Near resonant bubble acoustic cross-section corrections, including examples from oceanography, volcanology, and biomedical ultrasound

Abstract

The scattering cross-section sigma(s) of a gas bubble of equilibrium radius R(0) in liquid can be written in the form sigma(s)=4piR(0) (2)[(omega(1) (2)omega(2)-1)(2)+delta(2)], where omega is the excitation frequency, omega(1) is the resonance frequency, and delta is a frequency-dependent dimensionless damping coefficient. A persistent discrepancy in the frequency dependence of the contribution to delta from radiation damping, denoted delta(rad), is identified and resolved, as follows. Wildt's [Physics of Sound in the Sea (Washington, DC, 1946), Chap. 28] pioneering derivation predicts a linear dependence of delta(rad) on frequency, a result which Medwin [Ultrasonics 15, 7-13 (1977)] reproduces using a different method. Weston [Underwater Acoustics, NATO Advanced Study Institute Series Vol. II, 55-88 (1967)], using ostensibly the same method as Wildt, predicts the opposite relationship, i.e., that delta(rad) is inversely proportional to frequency. Weston's version of the derivation of the scattering cross-section is shown here to be the correct one, thus resolving the discrepancy. Further, a correction to Weston's model is derived that amounts to a shift in the resonance frequency. A new, corrected, expression for the extinction cross-section is also derived. The magnitudes of the corrections are illustrated using examples from oceanography, volcanology, planetary acoustics, neutron spallation, and biomedical ultrasound. The corrections become significant when the bulk modulus of the gas is not negligible relative to that of the surrounding liquid.

Quantification of undersea gas leaks from carbon capture and storage facilities, from pipelines and from methane seeps, by their acoustic emissions

“…At sea, there could be a wealth of phenomena (such as the effect of the chemical constituents on the bubble damping and stiffness) not covered by theory, while in the laboratory there are often many phenomena (such as tank reverberation) which can affect these relationships (Leighton et al 2002). Effects which are significant on single bubble dynamics (such as the generation of nonlinearities, Leighton et al 2004) or damping (Ainslie & Leighton 2009) can, when incorporated into populations of bubbles to determine the overall effect, have only modest influences. The effect on gas flux estimates when the suggested perturbations to the Minnaert relationship and bubble damping were included in the forward problem (to generate the acoustic spectrum) but neglected in the inversion (as if the experimenters were in ignorance that such an effect had occurred) were assessed here and found to be large, indicating the importance of identifying real factors affecting the passive acoustic emissions from the ocean bubbles in question, and distinguishing them from artefacts (e.g.…”

“…The bubble has a vector position x 0 with respect to the origin in a liquid (assumed to be incompressible) of density r 0 . In the limit of small amplitude oscillations, and for kR 0 1 (valid assumptions for most ocean gas bubbles pulsating at their natural frequencies; Ainslie & Leighton 2009), this approach can be used to find the time history of the pressure measured at vector position x, where x − x 0 = r. Assume for the moment that the bubble wall motion is simple harmonic and undamped, at some angular frequency u. The instantaneous value of the radius is R(t) and this oscillates about the equilibrium position R 0 .…”

Dolphin-Inspired Target Detection for Sonar and Radar

“…Humans have spent over a century researching this interaction for a range of applications (Ainslie, Leighton, 2009). These include attempts to derive beneficial effects from bubble acoustics, in fields as diverse as: climate science for air/sea transfer (Thorpe, 1992 ; the processing and monitoring of pharmaceuticals and food (Campbell, Mougeot, 1999;Skumiel et al, 2013), and of fuel and coolant (Leighton et al, 2012a); the generation of microfluidic devices (Carugo et al, 2011); ultrasonic cleaning (Leighton et al, 2005;Offin et al, 2014); and, in biomedicine, the provision of acoustic contrast agents and drug delivery vectors (Ferrara et al, 2007), and the use of cavitation as a therapy monitor (McLaughlan et al, 2010;Leighton et al, 2008a).…”

An Inversion of Acoustical Attenuation Measurements to Deduce Bubble Populations

“…This information is provided in an appendix because it does not affect the method described in this paper, although anyone using this method must carry out these calculations. The recent publications by Ainslie andLeighton (2009, 2011) have summarized some of the inconsistencies in the literature surrounding the damping calculations and provide advice on the most appropriate methods in different circumstances.…”