Eu, Byung Chan and Farhat, Hikmat (1997) Kinetic theory of fluidized granular matter. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 55 (4), 4187-4199. (doi:10.1103/PhysRevE.55.4187).
Abstract
In this paper, we present a statistical treatment of fluidized, elastic granular matter and a kinetic equation that describes the evolution of macroscopic properties of such matter. The present kinetic theory recognizes that the effects of excluded volume become dominant in the dynamic evolution of an assembly of granules and accordingly takes them into account in the formulation. On the basis of the equilibrium solution of the kinetic equation, a thermodynamics-like mathematical structure is constructed for the Boltzmann entropy of granular matter. The meaning of temperature in this mathematical structure is fixed by the shear rate. The equilibrium solution is shown to yield a density distribution comparable with the experimental data of Clement et al. [Europhys. Lett. 16, 133 (1991)]. The shear viscosity of granular matter is shown to increase with the packing fraction. This behavior is in qualitative agreement with experimental result by Hanes et al. [J. Fluid Mech. 150, 357 (1985)]. The viscosity also increases with the shear rate since the 'temperature' increases with the shear rate in the case of granular matter. Consequently, the granular matter is shown to be dilatant, as is experimentally known.
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