Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 172
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Abrahamsson, P.J. Sasic, S. and Rasmuson, A. 2016. On continuum modelling of dense inelastic granular flows of relevance for high shear granulation. Powder Technology, Vol. 294, p. 323.

    Liu, Chuanqi Sun, Qicheng and Zhou, Gordon G.D. 2016. Velocity profiles and energy fluctuations in simple shear granular flows. Particuology, Vol. 27, p. 80.

    Stranges, D.F. Khayat, R.E. and deBruyn, John 2016. Finite thermal convection of non-Fourier fluids. International Journal of Thermal Sciences, Vol. 104, p. 437.

    Takada, Satoshi Saitoh, Kuniyasu and Hayakawa, Hisao 2016. Kinetic theory for dilute cohesive granular gases with a square well potential. Physical Review E, Vol. 94, Issue. 1,

    Chamorro, Moisés G. Reyes, Francisco Vega and Garzó, Vicente 2015. Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow. Physical Review E, Vol. 92, Issue. 5,

    Kumaran, Viswanathan 2015. Kinetic theory for sheared granular flows. Comptes Rendus Physique, Vol. 16, Issue. 1, p. 51.

    Shirsath, Sushil S. Padding, Johan T. Kuipers, J. A. M. Hans and Clercx, Herman J. H. 2015. Simulation study of the effect of wall roughness on the dynamics of granular flows in rotating semicylindrical chutes. AIChE Journal, Vol. 61, Issue. 7, p. 2117.

    Abrahamsson, P.J. Sasic, S. and Rasmuson, A. 2014. On the continuum modeling of dense granular flow in high shear granulation. Powder Technology, Vol. 268, p. 339.

    Berdichevsky, Victor L. 2014. Overcoming paradoxes of Drucker–Prager theory for unconsolidated granular matter. International Journal of Engineering Science, Vol. 83, p. 174.

    Huntley, J. M. Tarvaz, T. Mantle, M. D. Sederman, A. J. Gladden, L. F. Sheikh, N. A. and Wildman, R. D. 2014. Nuclear magnetic resonance measurements of velocity distributions in an ultrasonically vibrated granular bed. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 372, Issue. 2015, p. 20130185.

    Khalil, Nagi Garzó, Vicente and Santos, Andrés 2014. Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases. Physical Review E, Vol. 89, Issue. 5,

    Kremer, Gilberto M. Santos, Andrés and Garzó, Vicente 2014. Transport coefficients of a granular gas of inelastic rough hard spheres. Physical Review E, Vol. 90, Issue. 2,

    Louge, M. Y. 2014. The surprising relevance of a continuum description to granular clusters. Journal of Fluid Mechanics, Vol. 742, p. 1.

    Pal, Raj Kumar and Geubelle, Philippe H. 2014. Impact response of elasto-plastic granular and continuum media: A comparative study. Mechanics of Materials, Vol. 73, p. 38.

    Soto, Rodrigo Risso, Dino and Brito, Ricardo 2014. Shear viscosity of a model for confined granular media. Physical Review E, Vol. 90, Issue. 6,

    Brito, Ricardo Risso, Dino and Soto, Rodrigo 2013. Hydrodynamic modes in a confined granular fluid. Physical Review E, Vol. 87, Issue. 2,

    Eshuis, Peter van der Weele, Ko Alam, Meheboob van Gerner, Henk Jan van der Hoef, Martin Kuipers, Hans Luding, Stefan van der Meer, Devaraj and Lohse, Detlef 2013. Buoyancy driven convection in vertically shaken granular matter: experiment, numerics, and theory. Granular Matter, Vol. 15, Issue. 6, p. 893.

    Garzó, Vicente Murray, J. Aaron and Vega Reyes, Francisco 2013. Diffusion transport coefficients for granular binary mixtures at low density: Thermal diffusion segregation. Physics of Fluids, Vol. 25, Issue. 4, p. 043302.

    Garzó, Vicente 2013. Grad's moment method for a granular fluid at moderate densities: Navier-Stokes transport coefficients. Physics of Fluids, Vol. 25, Issue. 4, p. 043301.

    Gunkelmann, Nina Serero, Dan and Pöschel, Thorsten 2013. Temperature of a granular gas with regard to the stochastic nature of particle interactions. New Journal of Physics, Vol. 15, Issue. 9, p. 093030.

  • Journal of Fluid Mechanics, Volume 361
  • April 1998, pp. 41-74

Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order

  • N. SELA (a1) and I. GOLDHIRSCH (a1)
  • DOI:
  • Published online: 01 April 1998

The Chapman–Enskog expansion is generalized in order to derive constitutive relations for flows of inelastically colliding spheres in three dimensions – to Burnett order. To this end, the pertinent (nonlinear) Boltzmann equation is perturbatively solved by performing a (double) expansion in the Knudsen number and the degree of inelasticity. One of the results is that the normal stress differences and the ‘temperature anisotropy’, characterizing granular fluids, are Burnett effects. The constitutive relations derived in this work differ, both qualitatively and quantitatively, from those obtained in previous studies. In particular, the Navier–Stokes (order) terms have a different dependence on the degree of inelasticity and the number density than in previously derived constitutive relations; for instance, the expression for the heat flux contains a term which is proportional to ε∇ log n, where ε is a measure of the degree of inelasticity and n denotes the number density. This contribution to the heat flux is of zeroth order in the density; a similar term, i.e. one that is proportional to ε∇n, has been previously obtained by using the Enskog correction but this term is O(n) and it vanishes in the Boltzmann limit. These discrepancies are resolved by an analysis of the Chapman–Enskog and Grad expansions, pertaining to granular flows, which reveals that the quasi-microscopic rate of decay of the temperature, which has not been taken into account heretofore, provides an important scale that affects the constitutive relations. Some (minor) quantitative differences between our results and previous ones exist as well. These are due to the fact that we take into account an isotropic correction to the leading Maxwellian distribution, which has not been considered before, and also because we consider the full dependence of the corrections to the Maxwellian distribution on the (fluctuating) speed.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *