Impact-induced viscoelastic bungee-jumper jets with uniform extension and stress

Abstract

We investigate the dynamics of a "bungee-jumper" jet induced by an impulsive force, which retracts after reaching its peak extension. Despite the strongly extensional and highly nonequilibrium nature of this motion, the jet exhibits simple and uniform rheological responses. To elucidate its extensional behavior in a highly extensional regime quantified by large Deborah and Reynolds numbers ($De \approx 2.1 \times 10^1 - 3.3 \times 10^3$, $Re \approx 2.8 \times 10^1 - 4.6 \times 10^2$), we use high-speed velocimetry and polarization-based stress imaging to measure the spatial distribution of velocity and stress throughout jets made of dilute polyethylene oxide (PEO) solutions. The bungee-jumper jets are found to exhibit two uniform characteristics despite the extreme $De$ conditions: a consistent spatial distribution of the extensional rate and a nearly uniform stress distribution during the jetting motion. These uniformities indicate that the seemingly complex jet dynamics can in fact be effectively represented using a constitutive model with spatially uniform coefficients. Comparison of several viscoelastic models shows that the Voigt model provides the best agreement with the measured dynamics, while the single-spring model captures the essential behavior when elasticity dominates.