Dust and gas mixtures with multiple grain species - a one-fluid approach

TL;DR

This paper develops a one-fluid formalism to model mixtures of gas and multiple dust species, enabling more accurate and efficient simulations of astrophysical dust dynamics, including phenomena like streaming instability and radial drift.

Contribution

It generalizes previous two-fluid models to a single-fluid approach for multiple dust phases, with analytic approximations for strong drag regimes and applications to astrophysical problems.

Findings

Non-monotonic velocity evolution due to multiple dust phases

Enhanced linear growth of streaming instability

Large grains can migrate outward in protoplanetary discs

Abstract

We derive the single-fluid evolution equations describing a mixture made of a gas phase and an arbitrary number of dust phases, generalising the approach developed in Laibe & Price (2014a). A generalisation for continuous dust distributions as well as analytic approximations for strong drag regimes are also provided. This formalism lays the foundation for numeri- cal simulations of dust populations in a wide range of astrophysical systems while avoiding limitations associated with a multiple-fluid treatment. The usefulness of the formalism is illustrated on a series of analytical problems, namely the dustybox, dustyshock and dustywave problems as well as the radial drift of grains and the streaming instability in protoplanetary discs. We find physical effects specific to the presence of several dust phases and multiple drag timescales, including non-monotonic evolution of the differential velocity between phases and increased efficiency of the linear growth of the streaming instability. Interestingly, it is found that under certain conditions, large grains can migrate outwards in protoplanetary discs. This may explain the presence of small pebbles at several hundreds of astronomical units from their central star.