Numerical study on the shape oscillation of an encapsulated microbubble in ultrasound field

• Published in: Physics of fluids (1994) Vol. 23; no. 4; pp. 041904 - 041904-13
• Main Authors: Liu, Yunqiao, Sugiyama, Kazuyasu, Takagi, Shu, Matsumoto, Yoichiro
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.04.2011
• Subjects: Acoustical measurements and instrumentation; Acoustics; Biological and medical sciences; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Investigative techniques, diagnostic techniques (general aspects); Medical sciences; Miscellaneous. Technology; Physics; Ultrasonic investigative techniques; Sonography; Geometrical shape; Bubble; Dynamics; Membrane; Finite volume method; Numerical simulation; Modeling; Medical application
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3578493

The shape oscillation of an encapsulated microbubble in an ultrasound field is numerically investigated. To predict the nonlinear process, the continuity equation and the Navier-Stokes equation are directly solved by means of a boundary-fitted finite-volume method on an orthogonal curvilinear coordinate system. The mechanics of neo-Hookean membrane is incorporated into the dynamic equilibrium at the bubble surface. The numerical results show that the membrane raises the natural frequency of an encapsulated bubble especially for small bubble, whereas this effect is attenuated as the initial bubble size grows. For a small encapsulated bubble of which the natural frequency is sufficiently higher than the driving frequency, the oscillation is stable, namely, the oscillatory amplitude is small; besides, the radial mode and shape modes are out of resonance so that no deformation emerges. As the bubble becomes larger, the natural frequencies of encapsulated and gas bubbles get closer, leading to the less apparent difference in oscillatory amplitude between them. Furthermore, shape modes of an encapsulated bubble are prone to be induced when twice of the higher-order natural frequency is approximately equal to the frequency of radial mode particularly when the bubble is at radial resonance for which the large-amplitude pulsation enhances the compressive stress developing in the membrane. In contrast, the shape oscillation is less likely to occur for a gas bubble with micrometer size since the surface tension suppresses the developments of nonspherical shape modes.