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/ in the range of 0. 1–300, the fallout height Zf is found to be Zf/a\, =\, (11 2) (Q^1/2/ (wₛa) ) ^0. 83. For high Reₚ particles, the fallout height assumes the simple form: Zf/a\, =\, (9 2) Nₚ^1/2. 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 particles fall out in the form of a bowl-shaped swarm at a height Zf\, \, 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.