Experimental Observation of the Nonlinear Response of Single Bubbles to AN Applied Acoustic Field.

An experimental technique for measuring the time -varying response of an oscillating, acoustically levitated bubble in water is developed. The bubble is levitated in a cell consisting of two concentric, cylindrical, piezoceramic transducers mounted on either end of a short glass tube. The entire apparatus forms, a closed-open cylindrical tube which is driven in the (r{,}theta {,}z) mode of (1,0,1) at a frequency f~24 kHz. Linearly polarized laser light (He-Ne 632.8, Ar-I 488.) 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. The scattered intensity I_{exp}(t) thus obtained contains, in principle, all of the dynamical information about the oscillating bubble, and various methods of analysis are employed to examine the behavior. For spherical bubbles, the scattered intensity I as a function of radius R and angle theta 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 theta . Using R(I) as a look-up table, the radius vs time (R(t)) response is calculated from the measured intensity vs time (I_ {exp}(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. (A. Prosperetti, L. A. Crum, and K. Commander, J. Acoust. Soc. Am. 83, 502 (1988)). Complex I_{exp}(t) behavior is also measured, with subharmonics and broad -band noise apparent in the Fourier spectra. This behavior is shown to exhibit high (>2) correlation dimension, indicating the presence of more than one degree of freedom in the motion. Possible explanations for this phenomenon are discussed, including shape oscillations and chaos.