Abstract
Granular flows present a host of interesting problems, both theoretical and experimental. For slow deformations, granular materials are glassy. They contain frozen disorder, and stresses propagate through the material via complex chains of contacts (Drescher et al., 1972; Drescher, 1976; Travers et al., 1986). In this case, granular materials are thought to behave plastically in response to a stress, once some narrow range of elastic response has been exceeded (Jackson, 1983). As the material deforms, contact chains are irreversibly broken and remade. At faster flow rates and lower densities, these materials are better modeled as a gas of particles, exhibiting random fluctuations (Bagnold, 1954; Haff, 1983; Jenkins and Savage, 1983). Unlike the case for large thermodynamic systems, the fluctuation energies can be comparable to the energy associated with large-scale motion. In both scenarios, the flows are inherently dissipative. For slow flows, energy is lost to Coulomb friction as grains slide across each other. For rapid flows, energy is lost because particle collisions are inherently inelastic.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bagnold, R.A., Experiments on a gravity-free dispersion of a large solid spheres in a newtonian fluid under shear, Proc. R. Soc. London, A225, 49–63, 1954.
Bak, P., Tang, C., and Wiesenfeld, K., Self-organized criticality: an explanation of 1/f noise, Phys. Rev. Lett., 59, 381–384, 1987.
Baxter, G.W. and Behringer, R.P., Pattern formation in flowing sand, Phys. Rev. Lett., 62, 2825–2828, 1989.
Baxter, G.W. and Behringer, R.P., Cellular automata models of granular flow, Phys. Rev. A, 42, 1017–1020, 1990a.
Baxter, G.W. and Behringer, R.P., Pattern formation and time-dependence in flowing sand, in Two Phase Flows and Waves, Springer-Verlag, New York, 1990b, pp. 1–29.
Baxter, G.W. and Behringer, R.P., Cellular automata models for the flow of granular materials, Physica D, 51, 465–471, 1991a.
Baxter, G.W. and Behringer, R.P., Time-dependence, scaling and pattern formation for flowing sand, Eur. J. Mech. B, 10, 181–186, 1991b.
Baxter, G.W. and Behringer, R.P., Experimental test of time-scales in flowing sand, Europhys. Lett., 21, 569–574, 1993.
Bransby, P.L. and Blair-Fish, P.M., Initial deformations during mass flow from a bunker: observations and idealizations, Powder Technol., 11, 273–288, 1975.
Bransby, P.L., Blair-Fish, P.M., and James, R.G., An investigation of the flow of granular materials, Powder Technol., 8, 197–206, 1973.
Cambou, B., Geomaterials: Constitutive Equations and Modelling, Elsevier, New York, 1990, pp. 263–282.
Campbell, C.S., The stress tensor for simple shear flows of a granular material, J. Fluid Mech., 203, 449–473, 1989.
Campbell, C.S. and Brennen, C.E., Computer simulation of granular shear flows, J. Fluid Mech., 151, 167–188, 1985.
Campbell, C.S. and Gong, A., The stress tensor in a two-dimensional granular shear flow, J. Fluid Mech., 164, 107–125, 1986.
Chang, C. and Misra, A., Constitutive laws for engineering materials, in Stress-Strain Modelling of Heterogeneous Solids Based on Micromechanics, American Society of Mechanical Engineers Press, 1991, pp. 501–504.
Cristofferson, J., Mehrabadi, M.M., and Nehmat-Nasser, S., A micromechanical description of granular material behavior. J. Appl. Mech., 48, 339–344, 1981.
Cundall, P. A. and Strack, O.D.L., A discrete numerical model for granular assemblies, Geotechnique, 29, 47–65, 1979.
Cutress, J.O. and Pulfer, R.F., X-Ray investigations of flowing powders. Powder Technol., 1, 213–220, 1967.
de Gennes, P.G., The Physics of Liquid Crystals, Clarendon Press, Oxford, 1974.
Drescher, A., An experimental investigation of flow rules for granular materials using optically sensitive glass particles, Geotechnique, 26, 591–601, 1976.
Drescher, A. and De Josselin De Jong, G., Photoelastic verification of a mechanical model for the flow of a granular material, J. Mech. Phys. Solids, 20, 337–351, 1972.
Drescher, A., Cousens, T.W., and Bransby, P.L., Kinematics of the mass flow of granular material through a plane hopper, Geotechnique, 28, 27–42, 1978.
Haff, P.K. and Werner, B.T., Computer simulation of the mechanical sorting of grains, Powder Technol., 48, 239–245, 1986.
Evesque, P. and Rajchenbach, J., Instability in a sand heap, Phys. Rev. Lett., 62, 44–46, 1989.
Feder, J., Fractals, Plenum, New York, 1988.
Frisch, U., Hasslacher, B., and Pomeau, Y., Lattice gas automata for the Navier-Stokes equation, Phys. Rev. Lett., 56, 1505–1508, 1986.
Haff, P.K., Booming dunes, Amer. Sci., 74, 376–381, 1986.
Haff, P.K., Grain flow as a fluid-mechanical phenomenon, J. Fluid Mech., 134, 401–430, 1983.
Held, G., Solina, D.H., Keane, D.T, Haag, W.J., Horne, P.M., and Grinstein, G. Experimental study of critical-mass fluctuation in an evolving sandpile, Phys. Rev. Lett., 65, 1120–1123, 1990.
Hettler, A. and Vardoulakis, I., Behavior of dry sand tested in a large triaxial apparatus, Geotechnique, 34, 183–197, 1984.
Jackson, R., in Some mathematical and physical aspects of continuum models for the motion of granular materials, in The Theory of Dispersed Multiphase Flow, Academic Press, New York, 1983, pp. 291–337.
Jaeger, H.M., Liu, C. and Nagel, S.R., Relaxation at the angle of repose, Phys. Rev. Lett., 62, 40–43, 1989.
Jenike, A.W., Gravity flow of bulk solids, Bull. Univ. Utah Eng. Exp. Station, 1961.
Jenike, A.W., Storage and flow of solids, Bull. Univ. Utah Eng. Exp. Station, 1964 (seventh printing, 1976 ).
Jenkins, J.T. and Savage, S.B., A theory for the rapid flow of identical, smooth, nearly elastic spherical particles, J. Fluid Mech., 130, 186–202, 1983.
Kadanoff, L.P., Nagel, S.R., Wu, L., and Zhou, S.M., Scaling and universality in avalanches, Phys. Rev. A, 39, 6524–6537, 1989.
Kruger, R.A. and Riederer, S.J., Basic Concepts of Digital Subtraction Angiography, G.K. Hall Medical Publishers, Boston, 1984.
Mandelbrot, B.B. and Van Ness, J.W., Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10, 422–437, 1968.
Mandelbrot, B.B. and Wallis, J.R., Noah, Joseph, and operational hydrology, Water Resour. Res., 4, 909–918, 1968.
Matsuoaka, H., A microscopic study on shear mechanism of granular materials, Soils Found, 14, 29–43, 1974.
Mello, T.M., Diamond, P.H., and Levine, H., Hydrodynamic modes of a granular shear flow, Phys. Fluids A, 3, 2067–2075, 1991.
Michalowski, R.L., Flow of granular material through a plane hopper, Powder Technol., 39, 29–40, 1984.
Oda, M., Initial fabrics and their relations to mechanical properties of granular material, Soils Found., 12, 17–36, 1972.
Otnes, R.K. and Enochson, L., Digital Time Series Analysis, John Wiley & Sons, New York, 1972.
Pariseau, W.G., Discontinuous velocity fields in gravity flows of granular materials through slots, Powder Technol., 3, 218–226, 1969.
Pitman, E.B. and Schaeffer, D.G., Stability of time dependent compressible granular flow in two dimensions, Commun. Pure Appl. Math., 40, 421–447, 1987.
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T., Numerical Recipes in C, Cambridge University Press, Cambridge, 1988.
Rosato, A., Strandburg, K.J., Prinz, F., and Swendsen, R.H., Why the brazil nuts are on top: size segregation of particulate matter by shaking, Phys. Rev. Lett., 58, 1038–1040, 1987.
Savage, S., Simulation of Couette flow of granular materials: spatiotemporal coherence and 1/f noise, 1993, to be published.
Schaeffer, D.G., Instability in the evolution equations describing incompressible granular flow, J. Diff. Eq., 66, 19–50, 1987.
Schofield, A. and Wroth, C, Critical State Soil Mechanics, McGraw-Hill, New York, 1968.
Thompson, P.A. and Grest, G.S., Friction and the dilatancy transition, Phys. Rev. Lett., 67, 1751–1754, 1991.
Travers, T., Bideau, D., Gervois, A., Troadec, J.P., and Messager, J.C., Uniaxial compression effects on 2d mixtures of “hard” and “soft” cylinders. J. Phys. A., 19, L1033–L1038, 1986.
Tuzun, U. and Nedderman, R.M., An investigation of the flow boundary during steady-state discharge from a funnel-flow bunker. Powder Technol., 31, 27–43, 1982.
Voss, R.F., Random fractals: self-affinity in noise, music, mountains and clouds, Physica D, 38, 362–371, 1988.
Walton, O.R. and Braun, R.L., Viscosity and temperature calculations for assemblies of inelastic frictions disks, J. Rheol., 30, 949–980, 1986a.
Walton, O.R. and Braun, R.L., Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mech., 63, 73–86, 1986b.
Walton, O.R., Braun, R.L., and Cervelli, D.M., Flow of granular solids: 3-dimensional discrete-particle computer modelling of uniform shear, in Micromechanics of Granular Materials, Elsevier, New York, 1987.
Wolfram, S., Cellular automata fluids. 1. Basic theory, J. Stat. Phys., 45, 471–472, 1986.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Behringer, R.P., Baxter, G.W. (1994). Pattern Formation and Complexity in Granular Flows. In: Mehta, A. (eds) Granular Matter. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4290-1_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4290-1_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8725-4
Online ISBN: 978-1-4612-4290-1
eBook Packages: Springer Book Archive