Analysis of time delay effects on a linear bubble chain system

Abstract

A chain of vertically rising discrete air bubbles represents a transition phenomenon from individual to continuum behavior in a bubbly liquid. Previous studies have reported that there is a preference for acoustic energy to propagate along the bubble chain and that this behavior could be explained by a coupled-oscillator model. However, it has recently been demonstrated that quantitative results from the coupled-oscillator model do not match experimental data. In this paper, it is shown how adding time delays to the coupled-oscillator model can produce results that are in better agreement with experimental data. In addition, the effects of time delays on the natural frequencies and damping o..