Non-integer asymptotic scaling of a thixotropic-viscoelastic model in large-amplitude oscillatory shear

We demonstrate that a simple thixotropic-viscoelastic constitutive model has a unique rheological fingerprint that fits data that no other model is known to fit. The key rheological signature is the non-integer power law scaling in asymptotically-nonlinear large-amplitude oscillatory shear (LAOS), sometimes called medium-amplitude oscillatory shear (MAOS). We begin with a minimalist constitutive model that contains only five material parameters, which we show to be the minimum required to capture all fundamental thixotropic and viscoelastic phenomena. We demonstrate that the low amplitude power-law scaling of the asymptotically nonlinear first and third harmonic stresses (scaling as input amplitude squared) is different than that observed in all other known constitutive model predictions (which predict nonlinearities to scale as input amplitude cubed). We then explore the effects of a sixth model parameter n (the most common addition to thixotropic models in the literature), introduced to govern the order of the kinetic rate equation. We show that this parameter gives further variability to this unique signature (with nonlinearities scaling as σ~γⁿ⁺¹). Finally, we compare these model signatures to the experimental signature of a real thixotropic material (Carbopol microgel suspension in water), demonstrating that models with non-integer amplitude scaling are required to match experimental observations.