Harmonic Analysis of the Scattered Pressure Field from a Single Bubble

Abstract

Pressure measurements were made on the first- and second-harmonic pressure fields scattered from single bubbles stable in a 20-kc/sec sound field at ambient-pressure amplitudes PA up to about 0.8 atm. The second-harmonic amplitude p2 proves to be a sensitive indicator of bubble behavior. Though p2 is usually an increasing function of PA at low amplitudes, tending to rise as PA2, pronounced exceptions are noted. Critical ranges of PA exist where p2 decreases, then increases rapidly, with increasing PA. In a critical range, obvious hissing occurs; in visual observations, a number of “microbubbles” (i.e., bubbles of diameter ≃15 μ or less) are seen near the original bubble. These microbubbles are generated when vigorous surface modes are set up on the original bubble, as described earlier by Willard. When PA increases to values of the order of 0.8 atm, the amplitudes of both first and second harmonics appear to approach limiting values, while higher harmonics and a subharmonic appear. A theory for the second harmonic was derived, assuming successive approximations to the Noltingk-Neppiras equation. The result for p2 is of the form DPA2, where D depends on frequency and bubble radius. [Supported in part by NIH Grant RG-8209.]