Free decay of shape oscillations of bubbles acoustically trapped in water and sea water

Abstract

Asymptotic results for the free decay of shape oscillations of viscous liquid spheres have been extended to include higher-order terms in the ratios of the inner and outer viscous penetration lengths to the radius. The new expressions are shown to be important for studies in which the two fluids have dissimilar densities and viscosities such as air/liquid systems. The analysis also includes an expansion for the frequency of maximum response of driven oscillations. The calculations are supported by measurements of the small-amplitude quadrupole mode free decay of nearly spherical bubbles acoustically levitated in clean water. The bubble radii ranged from 400 μm to 1400 μm. The results are interpreted in light of the initial-value problem. The lack of excess damping suggests that the interface behaves ideally for times up to two hours after bubble injection. Measurements were also carried out on bubbles in 0.5 m NaCl solution and in sea water. Larger bubbles (radius > 800 μm) in clean water exhibit damping two to four times larger than predicted by theory. The transition from this anomalous damping to theoretical damping is a very abrupt function of radius. All observations were carried out with similar acoustic fields for counteracting buoyancy. The excess damping appears to be associated with some nonlinear response of the bubble.