Nonlinear dynamical interaction between insonified microbubbles

Microbubbles are expected to be applied for ultrasonic therapy. In this research, considering two neighboring bubbles, we added to the Rayleigh-Plesset equation the term of nonlinear influence corresponding to pressure change caused by the neighboring bubbleâTMs oscillation, and numerical simulation was performed. It is known that the natural frequency of a microbubble decreases with increasing the bubblesâTM density. This fact agrees with our analytical prediction based on the Rayleigh-Plesset equation. Further, the natural frequency also depends on the diameter ratio of the two bubbles. Our numerical results show that superharmonic response reaches a peak at some distance between bubbles when they are driven at half their resonance frequency with their ratio of the natural frequency being two to one. Numerical simulation also shows that if the two bubbles of the same size exist at a close distance, the occurrence region of the subharmonics is larger than that of a single bubble.