Falling clouds of particles in viscous fluids

Abstract

We have investigated both experimentally and numerically the time evolution of clouds of particles settling under the action of gravity in an otherwise pure liquid at low Reynolds numbers. We have found that an initially spherical cloud containing enough particles is unstable. It slowly evolves into a torus which breaks up into secondary droplets which deform into tori themselves in a repeating cascade. Owing to the fluctuations in velocity of the interacting particles, some particles escape from the cloud toroidal circulation and form a vertical tail. This creates a particle deficit near the vertical axis of the cloud and helps in producing the torus which eventually expands. The rate at which particles leak from the cloud is influenced by this change of shape. The evolution toward the torus shape and the subsequent evolution is a robust feature. The nature of the breakup of the torus is found to be intrinsic to the flow created by the particles when the torus aspect ratio reaches a critical value. Movies are available with the online version of the paper.