Viscous effects on the interaction force between two small gas bubbles in a weak acoustic field

The relative motion of two gas bubbles in an acoustic field is investigated by calculating the time-averaged interaction force known as the secondary Bjerknes force. The surrounding medium is assumed to be an incompressible viscous liquid and the separation distance between the bubbles much larger than their radii. A refined formula for the interaction force is derived, which allows for translational oscillations of the bubbles, the vorticity of the linear scattered field, and acoustic streaming. The boundary condition of slippage on the gas-liquid interface is assumed. It is shown that viscous effects can cause small bubbles, driven well below resonance, to repel each other within a relatively wide parameter range. This result discloses a significant boundedness of the classical Bjerknes theory according to which bubbles of this sort are capable of mutual attraction alone.