Positional stability and radial dynamics of sonoluminescent bubbles under bi-harmonic driving: Effect of the high-frequency component and its relative phase

• SBSL in H2SO4 under bi-harmonic driving was experimentally and theoretically studied.
• The absence of sharp resonances peaks in the expansion ratio was numerically demonstrated.
• Numerical simulations of the main forces acting on the bubbles were performed.
• The effect of the order of the high-frequency harmonic component and its relative phase was studied.

The use of bi-frequency driving in sonoluminescence has proved to be an effective way to avoid the spatial instability (pseudo-orbits) developed by bubbles in systems with high viscous liquids like sulfuric or phosphoric acids. In this work, we present extensive experimental and numerical evidence in order to assess the effect of the high frequency component (PAcHF) of a bi-harmonic acoustic pressure field on the dynamic of sonoluminescent bubbles in an aqueous solution of sulfuric acid. The present study is mainly focused on the role of the harmonic frequency (Nf0) and the relative phase between the two frequency components (φbφb) of the acoustic field on the spatial, positional and diffusive stability of the bubbles. The results presented in this work were analyzed by means of three different approaches. First, we discussed some qualitative considerations about the changes observed in the radial dynamics, and the stability of similar bubbles under distinct bi-harmonic drivings. Later, we have investigated, through a series of numerical simulations, how the use of high frequency harmonic components of different order N  , affects the positional stability of the SL bubbles. Furthermore, the influence of φbφb in their radius temporal evolution is systematically explored for harmonics ranging from the second to the fifteenth harmonic (N=2–15N=2–15). Finally, a multivariate analysis based on the covariance method is performed to study the dependences among the parameters characterizing the SL bubble. Both experimental and numerical results indicate that the impact of PAcHF on the positional instability and the radial dynamics turns to be progressively negligible as the order of the high frequency harmonic component grows (i.e. N≫1N≫1), however its effectiveness on the reduction of the spatial instability remains unaltered or even improved.