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Shear-weakening of the transitional regime for granular flow

Published online by Cambridge University Press:  31 August 2007

KEVIN LU
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90025, USA
E. E. BRODSKY
Affiliation:
Department of Earth and Planetary Science, University of California, Santa Cruz, Santa Cruz, CA 95064, USA
H. P. KAVEHPOUR
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90025, USA

Abstract

This paper experimentally investigates the rheology of dense granular flow through itssolid-like to fluid-like transition. Between the well-established flow regimes – quasi-static and grain-inertial – the physical description of the transition remains elusive. Our experiment uses a top-rotating torsional shear cell capable of ± 1 μm accuracy in height and 5 decades (10−3 − 100 rad s−1) in rotation rate. The data on beach sand shows that shear and normal stresses exhibit an inverse rate-dependence under a controlledvolume environment in the transitional regime, while in the limiting regimes the results are in agreement with previous work. Theshear-weakening stresses illustrate a previouslyunknown ‘dip’ with increasingshear rate. Under a controlled-pressure environment, however, the shear-compacting volume-fraction ‘peaks’ with increasing shear-rate. We combine these results from both configurations to infer a constitutive law based on a rate-invariant granular fluid compressibility. The formulation provides an equation-of-state for dynamic granular systems, with state variables of pressure, strain rate and free-volume-fraction. Fitting parameters from independent constant-volume and constant-pressure data shows good agreement in validating our model. Moreover, the degree of grain jaggedness is essential to the rate-dependence within the transitional regime. The results on the solid–fluid transitionmay elucidate the evolution of granular flow anisotropies.

Type
Papers
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Aharonov, E. & Sparks, D. 2004 Stick-slip motion in simulated granular layers. J. Geophys. Res.-Solid Earth, 109.CrossRefGoogle Scholar
Bagnold, R. A. 1954 Experiments on a gravity free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 4963.Google Scholar
Behringer, R. P., Howell, D., Kondic, L., Tennakoon, S. & Veje, C. 1999 Predictability and granular materials. Physica D 133, 117.Google Scholar
Bocquet, L., Losert, W., Schalk, D., Lubensky, T. C. & Gollub, J. P. 2002 Granular shear flow dynamics and forces: experiment and continuum theory. Phys Rev E 65 (1), 011307.Google ScholarPubMed
Bossis, G., Grasselli, Y. & Volkova, O. 2004 Granular rheology in zero gravity. J. Phys. Cond. Matter. 16, 32793287.CrossRefGoogle Scholar
Campbell, C. S. 1990 Rapid granular flows. Annu. Rev. Fluid Mech. 22, 5792.CrossRefGoogle Scholar
Campbell, C. S. 2002 Granular shear flows at the elastic limit J. Fluid Mech. 465, 261291.CrossRefGoogle Scholar
Campbell, C. S. 2005 Stress-controlled elastic granular shear flows. J. Fluid Mech. 539, 273297.CrossRefGoogle Scholar
Campbell, C. S. 2006 Granular material flows – an overview. Powder Technol. 162, 208229.CrossRefGoogle Scholar
Cates, M. E., Wittmer, J. P., Bouchaud, J. P. & Claudin, P. 1999 Jamming and static stress transmission in granular materials. Chaos. 9, 511522.CrossRefGoogle ScholarPubMed
Cheng, D. C. H. & Richmond, R. A. 1978 Some observations on rheological behavior of dense suspensions. Rheol. Acta. 17, 446453.CrossRefGoogle Scholar
Corwin, E. I., Jaeger, H. M. & Nagel, S. R. 2005 Structural signature of jamming in granular media. Nature. 435, 10751078.CrossRefGoogle ScholarPubMed
daCruz, F. Cruz, F., Emam, S., Prochnow, M., Roux, J. N. & Chevoir, F. 2005 Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72, part 1 021309.Google Scholar
Dalton, F., Farrelly, F., Petri, A., Pietronero, L., Pitolli, L. & Pontuale, G. 2005 Shear stress fluctuations in the granular liquid and solid phases. Phys. Rev. Lett. 95 (13).CrossRefGoogle ScholarPubMed
Dartevelle, S. 2004 Numerical modeling of geophysical granular flows: 1. a comprehensive approach to granular rheologies and geophysical multiphase flows. Geochem. Geophys. Geosyst. 5.Google Scholar
Drake, T. G. 1990 Structural features in granular flows. J. Geophys. Res. 95 (B6), 86818696.CrossRefGoogle Scholar
Duran, J. 1999 Sands, Powders and Grains: An Introduction to the Physics of Granular Materials, 1st edn. Springer.Google Scholar
deGennes, P. G. Gennes, P. G. 1999 Granular matter: a tentative view. Rev. Mod. Phys. 71, S374S382.Google Scholar
Hanes, D. M. & Inman, D. L. 1985 Observations of rapidly flowing granular-fluid materials. J. Fluid Mech. 150, 357380.CrossRefGoogle Scholar
Hendy, S. C. 2005 Towards a theory of granular plasticity. J. Engng Math. 52, 137146.CrossRefGoogle Scholar
Howell, D. W., Behringer, R. P. & Veje, C. T. 1999 Fluctuations in granular media. Chaos. 9, 559572.CrossRefGoogle ScholarPubMed
Hsiau, S. S. & Shieh, Y. M. 2000 Effect of solid fraction on fluctuations and self-diffusion of sheared granular flows. Chem. Engng Sci. 55, 19691979.CrossRefGoogle Scholar
Jaeger, H. M., Nagel, S. R. & Behringer, R. P. 1996 Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 12591273.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2005 Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167192.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature. 441, 727730.CrossRefGoogle ScholarPubMed
Karion, A. & Hunt, M. L. 1999 Energy dissipation in sheared granular flows. Trans. ASME C: J. Heat Transfer. 121, 984991.CrossRefGoogle Scholar
Kavehpour, H. P. & McKinley, G. H. 2004 Tribo-rheometry: from gap-dependent rheology to tribology. Tribol. Lett. 17, 327335.CrossRefGoogle Scholar
Klausner, J. F., Chen, D. M. & Mei, R. W. 2000 Experimental investigation of cohesive powder rheology. Powder Technol. 112, 94101.CrossRefGoogle Scholar
Knight, J. B., Ehrichs, E. E., Kuperman, V. Y., Flint, J. K., Jaeger, H. M. & Nagel, S. R. 1996 Experimental study of granular convection. Phys. Rev. E 54, 57265738.Google ScholarPubMed
Larson, D. G. 1999 The Structure and Rheology of Complex Fluids. Oxford University Press.Google Scholar
Liu, A. J. & Nagel, S. R. 1998 Nonlinear dynamics – jamming is not just cool any more. Nature. 396, 2122.CrossRefGoogle Scholar
Lois, G., Lemaitre, A. & Carlson, J. M. 2005 Numerical tests of constitutive laws for dense granular flows. Phys. Rev. E 72, 051303.Google ScholarPubMed
Majmudar, T. S. & Behringer, R. P. 2005 Contact force measurements and stress-induced anisotropy in granular materials. Nature. 435, 10791082.CrossRefGoogle ScholarPubMed
Makse, H. A., Havlin, S., King, P. R. & Stanley, H. E. 1997 Spontaneous stratification in granular mixtures. Nature. 386, 379382.CrossRefGoogle Scholar
MiDi, G. D. R. 2004 On dense granular flows. Eur. Phys. J. E 14, 341365.Google Scholar
Nedderman, R. M. 1992 Static and Kinematics of Granular Materials, 1st edn. Cambridge University Press.CrossRefGoogle Scholar
Nowak, E. R., Knight, J. B., Povinelli, M. L., Jaeger, H. M. & Nagel, S. R. 1997 Reversibility and irreversibility in the packing of vibrated granular material. Powder Technol. 94, 7983.CrossRefGoogle Scholar
O'Hern, C. S., Langer, S. A., Liu, A. J. & Nagel, S. R. 2001 Force distributions near jamming and glass transitions. Phys. Rev. Lett. 86, 111114.CrossRefGoogle ScholarPubMed
O'Hern, C. S., Silbert, L. E., Liu, A. J. & Nagel, S. R. 2003 Jamming at zero temperature and zero applied stress: The epitome of disorder. Phys. Rev. E 68 (1), 011306.Google ScholarPubMed
Onoda, G. Y. & Liniger, E. G. 1990 Random loose packings of uniform spheres and the dilatancy onset. Phys. Rev. Lett. 64, 27272730.CrossRefGoogle ScholarPubMed
Ostojic, S., Somfai, E. & Nienhuis, B. 2006 Scale invariance and universality of force networks in static granular matter. Nature. 439, 828830.CrossRefGoogle ScholarPubMed
Reynolds, O. 1885 On the dilatancy of media composed of rigid particles in contact. Phil. Mag. 5, 469481.CrossRefGoogle Scholar
Savage, S. B. 1984 The mechanics of rapid granular flows. Adv Appl. Mech. 24, 289366.CrossRefGoogle Scholar
Savage, S. B. 1998 Analyses of slow high-concentration flows of granular materials. J. Fluid Mech. 377, 126.CrossRefGoogle Scholar
Savage, S. B. & Sayed, M. 1984 Stresses developed by dry cohesionless granular-materials sheared in an annular shear cell. J. Fluid Mech. 142, 391430.CrossRefGoogle Scholar
Savage, S. B., Nedderman, R. M., Tuzun, U. & Houlsby, G. T. 1983 The flow of granular-materials3. Rapid shear flows. Chem. Engng Sci. 38, 189195.CrossRefGoogle Scholar
Sawyer, W. G. & Tichy, J. A. 2001 Lubrication with granular flow: continuum theory, particle simulations, comparison with experiment. Trans. ASME J. Tribol. 123, 777784.CrossRefGoogle Scholar
Shinbrot, T. 2004 Granular materials – the brazil nut effect – in reverse. Nature. 429, 352353.CrossRefGoogle ScholarPubMed
Tardos, G. I., Khan, M. I. & Schaeffer, D. G. 1998 Forces on a slowly rotating, rough cylinder in a couette device containing a dry, frictional powder. Phys. Fluids. 10, 335341.CrossRefGoogle Scholar
Tardos, G. I., McNamara, S. & Talu, I. 2003 Slow and intermediate flow of a frictional bulk powder in the Couette geometry. Powder Technol. 131, 2339.CrossRefGoogle Scholar
Tuzun, U., Houlsby, G. T., Nedderman, R. M. & Savage, S. B. 1982 The flow of granular-materials2. Velocity distributions in slow flow. Chem. Engng Sci. 37, 16911709.CrossRefGoogle Scholar
Visscher, W. M. & Bolsterl, M. 1972 Random packing of equal and unequal spheres in 2 and 3 dimensions. Nature. 239, 504508.CrossRefGoogle Scholar
Yu, A. B., Zou, R. P. & Standish, N. 1996 Modifying the linear packing model for predicting the porosity of nonspherical particle mixtures. Indust. Engng Chem. Res. 35, 37303741.CrossRefGoogle Scholar
Zou, R. P. & Yu, A. B. 1996 Evaluation of the packing characteristics of mono-sized non-spherical particles. Powder Technol. 88, 7179.CrossRefGoogle Scholar