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Mechanisms of Cluster Formation in Force-Free GranularGases

Published online by Cambridge University Press:  18 July 2011

C. Salueña ,
L. Almazán  and
N. V. Brilliantov
C. Salueña
Affiliation:
Department of Mechanical Engineering, Universitat Rovira i Virgili, E-43007 Tarragona, Spain
L. Almazán
Affiliation:
Department of Mechanical Engineering, Universitat Rovira i Virgili, E-43007 Tarragona, Spain Centre de Recerca Matemàtica, 08193 Bellaterra, Spain
N. V. Brilliantov*
Affiliation:
Department of Mathematics University of Leicester, Leicester LE1 7RH, UK
*
⋆Corresponding author. E-mail: nb144@leicester.ac.uk
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Abstract

The evolution of a force-free granular gas with a constant restitution coefficient isstudied by means of granular hydrodynamics. We numerically solve the hydrodynamicequations and analyze the mechanisms of cluster formation. According to our findings, thepresently accepted mode-enslaving mechanism may not be responsible for the latterphenomenon. On the contrary, we observe that the cluster formation is mainly driven byshock-waves, which spontaneously originate and develop in the system. This agrees with apreviously suggested mechanism of formation of density singularities in one-dimensionalgranular gases.

Keywords

granular gascluster instabilityhydrodynamicsnumerical simulations

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Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 4: Granular hydrodynamics , 2011 , pp. 175 - 190
Copyright
© EDP Sciences, 2011

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References

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