著者

加賀見 俊介 金川 哲也

出版者

日本混相流学会

雑誌

混相流 (ISSN:09142843)

巻号頁・発行日

vol.35, no.2, pp.346-355, 2021-06-15 (Released:2021-07-08)

参考文献数

48

被引用文献数

4

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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.