Spontaneous concentrations of solids through two-way drag forces between gas and sedimenting particles

TL;DR

This paper investigates a non-linear instability in sedimenting particles within gas, revealing spontaneous formation of dense particle swarms that could influence planet formation and can be studied experimentally.

Contribution

It presents the first numerical analysis of non-linear evolution of particle sedimentation instability, showing formation of dense particle swarms in gas.

Findings

Particles form overdense swarms by at least a factor of 10.

The instability is driven by non-linear flow perturbations.

Potential implications for planet formation and dust opacity in protoplanetary discs.

Abstract

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.