Flow transitions in two-dimensional foams

TL;DR

This study investigates flow in two-dimensional foam models, revealing a transition from continuum to discrete flow regimes at a specific strain rate and flow region thickness, enhancing understanding of foam rheology.

Contribution

It provides detailed analysis of the discrete flow regime in 2D foam models, identifying the transition point from continuum to localized flow based on system size and strain rate.

Findings

Localized flow coexists with a power-law fluid and rigid body rotation.

Transition from continuum to discrete flow occurs at about 10 bubbles in the flow region.

The transition occurs at an applied strain rate of approximately 0.07 s^{-1}.

Abstract

For sufficiently slow rates of strain, flowing foam can exhibit inhomogeneous flows. The nature of these flows is an area of active study in both two-dimensional model foams and three dimensional foam. Recent work in three-dimensional foam has identified three distinct regimes of flow [S. Rodts, J. C. Baudez, and P. Coussot, Europhys. Lett. {\bf 69}, 636 (2005)]. Two of these regimes are identified with continuum behavior (full flow and shear-banding), and the third regime is identified as a discrete regime exhibiting extreme localization. In this paper, the discrete regime is studied in more detail using a model two dimensional foam: a bubble raft. We characterize the behavior of the bubble raft subjected to a constant rate of strain as a function of time, system size, and applied rate of strain. We observe localized flow that is consistent with the coexistence of a power-law fluid with rigid body rotation. As a function of applied rate of strain, there is a transition from a continuum description of the flow to discrete flow when the thickness of the flow region is approximately 10 bubbles. This occurs at an applied rotation rate of approximately $0.07 {\rm s^{-1}}$.