Acoustic nonlinearity and the generation of large tensile pressures to explain atomization in drop-chain acoustic fountains

Abstract

An ultrasound beam propagating upward in a liquid creates an acoustic fountain at a gas interface in the form of a drop chain. High-speed photography shows that one or several drops in such a fountain explode in less than a millisecond, resulting in liquid atomization [Simon et al. J. Fluid Mech., 2015, 766, pp. 129-146]. To explain this phenomenon, a nonlinear theory involving an isolated spherical drop is developed. The model considers an initial excitation in the form of a spherical standing acoustic wave at the lowest resonance frequency, i.e., when the drop diameter coincides with a wavelength. If higher harmonics are generated inside the drop due to acoustic nonlinearity, these harmonics will also have the form of standing spherical waves. At higher frequencies, more of the energy of each harmonic is localized near the drop center. Calculations demonstrate that harmonic generation can lead to large increases in both peak positive and peak negative acoustic pressure at the drop center. Such large tensile pressures may exceed the intrinsic cavitation threshold, leading to the nucleation of a bubble at the center and explosion of the drop as the bubble grows rapidly. [Work supported by RFBR 17-02-00261 and NIH R01EB007643.]