Phase transitions of perfluorocarbon nanoemulsion induced with ultrasound: A mathematical model

• This paper describes a mathematical model of ultrasonic acoustic droplet vaporization of perfluorocarbons.
• Liquid perfluoropentane droplets make larger gas bubbles than perfluorohexane at the same acoustic parameters.
• Increasing acoustic amplitude increased the bubble size.
• Insonation at lower frequencies forms larger bubbles than at higher frequencies.
• Higher temperatures create higher vapor pressures which in turn produces larger bubbles.

While ultrasound has been used in many medical and industrial applications, only recently has research been done on phase transformations induced by ultrasound. This paper presents a numerical model and the predicted results of the phase transformation of a spherical nanosized droplet of perfluorocarbon in water. Such a model has applications in acoustic droplet vaporization, the generation of gas bubbles for medical imaging, therapeutic delivery and other biomedical applications.The formation of a gas phase and the subsequent bubble dynamics were studied as a function of acoustic parameters, such as frequency and amplitude, and of the physical aspects of the perfluorocarbon nanodroplets, such as chemical species, temperature, droplet size and interfacial energy. The model involves simultaneous applications of mass, energy and momentum balances to describe bubble formation and collapse, and was developed and solved numerically. It was found that, all other parameters being constant, the maximum bubble size and collapse velocity increases with increasing ultrasound amplitude, droplet size, vapor pressure and temperature. The bubble size and collapse velocity decreased with increasing surface tension and frequency. These results correlate with experimental observations of acoustic droplet vaporization.