Derivation of Weakly Nonlinear Wave Equation for Focused Ultrasound in Bubbly Liquids Incorporating a Thermal Effect

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