Falling clouds of particles

Elisabeth Guazzelli
Aix-Marseille Universit\'e, CNRS, IUSTI UMR 7343, 13453 Marseille, France.

A cloud composed of solid spherical particles falling under gravity in a quiescent fluid can be regarded as an effective medium of excess mass and the problem can be related to that of the sedimentation of a spherical drop of heavy fluid in an otherwise lighter fluid. However, the cloud is unstable even in the complete absence of inertia and without needing to perturb its initial shape. It has been observed first to remain roughly spherical with a leakage of particles in a vertical tail and then to evolve into a torus which breaks up into two droplets in a repeating cascade. The discrete nature of the particles is fundamental in the understanding of these instabilities. Simple simulations using a point-particle approach, which contains the minimal physics of the long-range interactions, capture this dynamics. Faster breakup is observed for clouds of anisotropic particles such as fibers, due to the self motion of the anisotropic particles. When inertia is finite, the cloud also deforms into a flat torus that eventually destabilizes and breaks up into a number of secondary droplets but particle leakage is much weaker. While this evolution resembles that observed in the Stokes regime, the physical mechanisms involved are qualitatively different. The cloud evolution can be strongly determined by the importance of wake-mediated interactions. If the cloud settles now in a flowing fluid instead of a quiescent fluid, there is a coupling between particle-particle and particle-fluid interactions. This two-way coupling is evidenced for a cloud settling in a cellular flow field which is a simple model flow capturing key features of vortical effects on particles.
This work has been done in collaboration with L. Bergougnoux, G. Bouchet, J. E. Butler, M. L. Ekiel-Je\.{z}ewska, D. Lopez, B. Marchetti, B. Metzger, M. Nicolas, J. Park, F. Pignatel.