, Volume 84, Issue 4, pp 517–541 | Cite as

Oscillatory dynamics of a charged microbubble under ultrasound

  • J BALAKRISHNANEmail author


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.


Charged bubble dynamics acoustic cavitation nonlinear oscillations bifurcation diagrams largest Lyapunov exponents 


05.45.−a 05.90.+m 



TH acknowledges support through Rajiv Gandhi National Fellowship from the University Grants Commission, New Delhi.


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Copyright information

© Indian Academy of Sciences 2014

Authors and Affiliations

  1. 1.School of PhysicsUniversity of HyderabadHyderabadIndia
  2. 2.Centre for Complex Systems and Soft Matter PhysicsInternational Institute of Information Technology-BangaloreBangaloreIndia
  3. 3.School of Natural Sciences and Engineering, National Institute of Advanced StudiesIndian Institute of Science CampusBangaloreIndia

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