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

Abstract 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.