https://doi.org/10.1007/PL00011074
Velocity measurement of a settling sphere
École Normale Supérieure de Lyon, Laboratoire de
Physique, 46 Allée d'Italie, 69007 Lyon,
France
Received:
12
April
2000
Revised:
13
July
2000
Published online: 15 November 2000
We study experimentally the motion of a solid sphere settling
under gravity in a fluid at rest. The particle velocity is
measured with a new acoustic method. Variations of the sphere
size and density allow measurements at Reynolds numbers, based
on limit velocity, between 40 and 7 000.
At all Reynolds numbers, our observations are
consistent with the presence of a memory-dependent force
acting on the particle. At short times it has a 
behaviour as predicted by the unsteady Stokes equations and as
observed in numerical simulations. At long times, the decay of
the memory (Basset) force is better fitted by an exponential
behaviour.
Comparison of the dynamics of spheres of different densities
for the same Reynolds number show that the density is an
important control parameter. Light spheres show transitory
oscillations at 
, but reach a constant limit
speed.
PACS: 06.30.Gv – Velocity, acceleration, and rotation / 43.60.+d – Acoustic signal processing / 47.27.Vf – Wakes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
