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The approach of a sphere to a wall at finite Reynolds number

Published online by Cambridge University Press:  01 September 2010

A. MONGRUEL ,
C. LAMRIBEN ,
S. YAHIAOUI  and
F. FEUILLEBOIS
A. MONGRUEL*
Affiliation:
PMMH (CNRS UMR 7636, ESPCI, Université Pierre et Marie Curie-Paris 6 and Université Paris Diderot-Paris 7) 10, rue Vauquelin, 75231 Paris Cedex 05, France
C. LAMRIBEN
Affiliation:
PMMH (CNRS UMR 7636, ESPCI, Université Pierre et Marie Curie-Paris 6 and Université Paris Diderot-Paris 7) 10, rue Vauquelin, 75231 Paris Cedex 05, France
S. YAHIAOUI
Affiliation:
PMMH (CNRS UMR 7636, ESPCI, Université Pierre et Marie Curie-Paris 6 and Université Paris Diderot-Paris 7) 10, rue Vauquelin, 75231 Paris Cedex 05, France
F. FEUILLEBOIS
Affiliation:
LIMSI-CNRS, UPR 3251, B.P. 133, 91403 Orsay Cedex, France
*
†Email address for correspondence: [email protected]
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Abstract

The approach to a wall of a non-Brownian rigid spherical particle, settling in a viscous fluid with a Reynolds number of the order of unity, is studied experimentally. Far from the wall, the fluid motion around the particle is driven by inertia and viscosity forces. The particle Stokes number is also of the order of unity, so that the particle motion far from the wall is driven by inertia. In the close vicinity of the wall, however, the particle–wall hydrodynamic interaction decelerates the particle significantly. An interferometric device is used to measure the vertical displacement of a millimetric size spherical bead at distances from the wall smaller than 0.1 sphere radius, with a spatial resolution of 100 nm. For the range of impact Stokes number (St*, based on the limit velocity of the sphere in an unbounded fluid) explored here (up to St* ≅ 5), the measurements reveal that a small region of negligible particle inertia still exists just prior to contact of the sphere with the wall. In this lubrication-like region, the particle velocity decreases linearly with decreasing particle–wall distance and vanishes at contact, ruling out the possibility of a rebound. The vertical extent of this region decreases with increasing Stokes number and is e.g. only 10 μm large at impact Stokes number St* ≅ 5.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 661 , 25 October 2010 , pp. 229 - 238
Copyright
Copyright © Cambridge University Press 2010

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References

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