The Study Of The Bjerknes Force Between Two Bubbles Under The Action Of The Sound Field

Ultrasonic as an energy carrier, it will cause ultrasonic cavitation effect in liquid in the process of transmission of energy. Ultrasonic cavitation refers to the core of micro bubble in the liquid which is activated by ultrasonic wave with a series dynamic process of oscillation, growth, shrinkage and collapse of the bubble. Because this process is a complex process, often accompanied by the phenomena of high temperature, high pressure and light, so that in the development and utilization of the basic research and application of modern technology, such as physics, chemistry, biology, etc, it has a broad prospect. Under the stimulus of sound wave, there are a large number of random distribution of air bubbles in the liquid, and between bubbles will interact to produce secondary Bjerknes force, which make them to attract or repel each other. The secondary Bjerknes force not only has an important regulatory role to the distribution structure of air bubbles and the local area distribution of sound field, but also has a positive meaning to find out the vibration of the cluster and the internal mechanism of bubbles as well as the aggregation and separation of particles or air bubbles. Meanwhile, the most important is that the formation processes of acoustic cavitation and the principle of sonoluminescence will be understanded clearly. Thus, the study of secondary Bjerknes force between bubbles under the action of the ultrasonic wave has a quite important theoretical and practical significance.In this paper, the Lagrange function is used to deduce the coupling equations of the radial vibration and translational motion of bubbles, combineing the mathematical model and translational motion of single bubble in fluid. Then, numerical results of the secondary Bjerknes force are calculated for bubbles, and the influence on secondary Bjerknes force of bubble size, bubble spacing, sound pressure amplitude, heat transfer model and acoustic frequency is studied in detail. The results show that:1. Through the research of the effect of the bubble size on the secondary Bjerknes force between bubbles, It can be found that the bubble size has an effect on the secondary Bjerknes force. There is the attraction between the bubbles with the same size and the attraction increases as the bubble radius increases, eventually, the phenomena of collision or coalescence among bubbles are observed. The attraction and repulsion appear alternately because the phase of secondary Bjerknes force vary with time when the two bubbles have different size, but its time average force always tendency to attraction or repulsion. The bubbles attract each other when the radius of two bubbles greater or less than the resonance radius and the attraction increases as the bubble radius increases. The bubbles repel each other when the resonance radius is between the radius of two bubbles. When one of them is equal to the resonance radius, the bubbles firstly will attract, then, they come to a status of dynamic balance and do translational motion along with the fluid.2. Through the research of the effect of the bubble spacing on the secondary Bjerknes force between bubbles, it can be found that the secondary Bjerknes force between bubbles decreases as the bubble spacing increases. When spacing increases to a certain value, the interaction force between the two bubbles tends to zero, the movement characteristics of bubble similar to single bubble's. With decreasing of bubble spacing, the the secondary Bjerknes force between the two bubbles get strengthen, and the direction of the force will change when the radius of one bubble is equal to the resonance radius.3. Through the research of the effect of acoustic pressure amplitude on the secondary Bjerknes force between bubbles, It can be found that the secondary Bjerknes force between bubbles increases as acoustic pressure amplitude increases and the force direction will change due to the radius of bubbles. In addition, the translational status of the bubbles will be influenced for the different sound pressure.4. Through the research of the effect of the heat transfer models on the secondary Bjerknes force between bubbles, It can be found that the heat transfer models have not an obvious effect on the force.5. For the bubbles of the same radius, it always have attraction force between oscillating bubbles, whatever the driving frequency is. There is the side maximum of force below the resonant frequency area and the maximum of force in the resonant frequency. While, the force will decreases as the driving increases in above the resonant frequency. For the bubbles of the different radius, the driving frequency between the resonance frequencies of the two bubbles, the bubbles repulse each other and the relationship between force and frequency is nonlinear. The bubbles attract each other when the driving frequency greater or less than the resonance frequency and the attraction increases as driving increases below the resonant frequency area and the attraction decreases as driving increases in the resonant frequency area. For the micro bubbles in the liquid, under the driving of low frequency, they produce transient acoustic cavitation effect, conversely, produce steady acoustic cavitation effect by high frequency sound wave.