New Developments in ‘Rapid Granular Flows’

Abstract

The recent decade or so has witnessed much progress in the field of granular matter in general and granular gases (or rapid granular flows) in particular. On the theoretical side, there have been systematic developments of hydrodynamic models for granular gases based on the Chapman-Enskog expansion. The hard problem of establishing boundary conditions corresponding to these equations of motion has been successfully tackled. The role of microstructures, in particular the consequences of clustering have been studied in great detail. Among the major challenges posed by granular gases is the fact that they inherently lack scale separation (e.g., mean free times in steady shear flows are comparable to the inverse shear rate), are typically supersonic and break equipartition. This implies that corrections to the Navier-Stokes like hydrodynamic equations should be of importance and indeed it has e.g., been realized that the normal stress differences prevalent in granular gases are a manifestation of such corrections (Burnett). While the traditional experimental and theoretical paradigm for granular gases used to be shear flow it seems that the focus has shifted to vibrated systems, as the latter are easier to handle experimentally. Modern experimental techniques have enabled the measurement of single grain trajectories and full velocity distribution functions (which are often strongly non-Gaussian as systematic kinetic theories predict), convective patterns, shock waves and many other features of granular flows. Perhaps the most interesting finding is that the hydrodynamic theories and their extensions seem to ‘work’ far beyond their nominal range of validity. The dynamics of dense granular gases, the effects of frictional restitution (which are rarely accounted for) and the detailed behavior of granular mixtures are among the numerous exciting and open problems in this field.