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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. 1. Introduction Dispersions of particles in large volumes of liquid are of interest for many industrial applications or natural phenomena. When the particles are small or the liquid highly viscous, interactions between particles are governed by hydrodynamic forces, provided that surface forces, e.g. van der Waals forces, and Brownian motion are negligible. These hydrodynamic interactions lead to complex chaotic displacements of the particles despite the reversiblity of the Stokes equations. In this paper, we consider the motion under gravity of particles initially distributed in a viscous liquid with uniform concentration within a spherical boundary, namely the sedimentation of a spherical cloud of particles in an otherwise pure liquid at low Reynolds numbers, and enquire about its following time evolution. During the settling of the cloud, a striking collective motion of the particle arises and an observed outcome of this dynamic is that the cloud remains a cohesive entity for long times, maintaining a sharp boundary between its particle-filled interior and the clear fluid outside. The cloud has been often regarded as an effective medium of excess mass and the flow system related to that of the sedimentation of a spherical drop of heavy fluid in an otherwise lighter fluid solved by Hadamard (1911) and Rybczy´nskiRybczy´ Rybczy´nski (1911). However, the fluctuations in particle velocity causes some particles to cross the cloud boundary and be carried by the outside flow into a vertical tail emanating from the rear of the cloud. Moreover, the cloud has also been reported to undergo a complex shape evolution. It is indeed possible to observe that the cloud evolves into a torus that becomes unstable and breaks up into secondary droplets which deform into tori themselves in a repeating cascade.
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Bloen Metzger, Maxime Nicolas, Elisabeth Guazzelli. Falling clouds of particles in viscous fluids. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2007, ⟨10.1017/S0022112007005381⟩. ⟨hal-01440849⟩

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