Mathematical and numerical modeling of two-phase compressible flows with micro-inertia

The shock-induced collapse of a pre-existing nucleus near a solid surface in the focal region of a lithotripter is investigated. The entire flow field of the collapse of a single gas bubble subjected to a lithotripter pulse is simulated using a high-order accurate shock- and interface-capturing scheme, and the wall pressure is considered as an indication of potential damage. Results from the computations show the same qualitative behavior as that observed in experiments: a re-entrant jet forms in the direction of propagation of the pulse and penetrates the bubble during collapse, ultimately hitting the distal side and generating a water-hammer shock. As a result of the propagation of this wave, wall pressures on the order of 1 GPa may be achieved for bubbles collapsing close to the wall. The wall pressure decreases with initial stand-off distance and pulse width and increases with pulse amplitude. For the stand-off distances considered in the present work, the wall pressure due to bubble collapse is larger than that due to the incoming shockwave; the region over which this holds may extend to ten initial radii. The present results indicate that shock-induced collapse is a mechanism with high potential for damage in shockwave lithotripsy.

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Shock-induced collapse of a gas bubble in shockwave lithotripsy.

Medical ultrasound with microbubbles

https://www.colonius.caltech.edu/pdfs/AndoColoniusBrennen2011.pdf

Numerical simulation of shock propagation in a polydisperse bubbly liquid

Ultrasound medical applications, such as an ultrasound imaging with micro-bubble contrast agents, and high intensity focused ultrasound (HIFU) therapy have attracted much attention in recent years. These applications have a close relation to the motion of micro-bubbles, so that it is essential to understand their dynamics. The bubble motion is influenced by the internal phenomena and its interaction with the surrounding medium, such as the thermal diffusion, the mist formation, the mass diffusion, the heat and mass transfer through the bubble wall. It is important that the oscillation of micro bubbles generates a strong acoustic pressure for these medical applications. The strong pressure also appears in the case of a bubble cluster, like a cloud cavitation. As these dynamics of bubbles are strongly influenced by the thermal phenomena inside them, it is necessary to construct the model taking these phenomena into account to analyse the behaviour of the bubble cluster precisely. Thus, the following effects are considered: the evaporation and condensation of the liquid at the bubble wall, the heat transfer through the bubble wall, and the compressibility of the liquid. Then the spherical bubble cluster is numerically simulated. When the frequency of the ultrasound is sufficiently high, the bubble cluster hardly oscillates. On the contrary, when the frequency of the ultrasound is at the resonance of the bubble cluster, the pressure wave generates the shock wave and it focuses to the cluster centre. As a result, the pressure inside the bubble at the cluster centre becomes much higher than that of a single bubble. Though this extreme high pressure causes the severe cavitation erosion, it is thought that this high energy concentration has the potential to be utilized for medical applications.

Behaviour of a bubble cluster in an ultrasound field

An experimental and numerical study of transient shock wave phenomena in a liquid containing noncondensable gas bubbles is presented. Experiments are done in a shock tube with an upwardly directed bubbly flow to obtain a uniform spatial distribution of bubbles. The bubbly flow has an initial gas volume fraction of 0.2%. The bubbles have a radius of 0.6 mm. The liquid used is a silicone oil whose kinematic viscosity is 50×10−6 m2/s. Nitrogen and SF6 gas bubbles are tested to bring out the thermal effects of the bubble interior. The numerical calculation is performed using a modified mathematical model based on Kameda and Matsumoto [Phys. Fluids 8, 322 (1996)]. The transient pressure profiles determined in the experiment for the upwardly bubbly flow agree well quantitatively with those obtained by the numerical calculation using a uniform spatial distribution of bubbles. The SF6 experiment shows that the radial motion of the bubbles should be estimated by solving an equation in which the liquid compressibil...

Naoto Shimaura

Papers

Shock waves in a uniform bubbly flow