(518f) A Simple Paradigm for Strongly Nonlinear Large-Amplitude Oscillatory Shear (LAOS) Rheology

We quantify the dynamics of a dilute dispersion of nearly spherical particles that undergo Brownian rotations in an oscillatory shear flow, as a paradigm for large-amplitude oscillatory shear (LAOS) rheology. Our focus is on strongly nonlinear LAOS: β » 1 and β/α » 1, where β is a dimensionless shear-rate amplitude (or Weissenberg number) and α is a dimensionless oscillation frequency (or Deborah number). We derive an asymptotic solution for the long-time periodic orientation probability density function of the particles. Our analysis reveals that the orientation dynamics consists of periods of rapid oscillation (on the time-scale of the inverse shear-rate amplitude) separated by short "turning points" of  comparatively slow evolution when the imposed flow vanishes. Uniformly valid approximations to the shear stress and normal stress differences (NSDs) of the dispersion are then constructed: the particle contribution to the shear stress, first NSD, and second NSD, decays as β^-3/2, β^-1, and β^-1/2, respectively. These stress scalings originate from the orientation dynamics at the turning points; thus, it is the times when the flow vanishes that dominate the LAOS rheology of this paradigmatic complex fluid, surprisingly.