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.
