Mathematical and physical modelling of bubble growth due to ultrasound

Abstract

A mathematical model, combined with a physical model, has been developed to simulate the growth characteristics of a single bubble in liquid by the process of rectified diffusion. The mathematical model is based on the coupled momentum, energy and mass transport equations. The model forms a set of coupled, highly nonlinear and stiff differential equations and it is characterized by the fast moving boundary of the bubble. The model equations have been solved by the modified Gear method. The effects of initial bubble radius, initial concentration of dissolved gas in liquid and the amplitude and frequency of the imposed ultrasound field on the process of rectified diffusion are numerically studied. The results show that an air bubble in water grows when the ultrasonic pressure amplitude is more than the threshold pressure. In this case, the bubble volume rapidly reaches several times of its initial value and can gain sufficient buoyancy-force to float to the surface. Experiments have been carried out to simulate the growth of an air bubble in water under an ultrasonic pressure field. The experimental results of the bubble growth rate are compared with the results of the mathematical model which show a quite reasonable overall agreement between the experiments and the predictions.