Kinetic and Continuum Descriptions of Granular Flows

Abstract

Unlike the basic units of molecular systems, the elementary constituents of granular matter (the grains) experience dissipative interactions. This fact is the root cause of many of the difficulties encountered in the study of granular materials and among its major consequences are the existence of unique states and instabilities (e.g. collapse and clustering) as well as the multistable/metastable nature of most granular states. Another central consequence is the inherent lack of scale separation. The latter is responsible e.g. for the prominent normal stress differences (anisotropic pressures), long-range correlations, scale-dependent stress (and other) fields and, in general, the rheological nature of these materials. Constitutive relations and boundary conditions for dilute and near-elastic rapid granular flows have been derived from the pertinent Boltzmann equation with extensions to moderate densities obtained by employing the Enskog-Boltzmann equation or (systematically, via) response theory. Unlike the rapid flows, the dense, static and quasistatic regimes have not been treated in a systematic fashion heretofore. Preliminary results on elasticity in the static regime are presented.