Effects of translational motion on the Bjerknes forces of bubbles activated by strong acoustic waves

The motion of a small cavitation bubble is influenced by a neighboring large bubble, and these two bubbles can be mutually attractive or repulsive. The state of the bubble pair is strongly related to the secondary Bjerknes force in a strong acoustic field. Non-spherical oscillations are easily observed when a small cavitation bubble approaches a large bubble. The effects of translational motion and non-spherical oscillations of the small cavitation bubble on the secondary Bjerknes force are considered numerically in this paper, at large (greater than20 μm) and small (3 μm) bubble pair sizes. We show that the radial oscillation of the cavitation bubble is suppressed by the large bubble when the two are close to each other, and the magnitude and direction of the secondary Bjerknes force on the cavitation bubble are significantly different to those predicted results without considering translational motion. With the increase in size of the large bubble, the value of the secondary Bjerknes force varies from negative to positive, implying a transition between attraction and repulsion. The secondary Bjerknes force is sensitive to changes in the size of the large bubble, as there are many spikes in the curve in the range 20 μm < R10 < 100 μm. Moreover, the cavitation bubble is slightly repulsed when the large bubble is larger than 100 μm. There is a critical distance that can lead to a transition between mutual attraction and repulsion of bubbles. Cavitation bubbles can be driven toward the larger bubble by increasing acoustic pressure. The findings presented here will be helpful in understanding the complex behavior of cavitation bubbles in practical applications in which large bubbles exist and may interact with cavitation.