A model is developed to calculate the distribution of first-order velocity field caused by the coupled bubbles in an ultrasound field. Using this model, numerical investigations of velocity field have been made when the two identical bubbles are driven well below resonance by an acoustic field with pressure amplitude exceeding cavitation threshold. Three representative kinestates of the coupled bubbles were chosen for analyzing the velocity distribution of surrounding liquid. The results show that the nonlinear oscillations of a bubble pair affect violently the radial velocity distribution of surrounding liquid, especially in the expanding phase. Symmetry of the tangential velocity distribution implies a possibility of attraction or repulsion of the bubble pairs.
Using an appropriate approximation, we have formulated the interacting equation of multi-bubble motion for a system of a single bubble and a spherical bubble cluster. The behavior of the bubbles is observed in coupled and uncoupled states. The oscillation of bubbles inside the cluster is in a coupled state. The numerical simulation demonstrates that the secondary Bjerknes force can be influenced by the number density, initial radius, distance, driving frequency, and amplitude of ultrasound. However, if a bubble approaches a bubble cluster of the same initial radii, coupled oscillation would be induced and a repulsive force is evoked, which may be the reason why the bubble cluster can exist steadily. With the increment of the number density of the bubble cluster, a secondary Bjerknes force acting on the bubbles inside the cluster decreases due to the strong suppression of the coupled bubbles. It is shown that there may be an optimal number density for a bubble cluster which can generate an optimal cavitation effect in liquid for a stable driving ultrasound.
The dynamic responses of bubbles in ultrasonic field include the radial vibration, translation, and their interactions. Based on the radial vibration modal where the secondary radiation of neighboring bubbles was considered, and interaction forces of bubbles, the coupled motions of two bubbles with different size in a plane ultrasonic field was simulated numerically. The results show that the radial vibration of a big bubble has natural properties and its translation velocity is rapid relatively. The behavior and distribution of bubbles was observed experimentally by using high speed photography. It is shown that the big bubbles translate rapidly in bubble clouds and vibrate radially with small-amplitude. On the other hand, the phenomena of attraction and coalescence among bubbles is observed, which may attribute to the effects of secondary radiation between neighboring bubbles.
