Influnece of nonspherical effects on the secondary Bjerknes force in a strong acoustic field

The secondary Bjerknes force between bubbles in an acoustic field is a well-known acoustic phenomenon. The theoretical researches of the secondary Bjerknes force mainly focus on the case of two spherical bubbles. The secondary Bjerknes force between two spherical bubbles, calculated based on the linear equations, is very small and negligible. Therefore these theoretical researches donot give a good explanation for the phenomenon, such as “streamer formation” and multi-bubble sonoluminescence(MBSL). Experiments of sonoluminescence show that the shapes of the bubbles in a sound field are not entirely spherical. Nonspherical effects have an important influence on the secondary Bjerknes force when two bubbles come close to each other in a strong acoustic field(>1.0×105 Pa). How the shape distortion of a nonspherical bubble causes the secondary Bjerknes force between two bubbles to change, and how the secondary Bjerknes force affects the oscillations and movements of bubbles are major problems which we are to solve in the present research. The expression of the secondary Bjerknes force between a nonspherical bubble and a spherical bubble is obtained by considering the shape oscillation of a nonspherical bubble. We numerical simulate the secondary Bjerknes force between a nonspherical bubble and a spherical bubble based on the nonlinear oscillation equations of two bubbles, and compare the secondary Bjerknes force between a nonspherical bubble and a spherical bubble with the secondary Bjerknes force between two spherical bubbles in the same condition. We discuss the influence of nonspherical effects on the secondary Bjerknes force between two bubbles. The results show that when the amplitude of driving pressure is greater than the Blake threshold of a nonspherical bubble and makes the bubble oscillate stably, the secondary Bjerknes force between this nonspherical bubble and a spherical bubble is different from the secondary Bjerknes force between two spherical bubbles in direction and magnitude. The secondary Bjerknes force between a nonspherical bubble and a spherical bubble is much bigger than that between two spherical bubbles. The interactional distance of the secondary Bjerknes force between a nonspherical bubble and a spherical bubble is longer than that between two spherical bubbles. The secondary Bjerknes force between a spherical bubble and a nonspherical bubble depends on the radii of two bubbles, distance between two bubbles, shape mode of the nonspherical bubble and the amplitude of driving pressure. Our research is closer to the actual bubbles in liquid. We also prove that big mutual interaction between bubbles is the main cause for froming a stable structure between bubbles. For bubbles, big mutual interaction causing the cavitation becomes easier. These results are important for explaining the phenomenon in an acoustic field, such as “streamer formation” and MBSL.