Subwavelength droplets in nonlinear ultrasound fields: Simulation of focusing effects

Abstract

Ultrasound can trigger the evaporation of tiny droplets of emulsified, superheated fluids like perfluorocarbon. This acoustic droplet vaporization (ADV) effect is important because of its potential medical applications. For example, drug-loaded nanodroplets can penetrate the vessel wall and subsequently release their therapeutic load through acoustic activation. Until now, the medical application of ADV has been limited by lack of understanding of the acoustic activation mechanism. In an accompanying paper, a mechanism is proposed that can fully explain the experimentally observed phenomena such as a frequency dependent pressure threshold. The mechanism involves focusing of higher harmonics of the nonlinear activation field. In the current presentation it will be explained how the focusing effect is simulated. A particular problem here is that typical droplet sizes are in the order of micrometers, while typical wavelength sizes are in the order of hundreds of micrometers. This difference in scale will render the traditional analytic solution numerically useless. The problem is avoided by using appropriate expansions of the functions involved. Numerical results are presented that show a focusing effect inside the droplet for a range of incident harmonics. These results have enabled the demonstration of the mechanism in the accompanying paper.