Rheology of sediment transported by a laminar flow

TL;DR

This study extends a local rheology model to describe sediment transport in laminar flows, validating it across a range of conditions but revealing a creep regime at very low viscous numbers that the model cannot explain.

Contribution

The paper generalizes the Boyer et al. rheology model to include particle weight and tests it in a sediment transport experiment, revealing limitations at low viscous numbers.

Findings

Model validated for 10^{-5} ≤ Iv ≤ 1 with data collapsing onto a single curve.

Particles exhibit a creep regime at Iv < 10^{-5} where the model fails.

Friction coefficient decreases continuously in the creep regime, indicating non-local effects.

Abstract

Understanding the dynamics of fluid-driven sediment transport remains challenging, as it is an intermediate region between a granular material and a fluid flow. Boyer \textit{et al.}\citep{Boyer2011} proposed a local rheology unifying dense dry-granular and viscous-suspension flows, but it has been validated only for neutrally-buoyant particles in a confined system. Here we generalize the Boyer \textit{et al.}\citep{Boyer2011} model to account for the weight of a particle by addition of a pressure $P_0$, and test the ability of this model to describe sediment transport in an idealized laboratory river. We subject a bed of settling plastic particles to a laminar-shear flow from above, and use Refractive-Index-Matching to track particles' motion and determine local rheology --- from the fluid-granular interface to deep in the granular bed. Data from all experiments collapse onto a single curve of friction $\mu$ as a function of the viscous number $I_v$ over the range $10^{-5} \leq I_v \leq 1$, validating the local rheology model. For $I_v < 10^{-5}$, however, data do not collapse. Instead of undergoing a jamming transition with $\mu \rightarrow \mu_s$ as expected, particles transition to a creeping regime where we observe a continuous decay of the friction coefficient $\mu \leq \mu_s$ as $I_v$ decreases. The rheology of this creep regime cannot be described by the local model, and more work is needed to determine whether a non-local rheology model can be modified to account for our findings.