Yunqiao Liu

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

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 bubblesurface. 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.

Experimental and numerical study on bubble-sphere interaction near a rigid wall

This study is concerned with the interaction between a violently oscillating bubble and a movable sphere with comparable size near a rigid wall, which is an essential physical phenomenon in many applications such as cavitation, underwater explosion, ultrasonic cleaning, and biomedical treatment. Experiments are performed in a cubic water tank, and the underwater electric discharge technique (580 V DC) is employed to generate a bubble that is initiated between a rigid wall and a sphere in an axisymmetric configuration. The bubble-sphere interactions are captured using a high-speed camera operating at 52 000 frames/s. A classification of the bubble-sphere interaction is proposed, i.e., “weak,” “intermediate,” and “strong” interactions, identified with three distinct bubble shapes at the maximum volume moment. In the numerical simulations, the boundary integral method and the auxiliary function method are combined to establish a full coupling model that decouples the mutual dependence between the force and t...

Theoretical study on the shape instability of an encapsulated bubble in an ultrasound field

A theoretical study on the shape instability of a slightly deformed bubble encapsulated by a viscoelastic membrane in an ultrasound field is performed. The membrane effects of the inplane stress and the bending moment are incorporated into the traction jump condition at the bubble surface. The spherical motion of the bubble is numerically obtained by solving the Rayleigh-Plesset equation with the elastic stress. The deflection therefrom is linearized and expanded with respect to the Legendre polynomial. Two amplitudes for each shape mode are introduced because the membrane has mobility not only in the radial direction but also in the tangential direction. A simple expression for the natural frequency of shape mode is derived. Stability diagrams for the higherorder shape mode are mapped out in the phase space of driving amplitude versus driving frequency. The most unstable driving frequency is found to satisfy an integer multiple relationship with twice of the higher-order natural frequency. This finding is justified by a fact that the system with a boundary layer approximation is simplified into Mathieu’s equation. Liquid viscosity plays an important role in the shape stability due to the vorticity generation on the deformed membrane.A theoretical study on the shape instability of a slightly deformed bubble encapsulated by a viscoelastic membrane in an ultrasound field is performed. The membrane effects of the inplane stress and the bending moment are incorporated into the traction jump condition at the bubble surface. The spherical motion of the bubble is numerically obtained by solving the Rayleigh-Plesset equation with the elastic stress. The deflection therefrom is linearized and expanded with respect to the Legendre polynomial. Two amplitudes for each shape mode are introduced because the membrane has mobility not only in the radial direction but also in the tangential direction. A simple expression for the natural frequency of shape mode is derived. Stability diagrams for the higherorder shape mode are mapped out in the phase space of driving amplitude versus driving frequency. The most unstable driving frequency is found to satisfy an integer multiple relationship with twice of the higher-order natural frequency. This finding i...