Lamb-type waves generated by a cylindrical bubble oscillating between two planar elastic walls.

The volume oscillation of a cylindrical bubble in a microfluidic channel with planar elastic walls is studied. Analytical solutions are found for the bulk scattered wave propagating in the fluid gap and the surface waves of Lamb-type propagating at the fluid-solid interfaces. This type of surface wave has not yet been described theoretically. A dispersion equation for the Lamb-type waves is derived, which allows one to evaluate the wave speed for different values of the channel height h. It is shown that for h<λt, where λt is the wavelength of the transverse wave in the walls, the speed of the Lamb-type waves decreases with decreasing h, while for h on the order of or greater than λt, their speed tends to the Scholte wave speed. The solutions for the wave fields in the elastic walls and in the fluid are derived using the Hankel transforms. Numerical simulations are carried out to study the effect of the surface waves on the dynamics of a bubble confined between two elastic walls. It is shown that its resonance frequency can be up to 50% higher than the resonance frequency of a similar bubble confined between two rigid walls.

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.