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Inelastic microstructure in rapid granular flows of smooth disks

Phys. Fluids A 3, 47 (1991); doi:10.1063/1.857863

Issue Date: January 1991

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Mark A. Hopkins
Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755

Michel Y. Louge
Department of Mechanical Engineering, Cornell University, Ithaca, New York 14853
Computer simulations of two-dimensional rapid granular flows of uniform smooth inelastic disks under simple shear reveal a dynamic microstructure characterized by the local, spatially anisotropic agglomeration of disks. A spectral analysis of the concentration field suggests that the formation of this inelastic microstructure is correlated with the magnitude of the total stresses in the flow. The simulations confirm the theoretical results of Jenkins and Richman [J. Fluid Mech. 192, 313 (1988)] for the kinetic stresses in the dilute limit and for the collisional stresses in the dense limit, when the size of the periodic domain used in the simulations is a small multiple of the disk diameter. However, the kinetic and, to a lesser extent, collisional stresses both increase significantly with the size of the periodic domain, thus departing from the predictions of the theory that assumes spatial homogeneity and isotropy. Physics of Fluids A: Fluid Dynamics is copyrighted by The American Institute of Physics.
History: Received 30 March 1990; accepted 11 September 1990
Permalink: http://dx.doi.org/10.1063/1.857863
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KEYWORDS and PACS

Keywords
PACS
  • 61.20.Ja
    Structure of liquids and solids; crystallography Classical, semiclassical, and quantum theories of liquid structure Computer simulation of static and dynamic behavior
  • 46.30.Pa
    Classical mechanics and rheology Mechanics and rheology (including stability and structural mechanics of shells, plates, and beams) Friction, wear, adherence, hardness, mechanical contacts, tribology
  • YEAR: 1990-91

PUBLICATION DATA

ISSN:
0899-8213 (print)   1089-7666 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (15)
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  1. J. T. Jenkins, in Non-Classical Continuum Mechanics (Cambridge, U.P., Cambridge, 1987), pp. 213–225.
  2. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge U.P., Cambridge, 1970), 3rd ed.
  3. J. T. Jenkins and M. W. Richman, J. Fluid Mech. 192, 313 (1988).
  4. C. S. Campbell and C. E. Brennen, J. Fluid Mech. 151, 167 (1985).
  5. C. S. Campbell, Acta Mech. 63, 61 (1986).
  6. D. J. Evans, H. J. M. Hanley, and S. Hess, Phys. Today 37(1), 26 (1984).
  7. O. R. Walton, Mechanics of Granular Materials—New Models and Constitutive Relations, edited by J. T. Jenkins and M. Satalce (Elsevier, New York, 1983), pp. 327–338.
  8. O. R. Walton and R. L. Braun, J. Rheol. 30, 949 (1986).
  9. C. S. Campbell and A. Gong, J. Fluid Mech. 164, 107 (1986).
  10. M. A. Hopkins, Department of Civil and Environmental Engineering Report No. 87-7, Clarkson University, Potsdam, New York, 1987.
  11. C. S. Campbell, J. Fluid Mech. 203, 449 (1989).
  12. D. J. Evans and W. G. Hoover, Annu. Rev. Fluid. Mech. 18, 243 (1986).
  13. J. T. Jenkins and S. B. Savage, J. Fluid Mech. 130, 187 (1983).
  14. W. H. Press, B. P. Flannery, S. A. Teukolski, and W. T. Vetterling, Numerical Recipes; the Art of Scientific Computing (Cambridge U.P., Cambridge, 1986), pp. 449–453.
  15. R. N. Bracewell, The Fourier Transform and its Applications, Second Edition Revised (McGraw-Hill, New York, 1986), p. 246.

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