Individual and collective behavior of dust particles in a protoplanetary nebula

We study the interaction between gas and dust particles in a protoplanetary disk, comparing analytical and numerical results. We first calculate analytically the trajectories of individual particles undergoing gas drag in the disk, in the asymptotic cases of very small particles (Epstein regime) and very large particles (Stokes regime). Using a Boltzmann averaging method, we then infer their collective behavior. We compare the results of this analytical formulation against numerical computations of a large number of particles. Using successive moments of the Boltzmann equation, we derive the equivalent fluid equations for the average motion of the particles; these are intrinsically different in the Epstein and Stokes regimes. We are also able to study analytically the temporal evolution of a collection of particles with a given initial size-distribution provided collisions are ignored.Comment: 15 pages, 9 figures, submitted to Ap