Flow of dense granular material: towards simple constitutive laws

Recent experiments and numerical simulations of dry granular flows suggest that a simple rheological description in terms of a friction coefficient varying both with shear rate and pressure through a dimensionless inertial number may be sufficient to capture the major properties of granular flows. In this paper we first present the empirical constitutive laws and their interpretation using dimensional analysis, before analysing the prediction for different flow configurations. The successes and limits of the approach are discussed based on comparison with recent studies.

[1]  P. Mills,et al.  Model for a stationary dense granular flow along an inclined wall , 1999 .

[2]  Julio M. Ottino,et al.  Surface flow of granular materials: model and experiments in heap formation , 2001, Journal of Fluid Mechanics.

[3]  Farhang Radjai,et al.  Turbulentlike fluctuations in quasistatic flow of granular media. , 2002, Physical review letters.

[4]  Adrian Daerr,et al.  Dynamical equilibrium of avalanches on a rough plane , 2001 .

[5]  F. Dullien.  Porous Media: Fluid Transport and Pore Structure , 1979 .

[6]  Crucial role of sidewalls in granular surface flows: consequences for the rheology , 2005, Journal of Fluid Mechanics.

[7]  D Bonamy,et al.  Multiscale clustering in granular surface flows. , 2002, Physical review letters.

[8]  Jean-Noël Roux,et al.  Rheophysics of dense granular materials: discrete simulation of plane shear flows. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  James W. Landry,et al.  Granular flow down a rough inclined plane: Transition between thin and thick piles , 2003 .

[10]  F. Cruz.  Ecoulement de grains secs : frottement et blocage , 2004 .

[11]  Heinrich M. Jaeger,et al.  Signatures of granular microstructure in dense shear flows , 2000, Nature.

[12]  M. Rabaud,et al.  Granular avalanches in fluids. , 2002, Physical review letters.

[13]  Olivier Pouliquen,et al.  Submarine granular flows down inclined planes , 2005 .

[14]  Lev S. Tsimring,et al.  Patterns and collective behavior in granular media: Theoretical concepts , 2006 .

[15]  Wolfgang Losert,et al.  Superstable granular heap in a thin channel. , 2003, Physical review letters.

[16]  R. M. Nedderman,et al.  The thickness of the shear zone of flowing granular materials , 1980 .

[17]  M. Louge,et al.  Model for dense granular flows down bumpy inclines. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  I. Goldhirsch,et al.  RAPID GRANULAR FLOWS , 2003 .

[19]  G. Midi,et al.  On dense granular flows , 2003, The European physical journal. E, Soft matter.

[20]  S. Savage,et al.  The Mechanics of Rapid Granular Flows , 1984 .

[21]  Prabhu R. Nott,et al.  Frictional–collisional equations of motion for participate flows and their application to chutes , 1990, Journal of Fluid Mechanics.

[22]  Christian Veje,et al.  Stress Fluctuations in a 2D Granular Couette Experiment: A Continuous Transition , 1999 .

[23]  Olivier Pouliquen,et al.  Slow Dense Granular Flows as a Self-induced Process , 2001, Adv. Complex Syst..

[24]  O. Pouliquen,et al.  Stress fluctuations and shear zones in quasistatic granular chute flows. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  P. Coussot,et al.  A theoretical framework for granular suspensions in a steady simple shear flow , 1999 .

[26]  T S Komatsu,et al.  Creep motion in a granular pile exhibiting steady surface flow. , 2001, Physical review letters.

[27]  Olivier Pouliquen,et al.  A constitutive law for dense granular flows , 2006, Nature.

[28]  O Pouliquen.  Velocity correlations in dense granular flows. , 2004, Physical review letters.

[29]  Michael M. Khonsari,et al.  Granular Lubrication: Toward an Understanding of the Transition Between Kinetic and Quasi-Fluid Regime , 2004 .

[30]  Olivier Pouliquen,et al.  SCALING LAWS IN GRANULAR FLOWS DOWN ROUGH INCLINED PLANES , 1999 .