Translational motion of two interacting bubbles in a strong acoustic field

Using the Lagrangian formalism, equations of radial and translational motions of two coupled spherical gas bubbles have been derived up to terms of third order in the inverse distance between the bubbles. The equations of radial pulsations were then modified, for the purpose of allowing for effects of liquid compressibility, using Keller-Miksis' approach, and the equations of translation were added by viscous forces in the form of the Levich drag. This model was then used in a numerical investigation of the translational motion of two small, driven well below resonance, bubbles in strong acoustic fields with pressure amplitudes exceeding 1 bar. It has been found that, if the forcing is strong enough, the bubbles form a bound pair with a steady spacing rather than collide and coalesce, as classical Bjerknes theory predicts. Moreover, the viscous forces cause skewness in the system, which results in self-propulsion of the bubble pair. The latter travels as a unit along the center line in a direction that is determined by the ratio of the initial bubble radii. The results obtained are of immediate interest for understanding and modeling collective bubble phenomena in strong fields, such as acoustic cavitation streamers.