  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.
