Oscillatory dynamics of a charged microbubble under ultrasound

摘要

Nonlinear oscillations of a bubble carrying a constant charge and suspended in a fluid, undergoing periodic forcing due to incident ultrasound are studied. The system exhibits period-doubling route to chaos and the presence of charge has the effect of advancing these bifurcations. The minimum magnitude of the charge e?‘?min above which the bubblea€?s radial oscillations can occur above a certain velocity e?‘?1 is found to be related by a simple power law to the driving frequency e??” of the acoustic wave. We find the existence of a critical frequency $e??”_{H}$ above which uncharged bubbles necessarily have to oscillate at velocities below $c_{1}$. We further find that this critical frequency crucially depends upon the amplitude $P_{s}$ of the driving acoustic pressure wave. The temperature of the gas within the bubble is calculated. A critical value e?‘?tr of $P_{s}$ equal to the upper transient threshold pressure demarcates two distinct regions of e??” dependence of the maximal radial bubble velocity e?‘￡max and maximal internal temperature e?‘?max. Above this pressure, e?‘?max and e?‘￡max decrease with increasing e??”, while below e?‘?tr, they increase with e??”. The dynamical effects of the charge, the driving pressure and frequency of ultrasound on the bubble are discussed.