Steady flow of smooth, inelastic particles on a bumpy inclined plane: Hard and soft particle simulations

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

Volumn 81, Issue 4, 2010, Pages

  Tripathi, Anurag ^a   Khakhar, D V ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION DUE TO GRAVITY; ACCURATE PREDICTION; COMPUTATIONAL TIME; CONSTITUTIVE RELATIONS; DISCRETE-ELEMENT SIMULATIONS; EVENT DRIVEN; FIRST-PRINCIPLES; HARD PARTICLES; INCLINED PLANES; INELASTIC PARTICLE; MEAN VELOCITIES; PARTICLE DIAMETERS; SHALLOW LAYERS; SIMULATION RESULT; SOFT PARTICLES; SOFT-PARTICLE MODEL; SOLID VOLUME FRACTION; STIFFNESS CONSTANTS;

GRAVITATION; HEAT FLUX; MACHINERY; PARTICLE SIZE; STEADY FLOW; STIFFNESS; TITRATION; VISCOSITY;

KINETIC THEORY;

EID: 77951756357     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.041307     Document Type: Article

References (68)

1. E. Azanza, F. Chevoir, and P. Moucheront, J. Fluid Mech. 400, 199 (1999). 10.1017/S0022112099006461
2. C. Ancey, Phys. Rev. E 65, 011304 (2001). 10.1103/PhysRevE.65.011304
3. O. Pouliquen, Phys. Fluids 15, 1588 (1999).
4. S. B. Savage, J. Fluid Mech. 92, 53 (1979). 10.1017/S0022112079000525
5. C. S. Campbell and C. E. Brennen, Trans. ASME 52, 171 (1985).
6. O. R. Walton, Mech. Mater. 16, 239 (1993). 10.1016/0167-6636(93)90048-V
7. L. E. Silbert, D. Ertas, G. S. Grest, T. C. Halsey, D. Levine, and S. J. Plimpton, Phys. Rev. E 64, 051302 (2001). 10.1103/PhysRevE.64.051302
8. D. Ertaş, G. S. Grest, T. C. Halsey, D. Levine, and L. E. Silbert, Europhys. Lett. 56, 214 (2001). 10.1209/epl/i2001-00508-7
9. W. Bi, R. Delannay, P. Richard, N. Taberlet, and A. Valance, J. Phys.: Condens. Matter 17, S2457 (2005). 10.1088/0953-8984/17/24/006 (Pubitemid 40871963)
10. S. Dippel and D. Wolf, Comput. Phys. Commun. 121-122, 284 (1999). 10.1016/S0010-4655(99)00332-X (Pubitemid 32080841)
11. R. Delannay, M. Louge, P. Richard, N. Taberlet, and A. Valance, Nature Mater. 6, 99 (2007). 10.1038/nmat1813 (Pubitemid 46197645)
12. N. Taberlet, P. Richard, and R. Delannay, Comput. Math. Appl. 55, 230 (2008). 10.1016/j.camwa.2007.04.013 (Pubitemid 350235876)
13. L. E. Silbert, J. W. Landry, and G. S. Grest, Phys. Fluids 15, 1 (2003). 10.1063/1.1521719 (Pubitemid 36225350)
14. T. Poschel, J. Phys. II 3, 27 (1993). 10.1051/jp2:1993109
15. X. M. Zheng and J. M. Hill, Powder Technol. 86, 219 (1996). 10.1016/0032-5910(96)03030-6 (Pubitemid 126343839)
16. X. M. Zheng and J. M. Hill, Comput. Mech. 22, 160 (1998). 10.1007/s004660050349
17. L. E. Silbert, G. S. Grest, and S. J. Plimpton, Phys. Fluids 14, 2637 (2002). 10.1063/1.1487379
18. L. E. Silbert, D. Ertas, G. S. Grest, T. C. Halsey, and D. Levine, Phys. Rev. E 65, 051307 (2002). 10.1103/PhysRevE.65.051307 (Pubitemid 40606758)
19. S. Luding and S. McNamara, Granular Matter 1, 113 (1998). 10.1007/s100350050017
20. R. Brewster, L. E. Silbert, G. S. Grest, and A. J. Levine, Phys. Rev. E 77, 061302 (2008). 10.1103/PhysRevE.77.061302
21. J. Duran, Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials (Springer-Verlag, New York, 2000).
22. S. Luding, E. Clement, A. Blumen, J. Rajchenbach, and J. Duran, Phys. Rev. E 50, 4113 (1994). 10.1103/PhysRevE.50.4113
23. J. T. Jenkins and S. B. Savage, J. Fluid Mech. 130, 187 (1983). 10.1017/S0022112083001044
24. C. K. K. Lun, S. B. Savage, D. J. Jefferey, and N. Chepurniy, J. Fluid Mech. 140, 223 (1984). 10.1017/S0022112084000586
25. N. Mitarai and H. Nakanishi, Phys. Rev. E 67, 021301 (2003). 10.1103/PhysRevE.67.021301
26. W. R. Ketterhagen, J. S. Curtis, and C. R. Wassgren, Phys. Rev. E 71, 061307 (2005). 10.1103/PhysRevE.71.061307 (Pubitemid 41663742)
27. L. E. Silbert, G. S. Grest, R. Brewster, and A. J. Levine, Phys. Rev. Lett. 99, 068002 (2007). 10.1103/PhysRevLett.99.068002 (Pubitemid 47253884)
28. K. A. Reddy and V. Kumaran, Phys. Rev. E 76, 061305 (2007). 10.1103/PhysRevE.76.061305
29. S. Klongboonjit and C. S. Campbell, Phys. Fluids 20, 103301 (2008). 10.1063/1.2996134
30. R. D. Wildman, T. W. Martin, P. E. Krouskop, J. Talbot, J. M. Huntley, and D. J. Parker, Phys. Rev. E 71, 061301 (2005). 10.1103/PhysRevE.71.061301 (Pubitemid 41663736)
31. C. Bizon, M. D. Shattuck, J. B. Swift, and H. L. Swinney, Phys. Rev. E 60, 4340 (1999). 10.1103/PhysRevE.60.4340
32. M. Y. Louge, Phys. Fluids 6, 2253 (1994). 10.1063/1.868178 (Pubitemid 283890)
33. N. Mitarai and H. Nakanishi, Phys. Rev. Lett. 94, 128001 (2005). 10.1103/PhysRevLett.94.128001 (Pubitemid 40620580)
34. J. T. Jenkins and M. W. Richman, Arch. Ration. Mech. Anal. 87, 355 (1985). 10.1007/BF00250919
35. C. K. K. Lun, J. Fluid Mech. 233, 539 (1991). 10.1017/S0022112091000599
36. J. T. Jenkins and C. Zhang, Phys. Fluids 14, 1228 (2002). 10.1063/1.1449466 (Pubitemid 34305945)
37. D. K. Yoon and J. T. Jenkins, Phys. Fluids 17, 083301 (2005). 10.1063/1.2000768 (Pubitemid 41226569)
38. N. Mitarai and H. Nakanishi, Phys. Rev. E 75, 031305 (2007). 10.1103/PhysRevE.75.031305 (Pubitemid 46494745)
39. J. M. Montanero, V. Garzo, A. Santos, and J. J. Brey, J. Fluid Mech. 389, 391 (1999). 10.1017/S0022112099005182
40. A. Santos, J. M. Montanero, J. W. Dufty, and J. J. Brey, Phys. Rev. E 57, 1644 (1998). 10.1103/PhysRevE.57.1644
41. S. B. Savage and R. Dai, Mech. Mater. 16, 225 (1993). 10.1016/0167-6636(93)90047-U
42. M. Babic, Phys. Fluids 9, 2486 (1997). 10.1063/1.869367
43. M. Y. Louge, J. T. Jenknis, and M. A. Hopkins, Phys. Fluids A 2, 1042 (1990). 10.1063/1.857642
44. C. S. Chou, Proc. Natl. Sci. Counc., Repub. China, Part A: Phys. Sci. Eng. 24, 317 (2000).
45. M. Babić, ASME J. Appl. Mech. 60, 59 (1993). 10.1115/1.2900779
46. Y. Lan and A. Rosato, Phys. Fluids 7, 1818 (1995). 10.1063/1.868498
47. M. D. Shattuck, C. Bizon, J. B. Swift, and H. L. Swinney, Physica A 274, 158 (1999). 10.1016/S0378-4371(99)00433-1 (Pubitemid 30523121)
48. O. Herbst, P. Muller, and A. Zippelius, Phys. Rev. E 72, 041303 (2005). 10.1103/PhysRevE.72.041303 (Pubitemid 41777888)
49. R. Soto, Phys. Rev. E 69, 061305 (2004). 10.1103/PhysRevE.69.061305
50. Simulation of moderately thick layers h ≈ 20 d caused collapse near the base despite using TC model with most of the collisions being forced to be nondissipative.
51. J. P. Tignol, Galois' Theory of Algebraic Equations (World Scientific, Singapore, 2001).
52. L. E. Dickson, Elementary Theory of Equations (Wiley, New York, 1914).
53. S. Luding, E. Clement, A. Blumen, J. Rajchenbach, and J. Duran, Phys. Rev. E 49, 1634 (1994). 10.1103/PhysRevE.49.1634
54. P. Deltour and J. L. Barrat, J. Phys. I 7, 137 (1997). 10.1051/jp1:1997130
55. D. Goldman, M. D. Shattuck, C. Bizon, W. D. McCormick, J. B. Swift, and H. L. Swinney, Phys. Rev. E 57, 4831 (1998). 10.1103/PhysRevE.57.4831
56. We have also used velocity Verlet algorithm to integrate Eqs. and found that the results are identical using both integration schemes.
57. C. S. Campbell and A. Gong, J. Fluid Mech. 164, 107 (1986). 10.1017/S0022112086002495
58. C. S. Campbell, J. Fluid Mech. 203, 449 (1989). 10.1017/S0022112089001540
59. S. S. Hsiau and M. L. Hunt, ASME J. Heat Transfer 115, 541 (1993). 10.1115/1.2910720
60. A. D. Rosato, Y. Lan, and M. W. Richman, Powder Technol. 182, 228 (2008). 10.1016/j.powtec.2007.08.003 (Pubitemid 351186597)
61. J. T. Jenkins and F. Mancini, ASME J. Appl. Mech. 54, 27 (1987). 10.1115/1.3172990
62. D. V. Khakhar, J. J. McCarthy, and J. M. Ottino, Chaos 9, 594 (1999). 10.1063/1.166433
63. E. R. Dufresne, T. M. Squires, M. P. Brenner, and D. G. Grier, Phys. Rev. Lett. 85, 3317 (2000). 10.1103/PhysRevLett.85.3317
64. B. Lin, J. Yu, and S. A. Rice, Phys. Rev. E 62, 3909 (2000). 10.1103/PhysRevE.62.3909
65. J. T. Jenkins, Granular Matter 10, 47 (2007). 10.1007/s10035-007-0057-z (Pubitemid 350115272)
66. S. Torquato, Phys. Rev. E 51, 3170 (1995). 10.1103/PhysRevE.51.3170
67. Jenkins accounts for a chain length L of particles instead of d in Eq.. Since using this chain length enhances the discrepancy from simulation results, we use L = d.
68. V. Garzó and J. W. Dufty, Phys. Rev. E 59, 5895 (1999). 10.1103/PhysRevE.59.5895