Dynamics of acoustic resonance scattering from spherical targets: Application to gas bubbles in fluids

Abstract

In this study we investigate the dynamics of surface motion of a penetrable spherical body subjected to an incident plane acoustic wave. The results should be valid for objects of rather general internal consistency, since they are based on quite basic physical considerations, but they are illustrated here by the example of a gas bubble in a fluid. It is shown that surface waves generated in the scattering process circumnavigate the target sphere and, by a process of in-phase "resonance reinforcement," excite its multipole resonances at those eigenfrequencies at which n + 1/2 wavelengths (n being an integer) span the circumference. Phase matching is achieved here due to the fact that the surface wave suffers a phase jump of •r/2 at each of the two "caustic points" on the sphere at which the surface waves converge. Surface motions and circumferential waves on the bubble are graphically demonstrated, both on and off resonance. It is shown that the resonance manifests itself by a large-amplitude angular oscillation of the gas contained in the bubble.

Theory of Resonance Scattering

“…A detailed proof of this will now be given for the case of a spherical object (Murphy et aL, 1979;Uberall et aL, 1979). A detailed proof of this will now be given for the case of a spherical object (Murphy et aL, 1979;Uberall et aL, 1979).…”

“…In recent papers Uberall et aL, 1979;Gaunaurd and Uberall, 1980) the resonance theory has been applied to sound scattering from bubbles. The mentioned corrections were here not taken into account so that the theory applies to large bubbles only.…”

Shell waves and acoustic scattering from ultrasound contrast agents

“…The theory of acoustic scattering from spherical targets such as gas bubbles has been the subject of multiple studies [6]- [8]. This approach lends itself directly to investigating the contributions of the additional eigenfrequencies of the scattering object in the linear acoustic regime.…”

“…It is often difficult in scattering calculations to distinguish the scattering resonances from the background. To isolate the resonance peaks from the scattering background, theories such as "Resonance Scattering Theory" (RST) have been developed [6], [8], [12]. The implementation of this theory involves the subtraction of an appropriate background, which mimics how the object would behave as a rigid or soft scatter, to isolate the resonance peaks.…”

“…This approach lends itself directly to investigating the contributions of the additional eigenfrequencies of the scattering object in the linear acoustic regime. A comprehensive study of the acoustic scattering of gas bubbles, including thermal and viscous damping, was undertaken by Nishi [7].Überall et al [8] examined the higher order multipole scattering response of a gas bubble, Ye [9] implemented one of the first modal acoustic scattering solutions for contrast agents.…”