Abstract
Using the results of recent numerical simulations, we extend an existing kinetic theory for dense flows of identical, nearly elastic, frictionless spheres to identical, very dissipative, frictional spheres. The existing theory incorporates an additional length scale in the expression for the collisional rate of dissipation; this length scale is identified with the size of a cluster of correlated particles. Parameters of the theory for very dissipative, frictional spheres are set using the results of physical experiments on inclined flows of spheres over a rigid, bumpy base in the absence of sidewalls. The resulting theory is then tested against the results of physical experiments on flows of the same material over the surface of an erodible heap when frictional sidewalls are present.
Similar content being viewed by others
References
Mitarai N., Nakanishi H.: Velocity correlations in dense granular shear flows: effects on energy dissipation and normal stress. Phys. Rev. E 75, 031305 (2007)
Reddy K.A., Kumaran V.: Applicability of constitutive relations from kinetic theory for dense granular flow. Phys. Rev. E 76, 061305 (2007)
Lois G., Carlson J., Lemaitre A.: Numerical tests of constitutive laws for dense granular fows. Phys. Rev. E 72, 051303 (2005)
Lois G., Lemaitre A., Carlson J.: Emergence of multi-contact interactions in contact dynamics simulations. Europhys. Lett. 76, 318 (2006)
Mills P., Rognon P.G., Chevoir F.: Rheology and structure of granular materials near the jamming transition. Europhys. Lett. 81, 64005 (2008)
Goldman D.I., Swinney H.L.: Signatures of glass formation in a fluidized bed of hard spheres. Phys. Rev. Lett. 96, 145702 (2006)
Schröter M., Nägle S., Radin C., Swinney H.L.: Phase transition in a static granular system. Europhys. Lett. 78, 44004 (2007)
Hatano T., Otsuki M., Sasa S.: Criticality and scaling relations in a sheared granular material. J. Phys. Soc. Japan 76, 023001 (2007)
Ertas D., Halsey T.C.: Granular gravitational collapse and chute flow. Europhys. Lett. 60, 931 (2002)
Kumaran V.: The constitutive relation for the granular flow of rough particles and its application to the flow down an incline plane. J. Fluid Mech. 561, 1 (2006)
Jenkins J.T.: Dense shearing flows of inelastic disks. Phys. Fluids 18, 103307 (2006)
Jenkins J.T.: Dense inclined flows of inelastic spheres. Gran. Matt. 10, 47 (2007)
Garzo V., Dufty J.W.: Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 5895 (1999)
Pouliquen O.: Scaling laws in granular flows down a bumpy inclined plane. Phys. Fluids 11, 542 (1999)
Jop P., Forterre Y., Pouliquen O.: Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 451, 167 (2005)
Jenkins J.T., Richman M.W.: Grad’s 13-moment system for a dense gas of inelastic spheres. Arch. Ration. Mech. Anal. 87, 355 (1985)
MiDi G.D.R.: On dense granular flows. Eur. Phys. J. E 14, 341 (2004)
Da Cruz F., Emem S., Prochnow M., Roux J.-N., Chevoir F.: Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72, 021309 (2005)
Jenkins J.T., Zhang C.: Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14, 1228 (2002)
Yoon D.K., Jenkins J.T.: Kinetic Theory for identical, frictional, nearly elastic disks. Phys. Fluids 17, 083301 (2005)
Carnahan N.F., Starling K.E.: Equations of state of non-attracting rigid spheres. J. Chem. Phys. 51, 635 (1969)
Herbst O., Huthmann M., Zippelius A.: Dynamics of inelastically colliding spheres with Coulomb friction: dynamics of the relaxation of translational and rotational energy. Gran. Matt. 2, 211 (2000)
Foerster S.F., Louge M.Y., Chang H., Allia K.: Measurements of Collision properties of small spheres. Phys. Fluids 6, 1108 (1994)
Torquato S.: Nearest-neighbor statistics for packings of hard spheres and disks. Phys. Rev. E 51, 3170 (1995)
Richman M.W.: Boundary conditions based on a modified Maxwellian velocity distribution function for flows of identical, smooth, nearly elastic spheres. Acta Mech. 75, 227 (1988)
Jenkins J.T.: Boundary conditions for collisional grain flows at bumpy, frictional walls. In: Poschel, T., Luding, S. (eds) Granular Gases 125, Springer, Berlin (2001)
Pasini J.M., Jenkins J.T.: Aeolian transport with collisional suspension. Phil. Trans. Roy. Soc. 363, 1625 (2005)
Jenkins J.T., Hanes D.M.: The balance of momentum and energy at an interface between colliding and freely flying grains in a rapid granular flow. Phys. Fluids A 5, 781 (1993)
Silbert L.E., Ertas D., Grest G.S., Halsey T.C., Levine D., Plimpton S.J.: Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 51302 (2001)
Mitarai N., Nakanishi H.: Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow. Phys. Rev. Lett. 94, 128001 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jenkins, J.T., Berzi, D. Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granular Matter 12, 151–158 (2010). https://doi.org/10.1007/s10035-010-0169-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10035-010-0169-8