Stress-strain rate relation in plug-free flow of dense granular fluids: A first-principles derivation

We derive the macroscopic stress tensor for plug-free dense granular flow, using a first-principles coarse-graining of the intergranular forces. The derivation is based on the assumption, which defines the da Vinci fluid model, that the intergranular interactions are dominated by normal contact forces and solid friction. An explicit form for the stress - strain rate relation in the slow flow regime is obtained, providing, together with previously derived equations for the formation and growth dynamics of plug regions, a full closure for the rheology of dense granular fluids, in terms of well-defined material parameters. This relation allows us to quantify the strain rate, at which the flow crosses over from solid-friction-dominated to viscosity-dominated flow.