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

The two-dimensional 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-focusing 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.