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We study the dynamics of the Taylor-Couette flow of shear banding wormlike micelles. We focus on the high shear rate branch of the flow curve and show that for sufficiently high Weissenberg numbers, this branch becomes unstable. This instability is strongly sub-critical and is associated with a shear stress jump. We find that this increase of the flow resistance is related to the nucleation of turbulence. The flow pattern shows similarities with the elastic turbulence, so far only observed for polymer solutions. The unstable character of this branch led us to propose a scenario that could account for the recent observations of Taylor-like vortices during the shear banding flow of wormlike micelles.PACS numbers: Wormlike micelles are elongated, polymer-like structures resulting from the self-assembly of amphiphilic molecules in aqueous solution [1,2]. In contrast to regular polymers, they continuously break and fuse, providing an additional relaxation mechanism. In the fast breaking regime, Cates' reptation-reaction model [3] predicts that wormlike micelles solutions relax monoexponentially with a single time τ R ∼ √ τ b τ r , where τ b and τ r are the breaking and reptation times. In addition to their structural analogy, polymers and wormlike micellar solutions can exhibit flow instabilities when submitted to even moderate shear rates. In particular, many wormlike micelles solutions have been observed to undergo a shear banding transition. Under simple shear, the base scenario is the following [1,4] : below a critical shear rateγ l ∼ 1/τ R , the flow is homogeneous. Aboveγ l , the system becomes mechanically unstable. A phase of lower viscosity nucleates, inducing a banded state in which the initial viscous phase and the fluid phase coexist at constant stress. Increasing the imposed shear rate only affects the relative proportions of each bands, up to a second critical valueγ h , where the high shear rate phase entirely fills the flow geometry. Beyondγ h , the homogeneity of the flow is recovered. Albeit extremely well documented, the shear banding instability is still not fully understood [5][6][7]. In particular, it has been shown recently in cylindrical Couette geometry that contrary to the usual view, the shear banding flow may not be purely one-dimensional, but instead is organized into Taylor-like vortices stacked along the vorticity direction. These cellular structures are mainly localized in the high shear rate band and exhibit a complex dynamics depending on the applied shear rate [8].

Increasing antimicrobial and non-hemotoxic characteristics of polymers bearing thiazole and triazole groups by the appropriate selection of spacer and quaternization groups.