Acoustical scattering cross section of gas bubbles under dual-frequency acoustic excitation

The acoustical scattering cross section is a paramount parameter determining the scattering ability of cavitation bubbles when they are excited by the incident acoustic waves. This parameter is strongly related with many important applications of acoustic cavitation including facilitating the reaction of chemical process, boosting bubble sonoluminescence, and performing non-invasive therapy and drug delivery. In present paper, both the analytical and numerical solutions of acoustical scattering cross section of gas bubbles under dual-frequency excitation are obtained. The validity of the analytical solution is shown with demonstrating examples. The nonlinear characteristics (e.g., harmonics, subharmonics and ultraharmonics) of the scattering cross section curve under dual-frequency approach are investigated. Compared with single-frequency approach, the dual-frequency approach displays more resonances termed as "combination resonances" and could promote the acoustical scattering cross section significantly within a much broader range of bubble sizes due to the generation of more resonances. The influence of several paramount parameters (e.g., acoustic pressure amplitude, power allocations between two acoustic components, and the ratio of the frequencies) in the dual-frequency system on the predictions of scattering cross section has been discussed.