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

Guillaume Laibe*, Daniel J. Price

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


We derive the single-fluid evolution equations describing a mixture made of a gas phase and an arbitrary number of dust phases, generalizing the approach developed by Laibe & Price. A generalization for continuous dust distributions as well as analytic approximations for strong drag regimes is also provided. This formalism lays the foundation for numerical 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 time-scales, 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.

Original languageEnglish
Pages (from-to)1940-1956
Number of pages17
JournalMonthly Notices of the Royal Astronomical Society
Issue number2
Early online date5 Sept 2014
Publication statusPublished - 21 Oct 2014


  • Hydrodynamics
  • Methods: numerical
  • Protoplanetary discs
  • Dust, extinction
  • Smoothed particle hydrodynamics
  • Kelvin-Helmholtz instability
  • Tauri circumbinary ring
  • Protoplanetary disks
  • Radial-drift
  • Streaming instabilities
  • Planetesimal formation
  • Forming planetesimals
  • Size distribution
  • Solar nebula


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