We measure the turbulent diffusion coefficient of dust grains embedded in magnetorotational turbulence in a protoplanetary disc directly from numerical simulations and compare it to the turbulent viscosity of the flow .
The simulations are done in a local coordinate frame comoving with the gas in Keplerian rotation .
Periodic boundary conditions are used in all directions , and vertical gravity is not applied to the gas .
Using a two-fluid approach , small dust grains of various sizes ( with friction times up to \varOmega _ { 0 } \tau _ { f } = 0.02 ) are allowed to move under the influence of friction with the turbulent gas .
We measure the turbulent diffusion coefficient of the dust grains by applying an external sinusoidal force field acting in the vertical direction on the dust component only .
This concentrates the dust around the mid-plane of the disc , and an equilibrium distribution of the dust density is achieved when the vertical settling is counteracted by the turbulent diffusion away from the mid-plane .
Comparing with analytical expressions for the equilibrium concentration we deduce the vertical turbulent diffusion coefficient .
The vertical diffusion coefficient is found to be lower than the turbulent viscosity and to have an associated vertical diffusion Prandtl number of about 1.5 .
A similar radial force field also allows us to measure the radial turbulent diffusion coefficient .
We find a radial diffusion Prandtl number of about 0.85 and also find that the radial turbulent diffusion coefficient is around 70 % higher than the vertical .
As most angular momentum transport happens through magnetic Maxwell stresses , both the vertical and the radial diffusion coefficients are found to be significantly higher than suggested by the angular momentum transport by Reynolds stresses alone .
We also find evidence for trapping of dust grains of intermediate friction time in turbulent eddies .