Exponential Stress Relaxation Driven by Elementary Plastic Events in Non-Ageing Liquid Foams

TL;DR

This study reveals that non-ageing liquid foams relax stress exponentially through elementary plastic events, with in situ measurements showing linear relationships between stress, plastic activity, and coordination number, aligning with recent theoretical models.

Contribution

It demonstrates that stress relaxation in liquid foams is driven by individual plastic events rather than cascades, providing new insights into foam mechanics and validating recent theoretical predictions.

Findings

Stress relaxation follows an exponential decay governed by plastic event duration.

Linear relationships exist between shear stress, plastic activity, and coordination number.

Residual stress is linked to the orientation of the stress tensor.

Abstract

Liquid foams are archetypal athermal amorphous solids whose elasticity arises from the jamming of densely packed bubbles. We investigate the stress relaxation of non-ageing liquid foams following flow cessation, using fast X-ray tomo-rheoscopy. Thanks to in situ, time-resolved measurements, we uncover robust linear affine relationships between shear stress, plastic activity, and coordination number throughout the relaxation toward a residual stress state below the yield value. In contrast to previous studies on amorphous solids, we observe an exponential relaxation governed by the duration of individual plastic events, rather than by cascades of correlated ones associated with much longer, shear-rate-dependent timescales or power-law relaxations. Our results are consistent with a recent theoretical framework proposed by Cuny et al., suggesting that residual stress originates from the orientation of the stress tensor.