Time scales in shear banding of wormlike micelles

Transient stress and birefringence measurements are performed on wormlike micellar solutions that "shear band", i.e. undergo flow-induced coexistence of states of different viscosities along a constant stress "plateau". Three well-defined relaxation times are found after a strain rate step between two banded flow states on the stress plateau. Using the Johnson-Segalman model, we relate these time scales to three qualitatively different stages in the evolution of the bands and the interface between them: band destabilization, reconstruction of the interface, and travel of the fully formed interface. The longest timescale is then used to estimate the magnitude of the (unknown) "gradient" terms that must be added to constitutive relations to explain the history independence of the steady flow and the plateau stress selection.