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Evidence of higher-order effects in thermally driven rapid granular flows

  • C. M. HRENYA (a1), J. E. GALVIN (a1) (a2) and R. D. WILDMAN (a3)


Molecular dynamic (MD) simulations are used to probe the ability of Navier–Stokes-order theories to predict each of the constitutive quantities – heat flux, stress tensor and dissipation rate – associated with granular materials. The system under investigation is bounded by two opposite walls of set granular temperature and is characterized by zero mean flow. The comparisons between MD and theory provide evidence of higher-order effects in each of the constitutive quantities. Furthermore, the size of these effects is roughly one order of magnitude greater, on a percentage basis, for heat flux than it is for stress or dissipation rate. For the case of heat flux, these effects are attributed to super-Burnett-order contributions (third order in gradients) or greater, since Burnett-order contributions to the heat flux do not exist. Finally, for the system considered, these higher-order contributions to the heat flux outweigh the first-order contribution arising from a gradient in concentration (i.e. the Dufour effect)


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Alam, M. & Luding, S. 2003 Rheology of bidisperse granular mixtures via event-driven simulations. J. Fluid Mech. 476, 69.
Brey, J. J. & Ruiz-Montero, M. J. 2004 Simulation study of the Green–Kubo relations for dilute granular gases. Phys. Rev. E 70, 051301.
Brey, J. J., Dufty, J. W., Kim, C. S. & Santos, A. 1998 Hydrodynamics for granular flow at low density. Phys. Rev. E 58, 4638.
Brey, J. J., Ruiz-Montero, M. J. & Moreno, F. 2001 Hydrodynamics of an open vibrated system. Phys. Rev. E 63, 061305.
Brey, J. J., Ruiz-Montero, M. J., Maynar, P. & Garciade Soria, M. I. de Soria, M. I. 2005 Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases. J. Phys. Cond. Matter 17, S2489.
Brey, J. J., Dominguez, A., Garciade Soria, M. I. de Soria, M. I. & Maynar, P. 2006 Mesoscopic theory of critical fluctuations in isolated granular gases. Phys. Rev. Lett. 96, 158002.
Brilliantov, N. V. & Pöschel, T. 2004 Kinetic Theory of Granular Gases. Oxford University Press.
Campbell, C. S. 1990 Rapid granular flows. Annu. Rev. Fluid Mech. 22, 57.
Campbell, C. S. & Gong, A. 1986 The stress tensor in a two-dimensional granular shear flow. J. Fluid Mech. 164, 107.
Carnahan, N. F. & Starling, K. E. 1969 Equation of state of non-attracting rigid spheres. J. Chem. Phys. 51, 635.
Cercignani, C. 1987 The Boltzmann Equation and its Applications. Springer.
Ciccotti, G. & Tenebaum, A. 1980 Canonical ensemble and nonequilibrium states by molecular dynamics. J. Stat. Phys. 23, 767.
Clause, P. J. & Mareschal, M. 1988 Heat-transfer in a gas between parallel plates – moment method and molecular-dynamics. Phys. Rev. A 38, 4241.
Cordero, P. & Risso, D. 1998 Nonlinear transport laws for low density fluids. Physica A 257, 36.
Curtis, J. S. & vanWachem, B. Wachem, B. 2004 Modeling particle-laden flows: a research outlook. AIChE J. 50, 2638.
Dahl, S. R. & Hrenya, C. M. 2004 Size segregation in rapid, granular flows with continuous size distributions. Phys. Fluids 16, 1.
Ferziger, J. H. & Kaper, H. G. 1972 Mathematical Theory of Transport Processes in Gases. Elsevier.
Galvin, J. E., Dahl, S. R. & Hrenya, C. M. 2005 On the role of non-equipartition in the dynamics of rapidly flowing granular mixtures. J. Fluid Mech. 528, 207.
Galvin, J. E., Hrenya, C. M. & Wildman, R. D. 2007 On the role of the Knudsen layer in rapid granular flows. J. Fluid Mech. 585, 73.
Garz'o, V. & Dufty, J. 1999 Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 5895.
Garzo, V. & Montanero, J. M. 2002 Transport coefficients of a heated granular gas. Physica A 313, 336.
Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267.
Goldhirsch, I. & Sela, N. 1996 Origin of normal stress differences in rapid granular flows. Phys. Rev. E 54, 4458.
Goldhirsch, I. & Zanetti, G. 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619.
Goldhirsch, I., Noskowicz, S. H. & Bar-Lev, O. 2004 Theory of granular gases: some recent results and some open problems. J. Phys. Cond. Matter 17, 2591.
Haff, P. K. 1983 Grain flow as a fluid-mechanical problem. J. Fluid Mech. 134, 401.
Herbst, O., Müller, P., Otto, M. & Zippelius, A. 2004 Local equation of state and velocity distributions of a driven granular gas. Phys. Rev. E 70, 051313.
Herbst, O., Müller, P. & Zippelius, A. 2005 Local heat flux and energy loss in a two-dimensional vibrated granular gas. Phys. Rev. E 72, 141303.
Hopkins, M. & Louge, M. 1991 Inelastic microstructure in rapid granular flows of smooth disks. Phys. Fluids A 3, 47.
Jenkins, J. T. 1998 Kinetic theory for nearly elastic spheres. In Physics of Dry Granular Media (ed. Hermann, H. J., Hovi, J. P. & Luding, S.). Kluwer.
Jenkins, J. T. & Richman, M. W. 1988 Plane simple shear of smooth inelastic circular disks: the anisotropy of the second moment in dilute and dense limits. J. Fluid Mech. 192, 313.
Kumaran, V. 1997 Velocity distribution function for a dilute granular material in shear flow. J. Fluid Mech. 340, 319.
Kumaran, V. 2005 Kinetic model for sheared granular flows in the high Knudsen number limit. Phys. Rev. Lett. 95, 108001.
Lasinski, M. E., Curtis, J. S. & Pekny, J. F. 2004 Effect of system size on particle-phase stress and microstructure formation. Phys. Fluids 16, 265.
Liss, E. D. & Glasser, B. J. 2001 The influence of clusters on the stress in a sheared granular material. Powder Technol. 116, 116.
Mackowski, D., Papadopoulos, D. H. & Rosner, D. E. 1999 Comparison of Burnett and DSMC predictions of pressure distributions and normal stress in one-dimensional, strongly nonisothermal gases. Phys. Fluids 11, 2108.
Mareschal, M., Kestemont, E., Baras, F., Clementi, E. & Nicolis, G. 1987 Nonequilibrium states by molecular-dynamics – transport-coefficients in constrained fluids. Phys. Rev. A 35, 3883.
Martin, T. W., Huntley, J. M. & Wildman, R. D. 2006 Hydrodynamic model for a vibrofluidized granular bed. J. Fluid Mech. 535, 325.
MiDi, G. D. R. 2004 On dense granular flows. Eur. Phys. J. E 14, 341.
Montanero, J. M., Santos, A. & Garz'o, V. 2007 First-order Chapman–Enskog velocity distribution function in a granular gas. Physica A 376, 75.
Noskowicz, S. H., Bar-Lev, O., Serero, D. & Goldhirsch, I. 2007 Computer-aided kinetic theory and granular gases. Europhys. Lett. 79, 60001.
Pöschel, T. & Schwager, T. 2005 Computational Granular Dynamics. Springer.
Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. 1992 Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press.
Risso, D. & Cordero, P. 2002 Dynamics of rarefied gases. Phys. Rev. E 65, 021304.
Santos, A. & Garz'o, V. 1995 In Rarefied Gas Dynamics 19 (ed. Harvey, J. & Lord, G.). Oxford University Press.
Santos, A., Garzo, V. & Dufty, J. 2004 Inherent rheology of a granular fluid in uniform shear flow. Phys. Rev. E 061303.
Sela, N. & Goldhirsch, I. 1998 Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41.
Shattuck, M. D., Bizon, C., Swift, J. B. & Swinney, H. L. 1999 Computational test of kinetic theory of granular media. Physica A 274, 158.
Silbert, L. E., Grest, G. S., Brewster, R. & Levine, A. J. 2007 Rheology and contact lifetimes in dense granular flows. Phys. Rev. Lett. 99, 068002.
Soto, R., Mareschal, M. & Risso, D. 1999 Departure from Fourier's law for fluidized granular media. Phys. Rev. Lett. 83, 5003.
Sundaresan, S. 2000 Perspective: Modeling the hydrodynamics of multiphase flow reactors: Current status and challenges. AIChE J. 46, 1102.
Sunthar, P. & Kumaran, V. 2001 Characterization of the stationary states of a dilute vibrofluidized granular bed. Phys. Rev. E 64, 041303.
Tan, M.-L. & Goldhirsch, I. 1997 Intercluster interactions in rapid granular shear flows. Phys. Fluids 9, 856.
Walton, O. R. & Braun, R. L. 1986 Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mech. 63, 73.
Wassgren, C. & Curtis, J. S. 2006 The application of computational modeling to pharmaceutical materials science. MRS Bull. 31, 900.
Wildman, R. D., Huntley, J. M. & Parker, D. J. 2001 Granular temperature profiles in three-dimensional vibrofludized granular beds. Phys. Rev. E 63, 061311.
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Evidence of higher-order effects in thermally driven rapid granular flows

  • C. M. HRENYA (a1), J. E. GALVIN (a1) (a2) and R. D. WILDMAN (a3)


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