Resonances of deformed gas bubbles in liquids

Abstract

A T-matrix expansion technique has been used to investigate the monopole acoustical resonances of bubbles deformed into elongated axisymmetric objects (specifically: prolate spheroids and cylinders with hemispherical endcaps). The bubbles are modeled as air-filled inclusions in water. Scattering occurs because of the change of acoustical impedance at the interface between the two media. The results confirm that the resonance frequency of a bubble increases when it is deformed from a spherical shape. It increases more quickly with aspect ratio for cylindrical than for prolate spheroidal bubbles. The resonance frequency is also independent of the direction of excitation. For both cylindrical and prolate spheroidal bubbles the frequency width of the resonance increases with the deformation; but the corresponding values of Q fall more quickly for the cylindrical bubble. The scattering amplitude also decreases with the deformation, especially for endfire incidence. The angular distribution of acoustic scattering changes with the shape of the bubble. For spheroidal bubbles there is relatively little change from the spherical pattern obtained with an undeformed bubble; but for cylindrical bubbles the scattering may be irregular, with pronounced lobes in the broadside direction.

Broadband Models for Predicting Bistatic Bottom, Surface, and Volume Scattering Strengths

“…However, near resonance, it has been shown that the acoustic response, whether assuming a spherical, spheroidal, or cylindrical air-bubble model, generally varies by at most 30% [47][48]. Accordingly, as a first approximation we consider a spherical swimbladder, and then introduce corrections to account for real fish.…”

Acoustic Scattering by Axisymmetric Finite-Length Bodies: An Extension of a 2-Dimensional Conformal Mapping Method

“…In addition, low ka resonance scattering by gaseous bodies of higher aspect ratio (up to 100:1) was calculated with no difficulties relative to the numerical issues cited earlier. These ratios are much higher than what 39 has previously appeared in the literature (Strasberg, 1953;Weston, 1967;Feuillade and Werby, 1994;Ye and Hoskinson, 1998) There is great potential for further development of this model, including application to acous-tic scattering by elastic solids and shells. The implementation of better numerical integration techniques, the use of extended precision format of floating point arithmetic or various smoothing techniques (Yamashita, 1990) could delay the onset of ill-conditioned matrices, accelerating convergence.…”

“…Predictions from the T-matrix method and FMM are compared in Fig. 13 for aspect ratios up to 16:1; however, results for aspect ratios up to 20:1 were presented by Feuillade and Werby (1994) using the T-matrix method, as well as Ye and Hoskinson (1998) using the exact prolate spheroidal solution. In addition, low ka resonance scattering by gaseous bodies of higher aspect ratio (up to 100:1) was calculated with no difficulties relative to the numerical issues cited earlier.…”

“…Thus, the Oe in ha* is the equivalent spherical radius of the object, corresponding to the radius of the sphere (the 1:1 case shown) that has the same volume as the prolate spheroid. Results for aspect ratios up to 20:1 were tabulated by Feuillade and Werby (1994) using the T-matrix method, as well as Ye and Hoskinson (1998) using the exact prolate spheroidal solution.…”

Using one-dimensional waveguide resonators to measure phase velocities in bubbly liquids

“…Small variations from spherical conditions are not believed to significantly affect the bubble res-onance 18 since a prolate spheroid of aspect ratio of 1.414 only varies in resonance frequency and damping from a spherical bubble by less that 1%. 19 The volume of each balloon was measured through the water it displaced when submerged, then the equivalent spherical radius was determined as the radius that would displace the same volume of water. Six balloons with equivalent spherical radii of 2 cm were attached to a monofilament nylon line so that there was an L/6 distance between each balloon and an L/12 distance between each end balloon and a termination, where L is the length of the water column in the pipe.…”