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

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.