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Shear Flow of a Granular Material

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Abstract

The shear flow of a granular material between parallel plates is treated by means of the Boltzmann equation with pseudo-Maxwellian grains. The moments for reverse reflection boundary conditions are found explicitly. The shearing stress is found to depend quadratically on the shear rate.

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REFERENCES

  1. A. V. Bobylev, J. A. Carrillo, and I. A. Gamba, On some kinetic properties and hydrodynamics equations for inelastic interaction, Phys. Rev. (2000), to appear.

  2. A. V. Bobylev and C. Cercignani, Moment equations for a granular material in a thermal bath, submitted to J. of Stat. Phys. (2000).

  3. C. S. Campbell, Rapid granular flows, Ann. Rev. Fluid Mech. 22:57-92 (1990).

    Google Scholar 

  4. J. A. Carrillo, C. Cercignani, and I. A. Gamba, Steady states of a Boltzmann equation for driven granular media (2000), to appear.

  5. C. Cercignani and S. Cortese, Validation of a Monte Carlo simulation of the plane Couette flow of a rarefied gas, J. Stat. Phys. 75:817-838 (1994).

    Google Scholar 

  6. C. Cercignani, Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations (Cambridge University Press, Cambridge, 2000).

    Google Scholar 

  7. C. Cercignani, Existence of homoenergetic affine flows for the Boltzmann equation, Archive for Rational Mechanics and Analysis 105:377-387 (1989).

    Google Scholar 

  8. V. S. Galkin, On a solution of the kinetic equation, PMM (in Russian) 20:445-446 (1956).

    Google Scholar 

  9. A. Goldshtein and M. Shapiro, Mechanics of collisional motion of granular materials. Part I. General hydrodynamic equations, J. Fluid Mech. 282:75-114 (1995).

    Google Scholar 

  10. H. J. Herrmann, Simulation of granular media, Physica A 191:263-276 (1992).

    Google Scholar 

  11. K. Hutter and K. R. Rajagopal, On flows of granular materials, Continuum Mech. Thermodyn. 6:81-139 (1994).

    Google Scholar 

  12. H. M. Jaeger, S. R. Nagel, and R. P. Behringer, The physics of granular materials, Physics Today 32-38 (1996).

  13. C. K. K. Lun, Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres, J. Fluid Mech. 223:539-559 (1991).

    Google Scholar 

  14. N. Sela and I. Goldhirsch, Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order, J. Fluid Mech. 361:41-74 (1998).

    Google Scholar 

  15. C. Truesdell, On the pressures and the flux of energy in a gas according to Maxwell's kinetic theory, II, Journal of Rational Mechanics and Analysis 5:55-128 (1956).

    Google Scholar 

  16. C. Truesdell and R. G. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas (Academic Press, New York, 1980).

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    C. Cercignani

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  1. C. Cercignani
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Cercignani, C. Shear Flow of a Granular Material. Journal of Statistical Physics 102, 1407–1415 (2001). https://doi.org/10.1023/A:1004804815471

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