Nonlinear resonance of bubble cluster driven by ultrasound
Abstract
Due to the effects of secondary pressure radiation in bubble cluster, bubbles undergo coupled oscillation. Based on the dynamic equation of coupled oscillation, the nonlinear acoustic response of bubbles are research by an asymptotic method. The resonance response of bubbles are determined by the intrinsic properties of bubbles, such as the initial radius, the size of the bubble cluster, and the density distribution of bubbles in the cluster. Therefore, for a given bubble cluster, there is one natural resonance frequency. When bubbles in a cluster are driven to oscillate by ultrasound, some resonance regions can come into being. The acoustic response of bubbles has fundamental mode, first and second harmonics, first and second subharmonics. In term of the analytical expression of oscillating amplitude for the five modes, we analyzed the acoustic resonance in different frequency regions (<italic>w</italic> ≈<italic>w</italic><sub>0</sub>, <italic>w</italic> ≈<italic>w</italic><sub>0</sub>/2, <italic>w</italic> ≈<italic>w</italic><sub>0</sub>/3, <italic>w</italic> ≈2<italic>w</italic><sub>0</sub> and <italic>w</italic> ≈3<italic>w</italic><sub>0</sub>). The amplitude of each mode is affected by the intensity and frequency of ultrasound.The fundamental response of bubbles is easier to observe than other modes because it occurs at relatively low acoustic pressure. With the increase of the acoustic pressure, the response of bubbles goes from linear regime to nonlinear regime. When bubbles oscillate in nonlinear regime, the resonance response frequency will not be equal to the natural resonance one exactly, and a frequency region of multiple oscillating amplitude may exist according to the analytical expression of oscillating amplitude. The response of bubbles is also affected by the density of bubble numbers in cluster and the initial radius when of bubbles, while the effect of the relative position in the bubble cluster can be neglected. The resonance phenomena come into being after the driving pressure exceeds the thresholds for the sub-harmonics mode. With the increment of the equivalent radius of bubbles, the pressure thresholds related to of sub-harmonics resonance will decrease.
