KINETIC-THEORY OF FLUIDIZED GRANULAR MATTER

In this paper, we present a statistical treatment of fluidized, elasti c granular matter and a kinetic equation that describes the evolution of macroscopic properties of such matter. The present kinetic theory r ecognizes that the effects of excluded volume become dominant in the d ynamic evolution of an assembly of granules and accordingly takes them into account in the formulation. On the basis of the equilibrium solu tion of the kinetic equation, a thermodynamics-like mathematical struc ture 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 distr ibution comparable with the experimental data of Clement ct al. [Europ hys. Lett. 16, 133 (1991)]. The shear viscosity of granular matter is shown to increase with the packing fraction. This behavior is in quali tative agreement with experimental result by Hanes eT al. [J. Fluid Me ch. 150, 357 (1985)]. The viscosity also increases with the shear rate since the ''temperature'' increases with the shear rate in the case o f granular matter. Consequently, the granular matter is shown to be di latant, as is experimentally known.