  Dust is present in a large variety of astrophysical fluids, from tori around
supermassive black holes to molecular clouds, protoplanetary discs, and
cometary outflows. In many such fluids, shearing flows are present, leading to
the formation of Kelvin-Helmholtz instabilities (KHI) and changing the
properties and structures of the fluid through processes such as mixing and
clumping of dust. We investigate how dust changes the growth rates of the KHI
in 2D and 3D and how the it redistributes and clumps dust. We investigate if
similarities can be found between the structures in 3D KHI and those seen in
observations of molecular clouds. We do this by performing numerical
hydrodynamical dust+gas simulations with in addition to gas a number of dust
fluids. Each dust fluid represents a portion of the particle size-distribution.
We study how dust-to-gas mass density ratios between 0.01 and 1 alter the
growth rate in the linear phase of the KHI. We do this for a wide range of
perturbation wavelengths, and compare these values to the analytical gas-only
growth rates. As the formation of high-density dust structures is of interest
in many astrophysical environments, we scale our simulations with physical
quantities similar to values in molecular clouds. Large differences in dynamics
are seen for different grain sizes. We demonstrate that high dust-to-gas ratios
significantly reduce the growth rate of the KHI, especially for short
wavelengths. We compare the dynamics in 2D and 3D simulations, where the latter
demonstrates additional full 3D instabilities during the non-linear phase,
leading to increased dust densities. We compare the structures formed by the
KHI in 3D simulations with those in molecular clouds and see how the column
density distribution of the simulation shares similarities with log-normal
distributions with power-law tails sometimes seen in observations of molecular
clouds.
