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Stability of freely cooling granular mixtures at moderate densities

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  • Garzó, Vicente

Abstract

The formation of velocity vortices and density clusters is an intriguing phenomenon of freely cooling granular flows. In this work, the critical length scale Lc for the onset of instability is determined via stability analysis of the linearized Navier–Stokes hydrodynamic equations of d-dimensional granular binary mixtures at moderate densities. In contrast to previous attempts, the analysis is not restricted to nearly elastic systems since it takes into account the nonlinear dependence of the transport coefficients and the cooling rate on the collisional dissipation. As expected from previous results obtained in the very dilute regime, linear stability shows d−1transversal (shear) modes and a longitudinal (“heat”) mode to be unstable with respect to long enough wavelength excitations. The theoretical predictions also show that the origin of the instability is driven by the transversal component of the velocity field that becomes unstable when the system length L > Lc. An explicit expression of Lc is obtained in terms of the masses and diameters of the mixture, the composition, the volume fraction and the coefficients of restitution. Previous results derived in the limit of both mechanically equivalent particles and low-density mixtures are consistently recovered. Finally, a comparison with previous theoretical works which neglect the influence of dissipation on the transport coefficients shows quantitative discrepancies for strong dissipation.

Suggested Citation

  • Garzó, Vicente, 2015. "Stability of freely cooling granular mixtures at moderate densities," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 497-509.
  • Handle: RePEc:eee:chsofr:v:81:y:2015:i:pb:p:497-509
    DOI: 10.1016/j.chaos.2015.07.022
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    References listed on IDEAS

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    1. Garzó, Vicente & Santos, Andrés & Montanero, José María, 2007. "Modified Sonine approximation for the Navier–Stokes transport coefficients of a granular gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 94-107.
    2. A. Petri & A. Baldassarri & F. Dalton & G. Pontuale & L. Pietronero & S. Zapperi, 2008. "Stochastic dynamics of a sheared granular medium," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 64(3), pages 531-535, August.
    3. Andrea Gnoli & Andrea Puglisi & Alessandro Sarracino & Angelo Vulpiani, 2014. "Nonequilibrium Brownian Motion beyond the Effective Temperature," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-5, April.
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