Shear Thinning and Stress-Dependent Viscosity Activation Volumes: Combining Eyring and Carreau

The viscosity of fluids and their dependence on shear rate, known as shear thinning, plays a critical role in applications ranging from lubricants and coatings to biomedical and food-processing industries. Traditional models such as the Carreau and Eyring theories offer competing explanations for shear-thinning behavior. The Carreau model attributes viscosity reduction to molecular distortions, while the Eyring model describes shear thinning as a stress-induced transition over an activation energy barrier. This work proposes an extended-Eyring model that incorporates stress-dependent activation volumes, bridging key aspects of both theories. In modifying transition-state theory by using an Evans-Polanyi perturbation analysis, we derive a generalized viscosity equation that accounts for the molecular-scale rearrangements governing fluid flow. The model is validated against computational and experimental data, including shear-thinning behavior of pure squalane and polyethylene oxide (PEO) aqueous solutions. Comparative analysis with Carreau-Yasuda and conventional Eyring models demonstrates excellent accuracy in predicting viscosity trends over a wide range of shear rates. The introduction of stress-dependent activation volumes provides a description of molecular exchange kinetics accounting for structural reorganization under shear. These findings offer a unified framework for modeling shear thinning and have broad implications for designing advanced lubricants, polymer solutions, and complex fluids with tailored flow properties.