High-resolution bubble sizing through detection of the subharmonic response with a two-frequency excitation technique

Sizing bubbles in fluid using a two-frequency excitation technique is not prone to the same drawbacks of some other sizing methods—it has a global maximum at the bubble resonance frequency and allows good spatial resolution. The bubble is insonated with a high fixed imaging signal and a variable pumping signal tuned to the resonant frequency of the bubble, which are coupled at resonance by the high-amplitude oscillation of the bubble wall, with the formation of sum-and-difference terms. This paper examines both the resonance and off-resonance behavior of such combination frequency signals. A coupling of the subharmonic bubble response with the imaging frequency is shown to be a much more accurate and unambiguous detector of the bubble resonance than couplings involving the fundamental resonance. The characteristics of this subharmonic signal are examined using an automated sizing method, and the dependence of the response on the pumping signal amplitude and the frequency step size between two successive pumping frequencies is examined. The location of a definite subharmonic threshold is reported and quantified both for single bubbles held on a wire and for free rising bubbles moving through the focus of the transducers. This amplitude is found to be orders of magnitude lower than that predicted by traditional volumetric pulsation models, but agrees very closely with the theoretical onset of surface waves.