System of elastic hard spheres which mimics the transport properties of a granular gas

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 72, Issue 3, 2005, Pages

  Santos, Andrés ^a   Astillero, Antonio ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

FRICTION CONSTANT; INELASTIC HARD SPHERES (IHS);

APPROXIMATION THEORY; ELASTICITY; FLUIDIZED BEDS; GASES; KINETIC THEORY;

GRANULAR MATERIALS;

EID: 28844454668     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.031308     Document Type: Article

References (56)

1. C. S. Campbell, Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.22.1.57 22, 57 (1990).
2. I. Goldhirsch, Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.35.101101.161114 35, 267 (2003).
3. It is worth emphasizing that along this paper we understand by frictional elastic hard spheres a system of smooth and elastic particles, subject to an external drag force. This must be distinguished from a system of rough spheres with a coefficient of normal restitution α=1. The latter system has been considered, for instance, by C. S. Campbell and A. Gong, J. Fluid Mech. JFLSA7 0022-1120 164, 107 (1986);
4. C. S. Campbell, J. Fluid Mech. JFLSA7 0022-1120 203, 449 (1989);
5. S. J. Moon, J. B. Swift, and H. L. Swinney, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.011301 69, 011301 (2004).
6. T. P. C. van Noije and M. H. Ernst, Granular Matter GRMAFE 1434-5021 10.1007/s100350050009 1, 57 (1998).
7. V. Garzó, A. Santos, and J. J. Brey, Physica A PHYADX 0378-4371 10.1016/0378-4371(90)90150-Q 163, 651 (1990).
8. J. J. Brey, M. J. Ruiz-Montero, and D. Cubero, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.3664 54, 3664 (1996);
9. J. J. Brey, M. J. Ruiz-Montero, and D. Cubero, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.3150 60, 3150 (1999).
10. J. M. Montanero and A. Santos, Granular Matter GRMAFE 1434-5021 10.1007/s100350050035 2, 53 (2000).
11. A. Astillero and A. Santos, in The Physics of Complex Systems. New Advances and Perspectives, edited by, F. Mallamace, and, H. E. Stanley, (IOS Press, Amsterdam, 2004), pp. 475-480.
12. C. Cercignani, The Boltzmann Equation and Its Applications (Springer-Verlag, New York, 1988).
13. V. Garzó and A. Santos, Kinetic Theory of Gases in Shear Flows. Nonlinear Transport (Kluwer Academic Publishers, Dordrecht, 2003).
14. P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.94.511 94, 511 (1954);
15. P. Welander, Ark. Fys. AFYSA7 0365-2440 7, 507 (1954).
16. L. H. Holway, Phys. Fluids PFLDAS 0031-9171 10.1063/1.1761920 9, 1658 (1966).
17. A. Goldshtein and M. Shapiro, J. Fluid Mech. JFLSA7 0022-1120 282, 75 (1995).
18. J. J. Brey, J. W. Dufty, and A. Santos, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02181270 87, 1051 (1997);
19. J. W. Dufty, J. J. Brey, and A. Santos, Physica A PHYADX 0378-4371 10.1016/S0378-4371(97)00144-1 240, 212 (1997).
20. T. P. C. van Noije and M. H. Ernst, in Granular Gases, edited by, T. Pöschel, and, S. Luding, Vol. 564 of Lecture Notes in Physics (Springer-Verlag, Berlin, 2001), pp. 3-30.
21. J. J. Brey, J. W. Dufty, and A. Santos, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1004675320309 97, 281 (1999). Note a misprint in Eq. (C.11): The right-hand sides of the two equations should be multiplied by (d-1)(d+2)2 and d, respectively.
22. J. J. Brey, J. W. Dufty, C. S. Kim, and A. Santos, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.4638 58, 4638 (1998).
23. A. Astillero and A. Santos, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.031309 72, 031309 (2005), following paper.
24. S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases (Cambridge University Press, Cambridge, 1970).
25. V. Garzó and J. W. Dufty, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.5895 59, 5895 (1999).
26. J. J. Brey and D. Cubero, in Granular Gases, edited by, T. Pöschel, and, S. Luding, Vol. 564 of Lecture Notes in Physics (Springer-Verlag, Berlin, 2001), pp. 59-78.
27. V. Garzó and J. M. Montanero, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)00994-9 313, 336 (2002).
28. A. Santos, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)01005-1 321, 442 (2003).
29. For alternative estimates of a2HC, see Ref., and F. Coppex, M. Droz, J. Piasecki, and E. Trizac, Physica A PHYADX 0378-4371 10.1016/S0378-4371(03)00593-4 329, 114 (2003).
30. J. J. Brey, M. J. Ruiz-Montero, D. Cubero, and R. García-Rojo, Phys. Fluids PHFLE6 1070-6631 10.1063/1.870342 12, 876 (2000).
31. J. J. Brey and M. J. Ruiz-Montero, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.051301 70, 051301 (2004);
32. J. J. Brey, M. J. Ruiz-Montero, P. Maynar, and M. I. García de Soria, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/17/24/008 17, S2489 (2005).
33. J. M. Montanero, A. Santos, and V. Garzó, in Rarefied Gas Dynamics: 24th International Symposium on Rarefied Gas Dynamics, edited by, M. Capitelli, AIP Conf. Proc. No. 762 (American Institute of Physics, Melville, NY, 2005), pp. 797-802.
34. V. Garzó and J. M. Montanero, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.021301 69, 021301 (2004).
35. J. M. Montanero, A. Santos, and V. Garzó (in preparation).
36. J. W. Dufty, A. Baskaran, and L. Zogaib, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.051301 69, 051301 (2004).
37. J. T. Jenkins and M. W. Richman, J. Fluid Mech. JFLSA7 0022-1120 192, 313 (1988).
38. J. J. Brey, F. Moreno, and J. W. Dufty, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.445 54, 445 (1996).
39. J. J. Brey, M. J. Ruiz-Montero, and F. Moreno, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.2846 55, 2846 (1997).
40. V. Garzó, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66. 021308 66, 021308 (2002).
41. A. Santos, V. Garzó, and J. Dufty, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.061303 69, 061303 (2004).
42. V. Garzó, Physica A PHYADX 0378-4371 243, 113 (1997).
43. V. Garzó and M. López de Haro, Phys. Fluids PHFLE6 1070-6631 10.1063/1.869232 9, 776 (1997);
44. J. M. Montanero and V. Garzó, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.1836 58, 1836 (1998).
45. R. Soto, J. Piasecki, and M. Mareschal, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.031306 64, 031306 (2001).
46. V. Garzó, A. Santos, and J. W. Dufty (unpublished).
47. V. Garzó and J. W. Dufty, Phys. Fluids PHFLE6 1070-6631 10.1063/1.1458007 14, 1476 (2002).
48. V. Garzó and J. M. Montanero, Granular Matter GRMAFE 1434-5021 5, 156 (2003).
49. E. P. Gross and M. Krook, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.102.593 102, 593 (1956).
50. V. Garzó, A. Santos, and J. J. Brey, Phys. Fluids A PFADEB 0899-8213 10.1063/1.857458 1, 380 (1989).
51. P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1014033703134 106, 993 (2002).
52. J. W. Dufty, A. Santos, and J. J. Brey, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1270 77, 1270 (1996).
53. A. Santos, J. M. Montanero, J. W. Dufty, and J. J. Brey, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.57.1644 57, 1644 (1998).
54. M. H. Ernst and R. Brito, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1020437925931 109, 407 (2002).
55. V. Garzó, J. Stat. Phys. JSTPBS 0022-4715 112, 657 (2003).
56. V. Garzó and A. Astillero, J. Stat. Phys. JSTPBS 0022-4715 118, 936 (2005).