Superposition rheology of shear-banding wormlike micelles

Wormlike micelle solutions are submitted to small-amplitude oscillatory shear superimposed to steady shear in the shear banding regime. By imposing a shear oscillation, the interface between high- and low-shear regions oscillates in time. A two-fluid semi-phenomenological model is proposed for superposition rheology in the shear banding regime, which allows us to extract a characteristic velocity for the interface dynamics from experiments involving only a standard rheometer. Estimates of the stress diffusion coefficient ${\cal D}$ can also be inferred from such superposition experiments. The validity of our model is confirmed by directly recording the interface displacement using ultrasonic velocimetry.