# Rheological properties of the soft-disk model of two-dimensional foams

## TL;DR

This study uses a two-dimensional soft-disk model to explore foam rheology, revealing nonlinear stress behavior, shear localization, and the influence of boundary conditions, thereby connecting microscopic and continuum descriptions.

## Contribution

It demonstrates that linear viscous effects can produce nonlinear rheological behavior and provides a continuum model explaining shear localization in foam systems.

## Key findings

- Nonlinear (power-law) dependence of stress on strain rate observed.
- Shear localization occurs with wall drag and matches continuum model predictions.
- Localization length varies with boundary velocity, linking microscopic parameters to macroscopic behavior.

## Abstract

The soft-disk model previously developed and applied by Durian [D. J. Durian, Phys. Rev. Lett. 75, 4780 (1995)] is brought to bear on problems of foam rheology of longstanding and current interest, using two-dimensional systems. The questions at issue include the origin of the Herschel-Bulkley relation, normal stress effects (dilatancy), and localization in the presence of wall drag. We show that even a model that incorporates only linear viscous effects at the local level gives rise to nonlinear (power-law) dependence of the limit stress on strain rate. With wall drag, shear localization is found. Its nonexponential form and the variation of localization length with boundary velocity are well described by a continuum model in the spirit of Janiaud et al. [Phys. Rev. Lett. 97, 038302 (2006)]. Other results satisfactorily link localization to model parameters, and hence tie together continuum and local descriptions.