Nonlinear Couette flow in a low density granular gas

Journal of Statistical Physics

Volumn 103, Issue 5-6, 2001, Pages 1035-1068

  Tij, M ^a   Tahiri, E E ^a   Montanero, J M ^b   Garzo V ^b   Santos, A ^c   Dufty, J W ^c  

^a MOULAY ISMAIL UNIVERSITY   (Morocco)

^b UNIVERSITY OF EXTREMADURA   (Spain)

^c University of Florida ^*  (United States)

Author keywords

Boltzmann equation; Couette flow; Granular gases; Kinetic model; Rheological properties

Indexed keywords

EID: 0035536422     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010317207358     Document Type: Article

References (38)

1. C. S. Campbell, Ann. Rev. Fluid Mech. 22:57 (1990).
2. J. J. Brey, M. J. Ruiz-Montero, and D. Cubero, Phys. Rev. E 54:3664 (1996); J. J. Brey, D. Cubero, and M. J. Ruiz-Montero, ibid. 59:1256 (1999); S. Luding, M. Müller, and S. McNamara, in World Congress on Particle Technology (Brighton, 1998, CD: ISBN 0-85295-401-9); J. M. Montanero, and A. Santos, Gran. Matt. 2:53 (2000) and cond-mat/ 0002323.
3. J. J. Brey, M. J. Ruiz-Montero, and D. Cubero, Phys. Rev. E 54:3664 (1996); J. J. Brey, D. Cubero, and M. J. Ruiz-Montero, ibid. 59:1256 (1999); S. Luding, M. Müller, and S. McNamara, in World Congress on Particle Technology (Brighton, 1998, CD: ISBN 0-85295-401-9); J. M. Montanero, and A. Santos, Gran. Matt. 2:53 (2000) and cond-mat/ 0002323.
4. J. J. Brey, M. J. Ruiz-Montero, and D. Cubero, Phys. Rev. E 54:3664 (1996); J. J. Brey, D. Cubero, and M. J. Ruiz-Montero, ibid. 59:1256 (1999); S. Luding, M. Müller, and S. McNamara, in World Congress on Particle Technology (Brighton, 1998, CD: ISBN 0-85295-401-9); J. M. Montanero, and A. Santos, Gran. Matt. 2:53 (2000) and cond-mat/ 0002323.
5. J. J. Brey, M. J. Ruiz-Montero, and D. Cubero, Phys. Rev. E 54:3664 (1996); J. J. Brey, D. Cubero, and M. J. Ruiz-Montero, ibid. 59:1256 (1999); S. Luding, M. Müller, and S. McNamara, in World Congress on Particle Technology (Brighton, 1998, CD: ISBN 0-85295-401-9); J. M. Montanero, and A. Santos, Gran. Matt. 2:53 (2000) and cond-mat/ 0002323.
6. J. J. Brey, J. W. Dufty, C. S. Kim, and A. Santos, Phys. Rev. E 58:4638 (1998).
7. N. Sela and I. Goldhirsch, J. Fluid Mech. 361:41 (1998).
8. V. Garzó and J. W. Dufty, Phys. Rev. E 59:5895 (1999).
9. J. J. Brey, J. W. Dufty, and A. Santos, J. Stat. Phys. 97:281 (1999).
10. R. Zwanzig, J. Chem. Phys. 71:4416 (1979).
11. A. Santos, J. J. Brey, and V. Garzó, Phys. Rev. A 34:5047 (1986).
12. J. J. Brey, A. Santos, and J. W. Dufty, Phys. Rev. A 36:2842 (1987).
13. C. S. Kim, J. W. Dufty, A. Santos, and J. J. Brey, Phys. Rev. A 40:7165 (1989).
14. J. M. Montanero and V. Garzó, Phys. Rev. E 58:1836 (1998).
15. J. J. Brey, M. J. Ruiz-Montero, and F. Moreno, Phys. Rev. E 55:2846 (1997).
16. J. M. Montanero, V. Garzó, A. Santos, and J. J. Brey, J. Fluid Mech. 389:391 (1999).
17. J. T. Jenkins and S. B. Savage, J. Fluid Mech. 130:187 (1983); J. T. Jenkins and M. W. Richman, Phys. Fluids 28:3485 (1985); J. Fluid Mech. 192:313 (1988).
18. J. T. Jenkins and S. B. Savage, J. Fluid Mech. 130:187 (1983); J. T. Jenkins and M. W. Richman, Phys. Fluids 28:3485 (1985); J. Fluid Mech. 192:313 (1988).
19. J. T. Jenkins and S. B. Savage, J. Fluid Mech. 130:187 (1983); J. T. Jenkins and M. W. Richman, Phys. Fluids 28:3485 (1985); J. Fluid Mech. 192:313 (1988).
20. C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy, J. Fluid Mech. 140:223 (1984).
21. M. A. Hopkins and H. H. Shen, J. Fluid Mech. 244:477 (1992).
22. I. Goldhirsch and M. L. Tan, Phys. Fluids 8:1753 (1996); N. Sela, I. Goldhirsch, and S. H. Noskowicz, ibid. 8:2337 (1996).
23. I. Goldhirsch and M. L. Tan, Phys. Fluids 8:1753 (1996); N. Sela, I. Goldhirsch, and S. H. Noskowicz, ibid. 8:2337 (1996).
24. C. Cercignani, J. Stat. Phys. 102:1407 (2000).
25. M. W. Richman and C. S. Chou, J. Appl. Math. Phys. 39:885 (1988).
26. T. N. Hanes, J. T. Jenkins, and M. W. Richman, J. Appl. Mech. 55:969 (1988).
27. C. K. K. Lun, Phys. Fluids 8:2868 (1996).
28. M. Babic, Phys. Fluids 9:2486 (1997).
29. S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases (Cambridge University Press, Cambridge, 1970).
30. 0 = 0.94 kHz.
31. t, then the form for ζ used here is obtained. Again, this appears to be a good approximation. Confirmation of the quantitative agreement between the kinetic model and the Boltzmann equation for the state considered here is given in Section 4.
32. A. Santos and V. Garzó, Physica A 213:409 (1995); V. Garzó and A. Santos, ibid. 213:426 (1995).
33. A. Santos and V. Garzó, Physica A 213:409 (1995); V. Garzó and A. Santos, ibid. 213:426 (1995).
34. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, Oxford, 1994).
35. J. M. Montanero, A. Santos, and V. Garzó, Phys. Fluids 12:3060 (2000) and condmat/0003364; J. M. Montanero, M. Alaoui, A. Santos, and V. Garzó, Phys. Rev. E 49:367 (1994).
36. J. M. Montanero, A. Santos, and V. Garzó, Phys. Fluids 12:3060 (2000) and condmat/0003364; J. M. Montanero, M. Alaoui, A. Santos, and V. Garzó, Phys. Rev. E 49:367 (1994).
37. J. J. Brey and D. Cubero, Phys. Rev. E 57:2019 (1998).
38. R. Ramírez, D. Risso, R. Soto, and P. Cordero, Phys. Rev. E 62:2521 (2000).