  In this paper, we study the effect of MHD turbulence on the dynamics of dust
particles in protoplanetary disks. We vary the size of the particles and relate
the dust evolution to the turbulent velocity fluctuations. We performed
numerical simulations using two Eulerian MHD codes, both based on finite
difference techniques: ZEUS--3D and NIRVANA. These were local shearing box
simulations incorporating vertical stratification. Both ideal and non ideal MHD
simulations with midplane dead zones were carried out. The codes were extended
to incorporate different models for the dust as an additional fluid component.
Good agreement between results obtained using the different approaches was
obtained. The simulations show that a thin layer of very small dust particles
is diffusively spread over the full vertical extent of the disk. We show that a
simple description obtained using the diffusion equation with a diffusion
coefficient simply expressed in terms of the velocity correlations accurately
matches the results. Dust settling starts to become apparent for particle sizes
of the order of 1 to 10 centimeters for which the gas begins to decouple in a
standard solar nebula model at 5.2 AU. However, for particles which are 10
centimeters in size, complete settling toward a very thin midplane layer is
prevented by turbulent motions within the disk, even in the presence of a
midplane dead zone of significant size. These results indicate that, when
present, MHD turbulence affects dust dynamics in protoplanetary disks. We find
that the evolution and settling of the dust can be accurately modelled using an
advection diffusion equation that incorporates vertical settling. The value of
the diffusion coefficient can be calculated from the turbulent velocity field
when that is known for a time of several local orbits.
