Abstract
Recent theories for rapid deformations of granular materials have attempted to exploit the similarities between the grains of deforming granular mass and the molecules of a disequilibrated gas. Methods from the kinetic theory may then be used to determine, for example, the form of the balance laws for the means of density, velocity, and energy and to calculate specific forms for the mean fluxes of momentum and energy and, in these dissipative systems, the mean rate at which energy is lost in collisions.
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References
Bagnold, R. A. 1954. Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. London, A 255, 49–63.
Carnahan, N. F., Starling, K. E. 1969. Equation of state of nonattracting rigid spheres. J. Chem. Phys. 51, 635–636.
Chapman,S.,Cowling, T. G. 1970. The Mathematical Theory of Nonuniform Gases. Cambridge University Press: Cambridge.
Condiff, D. W., Lu, W.-K., Dahler, J. S. 1965. Transport properties of polyatomic fluids, A dilute gas of perfectly rough spheres. J. Chem. Phys. 42, 3445–3475.
Grad, H. 1949. On the kinetic theory of rarified gases. Comm. Pure and Appl. Math. 2, 331–407.
Hanes, D. M. 1983. Studies on the mechanics of rapidly flowing granular-fluid materials. Ph. D. Dissertation, University of California, San Diego.
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.
Lun, C., Savage, S. B., Jeffrey, D. J., Chepurniy, N. 1984. Kinetic theories of granular flow: simple shear of inelastic particles and general deformations of nearly elastic particles. J. Fluid Mech. 140, 223–256.
Reif, F. 1965. Fundamentals of Statistical Mechanics and Thermal Physics. McGraw-Hill: New York.
Savage, S. B. 1978. Experiments on shear flows of cohesionless granular materials. In Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials, (ed. S. C. COWIN & M. SATAKE) Gakujutsu Bunken Fukyu-Kal: Tokyo, 241–254.
Savage, S. B., Mckeown, S. 1983. Shear stresses developed during rapid shear of dense concentrations of large spherical particles between concentric rotating cylinders. J. Fluid Mech. 127, 453–472.
Savage, S. B., Sayed, M. 1984. Stresses developed by dry cohesionless granular materials sheared in an annular shear cell. J. Fluid Mech. 42, 391–430.
Sommerfeld, A. 1956. Thermodynamics and Statistical Mechanics. Academic Press: London and New York.
Stewart, G. R., Lin, D. N. C, Bodenheimer, V. 1984. Collision-Induced Transport Processes in Planetary Rings. In Planetary Rings (ed. R. GREENBERG & A. BRAHIC) Univ. Arizona Press: Tucson (pending publication).
Truesdell, C, Muncaster, R. G. 1980. Fundamentals of Maxwell’s Kinetic Theory of a Simple Monatomic Gas. Academic Press: New York.
Trulsen, J. 1971. Towards a theory of jet streams. Astro. Sp. Sci. 12, 329–348.
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For J. L. Ericksen on his 60th birthday
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© 1986 Springer-Verlag Berlin Heidelberg
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Jenkins, J.T., Richman, M.W. (1986). Grad’s 13-Moment System for a Dense Gas of Inelastic Spheres. In: The Breadth and Depth of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61634-1_31
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DOI: https://doi.org/10.1007/978-3-642-61634-1_31
Publisher Name: Springer, Berlin, Heidelberg
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