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The occurence of shear bands in a complex fluid is generally understood asresulting from a structural evolution of the material under shear, which leads(from a theoretical perspective) to a non-monotonic stationnary flow curverelated to the coexistence of different states of the material under shear. Inthis paper we present a scenario for shear-banding in a particular class ofcomplex fluids, namely foams and concentrated emulsions, which differs fromother scenarii in two important ways. First, the appearance of shear bands isshown to be possible both without any intrinsic physical evolution of thematerial (e.g. via a parameter coupled to the flow such as concentration orentanglements) and without any finite critical shear rate below which the flowdoes not remain stationary and homogeneous. Secondly, the appearance of shearbands depends on the initial conditions, i.e., the preparation of the material.In other words, it is history dependent. This behaviour relies on the tensorialcharacter of the underlying model (2D or 3D) and is triggered by an initiallyinhomogeneous strain distribution in the material. The shear rate displays adiscontinuity at the band boundary, whose amplitude is history dependent andthus depends on the sample preparation.

Non-linear oscillatory rheological properties of a generic continuum foam model: comparison with experiments and shear-banding predictions