- Access by Xinjiang University
Shearing instability of a dilute granular mixture
Phys. Rev. E 87, 022210 – Published 27 February, 2013
DOI: https://doi.org/10.1103/PhysRevE.87.022210
Abstract
The shearing instability of a dilute granular mixture composed of smooth inelastic hard spheres or disks is investigated. By using the Navier-Stokes hydrodynamic equations, it is shown that the scaled transversal velocity mode exhibits a divergent behavior, similarly to what happens in one-component systems. The theoretical prediction for the critical size is compared with direct Monte Carlo simulations of the Boltzmann equations describing the system, and a good agreement is found. The total energy fluctuations in the vicinity of the transition are shown to scale with the second moment of the distribution. The scaling distribution function is the same as found in other equilibrium and nonequilibrium phase transitions, suggesting the existence of some kind of universality.
Article Text
References (33)
- I. Goldhirsch, Ann. Rev. Fluid Mech. 35, 267 (2003).
- J. J. Brey, J. W. Dufty, and A. Santos, J. Stat. Phys. 87, 1051 (1997).
- I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993); I. Goldhirsch, M. L. Tan, and G. Zanetti, J. Sci. Comput. 8, 1 (1993).
- S. McNamara and W. R. Young, Phys. Rev. E 50, R28 (1994).
- N. V. Brilliantov and T. Pöschel, Kinetic Theory of Granular Gases (Oxford University Press, Oxford, 2004).
- J. J. Brey, M. J. Ruiz-Montero, and D. Cubero, Phys. Rev. E 60, 3150 (1999).
- P. P. Mitrano, V. Garzó, A. M. Hilger, C. J. Ewasko, and C. M. Hrenya, Phys. Rev. E 85, 041303 (2012).
- T. P. C. van Noije, M. H. Ernst, R. Brito, and J. A. G. Orza, Phys. Rev. Lett. 79, 411 (1997).
- J. J. Brey, F. Moreno, and M. J. Ruiz-Montero, Phys. Fluids 10, 2965 (1998).
- J. J. Brey, A. Domínguez, M. I. García de Soria, and P. Maynar, Phys. Rev. Lett. 96, 158002 (2006).
- V. Garzó and J. M. Montanero, J. Stat. Phys. 129, 27 (2007).
- V. Garzó, C. M. Hrenya, and J. W. Dufty, Phys. Rev. E 76, 031304 (2007).
- V. Garzó, J. M. Montanero, and J. W. Dufty, Phys. Fluids 18, 083305 (2006).
- V. Garzó and J. W. Dufty, Phys. Rev. E 60, 5706 (1999).
- J. W. Dufty, J. J. Brey, and J. Lutsko, Phys. Rev. E 65, 051303 (2002).
- A. Barrat and E. Trizac, Granular Matter 4, 57 (2002).
- J. J. Brey and M. J. Ruiz-Montero, Phys. Rev. E 84, 031302 (2011).
- S. R. Dahl, C. M. Hrenya, V. Garzó, and J. W. Dufty, Phys. Rev. E 66, 041301 (2002).
- J. M. Montanero and V. Garzó, Granular Matter 4, 17 (2002).
- M. J. Ruiz-Montero and J. J. Brey, AIP Conf. Proc. 1501, 977 (2012).
- J. J. Brey, J. W. Dufty, C. S. Kim, and A. Santos, Phys. Rev. E 58, 4638 (1998).
- V. Garzó and J. W. Dufty, Phys. Fluids 14, 1476 (2002).
- G. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, Oxford, 1994).
- A. García, Numerical methods for Physics (Prentice Hall, Englewood Hills, NJ, 2000).
- J. J. Brey, M. J. Ruiz-Montero, and D. Cubero, Phys. Rev. E 54, 3664 (1996).
- J. F. Lutsko, Phys. Rev. E 63, 061211 (2001).
- J. J. Brey, M. J. Ruiz-Montero, and F. Moreno, Phys. Rev. E 69, 051303 (2004).
- J. W. Dufty and J. J. Brey, Math. Model. Nat. Phenom. 6, 19 (2011).
- J. J. Brey, M. I. García de Soria, P. Maynar, and M. J. Ruiz-Montero, Phys. Rev. Lett. 94, 098001 (2005).
- J. J. Brey and M. J. Ruiz-Montero, Granular Matter 10, 53 (2007).
- J. J. Brey and M. J. Ruiz-Montero (unpublished).
- S. T. Bramwell, P. C. W. Holdsworth, and J.-F. Pinton, Nature (London) 396, 552 (1998).
- S. T. Bramwell, K. Christensen, J.-Y. Fortin, P. C. W. Holdsworth, H. J. Jensen, S. Lise, J. M. López, M. Nicodemi, J.-F. Pinton, and M. Sellitto, Phys. Rev. Lett. 84, 3744 (2000).