Thixotropic-viscoelastic rheological fingerprints in large amplitude oscillatory shear

In this work we demonstrate the use of large-amplitude oscillatory shear (LAOS) as a tool to characterize the behavior of constitutive models that exhibit both thixotropic and viscoelastic phenomena. We demonstrate this use of LAOS by first examining the strain controlled LAOS (LAOStrain) response of a Thixoelastic Jeffreys model. First, this canonical model is defined for capturing both viscoelasticity and thixotropy with a minimum number of model parameters. Then the use of LAOS is demonstrated as we explore this model response as a function of four dimensionless parameters: two LAOStrain deformation parameters (the Deborah number and the Wiessenberg number) and two material parameters (the ratio of viscoelastic to thixotropic timescales and the ratio of solvent viscosity to aggregate viscosity). We present an analytical solution for the asymptotic nonlinearities of this model in LAOS, as well as numerical results for the full nonlinearities. We present these results in a manner that eases the challenges of visualizing a response to four independent parameters. This canonical thixotropic-viscoelastic constitutive model, containing the minimum number of parameters required to capture both thixotropic and viscoelastic phenomena, predicts that short thixotropic timescales can be experimentally observed with nonlinear oscillatory deformation. This is relevant to recent suggestions in classifying thixotropic versus “simple” yield stress fluids with no observable thixotropy. Having established the signature of the simplest model that exhibits the features of interest, we then proceed to make two modifications, focusing on the fundamental characteristics of the kinetic rate equation. Expanding on the minimalist constitutive model that contains only five material parameters, we first examine the distinct rheological material function signatures produced when kinetic structure breakdown is dictated either by stress or by strain rate. We compare and contrast the behavior of these closely related models using asymptotic nonlinearities in LAOS. We also explore the differences between model responses in LAOStrain and in controlled stress oscillations (LAOStress). We then observe the effects of a sixth model parameter (the most common addition to simple models in the literature), introduced to govern the order of reaction of the kinetic rate equation. Finally, we give broader context as to where these models fit into the bigger picture by presenting a chart that summarizes models that are commonly used to describe yield-stress fluids in the literature. Overall, we show that LAOS provides a useful fingerprint for these thixotropic and viscoelastic models. Our analysis of the Thixoelastic Jeffreys model indicates that asymptotic scaling with respect to the amplitude of the input signal can identify the order of reaction. Furthermore it suggests that the amplitude-intrinsic nonlinearities are capable of identifying timescales that cannot be observed by step tests due to experimental limitations. Ultimately, these data can be used to inform constitutive model selection and therefore improve the accuracy of flow modeling of thixotropic viscoelastic fluids