A phase diagram of the pinch-off behavior of impulsively-induced viscoelastic liquid jets

TL;DR

This paper maps out the different behaviors of impulsively-induced viscoelastic liquid jets, identifying conditions for pinch-off versus no-pinch-off, and provides a phase diagram based on flow and rheological parameters.

Contribution

It introduces a phase diagram for viscoelastic jet behaviors using Reynolds and Weissenberg numbers, supported by a focused jet model with FENE-CR rheology.

Findings

Pinch-off jets occur at Re ≥ 23.4Wi for Wi ≥ 10.

No-pinch-off jets include retracting and returning types.

The phase diagram is explained by a focused jet model with FENE-CR.

Abstract

In this study, we systematically investigate the behaviors of viscoelastic liquid jets using an impulsive force, particularly in the high velocity and high elasticity regimes. The resulting jets are categorized into two types: (i) pinch-off jets, which break up during elongation after ejection, and (ii) no-pinch-off jets, which either retract to the nozzle after maximum elongation, known as `bungee-jumper jets' or return without elongation after ejection. We then propose criteria to delineate these regions using Reynolds number $Re$ and Weissenberg number $Wi$, reflecting the initial conditions at the jet ejection and the solution's rheological properties, respectively. We find that pinch-off jets occur at $Re \gtrsim 23.4Wi$ in high elasticity regimes ($Wi \gtrsim 10$), and at $Re \gtrsim 250$ in low elasticity regimes ($Wi \lesssim 10$). In addition, we demonstrate that the phase diagram of these behaviors can be rationalized through the focused jet modeling using the finitely extensible non-linear elastic dumbbell model with the Chilcott-Rallison closure approximation (FENE-CR).