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Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

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Published on: May 9, 2021

Nonlinear normal modes and localization in two bubble oscillators.

Naohiro Sugita¹, Toshihiko Sugiura¹

¹Department of Mechanical Engineering, Keio University, Yokohama 2238522, Japan.

|November 7, 2016

Summary

This study reveals energy localization in coupled bubble oscillations due to symmetry breaking. Localized nonlinear normal modes (NNMs) explain this phenomenon in acoustic fields.

Keywords:

Bubble dynamics Coupled nonlinear oscillation Nonlinear localization Nonlinear normal modes Perturbation analysis

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Area of Science:

Acoustics
Nonlinear Dynamics
Fluid Mechanics

Background:

Coupled nonlinear oscillations of bubbles in acoustic fields are complex phenomena.
Understanding energy localization is crucial for predicting bubble behavior.

Purpose of the Study:

To investigate the bifurcation structure of coupled nonlinear oscillations in two spherical gas bubbles.
To describe the energy localization phenomenon resulting from symmetry-breaking bifurcation.

Main Methods:

Nonlinear modal analysis was employed.
Approximate asymptotic solutions were derived using the method of multiple scales.
Analytical solutions were validated against numerical results.

Main Results:

Localized oscillation arises near localized nonlinear normal modes (NNMs).
Analytical and numerical results for steady-state oscillations show good agreement for small amplitudes.
A bifurcation diagram illustrates localized solutions for larger amplitudes, considering driving frequency, bubble separation, and thermal damping.

Conclusions:

Energy localization is a key feature of coupled bubble oscillations in acoustic fields.
The findings are relevant for practical experiments and simulations involving bubble dynamics.