Hiroyuki Takahira

Shock wave?bubble interaction near soft and rigid boundaries during lithotripsy: numerical analysis by the improved ghost fluid method

In the case of extracorporeal shock wave lithotripsy (ESWL), a shock wave-bubble interaction inevitably occurs near the focusing point of stones, resulting in stone fragmentation and subsequent tissue damage. Because shock wave-bubble interactions are high-speed phenomena occurring in tissue consisting of various media with different acoustic impedance values, numerical analysis is an effective method for elucidating the mechanism of these interactions. However, the mechanism has not been examined in detail because, at present, numerical simulations capable of incorporating the acoustic impedance of various tissues do not exist. Here, we show that the improved ghost fluid method (IGFM) can treat shock wave-bubble interactions in various media. Nonspherical bubble collapse near a rigid or soft tissue boundary (stone, liver, gelatin and fat) was analyzed. The reflection wave of an incident shock wave at a tissue boundary was the primary cause for the acceleration or deceleration of bubble collapse. The impulse that was obtained from the temporal evolution of pressure created by the bubble collapse increased the downward velocity of the boundary and caused subsequent boundary deformation. Results of this study showed that the IGFM is a useful method for analyzing the shock wave-bubble interaction near various tissues with different acoustic impedance.

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows

For the present study we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function

Numerical simulations of bubble motion in a vibrated cell under microgravity using level set and VOF algorithms.

Abstract: Understanding the stability of fluid interfaces subjected to small vibrations under microgravity conditions is important for designing future materials science experiments to be conducted aboard orbiting spacecraft. During the STS‐85 mission, experiments investigating the motion of a large bubble resulting from small, controlled vibrations were performed aboard the Space Shuttle Discovery. To better understand the experimental results, two‐and three‐dimensional simulations of the experiment were performed using level set and volume‐of‐fluid interface tracking algorithms. The simulations proved capable of predicting accurately the experimentally determined bubble translation behavior. Linear dependence of the bubble translation amplitude on the container translation amplitude was confirmed. In addition, the simulation model was used to confirm predictions of a theoretical inviscid model of bubble motion developed in a previous study.

Direct Numerical Simulations of Interaction of Strong Shock Waves with Nonspherical Gas Bubbles near Glass Boundaries in Mercury

The present study is concerned with the material damage of the liquid-mercury target systems induced by bubble collapse. The interaction of an incident strong shock wave with an initially spherical bubble near a glass wall in mercury is simulated using an improved Ghost Fluid Method (GFM), in which Riemann solutions are utilized to correct the values at boundary nodes. The mercury and glass are evaluated by using the equation of state for stiffened gas. The axi-symmetric motions of three phases for air, mercury, and glass are solved directly coupling the GFM with the level set method. The interaction of the shock wave with the bubble leads to the bubble deformation and the formation of liquid-jet during the collapse. The strong shock waves are generated in the mercury not only when the bubble rebounds but also when the liquid-jet impacts downstream surface of the bubble. It is shown that the impact of the shock waves on the glass wall leads to the formation of depression of the glass surface; the toroidal...

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows (Keynote)

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.Copyright

Numerical Simulations of Shock-Bubble Interactions Using an Improved Ghost Fluid Method

The present work is concerned with numerical simulations for the shock-bubble interactions using the Ghost Fluid Method (GFM) in which the interface is captured with level set methods. The GFM is applied to the interactions between an air shock wave and a cylindrical or spherical helium bubble to investigate the numerical diffusion in the reinitialization procedure of the level set function. It is shown that the interface is not captured accurately using the GFM without the reinitialization of the level set function. The numerical diffusion in the reinitialization procedure affects the formation of a re-entrant jet and vortex structures after a shock wave impacts the bubble. It is also shown that the results with the hybrid particle level set method agree with the experiments by Haas and Sturtevant. The hybrid particle level set method is superior in the mass conservation. Also, we have improved the GFM by correcting velocities, pressure and density at boundary nodes using the Riemann solutions to avoid numerical oscillations near the gas-liquid interface. We have succeeded in capturing the sharp interface for the shock-air bubble interaction in water by using the improved GFM coupling with the hybrid particle level set method. Mass conservation in the hybrid particle level set method is better than that in the standard level set method with high order discretization scheme.Copyright

Effects of Dynamic Surface Tension and Gas Permeation Resistance on the Stability of Microbubbles

To understand the stability of microbubbles, the shrinkage and growth of microbubbles under variation of a pressure field are observed with a CCD camera. The influence of gas diffusion is investigated for two kinds of microbubbles; one is Levovist which is an air microbubble coated by palmitic acid, and the other is Imavist which is a PFC gas microbubble covered by lipid and surfactant. It is shown that when the ambient liquid pressure increases, a tiny microbubble shrinks accompanied with surface depression, and does not return to the initial size even after the pressure is reduced. On the other hand, a large microbubble shrinks nearly spherically. The depression of bubble surface suggests the formation of multilayers of surfactant or lipid on bubble surface. It is also shown that air diffusion enhances the growth of the Imavist. A bubble model is also constructed by considering dynamic surface tension and gas permeation resistance of surfactant or lipid layers. The previous experimental results in which a microbubble was trapped with a laser trapping technique are compared with simulations based on the model. The results show that the rate of adsorption of surfactant is much faster than the shrinking speed of microbubbles. The decrease of surface tension due to the decrease of the surface area of a microbubble is a significant factor to determine the bubble profile. Also, the present experimental results are compared with simulations. The simulations considering the gas permeation resistance are in good agreement with the experiments for nearly spherical bubbles. The results also show that the increase of the permeation resistance during bubble shrinkage stabilizes microbubbles.Copyright

Observation of the growth of cavitation bubble cloud by the backscattering of focused ultrasound from a laser-induced bubble

The present study is concerned with the cavitation inception and the growth of a cavitation bubble cloud by the backscattering of focused ultrasound from a laser-induced bubble. The cavitation inception close to the interface of a laser-induced bubble has been observed by a high-speed video camera with the frame rate of up to 1.25 Mfps, and its location and the successive cavitation cloud growth are discussed for various ultrasound conditions. It is shown that the normalized distance between the cavitation inception location and the bubble interface by the wavelength of ultrasound is an increasing function of η = t0 / ts where the time t0 is the characteristic time for cavitation bubble collapse and the time ts the period of ultrasound. Also the magnitude of the dimensionless distance is about 0.05-0.3 times of the wavelength of ultrasound, and the positive pressure threshold of ultrasound for a cavitation inception is about 35 MPa. It is also shown that the cavitation bubble cloud by the backscattering of the incident ultrasound grows conically along the propagation axis of the focused ultrasound. As the incident focused ultrasound pressure at the focus becomes stronger or the duration of the focused ultrasound becomes longer, the cavitation bubble cloud grows larger. However, even though the ultrasound duration becomes longer, this growth ends up and reaches a limited value when the cavitation bubble cloud grows out of the focal region of the focused ultrasound.

Effects of Phospholipid Layers on the Motion of Microbubbles Under Pressure Variations

The shrinking and growth of microbubbles under pressure variations are observed with a CCD camera. The influence of gas diffusion on the stability of microbubbles covered with phospholipid layers is investigated. The microbubbles are made with acoustic liposomes encapsulating phosphate buffer solution and perfluoropropane gas. It is shown that when the ambient liquid pressure increases, the observed microbubbles shrink accompanied with the cyclic surface buckling and smoothing process. The bubble surface smoothing in the process shows that the excess phospholipid layers are removed from the surface, which results in the instantaneous bubble shrinkage. It is also shown that the smaller the initial radius is, the more the growth of microbubbles is reduced. The bubble model by Takahira and Ito, in which the dynamic surface tension and the gas permeation resistance of molecular layers are considered, is utilized to simulate the experiments. The simulation is in qualitative agreement with the experimental result except for the instantaneous bubble shrinkage. The model is improved so as to consider the instantaneous increase of surface tension. The instantaneous bubble shrinkage is simulated successfully with the improved model. The results suggest that the instantaneous increase of surface tension is caused by the shedding of the excess phospholipid layer material due to the zippering process proposed by Borden and Longo.Copyright