**Probing Shear-Banding Transitions of the VCM Model for Entangled Wormlike Micellar Solutions Using Large Amplitude Oscillatory Shearing (LAOS) Deformations**

By Lin Zhou, L.Pamela Cook, Gareth H. McKinley

We
explore the use of Large Amplitude Oscillatory Shear (LAOS) deformation
to probe the dynamics of shear-banding in soft entangled materials,
primarily wormlike

micellar solutions which are prone to breakage
and disentanglement under strong deformations. The state of stress in
these complex fluids is described by a class of viscoelastic

constitutive
models which capture the key linear and nonlinear rheological features
of wormlike micellar solutions, including the breakage and reforming of
an entangled network. At a frequency-dependent critical strain, the
imposed deformation field localizes to form a shear band, with a phase
response that depends on the frequency and amplitude of the forcing.
The different material responses are compactly represented in the form
of Lissajous (phase plane) orbits and a corresponding strain-rate and
frequency-dependent Pipkin diagram. Comparisons between the full
network model predictions and those of a simpler, limiting case are
presented.

Key words: LAOS, Pipkin diagram, shear banding