Local description of the two-dimensional flow of foam through a contraction

TL;DR

This study investigates the 2D flow of foam through a contraction in a Hele-Shaw cell, revealing how velocity, stress, and plasticity vary near the contraction, with insights into the effects of surfactants and flow conditions.

Contribution

It provides a detailed local description of foam flow behavior through contractions, highlighting the influence of surfactants and flow parameters on rheological features.

Findings

Velocity behavior differs at contraction entrance and exit.

Yielded region concentrates near the contraction.

Elastic stress depends on velocity and surfactant properties.

Abstract

The 2D flow of a foam confined in a Hele-Shaw cell through a contraction is investigated. Its rheological features are quantified using image analysis, with measurements of the elastic stress, rate of plasticity, and velocity. The behavior of the velocity strongly differs at the contraction entrance, where the flow is purely convergent, and at the contraction exit, where a velocity undershoot and a re-focussing of the streamlines are unraveled. The yielded region, characterized by a significant rate of plasticity and a maximal stress amplitude, is concentrated close to the contraction. These qualitative generic trends do not vary significantly with the flow rate, bubble area and contraction geometry, which is characteristic of a robust quasistatic regime. Using surfactants with a high surface viscoelasticity, a marked dependence of the elastic stress on the velocity is exhibited. The results show that the rate of plasticity does not only depend on the local magnitude of the deformation rate, but also crucially on the orientation of both elastic stresses and deformation rate. It is also discussed how the viscous friction controls the departure from the quasistatic regime.