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Planetesimals in gaseous protoplanetary disks may grow by collecting dustparticles. Hydrodynamical studies show that small particles generally avoidcollisions with the planetesimals because they are entrained by the flow aroundthem. This occurs when $St$, the Stokes number, defined as the ratio of thedust stopping time to the planetesimal crossing time, becomes much smaller thanunity. However, these studies have been limited to the laminar case, whereasthese disks are believed to be turbulent. We want to estimate the influence ofgas turbulence on the dust-planetesimal collision rate and on the impactspeeds. We used three-dimensional direct numerical simulations of a fixedsphere (planetesimal) facing a laminar and turbulent flow seeded with smallinertial particles (dust) subject to a Stokes drag. A no-slip boundarycondition on the planetesimal surface is modeled via a penalty method. We findthat turbulence can significantly increase the collision rate of dust particleswith planetesimals. For a high turbulence case (when the amplitude of turbulentfluctuations is similar to the headwind velocity), we find that the collisionprobability remains equal to the geometrical rate or even higher for $St\geq0.1$, i.e., for dust sizes an order of magnitude smaller than in the laminarcase. We derive expressions to calculate impact probabilities as a function ofdust and planetesimal size and turbulent intensity.

Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks