Scale dependence, correlations, and fluctuations of stresses in rapid granular flows

Abstract

It is shown that, unlike in simple molecular fluids, the stress field in granular fluids may be strongly scale, or resolution, dependent. This is a result of the intrinsic lack of scale separation in these fluids. Another consequence of the lack of scale separation in granular fluids is that microscopic stress fluctuations, whose origin (like in molecular fluids) is the underlying discreteness of the system, may appear as observables in macroscopic measurements; the correlation (or decay) time of the stress fluctuations is of the order of the mean-free time, which is also a macroscopic time. All of these properties are intrinsic to granular fluids and not (for example) results of the practical lack of scale separation that is dictated by the fact that grains are of macroscopic dimensions or the limited statistics in simulations. Numerical evidence, based on molecular-dynamic simulations of shear flows of smooth disks in a two-dimensional enclosure, serves to demonstrate the above phenomena.