Dust coagulation in protoplanetary disks: a rapid depletion of small   grains
  We model the process of dust coagulation in protoplanetary disks and calculate how it affects their observational appearance. Our model involves the detailed solution of the coagulation equation at every location in the disk. At regular time intervals we feed the resulting 3-D dust distribution functions into a continuum radiative transfer code to obtain spectral energy distributions. We find that, even if only the very basic -- and well understood -- coagulation mechanisms are included, the process of grain growth is much too quick to be consistent with infrared observations of T Tauri disks. Small grains are removed so efficiently that, long before the disk reaches an age of 1E6 years typical of T Tauri stars, the SED shows only very weak infrared excess. This is inconsistent with observed SEDs of most classical T Tauri stars. Small grains somehow need to be replenished, for instance by aggregate fragmentation through high-speed collisions. A very simplified calculation shows that when aggregate fragmentation is included, a quasi-stationary grain size distribution is obtained in which growth and fragmentation are in equilibrium. This quasi-stationary state may last 1E6 years or even longer, dependent on the circumstances in the disk, and may bring the time scales into the right regime. We conclude that a simple evolutionary scenario in which grains slowly grow from pristine 0.1 micron grains to larger grains over a period of a few Myr is most likely incorrect. 
C.P. Dullemond and C. Dominik