Mechanisms of Cluster Formation in Force-Free Granular Gases

C. Salueña¹ ; L. Almazán^1, 2 ; N. V. Brilliantov³

¹ Department of Mechanical Engineering, Universitat Rovira i Virgili, E-43007 Tarragona, Spain
² Centre de Recerca Matemàtica, 08193 Bellaterra, Spain
³ Department of Mathematics University of Leicester, Leicester LE1 7RH, UK

Mathematical modelling of natural phenomena, Tome 6 (2011) no. 4, pp. 175-190

Résumé

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.

Détail

DOI : 10.1051/mmnp/20127108

Bibliographie

[1] E. Ben-Naim, S. Y. Chen, G. D. Doolen, S. Redner Phys. Rev. Lett. 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 Phys. Rev. E 1998 4638 4653

[4] J. J. Brey, M. J. Ruiz-Montero, D. Cubero Phys. Rev. E 1999 3150 3157

[5] N. V. Brilliantov, T. Poeschel. Kinetic Theory of Granular Gases. University Press, Oxford, 2004.

[6] N. V. Brilliantov, T. Pöschel Phil. Trans. R. Soc. Lond. A 2001 415 428

[7] N. V. Brilliantov, T. Pöschel Phys. Rev. E 2003

[8] N. V. Brilliantov, C. Saluena, T. Schwager, T. Pöschel Phys. Rev. Lett. 2004

[9] N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, T. Pöschel Phys. Rev. E 1996 5382 5393

[10] R. Brito, M. H. Ernst Europhys. Lett. 1998 497 504

[11] J. A. Carrillo, T Pöschel, C. Salueña J. Fluid Mech. 2008 119 144

[12] E. Efrati, E. Livne, B. Meerson Phys. Rev. Lett. 2005

[13] V. Garzo. Enskog constitutive equations for hard disks. preprint (2008).

[14] V. Garzo, J. W. Dufty Phys. Rev. E 1999 5895 5911

[15] I. Goldhirsch, G. Zanetti Phys. Rev. Lett. 1993 1619 1622

[16] A. Goldshtein, M. Shapiro J. Fluid Mech. 1995 75 114

[17] S. A. Hill, G. F. Mazenko Phys. Rev. E 2003

[18] J. T. Jenkins, M. W. Richman Archives for Particle Mechanics and Analysis 1985 355 377

[19] E. Khain, B. Meerson Phys. Rev. E 2002

[20] G. Kuwabara, K. Kono Jpn. J. Appl. Phys. 1987 1230 1233

[21] C. K. K. Lun, S. B. Savage, D. J. Jeffrey, N. Chepurniy J. Fluid Mech. 1984 223 256

[22] J. F. Lutsko Phys. Rev. E 2005

[23] B. Meerson, A. Puglisi Europhys. Lett. 2005 478 484

[24] W. A. M. Morgado, I. Oppenheim Phys. Rev. E 1997 1940 1945

[25] X. Nie, E. Ben-Naim, S. Y. Chen Phys. Rev. Lett. 2002

[26] T. Pöschel, N. V. Brilliantov, editors. Granular Gas Dynamics, Lecture Notes in Physics Vol. 624. Springer, Berlin, 2003.

[27] T. Pöschel, N. V. Brilliantov, T. Schwager Physica A 2003 274 283

[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 Phys. Rev. E 2008

[30] R. Ramírez, T. Pöschel, N. V. Brilliantov, T. Schwager Phys. Rev. E 1999 4465 4472

[31] P. Resibois, M. de Leener. Classical Kinetic Theory of Fluids. Wiley Sons, New York, 1977.

[32] T. Schwager, T. Pöschel Phys. Rev. E 1998 650 654

[33] N. Sela, I. Goldhirsch J. Fluid Mech. 1998 41 74

[34] S. F. Shandarin, Ya. B. Zeldovich Rev. Mod. Phys. 1989 185 222

[35] F. Spahn, U. Schwarz, J. Kurths Phys. Rev. Lett. 1997 1596 1599

[36] S. Torquato Phys. Rev. E 1995 3170 3555