Granular Hydrodynamics

  • L. TrujilloEmail author
  • L. Di G. Sigalotti
  • J. Klapp
Part of the Environmental Science and Engineering book series (ESE)


Sand flowing through the constriction of an hourglass or jumping on a vibrating plate is fluidized in the sense that it moves analogously to a fluid. Dense flows of grains driven by gravity down inclines occur in nature and in industrial processes. Natural examples include rock avalanches and landslides. Applications are found in the chemical, pharmaceutical and petroleum industry. Grain flow can be modeled as a fluid-mechanical phenomenon. However, granular fluids teach us about an astounding complexity that emerges from simple, macroscopic particles. For example, starting from an homogenous fluidized system, structures evolve and a dilute granular fluid co-exists with much denser solid-like clusters. Another example is the so-called Brazil nut effect, whereby larger and heavier particles placed into an agitated granular bed rise to the top. We present an outlook of the hydrodynamic description of granular materials. Our purpose is to outline a theory of grain flow which is based upon the description of continuous matter fields derived from the kinetic theory for dense gases, as is usually encountered in fluid dynamics.


Granular Material Hydraulic Jump Velocity Distribution Function Granular System Granular Temperature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



L.T. acknowledges the organizer of the XVII Annual Meeting of the Fluid Dynamics Division (XVII-DDF) of the Mexican Physical Society, with special mention to Anne Cros. J. Klapp thank ABACUS, CONACyT grant EDOMEX-2011-C01-165873.


  1. Alam M, Luding S (2002) How good is the equipartition assumption for the transport properties of a granular mixture? Granul Matter 4:139–142CrossRefGoogle Scholar
  2. Alam M, Luding S (2003) Rheology of bidisperse granular mixtures via event-drivent simulations. J Fluid Mech 476:69–103CrossRefGoogle Scholar
  3. Arnarson BÖ, Willits JT (1998) Thermal diffusion in binary mixtures of smooth, nearly elastic spheres with and without gravity. Phys Fluids 10:1324–1328Google Scholar
  4. Alam M, Trujillo L, Herrmann HJ (2006) Hydrodynamic theory for reverse Brazil nut segregation and the non-monotonic ascension dynamics. J Stat Phys 124:587623CrossRefGoogle Scholar
  5. Alam M, Willits JT, Arnarson BÖ, Luding S (2002) Kinetic theory of a binary mixture of neraly elastic disks with size and mass disparity. Phys Fluids 14:4085–4087Google Scholar
  6. Arnarson BÖ, Jenkins JT (2000) Particle segregation in the context of the species momentum balances. In: Helbing D, Herrmann HJ, Schreckenberg M, Wolf DE (eds) Traffic and granular flow’99: social, traffic and granular dynamics. Springer, Berlin, pp 481–487Google Scholar
  7. Arnarson BÖ, Jenkins JT (2004) Binary mixtures of inelastic spheres: simplified constitutive theory. Phys Fluids 16:4543–4550Google Scholar
  8. Boudet JF, Amarouchene Y, Bonnier B, Kellay H (2007) The granular jump. J Fluid Mech 572:413–431CrossRefGoogle Scholar
  9. Brey JJ, Dufty JW, Kim CS, Santos A (1998) Hydrodynamics for granular flow at low density. Phys Rev E 58:4638–4653CrossRefGoogle Scholar
  10. Brey JJ, Ruiz-Montero MJ, Moreno F (2001) Hydrodynamics of an open vibrated granular system. Phys Rev E 63:061306CrossRefGoogle Scholar
  11. Brilliantov NV, Pöschel T (2004) Kinetic theory of granular gases. Oxford University Press, OxfordCrossRefGoogle Scholar
  12. Caballero G, Bergmann R, van der Meer D, Prosperetti A, Lohse D (2007) Role of air in granular jet formation. Phys Rev Lett 99:018001CrossRefGoogle Scholar
  13. Chapman S, Cowling TG (1970) The mathematical theory of nonuniform gases. Cambridge University Press, CambridgeGoogle Scholar
  14. Edwards SF, Oakeshott RBS (1989) Theory of powders. Physica A 157:1080–1090CrossRefGoogle Scholar
  15. Eshuis P, van der Weele K, van der Meer D, Lohse D (2005) Granular Leidenfrost effect: experiment and theory of floating particle clusters. Phys Rev Lett 95:258001CrossRefGoogle Scholar
  16. Eshuis P, van der Meer D, Alam M, van Gerner HJ, van der Weeke K, Lohse D (2010) Onset of convection in strongly shaken granular matter. Phys Rev Lett 104:038001CrossRefGoogle Scholar
  17. Feitosa K, Menon N (2002) Breakdown of energy equipartition in a 2D binary vibrated granular gas. Physical Review Letters 88:198301CrossRefGoogle Scholar
  18. Gallas JAC, Herrmann HJ, Sokołowski S (1992) Convection cells in vibrating granular media. Phys Rev Lett 69:1371–1373CrossRefGoogle Scholar
  19. García-Colín LS, Velasco RM, Uribe FJ (2008) Beyond the Navier-Stokes equations: Burnett hydrodynamics. Phys Rep 465:149–189CrossRefGoogle Scholar
  20. Garzó V (2008) Brazil-nut effect versus reverse Brazil-nut effect in a moderately dense granular fluid. Phys Rev E 78:020301CrossRefGoogle Scholar
  21. Garzó V, Dufty JW (1999) Dense fluid transport for inelastic hard spheres. Phys Rev E 59:5895–5911CrossRefGoogle Scholar
  22. Garzó V, Dufty JW, Hrenya CM (2007) Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport. Phys Rev E 76:031303Google Scholar
  23. Garzó V, Dufty JW, Hrenya CM (2007) Enskog theory for polydisperse granular mixtures. II. Sonine polynomial approximation. Phys Rev E 76:031304Google Scholar
  24. Garzó V, Vega-Reyes F, Montanero JM (2009) Modified Sonine approximation for granular binary mixtures. J Fluid Mech 623:387–411CrossRefGoogle Scholar
  25. Hong DC, Hayakawa H (1997) Thermodynamic theory of weakly excited granular systems. Phys Rev Lett 78:2764–2767CrossRefGoogle Scholar
  26. Hayakawa H, Yue S, Hong DC (1995) Hydrodynamic description of granular convection. Phys Rev Lett 75:2328–2331CrossRefGoogle Scholar
  27. Henrique C, Batrouni G, Bideau D (2000) Diffusion as a mixing mechanism in granular materials. Phys Rev E 63:011304CrossRefGoogle Scholar
  28. Herrmann HJ (1993) On the thermodynamics of granular media. J de Physique II (France) 3:427–433CrossRefGoogle Scholar
  29. Hong DC, Quinn PV, Luding S (2001) Reverse Brazil nut problem: competition between percolation and condensation. Phys Rev Lett 86:3423–3426CrossRefGoogle Scholar
  30. Huerta DA, Sosa V, Vargas MC, Ruiz-Suárez JC (2005) Archimedes’ principle in fluidized granular systems. Phys Rev E 72:031307CrossRefGoogle Scholar
  31. Ippolito I, Annic A, Lemaître J, Oger L, Bideau D (1995) Granular temperature: experimental analysis. Phys Rev E 52:2072–2075CrossRefGoogle Scholar
  32. Jaeger HM, Nagel SR, Behringer RP (1996) Granular solids, liquids, and gases. Rev Mod Phys 68:1259–1273CrossRefGoogle Scholar
  33. Jenkins JT (1998) Particle segregation in collisional flows of inelastic spheres. In: Herrmann HJ, Holvi J-P, Luding S (eds) Physics of dry granular media. Kluwer, Dordrecht, p 658Google Scholar
  34. Jenkins JT, Mancini F (1987) Balance laws and constitutive relations for plane flows of a dense, binary mixture of smooth, nearly elastic, circular disks. J Appl Mech 54:27–34CrossRefGoogle Scholar
  35. Jenkins JT, Mancini F (1989) Kinetic theory for binary mixtures of smooth, nearly elastic spheres. Phys Fluids A 1:2050–2057CrossRefGoogle Scholar
  36. Jenkins JT, Savage SB (1983) A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J Fluid Mech 130:187–202CrossRefGoogle Scholar
  37. Jenkins JT, Yoon DK (2002) Segregation in binary mixtures under gravity. Phys Rev Lett 88:194301CrossRefGoogle Scholar
  38. Jiang L, Liu M (2009) Granular solid hydrodynamics. Granul Matter 11:139–156CrossRefGoogle Scholar
  39. Kadanoff LP (1999) Built upon sand: theoretical ideas inspired by granular flows. Rev Mod Phys 71:435–444CrossRefGoogle Scholar
  40. Knight JB, Ehrichs EE, Kuperman V, Flint JK, Jaeger HM, Nagel SR (1996) Experimental study of granular convection. Phys Rev E 54:5726–5738CrossRefGoogle Scholar
  41. Leidenfrost JG (1966) On the fixation of water in diverse fire. Int J Heat Mass Transf 9:1153–1166CrossRefGoogle Scholar
  42. Lohse D, Bergmann R, Mikkelsen R, Zeilstra C, van der Meer D, Versluis M, van der Weele K, van der Hoef M, Kuipers H (2004) Impact on soft sand: void collapse and jet formation. Phys Rev Lett 93:198003CrossRefGoogle Scholar
  43. Lohse D, Rauhé R, Bergmann R, van der Meer D (2004) Creating a dry variety of quicksand. Nature 432:689–690CrossRefGoogle Scholar
  44. López de Haro M, Cohen EGD, Kincaid JM (1983) The Enskog theory for multicomponent mixtures. I Linear transport theory. J Chem Phys 78:2746–2759CrossRefGoogle Scholar
  45. Maes C, Thomas SR (2011) Archimedes’ law and its corrections for an active particle in a granular sea. J Phys A Math Theor 44:285001CrossRefGoogle Scholar
  46. McNamara S, Luding S (1998) Energy non-equipartition in systems of inelastic, rough spheres. Phys Rev E 58:2247CrossRefGoogle Scholar
  47. Möbius ME, Lauderdale BE, Nagel SR, Jaeger HM (2001) Size separation of granular particles. Nature 414:270CrossRefGoogle Scholar
  48. Schöter M, Ulrich S, Kreft J, Swift JB, Swinney HL (2006) Mechanisms in the size segregation of a binary granular mixture. Phys Rev E 74:011307CrossRefGoogle Scholar
  49. Serero D, Goldhirsch I, Noskowicz SH, Tan M-L (2008) Hydrodynamics of granular gases and granular mixtures. J Fluid Mech 554:237–258CrossRefGoogle Scholar
  50. Serero D, Noskowicz SH, Goldhirsch I (2007) Exact results versus mean field solutions for binary granular gas mixtures. Granul Matter 10:37–46CrossRefGoogle Scholar
  51. Shinbrot T, Muzzio FJ (1998) Reverse buoyancy in shaken granular beds. Phys Rev Lett 81:4365–4368CrossRefGoogle Scholar
  52. Trujillo L, Alam M, Herrmann HJ (2003) Segregation in a fluidized binary granular mixture: competition between buoyancy and geometric forces. Europhys Lett 64:190–196CrossRefGoogle Scholar
  53. Trujillo L, Herrmann HJ (2003) Hydrodynamic model for particle size segregation in granular media. Physica A 330:519–542CrossRefGoogle Scholar
  54. Wildman RD, Parker DJ (2002) Coexistence of two granular temperatures in binary vibrofluidized beds. Phys Rev Lett 88:064301CrossRefGoogle Scholar
  55. Willits JT, Arnarson BÖ (1999) Kinetic theory of a binary mixture of nearly elastic disks. Phys Fluids 11:3116–3122Google Scholar
  56. Yoon DK, Jenkins JT (2006) The influence of different species’ granular temperature on segregation in a binary mixture of dissipative grains. Phys Fluids 18:073303CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Centro de FísicaInstituto Venezolano de Investigaciones Científicas, IVICCaracasVenezuela
  2. 2.The Abdus SalamInternational Centre for Theoretical Physics, ICTPTriesteItaly
  3. 3.Instituto Nacional de Investigaciones Nucleares ININLa MarquesaMexico
  4. 4.Departamento de MatemáticasCinvestav del I.P.N.MexicoMéxico

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