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Stable bubble oscillations beyond Blake's critical threshold.

Ferenc Hegedűs1

  • 1Department of Hydrodynamic Systems, Budapest University of Technology and Economics, P.O. Box 91, 1521 Budapest, Hungary.

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Summary

This study proves stable bubble oscillation under ultrasonic radiation, even without nonlinear restrictions. The findings advance understanding of bubble dynamics in low-pressure environments.

Keywords:
Bifurcation theoryBubble dynamicsContinuation techniqueNonlinear dynamicsRayleigh–Plesset equation

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Area of Science:

  • Fluid Dynamics
  • Acoustics
  • Nonlinear Dynamics

Background:

  • Spherical bubble equilibrium radius depends on mechanical balance.
  • Below Blake's critical threshold, bubbles lack an equilibrium state.
  • Previous research sought evidence for stable bubble oscillation under harmonic forcing using linearized models.

Purpose of the Study:

  • To rigorously prove the existence of stable bubble motion under harmonic forcing in low-pressure regimes.
  • To overcome limitations of previous linearized or weakly nonlinear models.
  • To demonstrate a method applicable to more complex bubble dynamics.

Main Methods:

  • Application of modern nonlinear and bifurcation theory.
  • Numerical techniques to analyze bubble dynamics.
  • Utilized the Rayleigh-Plesset equation as a foundational model.

Main Results:

  • Existence of stable bubble motion proven without restrictions on nonlinearities.
  • Demonstrated a robust method for analyzing nonlinear bubble dynamics.
  • Validated theoretical predictions with numerical evidence.

Conclusions:

  • Stable bubble oscillation is achievable in low-pressure environments using ultrasonic radiation.
  • The employed nonlinear and bifurcation theory provides a powerful tool for bubble dynamics research.
  • The presented technique is extensible to more sophisticated bubble models.