Rheological modeling of both shear-thickening and thinning behaviors through constitutive equations

Abstract

Shear-thickening and thinning behaviors are often observed in the rheological measurements of dilute surfactant solutions with drag-reducing ability in wall-bounded turbulent flows. This study proposes a simple rheological modeling method based on combining constitutive equations, such as Giesekus and FENE-P models, with a fluidity equation to determine both thickening and thinning behaviors in simple shear flows simultaneously. The Giesekus and FENE-P models, which are typically used in numerical studies on turbulent drag reduction, cannot capture such complex behaviors. However, the proposed models, called f-Giesekus and f-FENE-P models, can predict the shear-thickening properties. The developed models are inspired by the Bautista–Manero–Puig model, where the Oldroyd-B model (upper-convected Maxwell model) is coupled with the fluidity equation. Parametric studies prove that the proposed models can accurately predict both the shear-thickening and shear-thinning properties. Notably, the f-FENE-P model shows prominent flexibility to determine the plateau region of the shear viscosity as a function of the shear rate. We verify that the analytical solutions of the f-FENE-P model agree with the experimental data of the shear viscosity in dilute drag-reducing surfactant solutions, except for the remarkable steep increase in the shear viscosity. The start-up shear flow is also studied to confirm various transitions accompanied by the overshoot and undershoot of the f-FENE-P model.