Dust Coagulation Regulated by Turbulent Clustering in Protoplanetary Disks

The coagulation of dust particles is a key process in planetesimal formation. However, the radial drift and bouncing barriers are not completely resolved, especially for silicate dust. Since the collision velocities of dust particles are regulated by turbulence in a protoplanetary disk, turbulent clustering should be properly treated. To that end, direct numerical simulations (DNSs) of the Navier-Stokes equations are requisite. In a series of papers, Pan & Padoan used a DNS with Reynolds number Re ∼ 1000. Here, we perform DNSs with up to Re = 16,100, which allow us to track the motion of particles with Stokes numbers of 0.01 ≲ St ≲ 0.2 in the inertial range. Through the DNSs, we confirm that the rms relative velocity of particle pairs is smaller by more than a factor of two, compared to that by Ormel & Cuzzi. The distributions of the radial relative velocities are highly non-Gaussian. The results are almost consistent with those by Pan & Padoan or Pan et al. at low Re. Also, we find that the sticking rates for equal-sized particles are much higher than those for different-sized particles. Even in the strong-turbulence case with α-viscosity of 10^-2, the sticking rates are as high as 50% and the bouncing probabilities are as low as ∼10% for equal-sized particles of St ≲ 0.01. Thus, turbulent clustering plays a significant role in the growth of centimeter-sized compact aggregates (pebbles) and also enhances the solid abundance, which may lead to the streaming instability in a disk.