Shear banding in reaction-diffusion models

Shear banding occurs in the flow of complex fluids: various types of shear thinning and shear thickening micelle solutions and liquid crystals. In ord er to cope with the strongly inhomogeneous interface between the bands, con stitutive models used in standard rheology must be supplemented by non-loca l terms. This leads rather generally to non-linear partial differential equ ations of the reaction-diffusion type. We use this formalism in order to ex plain some observed experimental features and as a guide for future researc h in this field.