Particle clouds in homogeneous and stratified environments

We examine the settling of monodisperse heavy particles released into a fluid when the resulting motion is sufficiently vigorous that the particle cloud initially assumes the form of a turbulent thermal. A laboratory study is complemented by numerical simulations of particle cloud dynamics in both homogeneous and stratified ambients. In the homogeneous ambient, the cloud generated by a total buoyancy excess Q= g'NₚVₚ , where $g'$ is the reduced gravity of the Nₚ spherical particles of volume Vₚ\,=\,4 a³/3 , evolves in a manner consistent with a classical fluid thermal. The cloud grows through turbulent entrainment and decelerates until its speed is exceeded by that of the individual particles wₛ , at which point the particles rain out as individuals. For particle Reynolds numbers Reₚ\,=\,wₛ a/ν in the range of 0.1–300, the fallout height Zf is found to be Zf/a\,=\,(11 ± 2) (Q1/2/(wₛa))0.83 . For high Reₚ particles, the fallout height assumes the simple form: Zf/a\,=\,(9 ± 2) Nₚ1/2 . Following fallout, the particles sink at their individual settling speeds in the form of a bowl-shaped swarm. In a stratified environment characterized by a constant Brunt–Väisälä frequency N , the mode of fallout depends explicitly on the stratified cloud number, Nₛ\,=\,wₛ Q-1/4 N-1/2 . For Nₛ\,<\,1 , the cloud overshoots, rebounds past, then intrudes at the neutral height, ZN , of the equivalent fluid thermal. The particles fall out between the depth of maximum penetration and the spreading neutral cloud, and may be distributed over a relatively broad area. For Nₛ\,>\,1 , the particles fall out in the form of a bowl-shaped swarm at a height Zf\,<\,ZN , thus giving rise to a relatively localized deposit. For Nₛ\,>\,4 , the fallout height is largely uninfluenced by the stratification and is adequately described by the homogeneous result. Regardless of Nₛ , following particle fallout in a stratified ambient, the fluid entrained by the thermal ascends and intrudes at a rebound height given to leading order by 3 Zf/4 . Criteria for three distinct modes of particle deposition in a stratified ambient are developed.