Dynamics of an oscillating cavitation bubble within a narrow gap

Abstract

The oscillation characteristics of a bubble in a confined space have important implications for various applications, including liquid pumping and mixing and particle conveyance in microfluidic devices. In this study, analytical solution with second-order accuracy and numerical solution are derived for the free oscillation of a single bubble in a narrow gap between parallel plates, and the applicability to dimensionless initial values of the analytical solutions is clarified. Moreover, the free-oscillation characteristics of the bubble within the gap are explored and described and are compared to those of a bubble in an infinite liquid. The primary conclusions are as follows: (1) The inherent nature of bubble oscillation in a gap is significantly influenced by the bubble equilibrium radius, and the oscillation amplitude of different orders of the analytical solution is significantly influenced by the dimensionless initial radius. (2) The difference between the natural frequency and acoustic damping constant during bubble oscillation in a gap and those in an infinite liquid decreases with increasing equilibrium radius, and the value of the difference is not less than 50%. (3) Within the gap, the bubble radius, wall velocity, and wall acceleration of a bubble in a narrow gap predicted by the bubble equation dramatically differ from those of a bubble in an infinite liquid, with the differences increasing with the dimensionless initial radius, where the values of the differences in the acceleration can be as high as the order of 104%.