  The behaviour of sedimenting particles depends on the dust-to-gas ratio of
the fluid. Linear stability analysis shows that solids settling in the Epstein
drag regime would remain homogeneously distributed in non-rotating
incompressible fluids, even when dust-to-gas ratios reach unity. However, the
non-linear evolution has not been probed before. Here, we present numerical
calculations indicating that in a particle-dense mixture solids spontaneously
mix out of the fluid and form swarms overdense in particles by at least a
factor 10. The instability is caused by mass-loaded regions locally breaking
the equilibrium background stratification. The driving mechanism depends on
non-linear perturbations of the background flow and shares some similarity to
the streaming instability in accretion discs. The resulting particle-rich
swarms may stimulate particle growth by coagulation. In the context of
protoplanetary discs, the instability could be relevant for aiding small
particles to settle to the midplane in the outer disc. Inside the gas envelopes
of protoplanets, enhanced settling may lead to a reduced dust opacity, which
facilitates the contraction of the envelope. We show that the relevant physical
set up can be recreated in a laboratory setting. This will allow our numerical
calculations to be investigated experimentally in the future.
