An improved Capillary Breakup Extensional Rheometer to characterize weakly rate-thickening fluids: Applications in synthetic automotive oils

Abstract

We describe a customized Capillary Breakup Extensional Rheometer (CaBER) with improved dynamic performance and added features for temperature control over the range from room temperature up to 250 °C. The system is aimed at characterizing the extensional rheological behavior of weakly rate-thickening fluids that are widely utilized in the automotive industry. We examine the shear rheology and filament-thinning dynamics of two commercially available automotive fluids with the same viscosity index. Comparisons of the rheological properties of the two samples reveal that although they have identical shear viscosities, they exhibit significant and distinct rate-thickening behavior in the strong extensional flow that is generated close to filament breakup. For the more elastic sample, the exponential filament-thinning dynamics are well-described by the Oldroyd-B model; however, this viscoelastic model poorly describes the response of the more weakly rate-thickening fluid. To address this limitation, we propose a simple Inelastic Rate-Thickening (IRT) model that more robustly describes the measured material response. The two constitutive parameters of the model represent the zero-shear-rate viscosity of the fluid and the rate of extensional thickening in the fluid. Numerical calculations with the IRT model show that the radii of thinning fluid filaments deviate from a linear decay in time and approach a quadratic dependence very close to breakup. By carefully fitting the measured temporal evolution of the mid-plane radius we can therefore systematically differentiate the extensional rheological response of the two oils. More generally, we show that the weakly rate-thickening regime can be distinguished from the well-known elasto-capillary response predicted by the Oldroyd-B model, via a constraint on the relaxation time (or more specifically the elasto-capillary number) of the fluid. The weakly rate-thickening behavior documented in these oils is representative of the relatively unstudied extensional rheology of many industrial fluids at large extensional strain rates (100–1000 s-1) and influences many complex industrial processes such as jetting, coating and stamping.