Mechanisms of Cluster Formation in Force-Free Granular Gases

C. Salueña; L. Almazán; N. V. Brilliantov

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 4, page 175-190
  • ISSN: 0973-5348

Abstract

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The evolution of a force-free granular gas with a constant restitution coefficient is studied by means of granular hydrodynamics. We numerically solve the hydrodynamic equations and analyze the mechanisms of cluster formation. According to our findings, the presently accepted mode-enslaving mechanism may not be responsible for the latter phenomenon. On the contrary, we observe that the cluster formation is mainly driven by shock-waves, which spontaneously originate and develop in the system. This agrees with a previously suggested mechanism of formation of density singularities in one-dimensional granular gases.

How to cite

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Salueña, C., Almazán, L., and Brilliantov, N. V.. "Mechanisms of Cluster Formation in Force-Free Granular Gases." Mathematical Modelling of Natural Phenomena 6.4 (2011): 175-190. <http://eudml.org/doc/222446>.

@article{Salueña2011,
abstract = {The evolution of a force-free granular gas with a constant restitution coefficient is studied by means of granular hydrodynamics. We numerically solve the hydrodynamic equations and analyze the mechanisms of cluster formation. According to our findings, the presently accepted mode-enslaving mechanism may not be responsible for the latter phenomenon. On the contrary, we observe that the cluster formation is mainly driven by shock-waves, which spontaneously originate and develop in the system. This agrees with a previously suggested mechanism of formation of density singularities in one-dimensional granular gases.},
author = {Salueña, C., Almazán, L., Brilliantov, N. V.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {granular gas; cluster instability; hydrodynamics; numerical simulations},
language = {eng},
month = {7},
number = {4},
pages = {175-190},
publisher = {EDP Sciences},
title = {Mechanisms of Cluster Formation in Force-Free Granular Gases},
url = {http://eudml.org/doc/222446},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Salueña, C.
AU - Almazán, L.
AU - Brilliantov, N. V.
TI - Mechanisms of Cluster Formation in Force-Free Granular Gases
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/7//
PB - EDP Sciences
VL - 6
IS - 4
SP - 175
EP - 190
AB - The evolution of a force-free granular gas with a constant restitution coefficient is studied by means of granular hydrodynamics. We numerically solve the hydrodynamic equations and analyze the mechanisms of cluster formation. According to our findings, the presently accepted mode-enslaving mechanism may not be responsible for the latter phenomenon. On the contrary, we observe that the cluster formation is mainly driven by shock-waves, which spontaneously originate and develop in the system. This agrees with a previously suggested mechanism of formation of density singularities in one-dimensional granular gases.
LA - eng
KW - granular gas; cluster instability; hydrodynamics; numerical simulations
UR - http://eudml.org/doc/222446
ER -

References

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  1. E. Ben-Naim, S. Y. Chen, G. D. Doolen, S. Redner. Shock-like dynamics of inelastic gases. Phys. Rev. Lett., 83 (1999), 4069–4072.  
  2. J. J. Brey, D. Cubero. Hydrodynamic transport coefficients of granular gases. In Pöschel and Luding [28], 59–78.  
  3. J. J. Brey, J. W. Dufty, C. S. Kim, A. Santos. Hydrodynamics for granular flow at low density. Phys. Rev. E, 58 (1998), 4638–4653.  
  4. J. J. Brey, M. J. Ruiz-Montero, D. Cubero. Origin of density clustering in a freely evolving granular gas. Phys. Rev. E, 60 (1999), 3150–3157.  
  5. N. V. Brilliantov, T. Poeschel. Kinetic Theory of Granular Gases. University Press, Oxford, 2004.  Zbl1155.76386
  6. N. V. Brilliantov, T. Pöschel. Hydrodynamics of granular gases of viscoelastic particles. Phil. Trans. R. Soc. Lond. A, 360 (2001), 415–428.  Zbl1002.76121
  7. N. V. Brilliantov, T. Pöschel. Hydrodynamics and transport coefficients for granular gases. Phys. Rev. E, 67 (2003), 061304.  
  8. N. V. Brilliantov, C. Saluena, T. Schwager, T. Pöschel. Transient structures in a granular gas. Phys. Rev. Lett., 93 (2004), 134301.  
  9. N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, T. Pöschel. Model for collisions in granular gases. Phys. Rev. E, 53 (1996), 5382–5393.  
  10. R. Brito, M. H. Ernst. Extension of Haff’s cooling law in granular flows. Europhys. Lett., 43 (1998), 497–504.  
  11. J. A. Carrillo, T Pöschel, C. Salueña. Granular hydrodynamics and pattern formation in vertically oscillated granular disk layers. J. Fluid Mech., 597 (2008), 119–144.  Zbl1170.76056
  12. E. Efrati, E. Livne, B. Meerson. Hydrodynamic singularities and clustering instability in a freely cooling inelastic gas. Phys. Rev. Lett., 94 (2005), 088001.  
  13. V. Garzo. Enskog constitutive equations for hard disks. preprint (2008).  
  14. V. Garzo, J. W. Dufty. Dense fluid transport for inelastic hard spheres. Phys. Rev. E, 59 (1999), 5895–5911.  
  15. I. Goldhirsch, G. Zanetti. Clustering instability in dissipative gases. Phys. Rev. Lett., 70 (1993), 1619-1622.  
  16. A. Goldshtein, M. Shapiro. Mechanics of collisional motion of granular materials. Part 1: General hydrodynamic equations. J. Fluid Mech., 282 (1995), 75–114.  Zbl0881.76010
  17. S. A. Hill, G. F. Mazenko. Granular clustering in a hydrodynamic simulation. Phys. Rev. E, 67 (2003), 061302.  
  18. J. T. Jenkins, M. W. Richman. Grad’s 13-moment system for a dense gas of inelastic spheres. Archives for Particle Mechanics and Analysis, 87 (1985), 355–377.  Zbl0617.76085
  19. E. Khain, B. Meerson. Symmetry-breaking instability in a prototypical driven granular gas. Phys. Rev. E, 66 (2002), 021306.  
  20. G. Kuwabara, K. Kono. Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys., 26 (1987), 1230–1233.  
  21. C. K. K. Lun, S. B. Savage, D. J. Jeffrey, N. Chepurniy. Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech., 140 (1984), 223–256 .  Zbl0553.73098
  22. J. F. Lutsko. Transport properties of dense dissipative hard-sphere fluids for arbitrary energy loss models. Phys. Rev. E, 72 (2005), 021306.  
  23. B. Meerson, A. Puglisi. Towards a continuum theory of clustering in a freely cooling inelastic gas. Europhys. Lett., 70 (2005), 478–484.  
  24. W. A. M. Morgado, I. Oppenheim. Energy dissipation for quasielastic granular particle collisions. Phys. Rev. E, 55 (1997), 1940–1945.  
  25. X. Nie, E. Ben-Naim, S. Y. Chen. Dynamics of freely cooling granular gases. Phys. Rev. Lett., 89 (2002), 204301.  
  26. T. Pöschel, N. V. Brilliantov, editors. Granular Gas Dynamics, Lecture Notes in Physics Vol. 624. Springer, Berlin, 2003.  Zbl1028.82534
  27. T. Pöschel, N. V. Brilliantov, T. Schwager. Long-time behavior of granular gases with impact-velocity dependent coefficient of restitution. Physica A, 325 (2003), 274–283.  Zbl1028.82534
  28. T. Pöschel, S. Luding, editors. Granular Gases, Lecture Notes in Physics Vol. 564. Springer, Berlin, 2001.  
  29. A. Puglisi, M. Assaf, I. Fouxon, B. Meerson. Attempted density blowup in a freely cooling dilute granular gas: Hydrodynamics versus molecular dynamics. Phys. Rev. E, 77 (2008), 021305.  
  30. R. Ramírez, T. Pöschel, N. V. Brilliantov, T. Schwager. Coefficient of restitution for colliding viscoelastic spheres. Phys. Rev. E, 60 (1999), 4465–4472.  
  31. P. Resibois, M. de Leener. Classical Kinetic Theory of Fluids. Wiley & Sons, New York, 1977.  Zbl0152.46503
  32. T. Schwager, T. Pöschel. Coefficient of restitution of viscous particles and cooling rate of granular gases. Phys. Rev. E, 57 (1998), 650–654.  
  33. N. Sela, I. Goldhirsch. Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech., 361 (1998), 41–74.  Zbl0927.76008
  34. S. F. Shandarin, Ya. B. Zeldovich. The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium. Rev. Mod. Phys., 61 (1989), 185–222.  
  35. F. Spahn, U. Schwarz, J. Kurths. Clustering of granular assemblies with temperature dependent restitution and under keplerian differential rotation. Phys. Rev. Lett., 78 (1997), 1596–1599.  
  36. S. Torquato. Nearest-neighbor statistics for packings of hard spheres and disks. Phys. Rev. E, 51 (1995), 3170–3555. 

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