Generalized friction and dilatancy laws for immersed granular flows consisting of large and small particles

The motion of fully immersed granular materials, composed of two distinct particle sizes, flowing down rough inclined planes is studied through fluid-particle numerical simulations. We focus on the effect of ambient fluids, as well as their interplay with particle size segregation, on the steady-state kinematic and rheological profiles of the granular-fluid mixture flow. Simulation results are analyzed in the framework of a visco-inertial rheological model, which is first validated in monodisperse flows with a wide range of the ambient fluid viscosity (i.e., from air to water and slurry) and then generalized for size-bidisperse mixtures. It is found that the local effective friction and volume fraction of mixtures with different particle sizes can be approximated from the rheology of single-component flows. While the presence of viscous ambient fluids slows down size segregation (perpendicular to the flow) depending on the mixture composition and flow viscosity, the effective bulk friction is shown to be independent of the state and progress of segregation.