A simple model of bubble cluster dynamics in an acoustic field

The dynamics of bubble clouds induced by ultrasound field are investigated in a regime where the cloud size is much smaller than the ultrasound wavelength. Two frequently used models describing the dynamics of individual bubbles inside a bubble cluster in an acoustic field are studied, one based on the homogeneity assumption, and the other based on the simultaneous motion assumption. A modified formula of the homogenization-based model is presented, and an inherent distinction in bubble-bubble interaction term is found in comparison to the simultaneous motion model. To gain insight into the mechanisms of such distinction, a reduced model unifying these two models is presented, and such distinction is explained by the spatial dependence of the bubble-bubble interaction in a bubble cluster accordingly. To validate the reduced model, the normalized distance γ_bb and the cloud interaction parameter B₀ are used as two scaling parameters, and the comparison between the present model and the coupled Rayleigh-Plesset type equations is made. A conclusion is that, in the weak bubble-bubble interaction case (γ_bb>10), the reduced model can well reproduce the radial motion of bubbles in the cluster during the growth stage and the collapse stage in each acoustic cycle; in the strong bubble-bubble interaction case (γ_bb<10), the growth phase of bubbles in the cluster can be accurately predicted by the reduced model only if B₀ or the amplitude of driving field is small.