EXISTENCE ANALYSIS OF OVER DAMPED SYSTEM IN BUBBLE DYNAMICS

Damping mechanisms play a crucial role in the dynamics of bubble, significantly impacting the motion of the bubble wall. The damping mechanisms can be classified into three types: viscous damping, thermal damping, and acoustic damping. This paper provides an in-depth study of the dynamics of the bubble wall through a detailed analysis of the dominant damping mechanisms governing their behavior and delineating the range of bubble radii. Through theoretical analysis and derivation of the equations governing bubble wall motion, the simplified damping ratio equation is established. This equation serves as evidence for the existence of an over-damped system in bubble dynamics. In contrast to the sub-damped system, where the bubble undergoes decaying reciprocal simple harmonic oscillations, the bubble in the over-damped system exhibits a distinct behavior. Rather than oscillating, the bubble gradually decays from its initial position towards its equilibrium position. This observation sheds light on the distinct behavior exhibited by bubble under different damping systems.