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 τ s = 10 −1 − 10 0 , one where τ s = 10 −4 − 10 −1 and finally one where τ 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, dN/da ∝ a −q , is either q = 3 or q = 4. We overall find that the steepness of the size distribution and the discrete versus continuous approach have little impact on the results. The level of diffusion and drift rates are mainly dictated by the range of particle sizes. 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.

The first stages of planet formation take place in protoplanetary disks that are largely made up of gas. Understanding how the gas affects planetesimals in the protoplanetary disk is therefore essential. In this paper, we discuss whether or not gas flow can erode planetesimals. We estimated how much shear stress is exerted onto the planetesimal surface by the gas as a function of disk and planetesimal properties. To determine whether erosion can take place, we compared this with previous measurements of the critical stress that a pebble-pile planetesimal can withstand before erosion begins. If erosion took place, we estimated the erosion time of the affected planetesimals. We also illustrated our estimates with two-dimensional numerical simulations of flows around planetesimals using the lattice Boltzmann method. We find that the wall shear stress can overcome the critical stress of planetesimals in an eccentric orbit within the innermost regions of the disk. The high eccentricities needed to reach erosive stresses could be the result of shepherding by migrating planets. We also find that if a planetesimal erodes, it does so on short timescales. For planetesimals residing outside of 1 au, we find that they are mainly safe from erosion, even in the case of highly eccentric orbits.

The streaming instability provides an efficient way of overcoming the growth barriers in the initial stages of the planet formation process. Considering the realistic case of a particle size distribution, the dynamics of the system is altered compared to the outcome of single size models. In order to understand the outcome of the multispecies streaming instability in detail, we perform a large parameter study in terms of particle number, particle size distribution, particle size range, initial metallicity, and initial particle scale height. We study vertically stratified systems and determine the metallicity threshold for filament formation. We compare these with a system where the initial particle distribution is unstratified and find that its evolution follows that of its stratified counterpart. We find that a change in the particle number does not result in significant variation in the efficiency and timing of filament formation. We also see that there is no clear trend for how varying the size distribution in combination with the particle size range changes the outcome of the multispecies streaming instability. Finally, we find that an initial metallicity of Zinit = 0.005 and Zinit = 0.01 both result in similar critical metallicity values for the start of filament formation. Our results show that the inclusion of a particle size distribution into streaming instability simulations, while changing the dynamics as compared to mono-disperse systems, does not result in overall unfavorable conditions for solid growth. We attribute the subdominant role of multiple species to the high-density conditions in the midplane, conditions under which linear stability analysis also predict little difference between single and multiple species.

We investigate the possibility of erosion of planetesimals in a protoplanetary disk. We use theory and direct numerical simulations (Lattice Boltzmann Method) to calculate the erosion of large -much larger than mean-free-path of gas molecules -bodies of different shapes in flows. We find that erosion follows a universal power-law in time, at intermediate times, independent of the Reynolds number of the flow and the initial shape of the body. Consequently, we estimate that planetesimals in eccentric orbits, of even very small eccentricity, rapidly (in about hundred years) erodes away if the semi-major axis of their orbit lies in the inner disk -less than about 10 AU. Even planetesimals in circular orbits erode away in approximately ten thousand years if the semi-major axis of their orbits are 0.6AU.