Direct observation of capillary waves due to high frequency ultrasound and their relation to atomized droplets

Abstract

Ultrasonic atomization has been studied and used in applications for decades, but a mechanistic understanding of droplet production does not exist at a quantitative level. Early work seemed to indicate that droplet size follows from the driving frequency according to Kelvin's equation. The underlying assumptions in this model do not hold at larger frequencies, and the model relies on a fitting parameter that has not been consistent across experimental studies. Additionally, modern experiments often indicate multi-modal droplet size distributions further complicating the physics. It is difficult to experimentally measure relevant quantities like capillary wavelength because of the time and length scales involved and the fact that the phenomenon occurs at a free liquid surface. We use a high speed digital holographic microscope, the only one of its kind in the world, to image the liquid surface—in full 3D and real time—fast enough to resolve capillary waves generated by 5–50 MHz ultrasound. We extract from this data the spectrum of capillary wavelengths and then compare these to droplet size distributions measured with laser diffraction particle sizing. Both thickness mode and surface acoustic wave lithium niobate transducers are included as well as a range of frequencies in each case. It is shown that droplet size does depend directly on capillary wavelength, but that capillary wavelength is not related to the driving frequency in a simple way.