Non-local effects in inhomogeneous flows of soft athermal disks

TL;DR

This study uses molecular dynamics to explore non-local rheological effects in inhomogeneous flows of soft athermal disks near jamming, revealing wave number dependence and the necessity of non-local models without diverging length scales.

Contribution

It demonstrates that non-local constitutive relations with fourth-order gradients are needed to accurately describe stress profiles in inhomogeneous soft disk flows near jamming.

Findings

Rheology is strongly wave number-dependent.

Particle migration alone cannot explain stress profiles.

Non-local models with fourth-order gradients effectively capture stress distributions.

Abstract

We numerically investigate non-local effects on inhomogeneous flows of soft athermal disks close to but below their jamming transition. We employ molecular dynamics to simulate Kolmogorov flows, in which a sinusoidal flow profile with fixed wave number is externally imposed, resulting in a spatially inhomogeneous shear rate. We find that the resulting rheology is strongly wave number-dependent, and that particle migration, while present, is not sufficient to describe the resulting stress profiles within a conventional local model. We show that, instead, stress profiles can be captured with non-local constitutive relations that account for gradients to fourth order. Unlike nonlocal flow in yield stress fluids, we find no evidence of a diverging length scale.