High-Frequency Acoustic Droplet Vaporization is Initiated by Resonance

Vaporization of low-boiling point droplets has numerous applications in combustion, process engineering, and in recent years, in clinical medicine. However, the physical mechanisms governing the phase conversion are only partly explained. Here, we show that an acoustic resonance can arise from the large speed of sound mismatch between a perfluorocarbon microdroplet and its surroundings. The fundamental resonance mode obeys a unique relationship $kR\sim 0.65$ between droplet size and driving frequency that leads to a threefold pressure amplification inside the droplet. Classical nucleation theory shows that this pressure amplification increases the nucleation rate by several orders of magnitude. These findings are confirmed by high-speed imaging performed at a timescale of 10 ns. The optical recordings demonstrate that droplets exposed to intense acoustic waves generated by interdigital transducers nucleate only if they match the theoretical resonance size.

Figure 1

(a) Calculated theoretical resonance curves for different driving frequencies. (b) Calculated resonance frequency $f_R$ as a function of size: droplet in free-field (red), droplet at a rigid wall (black), and bubble in free field (blue).

Figure 2

(a) Schematic of the experimental setup. The vaporization of PFP droplets is imaged using the Brandaris 128 ultra-high-speed camera. (b) A SAW device generates a longitudinal pressure wave in the fluid at the Rayleigh angle ${\theta }_R$. (c) Typical size distribution of the droplets used in this study.

Figure 3

Vaporization of PFP droplets driven at 19.6 (a) and 45.4 MHz (b) imaged at 15 Mfps. The nucleated droplets are marked by the red dotted circles. Stable bubbles are formed from all nucleated droplets as can be observed from the image captured 100 ms later. Number of nucleation events over time and the corresponding radius of the droplet at a driving frequency of 19.6 (c) and 45.4 MHz (d).

Figure 4

Resonant vaporization detected at a frequency of 19.6 (a) and 45.4 MHz (b). Calculated and simulated size-dependent pressure amplification factor within the droplet at a frequency of 19.6 (c) and 45.4 MHz (d). (e) Snapshot of the simulated pressure field for a $2.7\mu \mathrm{m}$ radius droplet resonant at a frequency of 45.4 MHz. (f) Droplet activation probability with and without the resonance effect, where “data” represents the experimental droplet activation probability.