Dynamics of Radially Expanding Liquid Sheets

The process of atomization often involves ejecting thin liquid sheets at high speeds from a nozzle that causes the sheet to flap violently and break up into fine droplets. The flapping of the liquid sheet has long been attributed to the sheet’s interaction with the surrounding gas phase. Here, we present experimental evidence to the contrary and show that the flapping is caused by the thinning of the liquid sheet as it spreads out from the nozzle exit. The measured growth rates of the waves agree remarkably well with the predictions of a recent theory that accounts for the sheet’s thinning but ignores aerodynamic interactions. We anticipate these results to not only lead to more accurate predictions of the final drop-size distribution but also enable more efficient designs of atomizers.

Figure 1

(a) Experimental set-up for generating radially expanding liquid sheet. Sinusoidal motion of the vibrating impactor generates sinuous waves that are convected radially outward. (b) Surface inclination angle, $\theta$, of the surface waves is related to the displacement, $d_3$, of the laser spot on the screen. (c) Measured dimensionless sheet radius versus ${\mathrm{We}}_d$ in the absence of forcing and at atmospheric pressure. The solid line represents, $2R/d={\mathrm{We}}_d/8$. The vertical dotted lines represent ${\mathrm{We}}_d$ at which the spatial growth rates of sinuous waves were determined.

Figure 2

Measured amplitude of surface inclination angle at different radial locations is compared with predictions (lines, (3)) in the smooth regime for a range of forcing frequencies and at 1 and 0.6 atm, (a) $\mathrm{W}{\mathrm{e}}_d=550$ and (b) $\mathrm{W}{\mathrm{e}}_d=700$.

Figure 3

Measured amplitude of surface inclination angle at different radial locations is compared with predictions (lines) in the flapping regime for a range of disturbance frequencies, (a) $\mathrm{W}{\mathrm{e}}_d=975$ at 1 and 0.6 atm. The inset shows the collapse of three sets of measurements for fixed $N$ across all $\mathrm{W}{\mathrm{e}}_d$ and varying $\overline{\omega }$ (legend: $\mathrm{W}{\mathrm{e}}_d$, frequency, $N$). The solid lines are theoretical predictions (4) for a fixed $N$, and (b) $\mathrm{W}{\mathrm{e}}_d=1200$ at 1 atm. Note that the frequencies at $\mathrm{W}{\mathrm{e}}_d=1200$ correspond to the highest natural modes in the system. The inset compares measurements with predictions of the aerodynamic theory (dotted lines) for $\mathrm{W}{\mathrm{e}}_d=975$ and 1200 (see Supplemental Material for details [31]).