Periodic jetting and monodisperse jet drops from oblique gas injection

When air is blown in a straw or tube near an air-liquid interface, typically one of two behaviors is observed: a dimple in the liquid's surface, or a frenzy of sputtering bubbles, waves, and spray. Here we report and characterize an intermediate regime that can develop when a confined air jet enters the interface at an angle. This regime is oscillatory with a distinct characteristic frequency and can develop periodic angled jets that can break up into monodisperse aerosols. The underlying mechanisms responsible for this highly periodic regime are not well understood. Here we flow a continuous stream of gas through a tube near a liquid surface, observing both optically and acoustically the deformation of the liquid-air interface as various parameters are systematically adjusted. We show that the Kelvin-Helmholtz instability is responsible for the inception of waves within a cavity formed by the gas. Inertia, gravity, and capillary forces both shape the cavity and govern the frequency and amplitude of these gas-induced cavity waves. The flapping cavity focuses the waves into a series of periodic jets that can break up into droplets following the Rayleigh-Plateau instability. We present scaling arguments to rationalize the fundamental frequencies driving this system, as well as the conditions that bound the periodic regime. These frequencies and conditions compare well with our experimental results.

Figure 1

Gas injection into a Petri dish of silicone oil can exhibit various dynamics. As the angle of the tube with the liquid surface is increased, there is a progression from a steady cavity to periodic waves, a stream of monodisperse droplets, and eventually a frenzy of bubbles and polydisperse droplets.

Figure 2

A schematic of the experimental setup. The liquid is placed in a tank on a microstage to precisely control the distance $\mathcal{Z}$ that the tube is submerged. The tube angle $\theta$ and flow rate $Q$ are also measured and varied.

Figure 3

An experimentally derived regime map illustrates the interplay between tube submersion distance $\mathcal{Z}$ and inclination angle $\theta$. Here the flow rate is $Q$ = 24 ml/s, the internal diameter of the tube is $d$ = 4.8 mm, and all other parameters are fixed.

Figure 4

Reducing dimensionality. (a) The regime map in Fig. 3 is nondimensionalized and plotted in terms of $\mathcal{Z}/(dcos\theta )$ and $\theta$. At low angles, the regime boundaries occur at constant values of $\mathcal{Z}/(dcos\theta )$ when all other parameters are fixed. Here the flow rate is $Q$ = 24 ml/s, the internal diameter $d$ = 4.8 mm. (b) The parameter $\mathcal{Z}/(dcos\theta )$ can be geometrically interpreted as the fraction of the tube outlet that is submerged $\ell /d$.

Figure 5

Acoustic signatures captured by the hydrophone for the various dynamic regimes: (a) wave regime ($\ell /d$ = 1.0, $Q$ = 47 ml/s), (b) breaking jet regime ($\ell /d$ = 1.4, $Q$ = 47 ml/s), and (c) irregular bubbling-sputtering regime ($\ell /d$ = 1.4, $Q$ = 16 ml/s). (d) A distinctly different acoustic signature appears for the bubbling regime at a low enough flow rate that a periodic stream of bubbles rise to the liquid surface and rupture ($\ell /d$ = 1.4, $Q$ = 8 ml/s). Each set of acoustic data is plotted in both the spatial domain (left) and the frequency domain (right). Here $d$ = 4.8 mm and $\theta ={30}^{\circ }$.

Figure 6

Experimental data illustrating the role of flow rate $Q$. (a) The regime map as a function of tube outlet fraction $\ell /d$ and flow rate $Q$ with $d$ = 4.8 mm. (b) The fundamental frequencies $f$ in the periodic regime (waves and breaking jet) as a function of flow rate $Q$ and tube outlet fraction $\ell /d$. Conditions with $\ell /d\gtrsim 1$ are repeated with a larger diameter $d$ = 6.2 mm tube. Here the tube angle is fixed at $\theta$ = ${30}^{\circ }$. The region marked with an asterisk represents the regime of regular bubbling observed at high tube submersion and low flow rates. The transition from the regular or periodic bubbling regime to irregular bubbling was not systematically investigated.

Figure 7

Transition for steady cavity to waves. (a) A schematic of the area of the tube outlet fraction available for the flow of gas. (b) Experimentally measured transition values for two different diameter tubes are plotted for various tube outlet fractions and nondimensional flow rates and compared to theory.

Figure 8

(a) A time series of high-speed images representing one period of the breaking jet regime. Here the tube is fully submerged a distance $H$ from the free surface. (b) The high-speed images from (a) thresholded with the tube masked to provide better visualization of the interface.

Figure 9

The frequency response [Fig. 6] for two different diameter tubes plotted using the dimensionless frequency and the dimensionless flow rate suggested from the proposed mechanism. The broken lines are visual aids bounding the region of periodicity.

Figure 10

Effect of viscosity on frequency response. The dimensionless frequency is plotted against an Ohnesorge number and indicates the relative contribution of viscosity to the dynamics of the phenomenon. The fluids used, in order of increasing viscosity, are water and silicone oils of viscosity 10, 100, 1000, 10 000 and 100 000 cSt.