気泡を含む液体中における集束超音波の熱的効果に着目した弱非線形波動方程式の導出

抄録

Weakly nonlinear focusing of quasi-planar ultrasound in a liquid nonuniformly containing many spherical microbubbles is theoretically investigated with a special focus on a thermal conduction at the bubble-liquid interface toward medical applications such as tumor coagulation by HIFU. Based on the previously derived Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation by our group (Kanagawa, J. Acoust. Soc. Am., 137 (2015), 2642), we derived a KZK equation newly incorporating the viscosity of bubbly liquids and the thermal conduction at the bubble-liquid interface by utilizing the energy equation inside bubble. As a result, two types of dissipation term were discovered in the resultant KZK equation: one is the second-order partial derivative term owing to the viscosity of bubbly liquids and the liquid compressibility and the other is a term without differentiation owing to the thermal conductivity. We found that the thermal conduction strongly contributes the dissipation effect.