Multi-State Rheology in Dense Particle-Liquid Channel Flows Over Bumpy Bed and Its Constitutive Modeling

Dense particle-liquid flows are common in natural flows processes. A primary challenge lies in the effective modeling of the granular stress, which is intrinsically related to the flowing state of the granular material. By developing non-invasive experimental technique and measurement methods for internal observations based on the refractive index matching (RIM) technique, the internal flow information of the particle-liquid channel flows over a bumpy bed is obtained. The flow shear and fluctuation are strong near the bottom while vanishing near the surface, with the interparticle interactions dominated by collision and friction, respectively, and a transitional layer in between. The granular rheology is controlled by the Bagnold number and presents a coexistence of frictional, viscous, and inertial regimes, corresponding to the granular quasi-static, liquid-like, and gas-like states, respectively. The multi-state stress can be modeled by integrating a frictional stress described by a rate-independent model and a collisional stress described by kinetic theory. The latter helps to explain the flow structure-dependence of the friction coefficient discovered in the heterogeneous flows studied here.