Non-Local Particle Flows Become Local When Considering Dissipative Stress

TL;DR

This study demonstrates that considering dissipative stress and geometric mixing-length effects can explain particle flow behavior in dense suspensions, challenging the notion of intrinsic non-local rheology.

Contribution

It introduces a shear-rate-weighted dissipative stress and a geometric mixing-length model to account for flow features traditionally attributed to non-local effects.

Findings

Replacing shear stress with dissipative stress restores local rheology.

A geometric mixing-length explains residual sub-yielding at flow reversals.

Much apparent non-locality arises from measurement and averaging artifacts.

Abstract

Dense granular and suspension flows under inhomogeneous shear exhibit persistent particle motion in regions where the local yield criterion is subcritical, an apparent breakdown of locality that has motivated the development of a generation of nonlocal rheological models. Using particle-resolved simulations of frictionless dense suspensions in two-dimensional Kolmogorov flow, we show that two independent considerations together account for this signature. First, replacing the conventional shear stress by a shear-rate-weighted dissipative stress $\tau_W=\langle \tau \dot \gamma \rangle/\langle \dot \gamma \rangle$, which isolates the component of stress that performs irreversible work, restores the homogeneous $\mu(J)$ law throughout the bulk of the flow, with the inferred friction remaining strictly above yield. Second, a simple geometric mixing-length construction, applied with conventional stresses and requiring no fluctuation input, accounts for the residual sub-yielding within a sub-diameter layer at flow reversals. Each approach is based on a different philosophy and mechanism, and together they suggest that much of the apparent non-locality in this geometry and frictionless case is an artefact of how stress is measured and averaged rather than an intrinsic breakdown of local rheology.