The constitutive relation for the granular flow of rough particles, and its application to the flow down an inclined plane

Journal of Fluid Mechanics

Volumn 561, Issue , 2006, Pages 1-42

  Kumaran, V ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ENERGY DISSIPATION; GRANULAR MATERIALS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; PERTURBATION TECHNIQUES; SHEAR FLOW; VISCOSITY MEASUREMENT; SURFACE ROUGHNESS; VISCOSITY;

COLLISION MODEL; GRANULAR FLOW; INCLINED PLANE; NAVIER-STOKES APPROXIMATION;

STEADY FLOW; FLOW OF SOLIDS;

APPROXIMATION THEORY; ENERGY DISSIPATION; GRANULAR MATERIALS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; PERTURBATION TECHNIQUES; SHEAR FLOW; STEADY FLOW; VISCOSITY MEASUREMENT; FLOW OF SOLIDS; SURFACE ROUGHNESS; VISCOSITY;

CONSTITUTIVE EQUATION; FLUID DYNAMICS; NAVIER-STOKES EQUATIONS; VISCOSITY; COMPUTATIONAL FLUID DYNAMICS;

BOLTZMANN EQUATION; BURNETT APPROXIMATION; FLOW DYNAMICS; GRANULAR FLOW; SHEAR VISCOSITY;

EID: 33747064654     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006000279     Document Type: Article

References (30)

1. Bocquet, L., Errami, J. & Lubensky, T. C. 2002 Hydrodynamic model for a dynamical jammed-to-flowing transition in gravity driven granular media. Phys. Rev. Lett. 89, 184 301-184 304.
2. Campbell, C. S. 1989 The stress tensor for simple shear flows of a granular material. J. Fluid Mech. 203, 449-473.
3. Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
4. Chou, C.-S. & Richman, M. W. 1998 Constitutive theory for homogeneous granular shear flows of highly inelastic spheres. Physica A 259, 430-448.
5. Ernst, M. H., Cichocki, B., Dorfman, J. R., Sharma, J. & Van Beijeren, H. 1978 Kinetic theory of nonlinear viscous flow in two and three dimensions. J. Stat. Phys. 18, 237-270.
6. Goldhirsch, I. 2003 Rapid granular flows, Annu. Rev. Fluid Mech. 35, 267-293.
7. Herbst, O., Huthmann, M. & Zippelius, A. 2000 Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy. Gran. Matt. 2, 211-219.
8. Jenkins, J. T. & Richman, M. W. 1985 Grad's 13-moment system for a dense gas of inelastic spheres. Arch. Rat. Mech. Anal. 87, 355-377.
9. Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic particles. J. Fluid Mech. 130, 186-202.
10. Jenkins, J. T. & Zhang, C. 2002 Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14, 1228-1235.
11. Kumaran, V. 2004 Constitutive relations and linear stability of a sheared granular flow. J. Fluid Mech. 506, 143.
12. Louge, M.-Y. 2003 Model for dense granular flows down bumpy surfaces. Phys. Rev. E 67, 061303-061313.
13. Louge, M.-Y. & Keast, S. C. 2001 On dense granular flows down flat frictional inclines. Phys. Fluids 13, 1213-1233.
14. Lun, C. K. K. 1991 Granular flow of dense spheres. J. Fluid Mech. 233, 539-559.
15. Lun, C. K. K. & Savage, S. B. 1987 A simple kinetic theory for granular flow of rough, inelastic, spherical particles. Trans. ASME E: J. Appl. Mech. 54, 47-53.
16. Lun, C. K. K., Savage, S. B., Jeffrey, D. J. & Chepurniy, N. 1984 Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223-256.
17. McCoy, B., Sandler, S. I. & Dahler, J. S. 1966 Transport theory of polyatomic fluids IV. The kinetic theory of a dense gas of perfectly rough spheres. J. Chem. Phys. 3485-3512.
18. Mitarai, N., Hayakawa, H. & Nakanishi, H. 2002 Collisional granular flow as a micropolar fluid. Phys. Rev. Lett. 88, 174301.
19. Mohan, L. S., Rao, K. K. & Nott, P. R. 2002 A frictional Cosserat model for the slow shearing of granular materials. J. Fluid Mech. 457, 377-409.
20. Pidduck, F. B. 1922 The kinetic theory of a special type of rigid molecule. Proc. R. Soc. Lond. A 101, 101-112.
21. Pouliquen, O. 1999 Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11, 542-548.
22. Pouliquen, O. & Chevoir, F. 2002 Dense flows of dry granular material. C. R. Phys. 3, 163-175.
23. Resibois, P. & de Leener, M. 1977 Classical Kinetic Theory of Fluids. Wiley.
24. Savage, S. B. & Jeffrey, D. J. 1981 The stress tensor in a granular flow at high shear rates. J. Fluid Mech. 110, 255-272.
25. Sela, N. & Goldhirsch, I. 1998 Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41-74.
26. Sela, N., Goldhirsch, I. & Noskowicz, S. H. 1996 Kinetic theoretical study of a simply sheared two dimensional granular gas to Burnett order. Phys. Fluids 8, 2337.
27. Silbert, L. E., Ertas, D., Grest, G. S., Halsey, T. C., Levine, D. & Plimpton, S. J. 2001 Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 51302.
28. Theodosopulu, M. & Dahler, J. S. 1974a Kinetic theory of polyatomic liquids. I. The generalised moment method. J. Chem. Phys. 9, 3567-3582.
29. Theodosopulu, M. & Dahler, J. S. 1974b Kinetic theory of polyatomic liquids. I. The rough sphere, rigid ellipsoid and square-well ellipsoid models. J. Chem. Phys. 9, 4048-4057.
30. Walton, O. R. & Braun, R. L. 1986 Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mech. 63, 74-86.