Quasi-static rheology of foams. Part 2. Continuous shear flow

The evolution of a bidimensional foam submitted to continuous quasi-static shearing is investigated both experimentally and numerically. We extract, from the images of the sheared foam, the plastic flow profiles as well as the local statistical properties of the stress field. When the imposed strain becomes larger than the yield strain, the plastic events develop large spatial and temporal correlations, and the plastic flow becomes confined to a narrow shear band. This transition and the steady-state regime of flow are investigated by first focusing on the elastic deformation produced by an elementary plastic event. This allows us to understand (i) the appearance of long-lived spatial heterogeneities of the stress field, which we believe are at the origin of the shear-banding transition, and (ii) the statistics of the dynamic fluctuations of the stress field induced by plastic rearrangements in the steady-state regime. Movies are available with the online version of the paper.