On the consistent modeling of shear-thickening polymer solutions

During the past few decades, the interest in understanding the peculiar rheological behavior of shear-thickening fluids has increased due to their potential use in various commercial applications. In such an endeavor, the optimal design of these fluids is essential, which necessitates our in-depth understanding of their properties from a modeling perspective. We herein introduce a continuum model to predict the rheological behavior of shear-thickening polymer solutions using non-equilibrium thermodynamics that guarantees, by construction, consistency with the laws of thermodynamics as extended to handle non-equilibrium systems. This is made possible by using a scalar structural variable that characterizes the formation of the shear-induced structure at sufficiently high shear rates, and a conformation tensor that characterizes the deformation of the polymer segments. The model predicts the exhibition of a shear-thickening behavior for all steady shear flow material functions (shear viscosity and normal stress coefficients), which is then followed by a shear-thinning behavior if finite extensibility or anisotropic effects are considered. We further document that these model predictions are in line with available shear viscosity rheological data for shear-thickening polymer solutions.