The Dynamics of Bubbles in a Corner'

Ultrasound cavitation has wide and important applications, including sonochemistry, ultrasound cleaning, medical ultrasonography and as well as therapeutic applications of ultrasound. The lack of predictable models for cavitation development is a core unresolved challenge in ultrasound cavitation.

Birmingham bubble group has been established for more than 30-years and is one of the world leading research groups in the mathematics of bubbles. In connection with the project, we have developed a tractable mathematical model for simulating the growth of bubbles for millions of oscillations subject to acoustic waves, based on multiscale perturbation and matched expansions. The approach has been well demonstrated by the excellent agreement of the model with experiments.

In this project, the PGR will develop mathematical and statistical modelling for the cavitation development due to acoustic waves. We assume that billions of nanobubbles pre-exist in liquids. When subject to acoustic waves, some of these bubbles grow and others diminish, through rectification, resulting in the variation of liquidized gas concentration in water.

The bubble size distribution is assumed following the Gaussian distribution. Its mean and standard deviation are updated by calculating the growth (diminish) of a sample set of O(100) bubbles using the tractable model. The gas concentration is then updated with the bubble size distribution and conservation of mass for the gas.

Multi-time scales are used in coupling the bubble growth and the gas concentration variation, because the diffusion over the macroscale of a bubble cloud takes much longer time than the growth of individual bubbles.