Planar dynamics of two interacting bubbles in an acoustic field

摘要

A theoretical study on the planar motion (relative 2-D) of two spherical gas bubbles, surrounded by a liquid subjected to an acoustic field is presented. Bubble interactions due to the secondary Bjerknes forces are considered. However, drag and gravitational forces are not considered. The relative motion is studied using a dynamical system approach. The possible patterns of relative planar motion of the bubbles, for each of the following categories of bubble interaction are analyzed: (a) Bubbles oscillating in phase, causing mutual attraction at all distances; (b) bubbles oscillating in opposite phase, causing mutual repulsion at all distances; and (c) resonant pairs of bubbles, featuring attraction at large distances and repulsion at small distances. The analytical study provides information on the influence of bubble sizes, forcing amplitude and frequency, energy and angular momentum levels, and physical properties of the gas and liquid phases on the geometry and kinematics of the trajectories. It is found that binary systems of bubbles may have bounded elliptical trajectories for certain ranges of the above parameters, as well as unbounded hyperbolical trajectories.