Viscous-inertial transition in dense sedimentary flows using particle-resolved Direct Numerical Simulations
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Dense sedimentary flows are central to many geophysical processes, such as river sediment transport and debris flows. Their complex behavior requires accurate rheological models linking particle-scale mechanisms to macroscopic flow. In particular, the transition from viscous- to inertia-dominated regimes remains poorly understood and is not represented in existing large-scale models. In this study, particle-resolved Direct Numerical Simulations (pr-DNS) are employed to investigate the viscous–inertial transition in two complementary configurations: (i) volume-imposed rheometry of dense suspensions composed of neutrally buoyant particles, and (ii) sheared sediment beds representative of sediment transport in shallow aquatic environments. High-fidelity pr-DNS data enable detailed analysis of microstructural features inaccessible in experiments. The volume-imposed simulations reproduce stress–strain trends consistent with experimental observations, capturing a continuous transition from viscous to inertial regimes at a transitional Stokes number. The results further demonstrate that wall roughness and confinement strongly influence the rheological response by modifying particle microstructure. Pronounced particle layering promotes inter-layer slip and reduced stresses, whereas enhanced confinement increases inter-layer mixing and leads to elevated effective viscosities, highlighting the role of boundary conditions in confined rheometry. Simulations of sheared sediment beds enable direct extraction of sediment-transport rheological parameters comparable to those from pressure-imposed rheometry. The rheology derived from sediment beds follows trends observed in recent numerical and experimental studies of dense suspensions in pressure-imposed rheometry and can be described using stress additivity based on combined viscous and inertial scales. However, distinct scaling coefficients are required to describe the evolution of the solid volume fraction and the effective friction coefficient. Overall, these results bridge idealized suspension rheometry and sediment transport by clarifying how inertia, wall boundaries, and particle-scale microstructure affect macroscopic rheological behavior in dense sedimentary flows. This provides a physically grounded basis for the development of constitutive models valid across viscous and inertial regimes.
