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Using velocity profile measurements based on dynamic light scattering andcoupled to structural and rheological measurements in a Couette cell, wepresent evidences for a shear-banding scenario in the shear flow of the oniontexture of a lyotropic lamellar phase. Time-averaged measurements clearly showthe presence of structural shear-banding in the vicinity of a shear-inducedtransition, associated to the nucleation and growth of a highly sheared band inthe flow. Our experiments also reveal the presence of slip at the walls of theCouette cell. Using a simple mechanical approach, we demonstrate that our dataconfirms the classical assumption of the shear-banding picture, in which theinterface between bands lies at a given stress $\sigma^\star$. We also outlinethe presence of large temporal fluctuations of the flow field, which are thesubject of the second part of this paper [Salmon {\it et al.}, submitted toPhys. Rev. E]

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