  The radial drift and diffusion of dust particles in protoplanetary disks
affect both the opacity and temperature of such disks as well as the location
and timing of planetesimal formation. In this paper, we present results of
numerical simulations of particle-gas dynamics in protoplanetary disks that
include dust grains with various size distributions. We consider three
scenarios in terms of particle size ranges, one where the Stokes number
$\tau_{\rm{s}} = 10^{-1} - 10^0$, one where $\tau_{\rm{s}} = 10^{-4} - 10^{-1}$
and finally one where $\tau_{\rm{s}} = 10^{-3} - 10^{0}$. Moreover, we consider
both discrete and continuous distributions in particle size. In accordance with
previous works we find in our multi-species simulations that different particle
sizes interact via the gas and as a result their dynamics changes compared to
the single-species case. The larger species trigger the streaming instability
and create turbulence that drives the diffusion of the solid materials. We
measure the radial equilibrium velocity of the system and find that the radial
drift velocity of the large particles is reduced in the multi-species
simulations and that the small particle species move on average outwards. We
also vary the steepness of the size distribution, such that the exponent of the
solid number density distribution, $\rm{d}\it{N}/\rm{d}\it{a} \propto
\it{a^{-q}}$, is either $q = 3$ or $q = 4$. We measure the scale height of the
particles and observe that small grains are stirred up well above the
sedimented midplane layer where the large particles reside. Our measured
diffusion and drift parameters can be used in coagulation models for planet
formation as well as to understand relative mixing of the components of
primitive meteorites (matrix, chondrules and CAIs) prior to inclusion in their
parent bodies.
