  Turbulent coagulation in protoplanetary disks is known to operate on
timescale far shorter than the lifetime of the disk. In the absence of
mechanisms that replenish the small dust grain population, protoplanetary disks
would rapidly lose their continuum opacity-bearing dust. This is inconsistent
with infrared observations of disks around T Tauri stars and Herbig Ae/Be
stars, which are usually optically thick at visual wavelengths and show
signatures of small (a<~ 3um) grains. A plausible replenishing mechanism of
small grains is collisional fragmentation or erosion of large dust aggregates,
which model calculations predict to play an important role in protoplanetary
disks. If optically thick disks are to be seen as proof for ongoing
fragmentation or erosion, then alternative explanations for the existence of
optically thick disks must be studied carefully. In this study we explore two
scenarios. First, we study the effect of residual, low-level infall of matter
onto the disk surface. We find that infall rates as low as 10^{-11} Msun/yr
can, in principle, replenish the small grain population to a level that keeps
the disk marginally optically thick. However, it remains to be seen if the
assumption of such inflow is realistic for star+disk systems at the age of
several Myrs, at which winds and jets are expected to have removed any residual
envelope. In summary, fragmentation or erosion still appear to be the most
promising processes to explain the abundant presence of small grains in old
disks.
