Granular Matter

, 20:15 | Cite as

Granular fluids with solid friction and heating

Original Paper


We perform large-scale molecular dynamics simulations to study heated granular fluids in three dimensions. Granular particles dissipate their kinetic energy due to solid frictional interaction with other particles. The velocity of each particle is perturbed by a uniformly-distributed random noise, which mimics the heating. At the early stage of evolution, the kinetic energy of the system decays with time and reaches a steady state at a later stage. The velocity distribution in the steady state shows a non-Gaussian distribution. This has been characterized by using the Sonine polynomial expansion for a wide range of densities. Particles show diffusive motion for densities below the jamming density \(\phi _\mathrm{J}\).


Granular gases Friction Cooling 



PD acknowledges financial support from Council of Scientific and Industrial Research, India. SP is grateful to UGC, India for support through an Indo-Israeli joint project. He is also grateful to DST, India for support through a J. C. Bose fellowship. The research of MS, Grant Number 839/14, was supported by the ISF within the ISF-UGC Joint Research Program Framework.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Jaeger, H.M., Nagel, S.R.: Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259–1273 (1996)ADSCrossRefGoogle Scholar
  2. 2.
    de Gennes, P.G.: Granular matter: a tentative view. Rev. Mod. Phys. 71, S374–S382 (1999)CrossRefGoogle Scholar
  3. 3.
    Aranson, I.S., Tsimring, L.S.: Patterns and collective behavior in granular media: theoretical concepts. Rev. Mod. Phys. 78, 641–692 (2006)ADSCrossRefGoogle Scholar
  4. 4.
    Duran, J.: Sands, Powders and Grains: An Introduction to the Physics of Granular Materials. Springer, New York (1994)Google Scholar
  5. 5.
    Brilliantov, N.V., Poschel, T.: Kinetic Theory of Granular Gases. Oxford University Press, Oxford (2004)CrossRefMATHGoogle Scholar
  6. 6.
    Das, P., Puri, S., Schwartz, M.: Clustering and velocity distributions in granular gases cooling by solid friction. Phys. Rev. E 94, 032907 (2016)ADSCrossRefGoogle Scholar
  7. 7.
    Blumenfeld, R., Edwards, S.F., Schwartz, M.: da Vinci fluids, catch-up dynamics and dense granular flow. Eur. Phys. J. E 32(4), 333–338 (2010)CrossRefGoogle Scholar
  8. 8.
    Schwartz, M., Blumenfeld, R.: Plug flow formation and growth in da Vinci fluids. Granul. Matter 13(3), 241–245 (2011)CrossRefGoogle Scholar
  9. 9.
    Pöschel, T., Luding, S.: Granular Gases. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Das, S.K., Puri, S.: Kinetics of inhomogeneous cooling in granular fluids. Phys. Rev. E 68, 011302 (2003)ADSCrossRefGoogle Scholar
  11. 11.
    Das, S.K., Puri, S.: Pattern formation in the inhomogeneous cooling state of granular fluids. Europhys. Lett. 61, 749–755 (2003)ADSCrossRefGoogle Scholar
  12. 12.
    Ahmad, S.R., Puri, S.: Velocity distributions in a freely evolving granular gas. Europhys. Lett. 75, 56–62 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    Ahmad, S.R., Puri, S.: Velocity distributions and aging in a cooling granular gas. Phys. Rev. E 75, 031302 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    Haff, P.K.: Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401–430 (1983)ADSCrossRefMATHGoogle Scholar
  15. 15.
    Goldhirsch, I., Zanetti, G.: Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619–1622 (1993)ADSCrossRefGoogle Scholar
  16. 16.
    Goldhirsch, I., Tan, M.-L., Zanetti, G.: A molecular dynamical study of granular fluids: the unforced granular gas. J. Sci. Comput. 8(1), 1–40 (1993)CrossRefMATHGoogle Scholar
  17. 17.
    Brilliantov, N.V., Krapivsky, P.L., Bodrova, A., Spahn, F., Hayakawa, H., Stadnichuk, V., Schmidt, J.: Size distribution of particles in Saturns rings from aggregation and fragmentation. Proc. Natl. Acad. Sci. USA 112, 9536–9541 (2015)ADSCrossRefGoogle Scholar
  18. 18.
    du Pont, S.C., Gondret, P., Perrin, B., Rabaud, M.: Granular avalanches in fluids. Phys. Rev. Lett. 90, 044301 (2003)ADSCrossRefGoogle Scholar
  19. 19.
    Gravish, N., Goldman, D.I.: Effect of volume fraction on granular avalanche dynamics. Phys. Rev. E 90, 032202 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    Montanero, J.M., Santos, A.: Computer simulation of uniformly heated granular fluids. Granul. Matter 2(2), 53–64 (2000)CrossRefGoogle Scholar
  21. 21.
    van Noije, T.P.C., Ernst, M.H.: Velocity distributions in homogeneous granular fluids: the free and the heated case. Granul. Matter 1(2), 57–64 (1998)CrossRefGoogle Scholar
  22. 22.
    Schmidt, J., Ohtsuki, K., Rappaport, N., Salo, H., Spahn, F.: Dynamics of Saturn’s dense rings. In: Dougherty, M.K., Esposito, L.W., Krimigis, S.M. (eds.) Saturn from Cassini-Huygens, the Structure of Saturn’s Rings, pp. 413–458. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  23. 23.
    Bridges, F.G., Hatzes, A., Lin, D.N.C.: Structure, stability and evolution of Saturn’s rings. Nature 309, 333–335 (1984)ADSCrossRefGoogle Scholar
  24. 24.
    Midi, G.D.R.: On dense granular flows. Eur. Phys. J. E 14(4), 341–365 (2004)CrossRefGoogle Scholar
  25. 25.
    Melo, F., Umbanhowar, P.B., Swinney, H.L.: Hexagons, kinks, and disorder in oscillated granular layers. Phys. Rev. Lett. 75, 3838–3941 (1995)ADSCrossRefGoogle Scholar
  26. 26.
    Umbanhowar, P.B., Melo, F., Swinney, H.L.: Localized excitations in a vertically vibrated granular layer. Nature 382, 793–796 (1996)ADSCrossRefGoogle Scholar
  27. 27.
    Ristow, G.H.: Pattern Formation in Granular Materials. Springer, Heidelberg (2000)Google Scholar
  28. 28.
    Zik, O., Levine, D., Lipson, S.G., Shtrikman, S., Stavans, J.: Rotationally induced segregation of granular materials. Phys. Rev. Lett. 73, 644–647 (1994)ADSCrossRefGoogle Scholar
  29. 29.
    Puri, S., Hayakawa, H.: Dynamical behaviour of rotated granular mixtures. Physica A 270, 115–124 (1999)ADSCrossRefGoogle Scholar
  30. 30.
    Puri, S., Hayakawa, H.: Segregation of granular mixtures in a rotating drum. Physica A 290, 218–242 (2001)ADSMathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Bocquet, L., Losert, W., Schalk, D., Lubensky, T.C., Gollub, J.P.: Granular shear flow dynamics and forces: experiment and continuum theory. Phys. Rev. E 65, 011307 (2001)ADSCrossRefGoogle Scholar
  32. 32.
    Wildman, R.D., Parker, D.J.: Coexistence of two granular temperatures in binary vibrofluidized beds. Phys. Rev. Lett. 88, 064301 (2002)ADSCrossRefGoogle Scholar
  33. 33.
    Feitosa, K., Menon, N.: Breakdown of energy equipartition in a 2D binary vibrated granular gas. Phys. Rev. Lett. 88, 198301 (2002)ADSCrossRefGoogle Scholar
  34. 34.
    Aranson, I.S., Olafsen, J.S.: Velocity fluctuations in electrostatically driven granular media. Phys. Rev. E 66, 061302 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    Snezhko, A., Aranson, I.S., Kwok, W.-K.: Structure formation in electromagnetically driven granular media. Phys. Rev. Lett. 94, 108002 (2005)ADSCrossRefGoogle Scholar
  36. 36.
    Salueña, C., Pöschel, T., Esipov, S.E.: Dissipative properties of vibrated granular materials. Phys. Rev. E 59, 4422–4425 (1999)ADSCrossRefGoogle Scholar
  37. 37.
    Barrat, A., Trizac, E.: Lack of energy equipartition in homogeneous heated binary granular mixtures. Granul. Matter 4, 57–63 (1998)CrossRefMATHGoogle Scholar
  38. 38.
    Pagnani, R., Marconi, U.M.B., Puglisi, A.: Driven low density granular mixtures. Phys. Rev. E 66, 051304 (2002)ADSCrossRefGoogle Scholar
  39. 39.
    Murayama, Y., Sano, M.: Transition from Gaussian to non-Gaussian velocity distribution functions in a vibrated granular bed. J. Phys. Soc. Jpn. 67, 1826–1829 (1998)ADSCrossRefGoogle Scholar
  40. 40.
    Peng, G., Ohta, T.: Scaling and correlations in heated granular materials. J. Phys. Soc. Jpn. 67, 2561–2564 (1998)ADSCrossRefGoogle Scholar
  41. 41.
    van Noije, T.P.C., Ernst, M.H., Trizac, E., Pagonabarraga, I.: Randomly driven granular fluids: large-scale structure. Phys. Rev. E 59, 4326–4341 (1999)ADSCrossRefGoogle Scholar
  42. 42.
    Kawarada, A., Hayakawa, H.: Non-Gaussian velocity distribution function in a vibrating granular bed. J. Phys. Soc. Jpn. 73, 2037–2040 (2004)ADSCrossRefMATHGoogle Scholar
  43. 43.
    Williams, D.R.M., MacKintosh, F.C.: Driven granular media in one dimension: correlations and equation of state. Phys. Rev. E 54, R9–R12 (1996)ADSCrossRefGoogle Scholar
  44. 44.
    Williams, D.R.M.: Driven granular media and dissipative gases: correlations and liquid-gas phase transitions. Physica A 233, 718–729 (1996)ADSCrossRefGoogle Scholar
  45. 45.
    Bodrova, A., Dubey, A.K., Puri, S., Brilliantov, N.V.: Intermediate regimes in granular Brownian motion: superdiffusion and subdiffusion. Phys. Rev. Lett. 109, 178001 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    Dubey, A.K., Bodrova, A., Puri, S., Brilliantov, N.V.: Velocity distribution function and effective restitution coefficient for a granular gas of viscoelastic particles. Phys. Rev. E 87, 062202 (2013)ADSCrossRefGoogle Scholar
  47. 47.
    Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Oxford University Press, Oxford (1987)MATHGoogle Scholar
  48. 48.
    Frenkel, D., Smit, B.: Understanding Molecular Simulation: From Algorithms to Applications. Academic Press, New York (2002)MATHGoogle Scholar
  49. 49.
    Rapaport, D.C.: The Art of Molecular Dynamics Simulation. Cambridge University Press, Cambridge (2004)CrossRefMATHGoogle Scholar
  50. 50.
    Santos, A.: Transport coefficients of \(d\)-dimensional inelastic Maxwell models. Physica A 321, 442–466 (2003)ADSMathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    Hayakawa, H.: Hydrodynamics of driven granular gases. Phys. Rev. E 68, 031304 (2003)ADSCrossRefGoogle Scholar
  52. 52.
    Chamorro, M.G., Vega Reyes, F., Garzo, V.: Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow. Phys. Rev. E 92, 052205 (2015)ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-uniform Gases. Cambridge University Press, Cambridge (1970)MATHGoogle Scholar
  54. 54.
    de Gennes, P.G.: Brownian motion with dry friction. J. Stat. Phys. 119, 953–962 (2005)ADSMathSciNetCrossRefMATHGoogle Scholar
  55. 55.
    Hayakawa, H.: Langevin equation with Coulomb friction. Physica D 205, 48–56 (2005)ADSCrossRefMATHGoogle Scholar
  56. 56.
    Das, P., Puri, S., Schwartz, M.: Single particle Brownian motion with solid friction. Eur. Phys. J. E 40, 60 (2017)CrossRefGoogle Scholar
  57. 57.
    Gnoli, A., Puglisi, A., Touchette, H.: Granular Brownian motion with dry friction. Europhys. Lett. 102, 14002 (2013)ADSCrossRefGoogle Scholar
  58. 58.
    Gnoli, A., Petri, A., Dalton, F., Pontuale, G., Gradenigo, G., Sarracino, A., Puglisi, A.: Brownian ratchet in a thermal bath driven by Coulomb friction. Phys. Rev. Lett. 110, 120601 (2013)ADSCrossRefGoogle Scholar
  59. 59.
    Burton, J.C., Lu, P.Y., Nagel, S.R.: Collision dynamics of particle clusters in a two-dimensional granular gas. Phys. Rev. E 88, 062204 (2013)ADSCrossRefGoogle Scholar
  60. 60.
    Berthier, L., Kob, W.: The Monte Carlo dynamics of a binary Lennard-Jones glass-forming mixture. J. Phys. Condens. Matter 19, 205130 (2007)ADSCrossRefGoogle Scholar
  61. 61.
    Santos, A., Montanero, J.M.: The second and third Sonine coefficients of a freely cooling granular gas revisited. Granul. Matter 11(3), 157–168 (2009)CrossRefMATHGoogle Scholar
  62. 62.
    Gao, Y., Kilfoil, M.L.: Intermittent and spatially heterogeneous single-particle dynamics close to colloidal gelation. Phys. Rev. E 79, 051406 (2009)ADSCrossRefGoogle Scholar
  63. 63.
    Fodor, E., Hayakawa, H., Visco, P., van Wijland, F.: Active cage model of glassy dynamics. Phys. Rev. E 94, 012610 (2016)ADSCrossRefGoogle Scholar
  64. 64.
    Reis, P.M., Ingale, R.A., Shattuck, M.D.: Caging dynamics in a granular fluid. Phys. Rev. Lett. 98, 188301 (2007)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Physical SciencesJawaharlal Nehru UniversityNew DelhiIndia
  2. 2.Beverly and Raymond Sackler School of Physics and AstronomyTel Aviv UniversityRamat AvivIsrael
  3. 3.Faculty of EngineeringHolon Institute of TechnologyHolonIsrael

Personalised recommendations