Effect of surface waves on the secondary Bjerknes force experienced by bubbles in a microfluidic channel.

An analytical expression is derived for the secondary Bjerknes force experienced by two cylindrical bubbles in a microfluidic channel with planar elastic walls. The derived expression takes into account that the bubbles generate two types of scattered acoustic waves: bulk waves that propagate in the fluid gap with the speed of sound and Lamb-type surface waves that propagate at the fluid-wall interfaces with a much lower speed than that of the bulk waves. It is shown that the surface waves cause the bubbles to form a bound pair in which the equilibrium interbubble distance is determined by the wavelength of the surface waves, which is much smaller than the acoustic wavelength. Comparison of theoretical and experimental results demonstrates good agreement.