Machine Learning-Based Derivation of a Multi-Variable Implicit Viscosity Model for Non-Newtonian Fluids

Viscosity, a crucial rheological property of fluids, plays an important role in understanding flow behavior and simulation of fluid flow. This thesis presents a novel data-driven viscosity model for shear-thinning, time-independent non-Newtonian fluids, particularly elastomeric compounds processed in polymer manufacturing. The work begins with a detailed rheological characterization based on high-pressure capillary rheometry, employing Bagley and Weissenberg–Rabinowitsch corrections to extract accurate shear stress and shear rate data. Classical viscosity models including the Carreau–Arrhenius formulation, were fitted using constrained nonlinear least squares to establish a physically meaningful baseline. The Carreau–Arrhenius model, due to its excellent performance across the experimental range and valid extrapolation into the Newtonian plateau, was selected for synthetic data generation . To overcome experimental limitations in low-shear regions, the validated classical model was used to augment the dataset with 2000 synthetic points. The enriched dataset enabled the development of the Multi-Variable Implicit (MVI) viscosity model, derived via symbolic regression using the PySR library. The MVI model produces a closed-form , algebraic expression that implicitly couples temperature and shear rate without relying on complex transcendental functions. This design ensures compatibility with CFD solvers, offering smoothness, numerical stability, and high computational efficiency. The model achieved an R² of 0.99 on unseen test data and generalized well across distinct polymers including thermoplastics, without retraining. It accurately reproduced the Newtonian plateau, transition region, and pseudoplastic regime., Although it does not capture the second Newtonian plateau at extreme shear rates. some non-Newtonian fluids show a second Newtonian plateau at very high shear rates, our specific compound did not show such behavior until extremely high shear rate which was almost outside of the values that a material experiences in a real-world industrial process. Therefore, the new derived viscosity model was not trained on extremely high shear rates and is not capable of capturing the second Newtonian plateau The proposed approach bridges data-driven modeling with classical rheology and offers a viable path toward interpretable AI-enhanced constitutive equations for engineering simulations.