  In protoplanetary disks, the distribution and abundance of small (sub)micron
grains are important for a range of physical and chemical processes. For
example, they dominate the optical depth at short wavelengths and their
surfaces are the sites of many important chemical reactions such as the
formation of water. Based on their aerodynamical properties (i.e., their strong
dynamical coupling with the surrounding gas) it is often assumed that these
small grains are well-mixed with the gas. Our goal is to study the vertical
(re)distribution of grains taking into account settling, turbulent diffusion,
as well as collisions with other dust grains. Assuming a fragmentation-limited
background dust population, we developed a Monte Carlo approach that follows
single monomers as they move through a vertical column of gas and become
incorporated in different aggregates as they undergo sticking and fragmenting
collisions. We find that (sub)micron grains are not necessarily well-mixed
vertically, but can become trapped in a thin layer with a scale-height that is
significantly smaller than that of the gas. This collisional trapping occurs
when the timescale for diffusion is comparable to or longer than the collision
timescale in the midplane and its effect is strongest when the most massive
particles in the size-distribution show significant settling. Based on
simulations and analytical considerations we conclude that for typical
dust-to-gas ratios and turbulence levels, the collisional trapping of small
grains should be a relatively common phenomenon. The absence of trapping could
then indicate a low dust-to-gas ratio, possibly because a large portion of the
dust mass has been removed through radial drift or is locked up in
planetesimals.
