  Gravitational instability (GI) controls the dynamics of young massive
protoplanetary discs. Apart from facilitating gas accretion on to the central
protostar, it must also impact on the process of planet formation: directly
through fragmentation, and indirectly through the turbulent concentration of
small solids. To understand the latter process, it is essential to determine
the dust dynamics in such a turbulent flow. For that purpose, we conduct a
series of 3D shearing box simulations of coupled gas and dust, including the
gas's self-gravity and scanning a range of Stokes numbers, from 0.001 to ~0.2.
First, we show that the vertical settling of dust in the midplane is
significantly impeded by gravitoturbulence, with the dust scale-height roughly
0.6 times the gas scale height for centimetre grains. This is a result of the
strong vertical diffusion issuing from (a) small-scale inertial-wave turbulence
feeding off the GI spiral waves and (b) the larger-scale vertical circulations
that naturally accompany the spirals. Second, we show that at R=50 AU
concentration events involving sub-metre particles and yielding order 1 dust to
gas ratios are rare and last for less than an orbit. Moreover, dust
concentration is less efficient in 3D than in 2D simulations. We conclude that
GI is not especially prone to the turbulent accumulation of dust grains.
Finally, the large dust scale-height measured in simulations could be, in the
future, compared with that of edge-on discs seen by ALMA, thus aiding detection
and characterisation of GI in real systems.
