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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Vega Reyes, Francisco and Santos, Andrés 2015. Steady state in a gas of inelastic rough spheres heated by a uniform stochastic force. Physics of Fluids, Vol. 27, Issue. 11, p. 113301.


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  • Journal of Fluid Mechanics, Volume 738
  • January 2014, R2

Kinetic-theory predictions of clustering instabilities in granular flows: beyond the small-Knudsen-number regime

  • Peter P. Mitrano (a1), John R. Zenk (a1), Sofiane Benyahia (a2), Janine E. Galvin (a2), Steven R. Dahl (a1) and Christine M. Hrenya (a1)
  • DOI: http://dx.doi.org/10.1017/jfm.2013.602
  • Published online: 04 December 2013
Abstract
Abstract

In this work we quantitatively assess, via instabilities, a Navier–Stokes-order (small-Knudsen-number) continuum model based on the kinetic theory analogy and applied to inelastic spheres in a homogeneous cooling system. Dissipative collisions are known to give rise to instabilities, namely velocity vortices and particle clusters, for sufficiently large domains. We compare predictions for the critical length scales required for particle clustering obtained from transient simulations using the continuum model with molecular dynamics (MD) simulations. The agreement between continuum simulations and MD simulations is excellent, particularly given the presence of well-developed velocity vortices at the onset of clustering. More specifically, spatial mapping of the local velocity-field Knudsen numbers ($K{n}_{u} $) at the time of cluster detection reveals $K{n}_{u} \gg 1$ due to the presence of large velocity gradients associated with vortices. Although kinetic-theory-based continuum models are based on a small-$Kn$ (i.e. small-gradient) assumption, our findings suggest that, similar to molecular gases, Navier–Stokes-order (small-$Kn$) theories are surprisingly accurate outside their expected range of validity.

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Email address for correspondence: hrenya@colorado.edu
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