Radial Flow of Dust Particles in Accretion Disks
  We study the radial migration of dust particles in accreting protostellar disks analogous to the primordial solar nebula. This study takes account of the two dimensional (radial and normal) structure of the disk gas, including the effects of the variation in the gas velocity as a function of distance from the midplane. It is shown that the dust component of disks accretes slower than the gas component. At high altitude from the disk midplane, the gas rotates faster than particles because of the inward pressure gradient force, and its drag force causes particles to move outward in the radial direction. Viscous torque induces the gas within a scale height from the disk midplane to flow outward, carrying small (size < 100 micron at 10 AU) particles with it. Only particles at intermediate altitude or with sufficiently large sizes (> 1 mm at 10 AU) move inward. When the particles' radial velocities are averaged over the entire vertical direction, particles have a net inward flux. At large distances from the central star, particles migrate inward with a velocity much faster than the gas accretion velocity. However, their inward velocity is reduced below that of the gas in the inner regions of the disk. The rate of velocity decrease is a function of the particles' size. While larger particles retain fast accretion velocity until they approach closer to the star, 10 micron particles have slower velocity than the gas in the most part of the disk (r < 100 AU). This differential migration of particles causes the size fractionation. Dust disks composed mostly of small particles (size < 10 micron) accrete slower than gas disks, resulting in the increase in the dust-gas ratio during the gas accretion phase. 
Taku Takeuchi and D.N.C. Lin