Navier-stokes transport coefficients of d-dimensional granular binary mixtures at low density

Journal of Statistical Physics

Volumn 129, Issue 1, 2007, Pages 27-58

  Garzó, Vicente ^a   Montanero, José María ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

DSMC method; Granular binary mixtures; Inelastic Boltzmann equation; Navier Stokes transport coefficients

Indexed keywords

EID: 34548628974     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9357-2     Document Type: Article

References (54)

1. Goldshtein, A., Shapiro, M.: Mechanics of collisional motion of granular materials, part 1: general hydrodynamic equations. J. Fluid Mech. 282, 75-114 (1995)
2. Brey, J.J., Dufty, J.W., Santos, A.: Dissipative dynamics for hard spheres. J. Stat. Phys. 87, 1051-1066 (1997)
3. Brilliantov, N.V., Pöschel, T.: Kinetic Theory of Granular Gases. Oxford University Press, Oxford (2004)
4. Chapman, S., Cowling, T.G.: The Mathematical Theory of Nonuniform Gases. Cambridge University Press, Cambridge (1970)
5. Brey, J.J., Dufty, J.W., Kim, C.S., Santos, A.: Hydrodynamics for granular flow at low-density. Phys. Rev. E 58, 4638-4653 (1998)
6. Brey, J.J., Cubero, D.: Hydrodynamic transport coefficients of granular gases. In: Pöschel T., Luding S. (eds.) Granular Gases. Lecture Notes in Physics, vol. 564, pp. 59-78. Springer, Berlin (2001)
7. Garzó, V., Montanero, J.M.: Transport coefficients of a heated granular gas. Physica A 313, 336-356 (2002)
8. Jenkins, J.T., Mancini, F.: Kinetic theory for binary mixtures of smooth, nearly elastic spheres. Phys. Fluids A 1, 2050-2057 (1989)
9. Zamankhan, P.: Kinetic theory for multicomponent dense mixtures of slightly inelastic spherical particles. Phys. Rev. E 52, 4877-4891 (1995)
10. Arnarson, B., Willits, J.T.: Thermal diffusion in binary mixtures of smooth, nearly elastic spheres with and without gravity. Phys. Fluids 10, 1324-1328 (1998)
11. Willits, J.T., Arnarson, B.: Kinetic theory of a binary mixture of nearly elastic disks. Phys. Fluids 11, 3116-3122 (1999)
12. Garzó, V., Dufty, J.W.: Homogeneous cooling state for a granular mixture. Phys. Rev. E 60, 5706-5713 (1999)
13. Martin, P.A., Piasecki, J.: Thermalization of a particle by dissipative collisions. Europhys. Lett. 46, 613-616 (1999)
14. Montanero, J.M., Garzó, V.: Monte Carlo simulation of the homogeneous cooling state for a granular mixture. Gran. Matt. 4, 17-24 (2002)
15. Barrat, A., Trizac, E.: Lack of energy equipartition in homogeneous heated binary granular mixtures. Gran. Matt. 4, 57-63 (2002)
16. Dahl, S.R., Hrenya, C.M., Garzó, V., Dufty, J.W.: Kinetic temperatures for a granular mixture. Phys. Rev. E 66, 041301 (2002)
17. Pagnani, R., Marconi, U.M.B., Puglisi, A.: Driven low density granular mixtures. Phys. Rev. E. 66, 051304 (2002)
18. Paolotti, D., Cattuto, C., Marconi, U.M.B., Puglisi, A.: Dynamical properties of vibrofluidized granular mixtures. Gran. Matt. 5, 75-83 (2003)
19. Krouskop, P., Talbot, J.: Mass and size effects in three-dimensional vibrofluidized granular mixtures. Phys. Rev. E 68, 021304 (2003)
20. Wang, H., Jin, G., Ma, Y.: Simulation study on kinetic temperatures of vibrated binary granular mixtures, Phys. Rev. E. 68, 031301 (2003)
21. Brey, J.J., Ruiz-Montero, M.J., Moreno, F.: Energy partition and segregation for an intruder in a vibrated granular system under gravity. Phys. Rev. Lett. 95, 098001 (2005)
22. Schröter, M., Ulrich, S., Kreft, J., Swift, J.B., Swinney, H.L.: Mechanisms in the size segregation of a binary granular mixture. Phys. Rev. E 74, 011307 (2006)
23. Wildman, R.D., Parker, D.J.: Coexistence of two granular temperatures in binary vibrofluidized beds. Phys. Rev. Lett. 88, 064301 (2002)
24. Feitosa, K., Menon, N.: Breakdown of energy equipartition in a 2D binary vibrated granular gas. Phys. Rev. Lett. 88, 198301 (2002)
25. Jenkins, J., Mancini, F.: Balance laws and constitutive relations for plane flows of a dense binary mixture of smooth, nearly elastic, circular disks. J. Appl. Mech. 54, 27-34 (1987)
26. Garzó, V., Dufty, J.W.: Hydrodynamics for a granular binary mixture at low density. Phys. Fluids 14, 1476-1490 (2002)
27. Garzó, V., Astillero, A.: Transport coefficients for inelastic Maxwell mixtures. J. Stat. Phys. 118, 935-971 (2005)
28. Garzó, V., Montanero, J.M., Dufty, J.W.: Mass and heat fluxes for a binary granular mixture at low-density. Phys. Fluids 18, 083305 (2006)
29. Garzó, V., Montanero, J.M.: Diffusion of impurities in a granular gas. Phys. Rev. E 69, 021301 (2004)
30. Montanero, J.M., Garzó, V.: Shear viscosity for a heated granular binary mixture at low-density. Phys. Rev. E 67, 021308 (2003)
31. Serero, D., Goldhirsch, I., Noskowicz, S.H., Tan, M.-L.: Hydrodynamics of granular gases and granular gas mixtures. J. Fluid Mech. 554, 237-258 (2006)
32. Warr, S., Huntley, J.M., Jacques, G.T.H.: Fluidization of a two-dimensional granular system: Experimental study and scaling behavior. Phys. Rev. E 52, 5583-5595 (1995)
33. Olafsen, J.S., Urbach, J.S.: Velocity distribution and density fluctuations in a granular gas. Phys. Rev. E 60, R2468-R2471 (1999)
34. Wildman, R.D., Huntley, J.M., Hansen, J.P.: Self-diffusion of grains in two-dimensional vibrofluidized bed. Phys. Rev. E 60, 7066-7075 (1999)
35. Rouyer, F., Menon, N.: Velocity fluctuations in a homogeneous 2D granular gas in steady state. Phys. Rev. Lett. 85, 3676-3679 (2000)
36. Blair, D.L., Kudrolli, A.: Velocity correlations in dense granular flows. Phys. Rev. E 64, 050301 (2001)
37. Horluck, S., van Hecke, M., Dimon, P.: Shock waves in two-dimensional granular flow: effects of rough walls and polydispersity. Phys. Rev. E 67, 021304 (2003)
38. Bird, G.A.: Molecular Gas Dynamics and the Direct Simulation Monte Carlo of Gas Flows. Clarendon, Oxford (1994)
39. Santos, A., Garzó, V., Dufty, J.W.: Inherent rheology of a granular fluid in uniform shear flow. Phys. Rev. E 69, 061303 (2004)
40. van Noije, T.P.C., Ernst, M.H.: Velocity distributions in inhomogeneous granular fluids: the free and the heated case. Gran. Matt. 1, 57-64 (1998)
41. Garzó, V.: Tracer diffusion in granular shear flows. Phys. Rev. E 66, 021308 (2002)
42. Brey, J.J., Ruiz-Montero, M.J., Moreno, F.: Hydrodynamic profiles for an impurity in an open vibrated granular gas. Phys. Rev. E 73, 031301 (2006)
43. Brey, J.J., Cubero, D.: Hydrodynamic transport coefficients of granular gases. In: Pöschel T, Luding S. (eds.) Granular Gases. Lecture Notes in Physics, pp. 59-78. Springer, Berlin (2001)
44. McLennan, J.A.: Introduction to Nonequilibrium Statistical Mechanics. Prentice-Hall, New Jersey (1989)
45. Brey, J.J., Ruiz-Montero, M.J., Cubero, D., García-Rojo, R.: Self-diffusion in freely evolving granular gases. Phys. Fluids 12, 876-883 (2000)
46. Garzó, V., Montanero, J.M.: Shear viscosity for a moderately dense granular binary mixture. Phys. Rev. E 68, 041302 (2003)
47. Montanero, J.M., Santos, A., Garzó, V.: DSMC evaluation of the Navier-Stokes shear viscosity of a granular fluid. In: Capitelli M. (ed.) Rarefied Gas Dynamics 24. AIP Conference Proceedings, vol. 762, pp. 797-802. American Institute of Physics, New York (2005), preprint arXiv: cond-mat/0411219
48. Brey, J.J., Ruiz-Montero, M.J.: Simulation study of the Green-Kubo relations for dilute granular gases. Phys. Rev. E 70, 051301 (2004)
49. Brey, J.J., Ruiz-Montero, M.J., Maynar, P., García de Soria, I.M.: Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases. J. Phys.: Condens. Matter 17, S2489-S2502 (2005)
50. Montanero, J.M., Santos, A., Garzó, V.: First-order Chapman-Enskog velocity distribution function in a granular gas. Physica A 376, 75-93 (2007)
51. Garzó, V., Santos, A., Montanero, J.M.: Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas. Physica A 376, 94-107 (2007)
52. López de Haro, M., Cohen, E.G.D., Kincaid, J.M.: The Enskog theory for multicomponent mixtures, I: linear transport theory. J. Chem. Phys. 78, 2746-2759 (1983)
53. Garzó, V., Dufty, J.W.: Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 5895-5911 (1999)
54. Ernst, M.H., Brito, R.: Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails. J. Stat. Phys. 109, 407-432 (2002)