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

摘要

Various models for interacting spherical bubbles in a compressible liquidbased on delay differential equations are considered. It is shown that mostpreviously proposed models for interacting spherical bubbles in a compressibleliquid based on the Keller-Miksis and Gilmore-Akulichev models are unstable forclosely spaced bubbles. A new model for a single spherical bubble in acompressible liquid is proposed and used to derive a stable model forinteracting bubbles. A qualitative comparison to the results of directnumerical integration of the fluid equations of motion suggests that the newmodel provides more accurate results than the standard Keller-Miksis orGilmore-Akulichev models for single bubble dynamics.