Context : Dust is present in a large variety of astrophysical fluids , ranging from tori around supermassive black holes to molecular clouds , protoplanetary discs , and cometary outflows .
In many such fluids , shearing flows are present , which can lead to the formation of Kelvin-Helmholtz instabilities ( KHI ) and may change the properties and structures of the fluid through processes such as mixing and clumping of dust .

Aims : We study the effects of dust on the KHI by performing numerical hydrodynamical dust+gas simulations .
We investigate how the presence of dust changes the growth rates of the KHI in 2D and 3D and how the KHI 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 .

Methods : We perform numerical multifluid hydrodynamical simulations with in addition to the 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 that are similar to values in molecular clouds .

Results : 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 .

Conclusions :