Stability analysis of the effect of harmonic waves on the shape stability of acoustic cavitation bubbles.

A liquid irradiated with high-power ultrasound generates harmonics and broad-band noise. The effect of ultrasound-containing harmonics on the bubble shape stability was numerically investigated in this study by solving the Keller-Miksis equation and the dynamic equation of distortion amplitude to identify the effect of harmonics on the equilibrium bubble size of acoustic cavitation. Numerical results indicated that the tendency of bubble stability changed for low- and high-pressure amplitudes, which could be attributed to decrease in the bubble expansion because of harmonic waves at high-pressure amplitude. The cavitation bubble became more unstable under low-pressure amplitude conditions, and more stable at high-pressure amplitude conditions because of harmonics; however, the discrepancy in the stable zones was small. The bubble wall velocity contributed to bubble stability under both amplitude conditions. The magnitude of the maximum bubble wall velocity increased with harmonic waves for the small pressure-amplitude conditions, resulting in an unstable bubble shape. The time that the bubble wall spent moving at high velocity was shortened with increasing harmonic waves under the high-pressure amplitude conditions, causing a stable bubble shape. Further, the phase shift of the harmonic wave affected bubble stability; bubble expansion was largely suppressed, and the bubble became more stable with an increase in the minimum pressure of the composite wave.