A model for acoustic vaporization of encapsulated droplets

Acoustic droplet vaporization (ADV) is the phase change of a liquid droplet triggered by an acoustic energy supply. It is the enabling mechanism behind a promising cancer treatment: inject droplets of a liquid that vaporises into a bubble under ultrasound, use them as contrast agents or as drug carriers that release their payload locally and controllably.

Modelling it is a coupling nightmare:

1. A radial dynamics problem for the vapor bubble;
2. A heat transfer problem across the liquid layer;
3. A nonlinear elasticity problem for the encapsulating shell.

A bubble/droplet/shell system

We built a model where the bubble is nested inside the droplet, the whole system wrapped in a hyperelastic shell — a crude but faithful representation of surfactant-stabilised droplets. The resulting ODEs couple the vapor pressure (thermodynamics), the acoustic forcing (nonlinear propagation) and the visco- hyperelastic response of the shell.¹

What we found

• The vaporization threshold depends strongly on geometrical and rheological parameters of the shell;
• There is a regime where the droplet only partially vaporises and the bubble recondenses — a fate directly connected to the acoustic parameters.²

This was supported by the Plan Cancer 2014–2019 project AIDA (Acoustically Induced Droplet Vaporization for Anti-cancer targeted drug delivery), a research project in physics, mathematics and engineering sciences applied to cancer research.

• PhD thesis (PDF)
• Movie