Title: Prolate spheroids settling in a quiescent fluid: clustering, microstructures and collisions

Abstract: In the present study, we investigate the settling of prolate spheroidal particles in a quiescent fluid by means of particle-resolved direct numerical simulations. By varying the particle volume fraction (phi) from 0.1% to 10%, we observe a non-monotonic variation of particle mean settling velocity with a local maximum at phi=1%. To explain this finding, we examine the spatial distribution and orientation of dispersed particles. The particle-pairs statistics show the tendency of particles to form column-like microsturctures, revealing the attraction and entrapment of paritcles in wake regions. This effect results in the formation of large-scale particle clusters at intermediate particle volume fractions. The most intense particle clustering at phi=1%, quantified by the standard deviation of Voronoi volume, induces a swarm effect and substantially enhances the particle settling rate by around 25%. While, in the very dilute suspension at phi=0.1%, the particle clustering is attenuated due to the long inter-particle distance. In dense suspensions, however, the crowded particle arrangement disrupts particle wakes, breaks particle microstructures and inhibits the particle clustering. Consequently, hindrance effect dominates and reduces the settling speed. In contrast to particle spatial distribution, the particle orientation plays a less important role in the mean settling velocity. At last, we examine the collision rate of settling particles by computing the collision kernel. As phi increases, the collision kernel decreases monotonically, which is primarily attributed to the decrease of radial distribution function. However, the radial relative velocity is almost a constant with the change of phi. These results reveal the importance of hydrodynamic interactions, including the wake-flow-induced attractions and the lubrication effect, in collisions among settling spheroids.