Kinetics and Dynamics of Rapid Granular Flows

Abstract

The dissipative nature of the interactions in granular systems has far reaching consequences: (i) There is an inherent lack of scale separation which is independent of the size of the system (in addition to the ‘practical’ scale separation due to the macroscopic sizes of typical grains); (ii) Both ‘geometrical’ (e.g. clusters, arches etc.) and ‘dynamical’ (e.g. stress chains) microstructures are of key importance in granular statics and dynamics; (iii) Many (rapid) flows are ‘supersonic’; (iv) Constitutive relations may be scale dependent. In many ways these systems are mesoscopic rather than macroscopic in nature. In addition, granular systems exhibit multi-stability and they are almost always in metastable states. Strongly excited granular matter can be entirely fluidized; this state is coined rapid granular flow and its dynamics is partially analogous to that of a classical gas. A perturbative solution of the pertinent inelastic Boltzmann equation yields constitutive relations which are different from those previously derived and this difference is related to a (previously unappreciated) quasi-microscopic time scale which characterizes the decay rate of the temperature. The normal stress differences (as well as the ‘anisotropic temperature’) are shown to result from Burnett corrections. The continuum equations of motion can be used to explain phenomena such as clustering and layering in granular systems and, to some extent, even the collapse phenomenon. The latter, unlike clustering, is not of hydrodynamic origin and the difference is explained. It is concluded that while statistical mechanical methods can be useful in the realm of granular materials, they should be applied with utmost care; in particular the above fundamental differences between molecular and granular systems must always be borne in mind.