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arXiv · 1310.2895

Delay differential equation models for single and coupled bubble dynamics in a compressible liquid

Derek C. Thomas·Yurii A. Ilinskii·Mark F. Hamilton
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Abstract

Various models for interacting spherical bubbles in a compressible liquid based on delay differential equations are considered. It is shown that most previously proposed models for interacting spherical bubbles in a compressible liquid based on the Keller-Miksis and Gilmore-Akulichev models are unstable for closely spaced bubbles. A new model for a single spherical bubble in a compressible liquid is proposed and used to derive a stable model for interacting bubbles. A qualitative comparison to the results of direct numerical integration of the fluid equations of motion suggests that the new model provides more accurate results than the standard Keller-Miksis or Gilmore-Akulichev models for single bubble dynamics.

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Derek C. Thomas, Yurii A. Ilinskii, Mark F. Hamilton. 2013-10-10. Delay differential equation models for single and coupled bubble dynamics in a compressible liquid. https://doi.org/10.1121/1.4830554

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