Analysis of the instability due to gas-dust friction in protoplanetary
  discs
  We study stability of a dust layer in a gaseous disc subject to the linear
axisymmetric perturbations. Instead of considering single-size particles,
however, the population of dust particles is assumed to consist of two grain
species. Dust grains exchange momentum with the gas via the drag force and
their self-gravity is also considered. We show that the presence of two grain
sizes can increase the efficiency of the linear growth of drag-driven
instability in the protoplanetary discs. A second dust phase with a small mass,
comparing to the first dust phase, would reduce the growth timescale even by a
factor of two or more especially when its coupling to the gas is weak. It means
that once a certain amount of large dust particles form, even though it is much
smaller than that of small dust particles, the dust layer becomes more unstable
and dust clumping are accelerated. Thus, presence of dust particles with
various sizes must be considered in studies of dust clumping in protoplanetary
discs where both large and small dust grains are present.
