Pinch-off of liquid jets at the finite scale of an interface

We derive self-similar continuum equations that govern the rupture of liquid threads at scales within the influence of interfacial dynamical effects. This regime and the obtained power-law solution for the evolution of the minimum neck radius, $h_{\min }=0.00107{(t_b-t)}^{2.34}$, fill a void in the literature in between the classical inertial-viscous regime and the stochastic formulation and reconcile flow features such as asymptotic slow boundary conditions far away from the singularity and symmetric profiles, respectively. Due to its inherent ties to the production of monosized droplets from jetting, this work can be utilized to approach, for example, the study of electrosprays or flow focusing at these critical scales for aerospace nano-thruster technology or single-biomolecule imaging with x-ray free-electron lasers.

Figure 1

Sketch about the minimum thickness of the pinching of a liquid thread. A detailed view in the vicinity of the minimum radius $h_{\min }$ and at a scale comparable in size to the interface thickness $\delta$ (in gray color gradient).

Figure 2

Inner interfacial solutions of ${\mathrm{\Phi }}_{\eta }$ for $\chi \in [0.625,1.125]$. The inset shows the relation between $N$ and $\chi$, with a divergent behavior of $N$ for $\chi <{\chi }_{\min }=0.745$ that corresponds to quasivertical blue curves in the main figure.

Figure 3

Family of self-similar solutions for $H$ as a function of $\chi$. There is only an even symmetric profile (blue, solid line) for $\chi =0.795$ (left vertical axis). The rest of the candidate curves are examples of how the symmetry is broken as $\chi$ varies (right vertical axis).

Figure 4

Family of self-similar solutions for $V$ as a function of $\chi$. There is only an odd symmetric profile (blue solid line) for $\chi =0.795$. The rest of the candidate curves are examples of how the symmetry is broken as $\chi$ varies.