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Pair-sphere trajectories in finite-Reynolds-number shear flow

Published online by Cambridge University Press:  17 January 2008

PANDURANG M. KULKARNI  and
JEFFREY F. MORRIS
PANDURANG M. KULKARNI
Affiliation:
Benjamin Levich Institute and Department of Chemical Engineering, The City College of New York, New York, NY 10031, USA
JEFFREY F. MORRIS
Affiliation:
Benjamin Levich Institute and Department of Chemical Engineering, The City College of New York, New York, NY 10031, USA
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Abstract

The pair trajectories of neutrally buoyant rigid spheres immersed in finite-inertia simple-shear flow are described. The trajectories are obtained using the lattice-Boltzmann method to solve the fluid motion, with Newtonian dynamics describing the sphere motions. The inertia is characterized by the shear-flow Reynolds number , where μ and ρ are the viscosity and density of the fluid respectively, is the shear rate and a is the radius of the larger of the pair of spheres in the case of unequal sizes; the majority of results presented are for pairs of equal radii. Reynolds numbers of 0 ≤ Re ≤ 1 are considered with a focus on inertia at Re = O(0.1). At finite inertia, the topology of the pair trajectories is altered from that predicted at Re = 0, as closed trajectories found in Stokes flow vanish and two new forms of trajectories are observed. These include spiralling and reversing trajectories in addition to largely undisturbed open trajectories. For Re = O(0.1), the limits of the various regions in pair space yielding open, reversing and spiralling trajectories are roughly defined.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 596 , 25 January 2008 , pp. 413 - 435
Copyright
Copyright © Cambridge University Press 2008

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