The secondary Bjerknes force between two gas bubbles under dual-frequency acoustic excitation

• Both analytical and numerical solutions of secondary Bjerknes force under dual-frequency sonic waves are obtained.
• Complicated patterns of the sign change of secondary Bjerknes force under dual-frequency excitation are revealed.
• Harmonics, subharmonics, and combination resonances are shown in dual-frequency approach.
• The influence of pressure amplitude, bubble distance and phase difference is discussed.

The secondary Bjerknes force is one of the essential mechanisms of mutual interactions between bubbles oscillating in a sound field. The dual-frequency acoustic excitation has been applied in several fields such as sonochemistry, biomedicine and material engineering. In this paper, the secondary Bjerknes force under dual-frequency excitation is investigated both analytically and numerically within a large parameter zone. The unique characteristics (i.e., the complicated patterns of the parameter zone for sign change and the combination resonances) of the secondary Bjerknes force under dual-frequency excitation are revealed. Moreover, the influence of several parameters (e.g., the pressure amplitude, the bubble distance and the phase difference between sound waves) on the secondary Bjerknes force is also investigated numerically.