Convective instability in sheared foam

This work provides evidence that anisotropic drainage in sheared foam is at the origin of convective instability in very long foam channels. Convective instability occurs in foam under forced drainage when a critical liquid fraction is exceeded. Liquid spontaneously accumulates at one side of the channel. The weight imbalance induces convection rolls in the foam. Experiments in a very long vertical foam channel demonstrate that the critical liquid fraction is smaller than in previous findings by a factor of five. The critical liquid fraction depends on both the channel length and the inhomogeneity of the liquid feed. Well below the critical liquid fraction, a static, elastic shear deformation of the foam structure occurs. At the critical liquid fraction, initial steady convection rolls are located at the lower region of the channel and expand as the liquid fraction further increases. Combining the drainage equation with both the elastic response of the foam and a model for anisotropic drainage, a critical liquid fraction for the growth of an initial liquid imbalance is derived analytically, which corresponds very well to experimental findings. Numerical simulations of the drainage equation and the elastic response of the foam reproduce these experimental and analytical findings.