Comparison of kinetic theory predictions with experimental results for a vibrated three-dimensional granular bed

Physics of Fluids

Volumn 18, Issue 11, 2006, Pages

  Viswanathan, H ^a   Wildman, R D ^a   Huntley, J M ^a   Martin, T W ^a  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; ENERGY TRANSFER; FINITE ELEMENT METHOD; FORECASTING; HEAT FLUX; TEMPERATURE DISTRIBUTION;

CONSERVATION EQUATIONS; FOURIER LAW; GRANULAR BED; MOMENTUM TRANSFER; TEMPERATURE GRADIENT;

KINETIC THEORY;

ANISOTROPY; ENERGY TRANSFER; FINITE ELEMENT METHOD; FORECASTING; HEAT FLUX; KINETIC THEORY; TEMPERATURE DISTRIBUTION;

EID: 33751559904     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2353398     Document Type: Article

References (47)

1. C. S. Campbell, "Rapid granular flows," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/annurev.fluid.22.1.57 22, 57 (1990).
2. I. Goldhirsch, "Rapid granular flows," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/annurev.fluid.35.101101.161114 35, 267 (2003).
3. P. Evesque, "Shaking dry powders and grains," Contemp. Phys.CTPHAF0010-7514 33, 245 (1992).
4. J. M. Ottino and D. V. Khakhar, "Mixing and segregation of granular materials," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/ annurev.fluid.32.1.55 32, 55 (2000).
5. J. Duran, Sands, Powders and Grains: An Introduction to the Physics of Granular Materials (Springer-Verlag, New York, 1999).
6. H. M. Jaeger and S. R. Nagel, "Physics of the granular state," ScienceSCIEAS0036-8075 255, 1523 (1992).
7. J. B. Knight, E. E. Ehrichs, V. Kuperman, J. K. Flint, H. M. Jaeger, and S. R. Nagel, "Experimental study of granular convection," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.54.5726 54, 5726 (1996).
8. E. Clément, L. Vanel, J. Rajchenbach, and J. Duran, "Pattern formation in a vibrated two-dimensional granular layer," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.53.2972 53, 2972 (1996).
9. C.-h. Liu and S. R. Nagel, "Sound in sand," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.68.2301 68, 2301 (1992).
10. C. Liu and S. R. Nagel, "Sound in a granular material: Disorder and nonlinearity," Phys. Rev. BPRBMDO0163-182910.1103/PhysRevB.48.15646 48, 15646 (1993).
11. S. Warr and J.-P. Hansen, "Relaxation of local density fluctuations in a fluidized granular medium," Europhys. Lett.EULEEJ0295-507510.1209/epl/i1996-00273-1 36, 589 (1996).
12. C. C. K. Lun, S. B. Savage, D. J. Jeffery, and N. Chepurniy, "Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flowfield," J. Fluid Mech.JFLSA70022-112010.1017/S0022112084000586 140, 223 (1984).
13. V. Kumaran, "Kinetic theory for a vibro-fluidized bed," J. Fluid Mech.JFLSA70022-112010.1017/S0022112098001050 364, 163 (1998).
14. J. T. Jenkins and S. B. Savage, "A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles," J. Fluid Mech.JFLSA70022-112010.1017/S0022112083001044 130, 187 (1983).
15. J. T. Jenkins, "Kinetic theory for nearly elastic spheres," Physics of Dry Granular Media (Kluwer Academic, Dordrecht, 1999), p. 353.
16. P. K. Haff, "Grain flow as a fluid-mechanical phenomenon," J. Fluid Mech.JFLSA70022-112010.1017/S0022112083003419 134, 401 (1983).
17. I. Goldhirsch and N. Sela, "Origin of normal stress differences in rapid granular flows," Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.54.4458 54, 4458 (1996).
18. J. J. Brey, M. J. Ruiz-Montero, and F. Moreno, "Steady uniform shear flow in a low density granular gas," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.55.2846 55, 2846 (1997).
19. N. Sela and I. Goldhirsch, "Hydrodynamic equations for rapid flows of smooth inelastic spheres to Burnett order," J. Fluid Mech.JFLSA70022-112010.1017/S0022112098008660 361, 41 (1998).
20. S. McNamara and S. Luding, "Energy flows in vibrated granular media," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.58.813 58, 813 (1998).
21. H. H. Shen and M. A. Hopkins, "Stresses in a rapid, simple shear flow of granular materials with multiple size grains," Part. Sci. Technol.PTCHDS0272-6351 6, 1 (1988).
22. C. Bizon, M. D. Shattuck, J. B. Swift, W. D. McCormick, and H. L. Swinney, "Patterns in 3D vertically oscillated granular layers: Simulation and experiment," Phys. Rev. Lett.PRLTAO0031-900710.1103/ PhysRevLett.80.57 80, 57 (1998).
23. I. Goldhirsch, "Scales and kinetics of granular flows," ChaosCHAOEH1054-150010.1063/1.166440 9, 659 (1999).
24. J. J. Brey, F. Moreno, and J. W. Dufty, "Model kinetic equation for low-density granular flow," Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.54.445 54, 445 (1996).
25. J. J. Brey, M. J. Ruiz-Montero, and F. Moreno, "Hydrodynamics of an open vibrated granular system," Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.63.061305 63, 061305 (2001).
26. J. J. Brey, J. W. Dufty, C. S. Kim, and A. Santos, "Hydrodynamics for granular flow at low density," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.58.4638 58, 4638 (1998).
27. K. Helal, M. Biben, and J.-P. Hansen, "Local fluctuations in a fluidized granular media," Physica APHYADX0378-437110.1016/ S0378-4371(97)00159-3 240, 361 (1997).
28. E. Clément and J. Rajchenbach, "Fluidization of a bidimensional powder," Europhys. Lett.EULEEJ0295-5075 16, 133 (1991).
29. S. Warr, J. M. Huntley, and G. T. H. Jacques, "Fluidization of a two-dimensional granular system: Experimental study and scaling behaviour," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.52.5583 52, 5583 (1995).
30. E. Azanza, F. Chevoir, and P. Moucheront, "Experimental study of collisional granular flows down an inclined plane," J. Fluid Mech.JFLSA70022-112010.1017/S0022112099006461 400, 199 (1999).
31. R. D. Wildman, J. M. Huntley, and J.-P. Hansen, "Self-diffusion of grains in a two-dimensional vibro-fluidized bed," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.60.7066 60, 7066 (1999).
32. R. D. Wildman, J. M. Huntley, and D. J. Parker, "Granular temperature profiles in three-dimensional vibrofluidized granular beds," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.63.061311 63, 061311 (2001).
33. R. D. Wildman, J. M. Huntley, J.-P. Hansen, and D. A. Allen, "Single-particle motion in three-dimensional vibrofluidized granular beds," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.62.3826 62, 3826 (2000).
34. R. D. Wildman, J.-P. Hansen, and D. J. Parker, "Velocity auto-correlation functions in three-dimensional vibro-fluidized granular beds," Phys. FluidsPHFLE61070-663110.1063/1.1420737 14, 232 (2002).
35. R. D. Wildman, J. M. Huntley, and D. J. Parker, "Convection in highly fluidized three-dimensional granular beds," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.86.3304 86, 3304 (2001).
36. R. D. Wildman and J. M. Huntley, "Scaling exponents for energy transport and dissipation in binary vibro-fluidized granular beds," Phys. FluidsPHFLE61070-663110.1063/1.1598960 15, 3090 (2003).
37. X. Yang and D. Candela, "Potential energy in a three-dimensional vibrated granular medium measured by NMR imaging," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.85.298 85, 298 (2000).
38. X. Yang, C. Huan, D. Candela, R. W. Mair, and R. L. Walsworth, "Measurements of grain motion in a dense, three dimensional granular fluid," Phys. Rev. Lett.PRLTAO0031-900710.1103/ PhysRevLett.88.044301 88, 044301 (2002).
39. C. Huan, X. Yang, D. Candela, R. W. Mair, and R. L. Walsworth, "NMR experiments on a three-dimensional vibrofluidized granular medium," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.69.041302 69, 041302 (2004).
40. T. W. Martin, J. M. Huntley, and R. D. Wildman, "Hydrodynamic model for a vibrofluidized granular bed," J. Fluid Mech.JFLSA70022-112010.1017/S0022112005004866 535, 325 (2005).
41. R. D. Wildman and D. J. Parker, "Coexistence of two granular temperatures in binary vibrofluidised beds," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.88.064301 88, 064301 (2002).
42. K. Feitosa and N. Menon, "Breakdown of energy equipartition in a 2D binary vibrated granular gas," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.88.198301 88, 198301 (2002).
43. J.-P. Hansen and I. McDonald, Theory of Simple Liquids, 2nd ed. (Academic, London, 1986).
44. N. F. Carnahan and K. E. Starling, "Equation of state for nonattracting rigid spheres," J. Chem. Phys.JCPSA60021-960610.1063/ 1.1672048 51, 635 (1969).
45. S. Warr and J. M. Huntley, "Energy input and scaling laws for a single particle vibrating in one-dimension," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.52.5596 52, 5596 (1995).
46. V. Kumaran, "Temperature of a granular material 'fluidised' by external vibrations," Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.57.5660 57, 5660 (1998).
47. M. W. Richman, "Boundary-conditions for granular flows at randomly fluctuating bumpy boundaries," Mech. Mater.MSMSD30167-663610.1016/ 0167-6636(93)90045-S 16, 211 (1993).