Experimental study on the kinetics of granular gases under microgravity

Journal of Fluid Mechanics

Volumn 641, Issue , 2009, Pages 521-539

  Tatsumi, Soichi ^a   Murayama, Yoshihiro ^b   Hayakawa, Hisao ^c   Sano, Masaki ^a  

^a UNIVERSITY OF TOKYO   (Japan)

^b TOKYO UNIVERSITY OF AGRICULTURE AND TECHNOLOGY   (Japan)

^c KYOTO UNIVERSITY   (Japan)

Author keywords

Cooling state; Granular gas; Kinetic theory; Microgravity; Steady state

Indexed keywords

COOLING; COOLING SYSTEMS; DISTRIBUTION FUNCTIONS; GRANULAR MATERIALS; KINETIC THEORY; KINETICS; MICROGRAVITY; MICROGRAVITY PROCESSING; WHITE NOISE;

AIRCRAFT FLYING; COOLING STATE; DRIVEN SYSTEM; FRICTIONAL FORCES; GRANULAR GAS; MICROGRAVITY CONDITIONS; PARABOLIC TRAJECTORIES; STEADY STATE;

GASES;

COOLING; EXPERIMENTAL STUDY; FRICTION; GAS; GRANULAR MEDIUM; GRAVITY; KINETICS; STEADY-STATE EQUILIBRIUM; VELOCITY; WHITE NOISE;

EID: 76249094311     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S002211200999231X     Document Type: Article

References (62)

1. Ahmad, S. R. & Puri, S. 2006 Velocity distributions in a freely evolving granular gas. Euro. Phys. Lett. 75 (1), 56-62.
2. Ahmad, S. R. & Puri, S. 2007 Velocity distributions and aging in a cooling granular gas. Phys. Rev. E 75, 031302.
3. Aranson, I. S. & Olafsen, J. S. 2002 Velocity fluctuations in electrostatically driven granular media. Phys. Rev. E 66, 061302.
4. Aspelmeier, T., Huthmann, M. & Zippelius, A. 2001 Free Cooling of Particles with Rotational Degrees of Freedom, Chapter 1, pp. 31-58. Lecture Notes in Physics, vol.564. Springer.
5. Baxter, G. W. & Olafsen, J. S. 2003 Kinetics: gaussian statistics in granular gases. Nature 425, 680.
6. Baxter, G. W. & Olafsen, J. S. 2007 Experimental evidence for molecular chaos in granular gases. Phys. Rev. Lett. 99, 028001.
7. Blair, D. L. & Kudrolli, A. 2001 Velocity correlations in dense granular gases. Phys. Rev. E 64, 050301(R).
8. Brilliantov, N. V., Poöschel, T., Kranz, W. T. & Zippelius, A. 2007 Translations and rotations are correlated in granular gases. Phys. Rev. Lett. 98, 128001.
9. Brilliantov, N. V. & Pöschel, T. 2000 Velocity distribution in granular gases of viscoelastic particles. Phys. Rev. E 61 (5), 5573-5587.
10. Brilliantov, N. V. & Pöschel, T. 2004 Kinetic Theory of Granular Gases. Oxford University Press.
11. Das, S. K. & Puri, S. 2003 Kinetics of inhomogeneous cooling in granular fluids. Phys. Rev. E 68, 011302.
12. Duran, J. 2000 Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials Series. Springer.
13. Ernst, M. H., Trizac, E. & Barrat, A. 2006 The Boltzmann equation for driven systems of inelastic soft spheres. J. Stat. Phys 124 (2-4), 549-586.
14. Esipov, S. E. & Pöschel, T. 1997 The granular phase diagram. J. Stat. Phys. 86 (5/6), 1385-1395. (Pubitemid 127357202)
15. Falcon, E., A u m a ̂itre, S., É vesque, P., Palencia, F., Lecoutre-Chabot, C., Fauve, S., Beysens, D. & Garrabos, Y. 2006 Collision statistics in a dilute granular gas fluidized by vibrations in low gravity. Europhys. Lett. 74 (5), 830-836.
16. Fiscina, J. E. & Cáceres, M. O. 2007 Evaporation transition in vibro-fluidized granular matter. Europhys. Lett. 80, 14007.
17. Géminard, J.-C. & Laroche, C. 2004 Pressure measurement in two-dimensional horizontal granular gases. Phys. Rev. E 70, 021301.
18. Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267-293.
19. Goldhirsch, I., Noskowicz, S. H. & Bar-Lev, O. 2005 Nearly smooth granular gases. Phys. Rev. Lett. 95 (6), 068002.
20. Goldhirsch, I. & Zanneti, G. 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70 (11), 1619-1622.
21. Goldshtein, A. & Shapiro, M. 1995 Mechanics of collisional motion of granular materials. Part 1. General hydrodynamics equations. J. Fluid Mech. 282, 75-114.
22. Haff, P. K. 1983 Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401-430.
23. Hayakawa, H. & Kawarada, A. 2005 Granular gas in an experimental accessible setup. In Powders and Grains, vol.2, pp. 1103-1106. A. A. Bakema Publ., Leiden.
24. Herbst, O., Cafiero, R., Zippelius, A., Hermann, H. J. & Luding, S. 2005 A driven two-dimensional granular gas with coulomb friction. Phys. Fluids 17, 107102.
25. Huthmann, M. & Zippelius, A. 1997 Dynamics of inelastically colliding rough spheres: relaxation of translational and rotational energy. Phys. Rev. E 56 (6), R6275.
26. Jaeger, H. M., Nagel, S. R. & Behringer, R. P. 1996 Granular solids, liquids, and gases. Rev. Mod. Phys. 68 (4), 1259-1273.
27. Jenkins, J. T. & Richman, M. W. 1985 Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28 (12), 3485.
28. Jenkins, J. T. & Zhang, C. 2002 Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14 (3), 1228.
29. Kawahara, R. & Nakanishi, H. 2004 Effects of velocity correlation on early stage of free cooling process of inelastic hard sphere system. J. Phys. Soc. Japan 73 (1), 68-75.
30. Kawarada, A. & Hayakawa, H. 2004 Non-Gaussian velocity distribution function in a vibrating granular bed. J. Phys. Soc. Japan 73 (8), 2037-2040.
31. Król, P. & Król, B. 2006 Determination of free surface energy values for ceramic materials and polyurethane surface-modifying aqueous emulsions. J. Eur. Ceram. Soc. 26 (12), 2241-2248.
32. Kudrolli, A., Wolpert, M. & Gollub, J. P. 1997 Cluster formation due to collisions in granular material. Phys. Rev. Lett. 78 (7), 1383-1386.
33. Labous, L., Rosato, A. D. & Dave, R. N. 1997 Measurements of collisional properties of spheres using high-speed video analysis. Phys. Rev. E 56 (5), 5717-5725.
34. Losert, W., Cooper, D. G. W., Delour, J., Kudrolli, A. & Gollub, J. P. 1999 Velocity statistics in excited granular media. Chaos 9 (3), 682-690.
35. Luding, S., Huthmann, M., McNamara, S. & Zippelius, A. 1998 Homogeneous cooling of rough, dissipative particles: theory and simulations. Phys. Rev. E 58 (3), 3416-3425.
36. Maaß, C. C., Isert, N., Maret, G. & Aegerter, C. M. 2008 Experimental investigation of the freely cooling granular gas. Phys. Rev. Lett. 100, 248001.
37. McNamara, S. & Young, W. R. 1994 Inelastic collapse in two dimensions. Phys. Rev. E 50 (1), R28-R31.
38. McNamara, S. & Young, W. R. 1996 Dynamics of a freely evolving, two-dimensional granular medium. Phys. Rev. E 53 (5), 5089-5100.
39. Miller, S. & Luding, S. 2004 Cluster growth in two-and three-dimensional granular gases. Phys. Rev. E 69, 031305.
40. Mischeler, S. & Mouhot, C. 2006 Cooling process for inelastic Boltzmann equations for hard spheres. Part I. Self-similar solutions and tail behaviour. J. Stat. Phys 124 (2-4), 703-746. (Pubitemid 44757207)
41. Mischeler, S., Mouhot, C. & Richard, M. R. 2006 Cooling process for inelastic Boltzmann equations for hard spheres. Part I. The Cauchy problem. J. Stat. Phys 124 (2-4), 655-702. (Pubitemid 44757206)
42. Moon, S. J., Swift, J. B. & Swinney, H. L. 2004 Steady-state velocity distributions of an oscillated granular gas. Phys. Rev. E 69, 011301.
43. Murayama, Y. & Sano, M. 1998 Transition from Gaussian to non-Gaussian velocity distribution functions in a vibrated granular bed. J. Phys. Soc. Japan 67 (6), 1826-1829.
44. Nie, X., Ben-Naim, E. & Chen, S. 2002 Dynamics of freely cooling granular gases. Phys. Rev. Lett. 89 (20), 204301.
45. Olafsen, J. S. & Urbach, J. S. 1998 Clustering, order, and collapse in a driven granular monolayer. Phys. Rev. Lett. 81 (20), 4369-4372.
46. Olafsen, J. S. & Urbach, J. S. 1999 Velocity distributions and density fluctuations in a granular gas. Phys. Rev. E 60 (3), R2468-R2471.
47. Painter, B., Dutt, M. & Behringer, R. P. 2003 Energy dissipation and clustering for a cooling granular material on a substrate. Physica D 175 (1), 43-68.
48. Pöschel, T., Brilliantov, N. V. & Formella, A. 2006 Impact of high-energy tails on granular gas properties. Phys. Rev. E 74, 041302.
49. Reis, P. M., Ingale, R. A. & Shattuck, M. D. 2007 Forcing independent velocity distributions in an experimental granular fluid. Phys. Rev. E 75, 051311.
50. Rouyer, F. & Menon, N. 2000 Velocity fluctuations in a homogeneous two-dimensional granular gas in steady state. Phys. Rev. Lett. 85 (17), 3676-3679.
51. Saitoh, K. & Hayakawa, H. 2007 Rheology of a granular gas under a plane shear. Phys. Rev. E 75 (2), 021302.
52. Santos, A. 2003 Transport coefficients of d-dimensional inelastic Maxwell models. Physica A 321 (3), 442.
53. Santos, A., Brey, J. J., Kim, C. S. & Dufty, J. W. 1989 Velocity distribution for a gas with steady heat flow. Phys. Rev. A 39 (1), 320-327.
54. Thornton, C. & Ning, Z. 1998 A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres. Powder Technol. 99 (2), 154-162.
55. van Noije, T. P. C. & Ernst, M. H. 1998 Velocity distributions in homogeneous granular fluids: the free and the heated case. Gran. Mat. 1, 57-64.
56. van Noije, T. P. C., Ernst, M. H. & Brito, R 1998 Ring kinetic theory for an idealized granular gas. Physica A 251 (1), 266-283.
57. van Zon, J. S., Kreft, J., Goldman, Daniel I., Miracle, D., Swift, J. B. & Swinney, Harry L. 2004 Crucial role of sidewalls in velocity distributions in quasi-two-dimensional granular gases. Phys. Rev. E 70, 040301(R).
58. van Zon, J. S. & MacKintosh, F. C. 2005 Velocity distributions in dilute granular systems. Phys. Rev. E 72, 051301.
59. Villani, C. 2006 Mathematics of granular materials. J. Stat. Phys. 124 (2-4), 781-822.
60. Wang, H.-Q. & Menon, N. 2008 Heating mechanism affects equipartition in a binary granular system. Phys. Rev. Lett. 100, 158001.
61. Weir, G. & Tallon, S. 2005 The coefficient of restitution for normal incident, low velocity particle impacts. Chem. Engng Sci. 60 (13), 3637-3647.
62. Xu, H., Reeves, A. P. & Louge, M. Y. 2004 Measurement errors in the mean and fluctuation velocities of spherical grains from a computer analysis of digital images. Rev. Sci. Instrum. 75 (4), 811.