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 Q min above which the bubble’s radial oscillations can occur above a certain velocity c 1 is found to be related by a simple power law to the driving frequency ω of the acoustic wave. We find the existence of a critical frequency ω 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 P tr of P s equal to the upper transient threshold pressure demarcates two distinct regions of ω dependence of the maximal radial bubble velocity v max and maximal internal temperature T max. Above this pressure, T max and v max decrease with increasing ω, while below P tr, they increase with ω. The dynamical effects of the charge, the driving pressure and frequency of ultrasound on the bubble are discussed.
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TH acknowledges support through Rajiv Gandhi National Fellowship from the University Grants Commission, New Delhi.
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HONGRAY, T., ASHOK, B. & BALAKRISHNAN, J. Oscillatory dynamics of a charged microbubble under ultrasound. Pramana - J Phys 84, 517–541 (2015). https://doi.org/10.1007/s12043-014-0846-y
- Charged bubble dynamics
- acoustic cavitation
- nonlinear oscillations
- bifurcation diagrams
- largest Lyapunov exponents