Rheology of sedimentary flows across the viscous–inertial transition

Dense sedimentary flows underpin a wide range of geomorphic processes, from bedload transport in rivers to debris-laden shallow flows, yet their rheological description across regimes remains incomplete. In particular, the transition from viscous-dominated to inertia-dominated behavior in dense suspensions poses a central challenge for constitutive modeling of subaqueous sediment transport. Here, we present a unified numerical investigation of the viscous–inertial transition in sheared sedimentary flows using particle-resolved Direct Numerical Simulations (pr-DNS), spanning idealized rheometric configurations and flow-driven sediment beds.

We employ both pressure-imposed and volume-imposed rheological frameworks to systematically probe the role of fluid viscosity, shear rate, granular pressure, particle friction, confinement, and boundary roughness. Across configurations, we characterize rheology in terms of the macroscopic friction and solid volume fraction expressed as functions of combined viscous and inertial control parameters. Our results confirm that the transition can be described by an additive scaling of visco-inertial stresses but reveal that different rheological quantities respond differently to inertia.

In pressure-imposed simulations of dense frictional suspensions, we find that the viscous–inertial transition occurs at Stokes numbers ranging from 5 to around 8, consistent with recent experiments. Notably, shear stress exhibits a more gradual transition than particle pressure, indicating a decoupling of stress components. Microstructural analysis shows that this behavior arises from the combined action of lubrication and tangential contact forces, as particles progressively shift from rolling to sliding contacts. This shift is governed not only by the Stokes number, but also by proximity to jamming and inter-particle friction.

Complementary volume-imposed simulations between rough confining walls demonstrate that boundary conditions strongly influence the measured rheology through particle layering and inter-layer mixing. Wall roughness and cell height modulate stress levels and effective friction, including weakening of the macroscopic friction during the transition, while preserving a consistent viscous–inertial scaling across cases. Despite a reduction in contact number, increased force magnitudes on remaining contacts drive the inertial regime.

Finally, simulations of pressure-driven shallow flows over sediment beds show that the transition occurs at Stokes numbers comparable to those of our numerical and experimental results of pressure-imposed rheometry, with distinct scaling coefficients for volume fraction and macroscopic friction. Together, these results highlight the complex, multi-scale nature of sediment rheology and underscore the need for refined constitutive laws that explicitly account for microstructure, confinement, and stress anisotropy in geomorphic sediment transport.