  We investigate the two-dimensional flow of a liquid foam around circular
obstacles by measuring all the local fields necessary to describe this flow:
velocity, pressure, bubble deformations and rearrangements. We show how our
experimental setup, a quasi-2D "liquid pool" system, is adapted to the
determination of these fields: the velocity and bubble deformations are easy to
measure from 2D movies, and the pressure can be measured by exploiting a
specific feature of this system, a 2D effective compressibility. To describe
accurately bubble rearrangements, we propose a new, tensorial descriptor. All
these quantities are evaluated via an averaging procedure that we justify
showing that the fluctuations of the fields are essentially random. The flow is
extensively studied in a reference experimental case; the velocity presents an
overshoot in the wake of the obstacle, the pressure is maximum at the leading
side and minimal at the trailing side. The study of the elastic deformations
and of the velocity gradients shows that the transition between plug flow and
yielded regions is smooth. Our tensorial description of T1s highlight their
correlation both with the bubble deformations and the velocity gradients. A
salient feature of the flow, notably on the velocity and T1 repartition, is a
marked asymmetry upstream/downstream, signature of the elastic behaviour of the
foam. We show that the results do not change qualitatively when various control
parameters vary, identifying a robust quasistatic regime. These results are
discussed in the frame of the actual foam rheology literature, and we argue
that they constitute a severe test for existing rheological models, since they
capture both the elastic, plastic and fluid behaviour of the foam.
