Timescales and instabilities of shear thinning solutions of wormlike micelles
Résumé
Shear thinning solutions of surfactant wormlike micelles are multi-scale systems with complex rheology. Transient kinetics of semidilute solu-
tions is studied using a simple rheo-optical device with cylindrical Couette geometry. During a start-up of flow experiment, we observe the nuc-
leation of the induced structures followed by the organization of the flow into two bands. The building of this banding structure begins with the
formation of a diffuse interface that rapidly migrates towards the inner wall and sharpens (typical time scale: 5s). When its profile is sharp, the
interface continues to move slowly up to its stationary position in the gap (typical time scale: 20s). This process is followed by the growth of an
interface instability with wave vector along the cylinder axis that saturates on time scale of the order of 40 – 50s. We reproduce this behaviour
using a non-monotone constitutive model including diffusion terms to cope with the strong gradients in the region of the sharp interface. The
second timescale, corresponding to the displacement of the sharp interface to its equilibrium position, is used to estimate the interface width and
the stress diffusion coefficient. Finally, in order to identify the origin of the longest time scale we study the growth of the interface instability in
the model.