Superposition rheology of shear-banding wormlike micelles

TL;DR

This paper introduces a semi-phenomenological model for superposition rheology in shear-banding wormlike micelles, enabling extraction of interface dynamics and stress diffusion coefficients from standard rheometer experiments, validated by ultrasonic velocimetry.

Contribution

A novel model linking superposition rheology to interface dynamics in shear-banding micelles, allowing parameter estimation from simple rheometry.

Findings

Interface oscillations can be characterized by the model.

Stress diffusion coefficient can be estimated from experiments.

Model validated by ultrasonic velocimetry measurements.

Abstract

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.