Non-Local Particle Flows Become Local When Considering Dissipative Stress
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.