Discrete rearranging disordered patterns, part II: 2D plasticity, elasticity and flow of a foam

TL;DR

This paper investigates the plastic flow of 2D foams through experiments and develops a phenomenological model linking bubble rearrangements to continuous plasticity, elastic, and fluid behavior.

Contribution

It introduces a new phenomenological equation predicting foam plastic strain rate based on local elastic strain and elongation rate, validated by experiments.

Findings

Good agreement between model predictions and experimental measurements.

Foam can be modeled as a continuous medium with fluid, elastic, and plastic properties.

Derived constitutive equations successfully describe foam behavior.

Abstract

The plastic flow of a foam results from bubble rearrangements. We study their occurrence in experiments where a foam is forced to flow in 2D: around an obstacle; through a narrow hole; or sheared between rotating disks. We describe their orientation and frequency using a topological matrix defined in the companion paper (Graner et al., preprint), which links them with continuous plasticity at large scale. We then suggest a phenomenological equation to predict the plastic strain rate: its orientation is determined from the foam's local elastic strain; and its rate is determined from the foam's local elongation rate. We obtain a good agreement with statistical measurements. This enables us to describe the foam as a continuous medium with fluid, elastic and plastic properties. We derive its constitutive equation, then test several of its terms and predictions.