Ejection of Uniform Micrometer-Sized Droplets from Faraday Waves on a Millimeter-Sized Water Drop

This Letter reports the first observation and theoretical analysis of a new phenomenon: one large spherical water drop ejecting simultaneously a very large number of monodisperse microdroplets. An ultrasonic nozzle with multiple-Fourier horns in resonance enables controlled excitation of megahertz Faraday waves on the free water surface. The temporal instability of such waves leads to the ejection of $3.5–4.4\mu \mathrm{m}$ monodisperse droplets at a high rate ($>4.0\times {10}^7\mathrm{droplets}/\sec$). This is in stark contrast to the Rayleigh-Plateau instability, which ejects one droplet at a time.

Figure 1

(a) 3D architecture of the MHz multiple-Fourier horn ultrasonic nozzle. The nozzle is comprised of a drive section with a pair of piezoelectric transducers and a resonator section with central channel dimensions of $200\mu \mathrm{m}\times 200\mu \mathrm{m}$ and $150\mu \mathrm{m}\times 150\mu \mathrm{m}$ for the 1.0 MHz three- and 1.5 MHz four-Fourier horn nozzles, respectively, and the corresponding end face dimensions of $700\mu \mathrm{m}\times 1060\mu \mathrm{m}$ and $482\mu \mathrm{m}\times 1060\mu \mathrm{m}$. (b) Photograph of the 1.0 MHz and 1.5 MHz nozzles. (c) Geometry of the nozzle end face and liquid layer $d$ in depth. (d),(e) Nozzle end face–liquid sphere geometry, top view and side view, respectively.

Figure 2

Droplet ejection. The droplet ejection experiments were carried out using a bench-scale setup [22]. Water was transported to the nozzle end face at flow rates controlled by a syringe pump ($kd$ Scientific Model #101). (a) Time sequences of the water drop on the end face of the 1.0 MHz nozzle leading to droplet ejection. (b) Transparent water drop in the absence of droplet ejection. (c),(d) Droplets ejected from bright surfaces of the water drops at the drive frequency of 0.960 and $1.447\pm 0.001\mathrm{MHz}$, respectively. (e) Imaging of the droplets ejected from the free surface of the water layer. Note that the scale bars in (b) and (c), (d), and (e) are 350, 250, and $50\mu \mathrm{m}$, respectively.

Figure 3

Measured droplet sizes and size distributions in logarithmic scale from the water sphere using (a) the 1.0 MHz nozzle and (b) the 1.5 MHz nozzle. Note: Volume frequency designates volume percent in each size range of the histogram. The GSD and geometric mean of a data set with a log-normal distribution are, respectively, equivalent to the standard deviation and arithmetic mean of a data set with normal distribution.

Figure 4

Comparison of measured water droplet diameters with theoretical predictions.