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A number of commercial fluids, including synthetic automotive oils, food andconsumer products containing polymer additives exhibit weakly rate-thickeningresponses in the final stages of capillarity-driven thinning, where a largeaccumulated strain and high extensional strain rate alter the thinning dynamicsof the slender liquid filament. Consequently, the capillarity-driven thinningdynamics typically feature two distinct regions at the early and late stages ofthe filament breakup process, each dominated by distinct mechanisms. Thesefeatures have been incorporated in a simple Inelastic Rate-Thickening (IRT)model with linear and quadratic contributions to the constitutive stress-strainrate relationship, where the apparent extensional viscosity slowly thickens athigh strain rates. We numerically compute the thinning dynamics of the IRTmodel assuming an axially-slender axisymmetric filament and no fluid inertia.The computational results motivate a new self-similar solution dominated by thesecond-order stress obtained through a similarity transformation. The newasymptotic solution leads to a self-similar filament shape that is more slenderthan the Newtonian counterpart and results in a quadratic thinning of themid-point radius of the filament with time to breakup close to singularity. Anew and distinct asymptotic geometric correction factor, $X\approx 0.5778$ isobtained, from which a more accurate true extensional viscosity can berecovered from an interpolated time-varying geometric correction factor basedon the magnitudes of different stress components. Finally, we propose astatistics-based protocol to select the best-fit constitutive model using aparameter-free criterion, enabling us to quantify the extensional rheologicalbehavior through capillarity-driven thinning dynamics more systematically oncomplex rate-thickening viscoelastic fluids.

Capillarity-driven thinning and breakup of weakly rate-thickening fluids