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Context. Circumstellar disks are known to contain a significant mass in dustranging from micron to centimeter size. Meteorites are evidence that individualgrains of those sizes were collected and assembled into planetesimals in theyoung solar system. Aims. We assess the efficiency of dust collection of aswarm of non-drifting planetesimals {\rev with radii ranging from 1 to$10^3$\,km and beyond. Methods. We calculate the collision probability of dustdrifting in the disk due to gas drag by planetesimal accounting for severalregimes depending on the size of the planetesimal, dust, and orbital distance:the geometric, Safronov, settling, and three-body regimes. We also include ahydrodynamical regime to account for the fact that small grains tend to becarried by the gas flow around planetesimals. Results. We provide expressionsfor the collision probability of dust by planetesimals and for the filteringefficiency by a swarm of planetesimals. For standard turbulence conditions(i.e., a turbulence parameter $\alpha=10^{-2}$), filtering is found to beinefficient, meaning that when crossing a minimum-mass solar nebula (MMSN) beltof planetesimals extending between 0.1 AU and 35 AU most dust particles areeventually accreted by the central star rather than colliding withplanetesimals. However, if the disk is weakly turbulent ($\alpha=10^{-4}$)filtering becomes efficient in two regimes: (i) when planetesimals are allsmaller than about 10 km in size, in which case collisions mostly take place inthe geometric regime; and (ii) when planetary embryos larger than about 1000 kmin size dominate the distribution, have a scale height smaller than one tenthof the gas scale height, and dust is of millimeter size or larger in which casemost collisions take place in the settling regime. These two regimes have verydifferent properties: we find that the local filtering efficiency$x_{filter,MMSN}$ scales with $r^{-7/4}$ (where $r$ is the orbital distance) inthe geometric regime, but with $r^{-1/4}$ to $r^{1/4}$ in the settling regime.This implies that the filtering of dust by small planetesimals should occurclose to the central star and with a short spread in orbital distances. On theother hand, the filtering by embryos in the settling regime is expected to bemore gradual and determined by the extent of the disk of embryos. Dustparticles much smaller than millimeter size tend only to be captured by thesmallest planetesimals because they otherwise move on gas streamlines and theircollisions take place in the hydrodynamical regime. Conclusions. Our resultshint at an inside-out formation of planetesimals in the infant solar systembecause small planetesimals in the geometrical limit can filter dust much moreefficiently close to the central star. However, even a fully-formed belt ofplanetesimals such as the MMSN only marginally captures inward-drifting dustand this seems to imply that dust in the protosolar disk has been filtered byplanetesimals even smaller than 1 km (not included in this study) or that ithas been assembled into planetesimals by other mechanisms (e.g., orderlygrowth, capture into vortexes). Further refinement of our work concerns, amongother things: a quantitative description of the transition region between thehydro and settling regimes; an assessment of the role of disk turbulence forcollisions, in particular in the hydro regime; and the coupling of our model toa planetesimal formation model.

On the filtering and processing of dust by planetesimals 1. Derivation of collision probabilities for non-drifting planetesimals