interacting through their outer regions, the migration velocity of each particle is the sum of the velocity of an isolated particle and of a disturbance velocity induced by the other one. Particles placed in the normal or transversal directions repel each other. When each particle is located in a wake of the other one, they may either attract or repel each other.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 449 - 470
Copyright
Copyright © Cambridge University Press 2010

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