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Bubble interaction model for hydrodynamic unstable mixing.

Sung-Ik Sohn1

  • 1Department of Mathematics, Kangnung National University, Kangnung 210-702, Korea. sohnsi@kangnung.ac.kr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 7, 2007
PubMed
Summary

This study introduces an analytic model for Rayleigh-Taylor mixing, accurately predicting single and multiple bubble evolution. The model reveals key dynamics like bubble competition and provides insights into growth coefficients and self-similar behaviors.

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Area of Science:

  • Fluid dynamics
  • Plasma physics
  • Astrophysical phenomena

Background:

  • Rayleigh-Taylor (RT) instability is crucial in various physical systems, including inertial confinement fusion and astrophysical processes.
  • Understanding bubble evolution in RT mixing is essential for accurate modeling and prediction.
  • Existing models often struggle with arbitrary density ratios and complex multi-bubble interactions.

Purpose of the Study:

  • To develop an analytic model for single and multiple bubble evolution in Rayleigh-Taylor mixing across arbitrary density ratios.
  • To extend Zufiria's potential theory for enhanced predictive capabilities.
  • To investigate bubble competition dynamics and scaling laws.

Main Methods:

  • Extension of Zufiria's potential theory using velocity potential with point sources.
  • Derivation of solutions for single bubble velocity and curvature.
  • Analysis of multiple bubble interactions, including competition and growth dynamics.
  • Investigation of scaling laws and self-similar behavior in bubble evolution.

Main Results:

  • The analytic model shows good agreement with numerical results for single bubble velocity and curvature.
  • The model captures the dynamics of bubble competition, where larger bubbles consume smaller ones.
  • The growth coefficient (alpha) depends on the Atwood number and perturbation amplitude.
  • Bubble aspect ratio exhibits self-similar behavior, independent of the Atwood number.

Conclusions:

  • The developed analytic model provides a robust framework for studying Rayleigh-Taylor mixing.
  • The model accurately predicts key parameters like bubble growth and competition dynamics.
  • Findings offer valuable insights for simulations and experiments in fluid dynamics and astrophysics.