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

¹ Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, 22100 Lund, Sweden
e-mail: michiel@astro.lu.se
² Laboratoire Lagrange, UMR 7293, Université de Nice Sophia-Antipolis, Observatoire de la Côte d’Azur, Boulevard de l’Observatoire, 06304 Nice Cedex 4, France
³ Max Planck Institute for Dynamics and Self-Organization, (MPIDS), 37077 Göttingen, Germany
⁴ Institut für Geophysik und extraterrestrische Physik, Technische Universität Braunschweig, Mendelssohnstr. 3, 38106 Braunschweig, Germany

Received: 7 April 2015
Accepted: 16 March 2016

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 nonlinear 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 that are 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 nonlinear 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.