Using statistical methods analogous to those used in the kinetic theory of dense gases, conservation equations and constitutive equations are derived for the flow of an idealized granular material consisting of uniform, rough, inelastic spherical particles. Simple forms for the singlet and pair velocity distribution functions are employed to study the effects of particle rotary inertia in the specific case of Couette flow of such materials. A constant coefficient of restitution e is used to characterize the inelasticity of the particles and a roughness coefficient β is adopted to characterize the effects of surface friction in collisions between particles. During collisions, surface friction causes particle rotational velocity fluctuations. As a result of particle rotary inertia, the stress tensor is found to be asymmetric during general deformations. However, for the special case of steady Couette flow which is studied in detail, the stress tensor remains symmetric. The partition of fluctuation kinetic energy between the translational and rotational modes is examined; equipartition is achieved only for the case of perfectly rough particles. In agreement with previous investigations, the stresses are found to decrease with decreasing e. Except for the case of almost perfectly rough particles, the effects of rotary inertia generally reduce the stresses. However, the normal stresses are reduced more than the shear stresses, and the predicted ratio of shear to normal stress (the dynamic friction angle) is higher for rough particles than for smooth ones. The inclusion of roughness in the analysis yields shear to normal stress ratios that agree more closely with experimental measurements.
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March 1987
Research Papers
A Simple Kinetic Theory for Granular Flow of Rough, Inelastic, Spherical Particles
C. K. K. Lun,
C. K. K. Lun
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada H3A 2K6
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S. B. Savage
S. B. Savage
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada H3A 2K6
Search for other works by this author on:
C. K. K. Lun
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada H3A 2K6
S. B. Savage
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada H3A 2K6
J. Appl. Mech. Mar 1987, 54(1): 47-53 (7 pages)
Published Online: March 1, 1987
Article history
Received:
November 28, 1983
Revised:
July 10, 1986
Online:
July 21, 2009
Citation
Lun, C. K. K., and Savage, S. B. (March 1, 1987). "A Simple Kinetic Theory for Granular Flow of Rough, Inelastic, Spherical Particles." ASME. J. Appl. Mech. March 1987; 54(1): 47–53. https://doi.org/10.1115/1.3172993
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