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 of individual eigenmodes of the vertical bubble chain are also investigated. It was found that adding time delays can dramatically change the damping of the different modes of the system while having less dramatic impact on the natural frequencies of the individual eigenmodes. Counterintuitively, it is found that the effects of time delays appear to be more important when the bubbles are closer together than when they are farther apart.

Eigenmodal resonances of polydisperse bubble systems on a rigid boundary

“…More recently, systems consisting of many interacting bubbles have been studied by various investigators. [6][7][8][9][10][11][12][13][14][15] A short review of some recent studies can be found in the article by Manasseh and Ooi. 16 As one might expect, bubbles can interact acoustically with each other, causing the natural frequencies of the system to change from that of isolated bubbles, and it was found that the interaction has a greater effect when the bubbles are closer.…”

Ultrasound contrast agents: bubbles drops and particles

“…During the subsequent transportation, vortical flow structures displayed by the detached liposomes were captured in this study (results not shown here). These flow structures and the flow velocity are on the same order of magnitude as previously reported micro-scale steady streaming generated around an oscillating bubble 190,199,208 . A further calculation of the Stokes number (S t ) for the liposomes based on the experimental conditions gives S t ≈ 0.01 (« 1), implying that the shed particles can closely follow the streaming field generated by an oscillating MB.…”

Measurement of pressure on a surface using bubble acoustic resonances

“…The concept of an image bubble was originally introduced by [Strasberg, 1953], who used an approximation intended to deal with the issues of multiple re-reflexions. However, in order to compare pressure measurements with theory, a coupled-oscillator model under the self-consistent assumption [Tolstoy, 1986, Feuillade, 2001, Allen et al, 2003, Ida, M. et al, 2007, Yasui, K. et al, 2009, Ooi et al, 2008 gives an exact prediction.This image theory assumes a rigid boundary. The stress required to deform the boundary by a significant fraction of the bubble radius is orders of magnitude greater than the pressures created by the bubble response and so the boundary in the present experiment is considered rigid.…”

“…The factor 2/3 is approximately 0.816. Strasberg (1953) calculated a factor of 0.833 by a completely different method that is an approximation if pressure is measured, whereas (6) is in principle exact; the difference between the theories is discussed in detail in [Manasseh & Ooi 2009]. It is worth noting that as the number of bubbles increases, the number of possible modes of oscillation increases, giving rise to unusual, anisotropic propagation of sound ( [Manasseh et al, 2004, Leroy et al, 2005, Nikolovska et al, 2007).…”