Numerical study of the nonlinear dynamics of the acoustic drops and bubbles

Abstract

The dynamics of liquid drops and bubbles held together by surface tension and perturbed by small disturbances is of great interest to many researchers. Its essential physical nature is characterized by a nonlinear moving-boundary problem complicated by the interfacial stress interaction between two domains, each governed by their own dynamical systems respectively. In this thesis, the dynamics of an acoustically levitated drop is investigated. A low dimensional phase plane approach is used to interpret the nonlinear dynamics of the drop motions. It is found that the stability of shape oscillations imposes an upper limit on the acoustic bond number that can be used, while the lower limit is set by the stability of translational motion. The static equilibrium shapes can be obtained by incorporating the artificial damping into the system. The static equilibrium shapes thus found agree very well with the experimental data. In addition, that two-to-one internal resonance of a single bubble between the volume mode and one of the shape modes is carefully examined. instability wedges for unstable volume oscillations on the plane of volume oscillation amplitude versus frequency are identified numerically. Furthermore, the dynamical behaviors of the bubbles with parameters within the instability wedges can be divided into stable bubble oscillations and transient bubble oscillations. Attention is focused on the transient bubble oscillations. Numerical simulation shows that liquid jets form at t.he two poles of the transient bubble and lead to the breakup of the bubble. A possible mechanism resulting in the formation of the liquid jets is proposed and demonstrated with numerical simulation examples. Bjerknes forces between two bubbles are also investigated. It is found that the Bjerknes forces between two attracting bubbles can be predicted with a formula derived by Crum with amazing accuracy. However, numerical simulations indicate that a multiplication factor is needed for the cases of two repelling bubbles within short distance. The effect of shape oscillations on the translational motions of two bubbles is also examined. Interestingly, the shape oscillation has little effect on attracting bubbles, while significant effect on the translational motion of two repelling bubbles within short distance is observed.