Acoustically forced oscillations of air bubbles in water: Experimental results

Abstract

An experimental technique for measuring the time-varying response of an oscillating, acoustically levitated air bubble in water is developed. The bubble is levitated in a resonant cell driven in the (r,θ,z) mode of (1,0,1) at a frequency fd≊24 kHz. Linearly polarized laser light (Ar–I 488.0 nm) is scattered from the bubble, and the scattered intensity is measured with a suitable photodetector positioned at some known angle from the forward, subtending some solid acceptance angle. The output photodetector current, which is linearly proportional to the light intensity, is converted into a voltage, digitized, and then stored on a computer for analysis. For spherical bubbles, the scattered intensity Iexp(t) as a function of radius R and angle θ is calculated theoretically by solving the boundary value problem (Mie theory) for the water/bubble interface. The inverse transfer function R(I) is obtained by integrating over the solid angle centered at some constant θ. Using R(I) as a look-up table, the radius versus time [R(t)] response is calculated from the measured intensity versus time [Iexp(R,t)]. Fourier and phase space analyses are applied to individual R(t) curves. Resonance response curves are also constructed from the R(t) curves for equilibrium radii ranging from 20 to 90 microns, and harmonic resonances are observed. Comparisons are made to a model for bubble oscillations developed by Prosperetti et al. [Prosperetti et al., J. Acoust. Soc. Am. 83, 502 (1988)]. Complex Iexp(t) behavior is also measured, with subharmonics and broadband noise apparent in the Fourier spectra. Possible explanations for this phenomenon are discussed, including shape oscillations and chaos.