Nonlinear acoustic theory on flowing liquid containing multiple microbubbles coated by a compressible visco-elastic shell: Low and high frequency cases

Microbubbles coated by visco-elastic shells are important for ultrasound diagnosis using contrast agents, and the dynamics of single bubbles has been investigated in literature. However, although a high number agents used practical situations, there long an absence nonlinear acoustic theory multiple bubbles, except our recent work Kikuchi Kanagawa [“Weakly on propagation liquids containing many microbubbles encapsulated shell,” Jpn. J. Appl. Phys. 60, SDDD14 (2021)], under several assumptions to be excluded. Aiming generalization, this study, we theoretically investigate weakly liquid shell with compressibility. Leveraging method scales, both Korteweg–de Vries–Burgers (KdVB) equation low-frequency wave Schrödinger (NLS) high-frequency short derived from volumetric averaged equations bubbly based two-fluid model up-to-date Neglected factors previous paper, i.e., compressibility liquid, drag force acting bubble translation, thermal conduction, incorporated present KdVB NLS equations; proposed will regarded as generic physico-mathematical model. The results show that attenuated strongly decreased nonlinearity ultrasound. Finally, compared magnitudes six dissipation (shell compressibility, viscosity, effect, force) five typical similar tendency between was revealed.