The effects of interfacial viscosity on the attenuation and phase speed of acoustic waves in bubbly liquids

The attenuation and phase speed of bubbly fluids have been shown to be highly dispersive due in part to the resonance response of individual bubbles. Surface-active materials, or surfactants, are known to dramatically alter the viscoelastic dynamics of an interface without affecting the bulk fluid properties. In this theoretical model the effects of surface viscosity on the propagation of linear pressure waves through a bubbly fluid are examined. The attenuation and phase speed are calculated for varying radii, void fraction, and interfacial viscosity for air bubbles in water. The results show an increase in attenuation for frequencies far removed from the bubble resonance for radii less than 100 microns. There is no significant increase in attenuation for larger bubbles (order 1 mm). Interestingly, near resonance, the interfacial viscous case has a lower attenuation than the clean interface, most likely due to the reduced radiation damping associated with smaller radial excursions. Likewise, resonance effects on the phase speed dispersion curve are also significantly diminished due to the interfacial viscosity. These results could be important for understanding propagation near the surface of the ocean, where surface-active materials can dramatically affect the dynamics of micron-sized bubbles and bubble distributions. [Work supported by ONR.]