Particle fluctuations and their effects on the rheological behavior of sheared granular flows

We present numerical simulations of plane-sheared granular flows in two pressure-controlled configurations and investigate the particle fluctuations over a wide range of the inertial number I. Quantities affecting the velocity fluctuations, including the granular temperature and the stress ratio, are shown to be intrinsically related and to exhibit similar I-dependent characteristics. We first propose a scaling law describing the one-to-one relationship between the granular temperature and I in both the inertial and collisional regimes, where the volume fraction plays an important role. This relation differs from the power-law dependence between the stress ratio and I. However, for low values of I, these two velocity fluctuation quantities deviate from the one-to-one relation, similar to the effective friction coefficient μ. Based on the obtained inverse power law, we propose a new unified model incorporating the stress ratio to describe the rheological behaviors in the quasistatic, inertial, and collisional regimes. The proposed model is more applicable than the one that integrates the granular temperature, allowing nonlocal effects to be roughly eliminated at low values of I and the rheological dependence on the volume fraction to be effectively removed at high values of I. This provides an alternative approach for developing rheological models for granular materials under complex flow conditions.