Bubble Dynamics

Part of the SpringerBriefs in Molecular Science book series (BRIEFSMOLECULAR)


Bubble pulsation is mathematically described by the Rayleigh–Plesset equation and by Keller equation. Derivation of the equations is fully described herein. Using the Rayleigh–Plesset equation, the violent collapse of a bubble is discussed. A method of numerical simulations of bubble pulsation is also described. In relation to numerical simulations, non-equilibrium evaporation and condensation of water vapor at the bubble wall, the variation in liquid temperature at the bubble wall, the gas diffusion across the bubble wall, and the chemical reactions inside a bubble are discussed. Comparison between numerical results and experimental data for a single-bubble system is shown. The main oxidants created inside a bubble are described based upon numerical simulations data. Linear and nonlinear resonance radius of a bubble is discussed as well as the analytical solution of the linearized equation of bubble pulsation. The mechanism of shock wave emission from a bubble into surrounding liquid is discussed. Inside a collapsing bubble, a shock wave is seldom formed due to lower temperature near the bubble wall. A liquid jet penetrates into a collapsing bubble near the solid surface. The bubble pulsation is influenced by the acoustic emissions from the surrounding bubbles, which is called bubblebubble interaction. The origin of acoustic cavitation noise is discussed based upon results of numerical simulations. It is shown that surfactants and salts strongly retard bubble–bubble coalescence.


Rayleigh–Plesset equation Keller equation Rayleigh collapse Resonance radius Shock wave Jetting Primary and secondary Bjerkens forces Bubble–bubble interaction Acoustic cavitation noise Acoustic streaming 


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.National Institute of Advanced Industrial Science and Technology (AIST)Moriyama-ku, NagoyaJapan

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