Translational motion of a spherical bubble in an acoustic standing wave of high intensity

Using the Lagrangian formalism, coupled equations of radial and translational motions of a spherical gas bubble in an acoustic wave field are derived. The equation of radial motion is then modified, for the purpose of allowing for effects of liquid compressibility, using Keller–Miksis’ approach, and the equation of translation is added by the primary Bjerknes force and the viscous force in the form of the Levich drag. The resulting equations are solved numerically for the purpose of studying the translational motion of a bubble in a plane standing wave. It is shown that, if the acoustic pressure amplitude is high enough, a bubble driven below resonance, instead of moving to the pressure antinode as it does in a weak field, reciprocates about the pressure node plane. This result is of interest for an understanding of irregular bubble motions observed experimentally in strong acoustic fields.