Shear banding in a lyotropic lamellar phase. I. Time-averaged velocity profiles

Using velocity profile measurements based on dynamic light scattering and coupled to structural and rheological measurements in a Couette cell, we present evidences for a shear banding scenario in the shear flow of the onion texture of a lyotropic lamellar phase. Time-averaged measurements clearly show the presence of structural shear banding in the vicinity of a shear-induced transition, associated with the nucleation and growth of a highly sheared band in the flow. Our experiments also reveal the presence of slip at the walls of the Couette cell. Using a simple mechanical approach, we demonstrate that our data confirm the classical assumption of the shear banding picture, in which the interface between bands lies at a given stress sigma(*). We also outline the presence of large temporal fluctuations of the flow field, which are the subject of the second part of this paper [Salmon et al., Phys. Rev. E 68, 051504 (2003)].