Bubble response to the amplitude modulation signal near the threshold of dynamical stability

Abstract

There is a range of acoustic techniques for characterizing bubble populations within liquids [Leighton et al., Ultrasonics 34, 661–667 (1996)]. The linear resonant backscattering was the first detection technique. The great difference between the compressibility of gas in the bubble and surrounding liquid leads to the easy manifestation of nonlinear effects, the simplest of which is the presence of harmonics at 2ωp, 3ωp, etc., of the pure tone driving frequency ωp in the scattering signal. However, bubble pulsation of finite amplitude results not only in the harmonics generation. The nonlinear resonance characterized by multistable oscillation states arising from the saddle-node bifurcations is a significant example. The emphasis of this study is to propose a technique for bubble sizing by using the ability of a bubble as a nonlinear oscillatory system to amplify weak signals near the threshold of dynamical stability. The analytical as well as numerical solutions have been derived for the nonlinear bubble response to the modulation driving pressure. The magnitude and the form of the acoustical signal reradiated near the threshold of dynamical stability are drastically different from the modulation of incident wave and enable the characterization of the bubble population in liquid.