Nonlinear attenuation of sound waves by inertial cavitation bubbles

Acoustic cavitation fields generally involve clouds of inertial bubbles, expanding to many time their initial radius, and then collapsing. A correct estimation of the wave attenuation in such media requires a realistic estimation of the power dissipated by the oscillation of each bubble. This power loss originates mainly from thermal diffusion in the gas and viscous friction in the liquid, and is calculated numerically for a single inertial bubble, by solving the bubble dynamics in a typical parameter range at 20 kHz, using a convenient model accounting for the thermal behavior of the gas. These estimations are then injected in the nonlinear Caflish equations, which describe wave propagation in a bubbly media, conveniently recast in an energy conservation equation. A nonlinear attenuation coefficient is deduced and found to be several orders of magnitude higher than the linear prediction.