Fast bubble dynamics and sizing

Single bubble sizing is usually performed by measuring the resonant bubble response using the Dual Frequency Ultrasound Method. However, in practice, the use of millisecond-duration chirp-like waves yields nonlinear distortions of the bubble oscillations. In comparison with the resonant curve obtained under harmonic excitation, it was observed that the bubble dynamic response shifted by up to 20 percent of the resonant frequency with bubble radii of less than 100 μm. In the case of low pressure waves (P<5kPa), an approximate formula for the apparent frequency shift is derived. Simulated and experimental bubble responses are analyzed in the time-frequency domain using an enhanced concentrated (reassigned) spectrogram. The difference in the resonant frequency resulted from the persistence of the resonant mode in the bubble response. Numerical simulations in which these findings are extended to pairs of coupled bubbles and to bubble clouds are also presented.