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Experimental investigation and kinetic-theory-based model of a rapid granular shear flow

Published online by Cambridge University Press:  25 April 2008

R. D. WILDMAN ,
T. W. MARTIN ,
J. M. HUNTLEY ,
J. T. JENKINS ,
H. VISWANATHAN ,
X. FEN  and
D. J. PARKER
R. D. WILDMAN
Affiliation:
School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough LE11 3TU, UK
T. W. MARTIN
Affiliation:
School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough LE11 3TU, UK
J. M. HUNTLEY
Affiliation:
School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough LE11 3TU, UK
J. T. JENKINS
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853USA
H. VISWANATHAN
Affiliation:
School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough LE11 3TU, UK
X. FEN
Affiliation:
School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
D. J. PARKER
Affiliation:
School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
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Abstract

An experimental investigation of an idealized rapidly sheared granular flow was performed to test the predictions of a model based on the kinetic theory of dry granular media. Glass ballotini beads were placed in an annular shear cell and the lower boundary rotated to induce a shearing motion in the bed. A single particle was tracked using the positron emission particle tracking (PEPT) technique, a method that determines the location of a particle through the triangulation of gamma photons emitted by a radioactive tracer particle. The packing fraction and velocity fields within the three-dimensional flow were measured and compared to the predictions of a model developed using the conservation and balance equations applicable to dissipative systems, and solved incorporating constitutive relations derived from kinetic theory. The comparison showed that kinetic theory is able to capture the general features of a rapid shear flow reasonably well over a wide range of shear rates and confining pressures.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 602 , 10 May 2008 , pp. 63 - 79
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Arnarson, B. O. & Jenkins, J. T. 2004 Binary mixtures of inelastic spheres: Simplified constitutive theory. Phys. Fluids 16, 4543–4550.CrossRefGoogle Scholar
Bizon, C., Shattuck, M. D., Swift, J. B., McCormick, W. D. & Swinney, H. L. 1998 Patterns in 3d vertically oscillated granular layers: Simulation and experiment. Phys. Rev. Lett. 80, 57–60.CrossRefGoogle Scholar
Brey, J. J., Dufty, J. W., Kim, C. S. & Santos, A. 1998 Hydrodynamics for granular flow at low density. Phys. Rev. E 58, 4638–4653.Google Scholar
Brey, J. J., Ruiz-Montero, M. J. & Moreno, F. 2001 Hydrodynamics of an open vibrated granular system. Phys. Rev. E 63, 061305.Google ScholarPubMed
Campbell, C. S. 2002 Granular shear flows at the elastic limit. J. Fluid Mech. 465, 261–291.CrossRefGoogle Scholar
Carnahan, N. F. & Starling, K. E. 1969 Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635–636.CrossRefGoogle Scholar
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-uniform Gases. Cambridge University Press.Google Scholar
Clement, E. & Rajchenbach, J. 1991 Fluidization of a bidimensional powder. Europhys. Lett. 16, 133–138.CrossRefGoogle Scholar
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, 73–92.CrossRefGoogle Scholar
Garzo, V. & Dufty, J. W. 1999 Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 5895–5911.Google ScholarPubMed
Helal, K., Biben, T. & Hansen, J. P. 1997 Local fluctuations in a fluidized granular medium. Physica A 240, 361–373.CrossRefGoogle Scholar
Hsiau, S. S. & Shieh, Y. M. 1999 Fluctuations and self-diffusion of sheared granular material flows. J. Rheol. 43, 1049–1066.CrossRefGoogle Scholar
Huan, C., Yang, X. Y., Candela, D., Mair, R. W. & Walsworth, R. L. 2004 NMR experiments on a three-dimensional vibrofluidized granular medium. Phys. Rev. E 69, 041302.Google ScholarPubMed
Jenkins, J. T. & Askari, E. 1999 Hydraulic theory for a debris flow supported on a collisional shear layer. Chaos 9, 654–658.CrossRefGoogle ScholarPubMed
Jenkins, J. T. & Mancini, F. 1989 Kinetic-theory for binary-mixtures of smooth, nearly elastic spheres. Phys. Fluids A 1, 2050–2057.CrossRefGoogle Scholar
Jenkins, J. T. & Richman, M. W. 1985 a Grads 13-moment system for a dense gas of inelastic spheres. Arch. Rat. Mech. Anal. 87, 355–377.CrossRefGoogle Scholar
Jenkins, J. T. & Richman, M. W. 1985 b Kinetic-theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28, 3485–3494.CrossRefGoogle Scholar
Jenkins, J. T. & Richman, M. W. 1986 Boundary-conditions for plane flows of smooth, nearly elastic, circular disks. J. Fluid Mech. 171, 53–69.CrossRefGoogle Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical-particles. J. Fluid Mech. 130, 187–202.CrossRefGoogle Scholar
Johnson, P. C., Nott, P. & Jackson, R. 1990 Frictional collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 501–535.CrossRefGoogle Scholar
Kierzenka, J. & Shampine, L. F. 2001 A bvp solver based on residual control and the MATLAB PSE. ACM Trans. Math. Software. 27, 299–316.CrossRefGoogle Scholar
Kumaran, V. 1998 a Kinetic theory for a vibro-fluidized bed. J. Fluid Mech. 364, 163–185.CrossRefGoogle Scholar
Kumaran, V. 1998 b Temperature of a granular material “fluidized” by external vibrations. Phys. Rev. E 57, 5660–5664.Google Scholar
Louge, M. Y. 2003 Model for dense granular flows down bumpy inclines. Phys. Rev. E 67, 061303.Google ScholarPubMed
Lu, H. L., Gidaspow, D. & Manger, E. 2001 Kinetic theory of fluidized binary granular mixtures. Phys. Rev. E 6406, 061301.Google Scholar
Luding, S., Herrmann, H. J. & Blumen, A. 1994 Simulations of 2-dimensional arrays of beads under external vibrations – scaling behavior. Phys. Rev. E 50, 3100–3108.Google Scholar
Martin, T. W., Huntley, J. M. & Wildman, R. D. 2005 Hydrodynamic model for a vibrofluidized granular bed. J. Fluid Mech. 535, 325–345.CrossRefGoogle Scholar
McNamara, S. & Luding S. 1998 Energy nonequipartition in systems of inelastic, rough spheres. Phys. Rev. E 58, 2247–2250.Google Scholar
Midi, G. D. R. 2004 On dense granular flows. Eur. Phys. J. E 14, 341–365.Google Scholar
Mitarai, N. & Nakanishi, H. 2005 Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow. Phys. Rev. Lett. 94, 128001.CrossRefGoogle ScholarPubMed
Parker, D. J., Allen, D. A., Benton, D. M., Fowles, P., McNeil, P. A., Tan, M. & Beynon, T. D. 1997 Developments in particle tracking using the birmingham positron camera. Nucl. Instrum. Meth. Phys. Res. 392, 421–426.CrossRefGoogle Scholar
Richman, M. W. 1993 Boundary-conditions for granular flows at randomly fluctuating bumpy boundaries. Mech. Mater. 16, 211–218.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, 391–430.CrossRefGoogle Scholar
Sela, N. & Goldhirsch, I. 1998 Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41–74.CrossRefGoogle Scholar
Slattery, J. C. 1972 Momentum, Energy and Mass Transfer in Continua. McGraw-Hill.Google Scholar
Sunthar, P. & Kumaran, V. 1999 Temperature scaling in a dense vibrofluidized granular material. Phys. Rev. E 60, 1951–1955.Google Scholar
Talbot, J. & Viot, P. 2002 Wall-enhanced convection in vibrofluidized granular systems. Phys. Rev. Lett. 89, 064301.CrossRefGoogle ScholarPubMed
Tsuji, Y., Morikawa, Y. & Shiomi, H. 1984 LDV measurements of an air solid 2-phase flow in a vertical pipe. J. Fluid Mech. 139, 417–434.CrossRefGoogle Scholar
Umbanhowar, P. B., Melo, F. & Swinney, H. L. 1996 Localized excitations in a vertically vibrated granular layer. Nature 382, 793–796.CrossRefGoogle Scholar
Viswanathan, H., Wildman, R. D., Huntley, J. M. & Martin, T. W. 2006 Comparison of kinetic theory predictions with experimental results for a vibrated three-dimensional granular bed. Phys. Fluids 18, 113302.CrossRefGoogle Scholar
Volfson, D., Tsimring, L. S. & Aranson, I. S. 2003 Order parameter description of stationary partially fluidized shear granular flows. Phys. Rev. Lett. 90, 254301.CrossRefGoogle ScholarPubMed
Warr, S., Huntley, J. M. & Jacques, G. T. H. 1995 Fluidization of a 2-dimensional granular system – experimental study and scaling behavior. Phys. Rev. E 52, 5583–5595.Google Scholar
Wildman, R. D. & Huntley, J. M. 2000 Novel method for measurement of granular temperature distributions in two-dimensional vibro-fluidised beds. Powder Technol. 113, 14–22.CrossRefGoogle Scholar
Wildman, R. D., Huntley, J. M., Hansen, J. P., Parker, D. J. & Allen, D. A. 2000 Single-particle motion in three-dimensional vibrofluidized granular beds. Phys. Rev. E 62, 3826–3835.Google ScholarPubMed
Wildman, R. D., Huntley, J. M. & Parker, D. J. 2001 a Convection in highly fluidized three-dimensional granular beds. Phys. Rev. Lett. 86, 3304–3307.CrossRefGoogle ScholarPubMed
Wildman, R. D., Huntley, J. M. & Parker, D. J. 2001 b Granular temperature profiles in three-dimensional vibrofluidized granular beds. Phys. Rev. E 6306, 061311.Google Scholar
Wildman, R. D. & Parker, D. J. 2002 Coexistence of two granular temperatures in binary vibrofluidized beds. Phys. Rev. Lett. 88, 064301.CrossRefGoogle ScholarPubMed
Yang, X. Y., Huan, C., Candela, D., Mair, R. W. & Walsworth, R. L. 2002 Measurements of grain motion in a dense, three-dimensional granular fluid. Phys. Rev. Lett. 88, 044301.CrossRefGoogle Scholar
Zamankhan, P. 1995 Kinetic-theory of multicomponent dense mixtures of slightly inelastic spherical-particles. Phys. Rev. E 52, 4877–4891.CrossRefGoogle ScholarPubMed