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= gʹN_pV_p, where gʹ is the reduced gravity of the N_p spherical particles of volume V_p,{=},{4upi a^3}/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 w_s, at which point the particles rain out as individuals. For particle Reynolds numbers hbox{it Re}_p,{=},w_s a/nu in the range of 0.1–300, the fallout height Z_f is found to be Z_f/a,{=},(11 pm 2) (Q^{1/2}/(w_sa))^{0.83}. For high hbox{it Re}_p particles, the fallout height assumes the simple form: Z_f/a,{=},(9 pm 2) N_p^{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–V?is?l? frequency N, the mode of fallout depends explicitly on the stratified cloud number, N_s,{=},w_s Q^{-1/4} N^{-1/2}. For N_s,{<},1, the cloud overshoots, rebounds past, then intrudes at the neutral height, Z_N, 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 N_s,{>},1, the particles fall out in the form of a bowl-shaped swarm at a height Z_f,{<},Z_N, thus giving rise to a relatively localized deposit. For N_s,{>},4, the fallout height is largely uninfluenced by the stratification and is adequately described by the homogeneous result. Regardless of N_s, 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} Z_f/4. Criteria for three distinct modes of particle deposition in a stratified ambient are developed.