Skip to main content
Log in

On the development of inhomogeneities in freely evolving granular gases: The shear state and beyond

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

The understanding of the mechanisms leading to the formation of inhomogeneities in freely evolving granular gases is important to establish, for instance, the time scale for pattern formation. In this work, the shear state of an isolated granular gas will be analyzed. This is a two-band shear state with a steady density profile and an average temperature that decays in time with a Haff like law, but controlled by the viscosity of the gas. Hydrodynamics predicts that this state can only exist if the size of the system is larger than the critical size for the stability of the homogeneous cooling state, and expressions for the hydrodynamic fields in the limit of not too large inhomogeneities can be obtained. The theoretical predictions are compared with computer simulation results of a system of inelastic hard disks for several values of the coefficient of restitution, well beyond the quasi-elastic limit. It will be shown that the shear state is indeed exhibited by the system if its size is larger, but not much larger, than the critical size. The behaviour of the system and the way in which it deviates from the shear state as its size is increased will also be discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N.V. Brilliantov, T. Pöschel, Kinetic Theory of Granular Gases (Oxford University Press, Oxford, 2004)

  2. I. Goldhirsch, Annu. Rev. Fluid Mech. 35, 267 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  3. J.W. Dufty, J. Phys. Cond. Matter 12, A47 (2000)

    Article  ADS  Google Scholar 

  4. I. Goldhirsch, G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993)

    Article  ADS  Google Scholar 

  5. I. Goldhirsch, M.L. Tan, G. Zannetti, J. Sci. Comp. 8, 1 (1993)

    Article  MATH  Google Scholar 

  6. S. McNamara, W.R. Young, Phys. Rev. E 53, 5089 (1996)

    Article  ADS  Google Scholar 

  7. J.J. Brey, J.W. Dufty, C.S. Kim, A. Santos, Phys. Rev. E 58, 5638 (1998)

    Article  ADS  Google Scholar 

  8. R. Soto, M. Mareschal, M.M. Mansour, Phys. Rev. E 62, 3836 (2000)

    Article  ADS  Google Scholar 

  9. J. Wakou, R. Brito, M.H. Ernst, J. Stat. Phys. 107, 3 (2002)

    Article  MATH  Google Scholar 

  10. C.K.K. Lun, S.B. Savage, D.J. Jeffrey, N. Chepurniy, J. Fluid Mech. 140, 223 (1984)

    Article  MATH  ADS  Google Scholar 

  11. N. Sela, I. Goldhirsch, S.H. Noskowicz, Phys. Fluids 8, 2337 (1996)

    Article  MATH  ADS  Google Scholar 

  12. J.J. Brey, M.J. Ruiz-Montero, F. Moreno, Phys. Rev. E 55, 2845 (1997)

    Article  ADS  Google Scholar 

  13. J.J. Brey, M.J. Ruiz-Montero, A. Domínguez, Phys. Rev. E 78, 041301 (2008)

    Article  ADS  Google Scholar 

  14. J.J. Brey, D. Cubero, Granular Gases (Springer-Verlag, Berlin, 2000), p. 59

  15. G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, 1994)

  16. A.L. García, Numerical Methods for Physics (Prentice Hall Englewood Cliffs, NJ, 2000)

  17. J.J. Brey, M.J. Ruiz-Montero, Phys. Rev. E 69, 011305 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  18. J.J. Brey, M.J. Ruiz-Montero, D. Cubero, Phys. Rev. E 54, 3664 (1996)

    Article  ADS  Google Scholar 

  19. J.F. Lutsko, Phys. Rev. E 63, 061211 (2001)

    Article  ADS  Google Scholar 

  20. J.J. Brey, M.J. Ruiz-Montero, F. Moreno, Phys. Rev. E 69, 051303 (2004)

    Article  ADS  Google Scholar 

  21. J.J. Brey, M.J. Ruiz-Montero, F. Moreno, Phys. Fluids 10, 2976 (1998)

    Article  ADS  Google Scholar 

  22. I. Pagonabarraba, E. Trizac, T.P.C. van Noije, M.H. Ernst, Phys. Rev. E 65, 011303 (2001)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruiz-Montero, M., Javier Brey, J. On the development of inhomogeneities in freely evolving granular gases: The shear state and beyond. Eur. Phys. J. Spec. Top. 179, 249–262 (2009). https://doi.org/10.1140/epjst/e2010-01206-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2010-01206-3

Keywords

Navigation