A two-dimensional flow instability in Large Amplitude Oscillatory Shear of entangled polymers

Large amplitude oscillatory shear (LAOS) flows are an important tool for characterizing soft materials, providing independent control over the timescale and nonlinearity of the imposed deformation. However, LAOS measurements can be complicated due to interpret than small amplitude oscillatory shear measurements, due to the nonlinear and unsteady nature of the measurements. In this talk, we present a further complication: there is emerging computational support for a two-dimensional flow instability in LAOS, creating a disconnect between the macroscopically imposed deformation and the microscopic flow experienced by individual fluid elements. The instability develops from plane-wave perturbations to the polymer configuration aligned off-axis to the velocity gradient, and is distinct (in several ways) from traditional shear banding instabilities. We present preliminary results from a linear stability analysis as well as nonlinear quasi one-dimensional flow calculations. Results show that the instability only emerges for sufficiently entangled systems in a bounded range of strain amplitudes/frequencies, and tends to favor flow heterogeneity on lengthscales set by stress diffusion.