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Direct numerical simulation of the gravity-induced settling of finite-sizeparticles in triply-periodic domains has been performed under diluteconditions. For a single solid-to-fluid density ratio of 1.5 we have consideredtwo values of the Galileo number corresponding to steady vertical motion(Ga=121) and to steady oblique motion (Ga=178) in the case of one isolatedsphere. For the multi-particle system we observe strong particle clusteringonly in the latter case. The geometry and time scales related to clustering aredetermined from Voronoi tesselation and particle-conditioned averaging. As aconsequence of clustering, the average particle settling velocity is increasedby 12% as compared to the value of an isolated sphere; such a collective effectis 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 shownthat the observed enhancement of the settling velocity is due to the fact thatthe downward fluid motion (with respect to the global average) which is inducedin the cluster regions is preferentially sampled by the particles. It isfurther observed that the variance of the particle velocity is stronglyenhanced in the clustering case. With the aid of a decomposition of theparticle velocity it is shown that this increase is due to enhanced fluidvelocity fluctuations (due to clustering) in the vicinity of the particles.Finally, we discuss a possible explanation for the observation of a criticalGalileo number marking the onset of clustering under dilute conditions.

Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion