Shear localisation with 2D Viscous Froth and its relation to the Continuum Model

TL;DR

This study uses 2D Viscous Froth simulations to explore shear localisation in foam samples, linking microscopic parameters to a continuum model and revealing how localisation depends on shear conditions and foam properties.

Contribution

It extends the continuum model to include yield and limit stresses, relating these to VF model parameters and demonstrating shear localisation dependence on shear velocity and wall friction.

Findings

Shear localisation is clearly demonstrated in simulations.

Localisation length depends on the product of shear velocity and wall friction.

The extended continuum model accurately describes foam behaviour with a Herschel-Bulkley exponent of 0.3.

Abstract

Simulations of monodisperse and polydisperse ($\mu_2(A)=0.13\pm0.002$) 2D foam samples undergoing simple shear are performed using the 2D Viscous Froth (VF) Model. These simulations clearly demonstrate shear localisation. The dependence of localisation length on the product $\lambda V$ (shearing velocity $V$ times external wall friction coefficient $\lambda$) is examined and is shown to agree qualitatively with other published experimental data. A wide range of localisation lengths is found at low $\lambda V$, an effect which is attributed to the existence of distinct yield and limit stresses. The general Continuum Model is extended to incorporate such an effect and its parameters are subsequently related to those of the VF Model. A Herschel-Bulkley exponent of $a=0.3$ is shown to accurately describe the observed behaviour. The localisation length is found to be independent of $\lambda V$ for monodisperse foam samples.