Shear-banding in a lyotropic lamellar phase, Part 2: Temporal fluctuations

We analyze the temporal fluctuations of the flow field associated to a shear-induced transition in a lyotropic lamellar phase: the layering transition of the onion texture. In the first part of this work [Salmon et al., submitted to Phys. Rev. E], we have evidenced banded flows at the onset of this shear-induced transition which are well accounted for by the classical picture of shear-banding. In the present paper, we focus on the temporal fluctuations of the flow field recorded in the coexistence domain. These striking dynamics are very slow (100--1000s) and cannot be due to external mechanical noise. Using velocimetry coupled to structural measurements, we show that these fluctuations are due to a motion of the interface separating the two differently sheared bands. Such a motion seems to be governed by the fluctuations of $\sigma^\star$, the local stress at the interface between the two bands. Our results thus provide more evidence for the relevance of the classical mechanical approach of shear-banding even if the mechanism leading to the fluctuations of $\sigma^\star$ remains unclear.