(659b) Richer Descriptions of Viscoelastic Nonlinearity in Time-Varying Flows

Many Fast Moving Consumer Goods (FMCGs), such as packaged foods, cosmetics, and over-the-shelf pharmaceuticals are complex fluids, or involve complex fluids during their processing steps. These materials are viscoelastic, exhibiting both viscous “fluid-like” and elastic “solid-like” behavior. A detailed knowledge of the rheology (i.e. flow properties) of these materials enables optimization of the processing steps in their industrial production, leading to efficient use of materials and lower cost of production. Additionally, rheology helps to characterize the material, providing a "fingerprint" that enables unambiguous identification of materials and bounds on product specifications for quality assurance. One such rheological protocol is Large Amplitude Oscillatory Shear (LAOS), which is now well-established as a key technique for characterizing nonlinear viscoelasticity across many fields, from the response of polymer melts to foods, additive manufacturing feedstocks and other soft materials. Unlike the often-studied shear stress in LAOS, the nonlinear oscillatory response of the first normal stress difference (N₁(t; ω, γ)) has been comparatively less studied, despite its importance in many free surface processing operations (e.g. die swell/extrusion). At sufficiently large strains for many viscoelastic materials such as polymer melts, N₁ can become much larger than the shear stress, thus serving as a very sensitive probe of the material’s nonlinear characteristics.

We introduce a Fourier-Tschebyshev framework appropriate for the quantitative description of N₁ and a physical interpretation for the corresponding material coefficients, similar to the elastic and viscous Tschebyshev expansion commonly used to describe shear thinning or thickening in the shear stress response. This new decomposition is first illustrated through analysis of the second-order and fourth-order responses of the quasilinear Upper Convected Maxwell model and the fully nonlinear Giesekus model. We then use this new framework to analyze experimental data on a silicone fluid and a thermoplastic polyurethane melt. Furthermore, we apply the recently developed Gaborheometry strain sweep technique to enable rapid and quantitative determination of experimental N₁ data from small to large strain amplitudes. We verify that asymptotic analytical connections between the oscillatory shear stress and N₁ in the quasilinear limit are met for the experimental data. We then use machine learning techniques to learn a tensorial constitutive equation (also known as a Rheological Universal Differential Equation (RUDE)) that accurately describes the fluid’s extended rheological fingerprint, generating a digital fluid twin that enables the prediction of the fluid response under different processing conditions. This framework for analyzing normal stress differences is complementary to the established framework for analyzing the shear stresses in LAOS, and augments the content of material-specific data sets, hence more fully quantifying the important nonlinear viscoelastic properties of a wide range of soft materials.