Velocity analysis for collapsing cavitation bubble near a rigid wall under an ultrasound field

Acoustic cavitation bubble and its production extreme physics such as shockwaves and micro-jets on a solid wall have attracted great interest in the application of ultrasound (e.g., ultrasonic medical, ultrasonic cleaning, and ultrasonic machining). However, the prediction and control of micro-jets induced by ultrasonic field have been a very challenging work, due to the complicated mechanisms of collapsing of cavitation bubbles. In order to determine the interaction of micro-jet with the key parameters that influence the acoustic cavitation, the dynamics of bubble growth and collapse near a rigid boundary in water is investigated. Using the method of mirror image, a revised bubble dynamics equation in radial oscillation for a bubble near a plane rigid wall is derived from the double-bubble equation (the Doinikov equation). In the present equation, the gas inside the bubble is assumed to be the van der Waals gas, and the weak compressibility of the liquid is also assumed. The revised equation is then employed to simulate numerically the dynamical behaviors of a bubble, using the fourth-order Runge-Kutta method with variable step size adaptive control. Numerical simulations of the motion characteristics and collapse velocities of a bubble near a rigid boundary or a free boundary have been performed, under various conditions of initial bubble radius, spacing between the center of the bubble and the wall, acoustic pressure and ultrasonic frequency, in order to explain the effects of these key parameters on the acoustic cavitation intensity. It is shown that, compared with free boundary, the effect of rigid boundary on the bubble plays a significant role in suppressing the bubble oscillation. The intensity of bubble collapsing is reduced as the increase of the initial bubble radius and ultrasonic frequency, and increased by enlarging the spacing between the center of the bubble and the wall. There exists an optimal acoustic pressure (almost 3.5 times bigger than the ambient pressure), at which the collapse of a bubble near a rigid wall can be the most violent. Furthermore, the relationship between the collapse velocity of a bubble near a rigid boundary and its micro-jet is described. Results demonstrate that the velocity of micro-jet is dependent on that of bubble collapse, and it can be controlled by adjusting the velocity of bubble collapse indirectly. Calculation results of the micro-jet in this paper are compared with some numerical and experimental results given in the literature and good apparent trends between them are obtained. These results will give important implications for further understanding the dynamics of cavitation bubble on a solid wall induced by the ultrasonic field and its different requirements in engineering applications.