  Direct numerical simulation of the gravity-induced settling of finite-size
particles in triply-periodic domains has been performed under dilute
conditions. For a single solid-to-fluid density ratio of 1.5 we have considered
two values of the Galileo number corresponding to steady vertical motion
(Ga=121) and to steady oblique motion (Ga=178) in the case of one isolated
sphere. For the multi-particle system we observe strong particle clustering
only in the latter case. The geometry and time scales related to clustering are
determined from Voronoi tesselation and particle-conditioned averaging. As a
consequence of clustering, the average particle settling velocity is increased
by 12% as compared to the value of an isolated sphere; such a collective effect
is not observed in the non-clustering case. By defining a local (instantaneous)
fluid velocity average in the vicinity of the finite-size particles it is shown
that the observed enhancement of the settling velocity is due to the fact that
the downward fluid motion (with respect to the global average) which is induced
in the cluster regions is preferentially sampled by the particles. It is
further observed that the variance of the particle velocity is strongly
enhanced in the clustering case. With the aid of a decomposition of the
particle velocity it is shown that this increase is due to enhanced fluid
velocity fluctuations (due to clustering) in the vicinity of the particles.
Finally, we discuss a possible explanation for the observation of a critical
Galileo number marking the onset of clustering under dilute conditions.
