In laboratory experiments , we study the motion of levitated , sedimenting clouds of sub-mm grains at low ambient pressure and at high solid-to-gas ratios \epsilon .
The experiments show a collective behavior of particles , i.e .
grains in clouds settle faster than an isolated grain .
In collective particle clouds , the sedimentation velocity linearly depends on \epsilon and linearly depends on the particle closeness C .
However , collective behavior only sets in at a critical value \epsilon _ { crit } which linearly increases with the experiment Stokes number St. For St < 0.003 particles always behave collectively .
For large Stokes numbers , large solid-to-gas ratios are needed to trigger collective behavior , e.g . \epsilon _ { crit } = 0.04 at St = 0.01 .
Applied to protoplanetary disks , particles in dense environments will settle faster .
In balance with upward gas motions ( turbulent diffusion , convection ) the thickness of the midplane particle layer will be smaller than calculated based on individual grains , especially for dust .
For pebbles , large solid-to-gas ratios are needed to trigger instabilities based on back-reaction .