On granular flows: From kinetic theory to inertial rheology and nonlocal constitutive models

Abstract

Previous results of discrete simulations of steady, unidirectional particle flows, here collected and critically reanalyzed, permit to make the case that the kinetic theory of granular gases, extended to include the correlations in the velocity fluctuations and the role of friction in collisions, provides the long-sought universal framework to predict the flow of realistic particles over the entire range of solid volume fraction from dilute to very dense - the upper limit being the critical value at which rate-independent components of the stresses arise. The case is made even stronger by the explicit derivation of the popular inertial rheology and its nonlocal extension to deal with heterogeneities based on the granular fluidity concept as special limits of the kinetic theory. In the process, common statements about the frictional-collisional duality in the granular stresses and the importance of long-lasting contacts creating a percolating network are shown to be greatly exaggerated for granular flows in practical applications.