Surface-wave instabilities, period doubling, and an approximate universal boundary of bubble stability at the upper threshold of sonoluminescence

Bubble shape instability of acoustic cavitation in molten metal used in ultrasonic casting

In this study, we estimated the equilibrium bubble size of acoustic cavitation in a molten metal, which is basic information in ultrasonic casting. For this, the bubble shape instability of acoustic cavitation in the melt was numerically investigated by solving the Keller-Miksis equation and dynamic equation of the distortion amplitude. The acoustic cavitation bubbles are more stable in aluminum and magnesium melts than in water, and the parametric instability mainly determines the bubble stability at 20-160 kHz in molten metals. However, the afterbounce instability does not significantly affect the bubble stability in molten metals owing to the small number of bubble oscillations after the first rapid compression, and the distortion amplitude cannot grow significantly after the first compression. The bubbles in the melt become more unstable with an increase in the ultrasonic frequency owing to the corresponding increase in the bubble wall velocity. Through this stability analysis, we can estimate that the stable bubble size in the aluminum or magnesium melt is approximately three or four times larger than that in water at the same ultrasonic pressure amplitude.

GPU accelerated numerical investigation of the spherical stability of an acoustic cavitation bubble excited by dual-frequency

The spherical stability of an acoustic cavitation bubble under dual-frequency excitation is investigated numerically. The radial dynamics is described by the Keller-Miksis equation, which is a second-order ordinary differential equation. The surface dynamics is modelled by a set of linear ordinary differential equation according to Hao and Prosperetti (1999), which takes into account the effect of vorticity by boundary layer approximation. Due to the large amount of investigated parameter combinations, the numerical computations were carried out on graphics processing units. The results showed that for bubble size between R_E=2μm and 4μm, the combination of a low and a high frequency, and the combination of two close but not equal frequencies are important to prevent the bubble losing its shape stability, while reaching the chemical threshold (R_max/R_E=3) (Kalmár et al., 2020). The phase shift between harmonic components of dual-frequency excitation has no effect on the shape stability.

GPU accelerated study of a dual-frequency driven single bubble in a 6-dimensional parameter space: The active cavitation threshold

The active cavitation threshold of a dual-frequency driven single spherical gas bubble is studied numerically. This threshold is defined as the minimum intensity required to generate a given relative expansion (R_max-R_E)/R_E, where R_E is the equilibrium size of the bubble and R_max is the maximum bubble radius during its oscillation. The model employed is the Keller-Miksis equation that is a second order ordinary differential equation. The parameter space investigated is composed by the pressure amplitudes, excitation frequencies, phase shift between the two harmonic components and by the equilibrium bubble radius (bubble size). Due to the large 6-dimensional parameter space, the number of the parameter combinations investigated is approximately two billion. Therefore, the high performance of graphics processing units is exploited; our in-house code is written in C++ and CUDA C software environments. The results show that for (R_max-R_E)/R_E=2, the best choice of the frequency pairs depends on the bubble size. For small bubbles, below 3μm, the best option is to use just a single frequency of a low value in the giant response region. For medium sized bubbles, between 3μm and 6μm, the optimal choice is the mixture of low frequency (giant response) and main resonance frequency. For large bubbles, above 6μm, the main resonance dominates the active cavitation threshold. Increasing the prescribed relative expansion value to (R_max-R_E)/R_E=3, the optimal choice is always single frequency driving with the lowest value (20kHz here). Thus, in this case, the giant response always dominates the active cavitation threshold. The phase shift between the harmonic components of the dual-frequency driving (different frequency values) has no effect on the threshold.

Study of non-spherical bubble oscillations under acoustic irradiation in viscous liquid

The effect of dissipation on the shape stability of a harmonically excited bubble is investigated. The employed liquid is the highly viscous glycerine. The rate of the dissipation is controlled through the alteration of viscosity of the liquid by varying its temperature. The mean radius of the bubble during its radial oscillation is described by the Keller-Miksis equation. Two approaches are used to describe the surface oscillations. The first model solves the surface dynamics equations of each mode together with the transport equation of the vorticity in the liquid domain. The second model approximates the transport equation, which is a partial differential equation, with a boundary layer approximation reducing the required computational resources significantly. The comparison of the surface models shows qualitative agreement at low dissipation rate; however, at high viscosity the application of the full transport equation is mandatory. The results show that an increasing rate of dissipation can significantly extend the shape stable domains in the excitation frequency-pressure amplitude parameter plane. Nevertheless, the collapse strength is decreasing due to the highly damped oscillations. It has been found that an optimal range of dissipation rate in terms of temperature can be defined expressing a good compromise between the collapse strength and surface stability. The computations are carried out by an in-house GPU accelerated initial value problem solver.

Bubble dynamics in boiling histotripsy

Boiling histotripsy is a non-invasive, cavitation-based ultrasonic technique which uses a number of millisecond pulses to mechanically fractionate tissue. Though a number of studies have demonstrated the efficacy of boiling histotripsy for fractionation of solid tumours, treatment monitoring by cavitation measurement is not well studied because of the limited understanding of the dynamics of bubbles induced by boiling histotripsy. The main objectives of this work are to (a) extract qualitative and quantitative features of bubbles excited by shockwaves and (b) distinguish between the different types of cavitation activity for either a thermally or a mechanically induced lesion in the liver. A numerical bubble model based on the Gilmore equation accounting for heat and mass transfer (gas and water vapour) was developed to investigate the dynamics of a single bubble in tissue exposed to different High Intensity Focused Ultrasound fields as a function of temperature variation in the fluid. Furthermore, ex vivo liver experiments were performed with a passive cavitation detection system to obtain acoustic emissions. The numerical simulations showed that the asymmetry in a shockwave and water vapour transport are the key parameters which lead the bubble to undergo rectified growth at a boiling temperature of 100°C. The onset of rectified radial bubble motion manifested itself as (a) an increase in the radiated pressure and (b) the sudden appearance of higher order multiple harmonics in the corresponding spectrogram. Examining the frequency spectra produced by the thermal ablation and the boiling histotripsy exposures, it was observed that higher order multiple harmonics as well as higher levels of broadband emissions occurred during the boiling histotripsy insonation. These unique features in the emitted acoustic signals were consistent with the experimental measurements. These features can, therefore, be used to monitor (a) the different types of acoustic cavitation activity for either a thermal ablation or a mechanical fractionation process and (b) the onset of the formation of a boiling bubble at the focus in the course of HIFU exposure.

Perturbation of a radially oscillating single-bubble by a micron-sized object

A single bubble oscillating in a levitation cell is acoustically monitored by a piezo-ceramics microphone glued on the cell external wall. The correlation of the filtered signal recorded over distant cycles on one hand, and its harmonic content on the other hand, are shown to carry rich information on the bubble stability and existence. For example, the harmonic content of the signal is shown to increase drastically once air is fully dissociated in the bubble, and the resulting pure argon bubble enters into the upper branch of the sonoluminescence regime. As a consequence, the bubble disappearance can be unambiguously detected by a net drop in the harmonic content. On the other hand, we perturb a stable sonoluminescing bubble by approaching a micron-sized fiber. The bubble remains unperturbed until the fiber tip is approached within a critical distance, below which the bubble becomes unstable and disappears. This distance can be easily measured by image treatment, and is shown to scale roughly with 3-4 times the bubble maximal radius. The bubble disappearance is well detected by the drop of the microphone harmonic content, but several thousands of periods after the bubble actually disappeared. The delay is attributed to the slow extinction of higher modes of the levitation cell, excited by the bubble oscillation. The acoustic detection method should however allow the early detection and imaging of non-predictable perturbations of the bubble by foreign micron-sized objects, such as crystals or droplets.

The effect of high viscosity on the collapse-like chaotic and regular periodic oscillations of a harmonically excited gas bubble

In the last decade many industrial applications have emerged based on the rapidly developing ultrasonic technology such as ultrasonic pasteurization, alteration of the viscosity of food systems, and mixing immiscible liquids. The fundamental physical basis of these applications is the prevailing extreme conditions (high temperature, pressure and even shock waves) during the collapse of acoustically excited bubbles. By applying the sophisticated numerical techniques of modern bifurcation theory, the present study intends to reveal the regions in the excitation pressure amplitude-ambient temperature parameter plane where collapse-like motion of an acoustically driven gas bubble in highly viscous glycerine exists. We report evidence that below a threshold temperature the bubble model, the Keller-Miksis equation, becomes an overdamped oscillator suppressing collapse-like behaviour. In addition, we have found periodic windows interspersed with chaotic regions indicating the presence of transient chaos, which is important from application point of view if predictability is required.

Saturation of shape instabilities in single-bubble sonoluminescence

Excitation of shape instabilities represents one route to bubble death in single-bubble sonoluminescence. This feature is satisfactorily explained by an expansion to first order in the amplitude of a shape distortion in the form of a spherical harmonic. By taking the expansion to second order, it is found that regions of parameter space exist where the exponential growth into bubble disruption is checked and a saturated stable state of shape distortion is possible. Experimental evidence provided by Mie scattering is presented, and a possible connection to simultaneous spatially anisotropic light emission is discussed.

Concomitance in single bubble sonoluminescence of period doubling in emission and shape distortion

We report the first direct observation for a single stable sonoluminescing bubble of a shape instability. Furthermore we show that stable saturation of the shape distortion caused by the instability for a certain range of parameters is experimentally possible and furthermore is directly linked to the curious phenomenon of flash by flash period doubling of the sonoluminescent emission as the afterbounce instability causing the shape distortion is always period doubled whenever the emission is & vice versa.

Temperature and intensity of sonoluminescence radiation in sulfuric acid

The spectral radiation of sonoluminescence (SL) from sulfuric acid doped with various Xe concentrations has been studied in a hydrochemical simulation, including radiation effects of both continuum and line emissions. The simulation considers the same temperature for both continuum and line parts of the SL spectrum and gives results in agreement with the experiment. Also, it can properly show period-doubling dynamics for a 50 torr bubble. For most of the allowable driving pressures, it is shown that both the temperature and the intensity of SL for a 4 torr bubble are greater than those of a 50 torr bubble. However, for the range of pressures near the maximum driving conditions of the 50 torr bubble, the SL intensity of this bubble can be up to three orders of magnitude greater than the 4 torr bubble. This case, which is in agreement with the experiment, is obtained when the light-emitting region of the 50 torr bubble is about three orders of magnitude greater than the 4 torr bubble.

Bubble dynamics in a standing sound field: the bubble habitat

Bubble dynamics is investigated numerically with special emphasis on the static pressure and the positional stability of the bubble in a standing sound field. The bubble habitat, made up of not dissolving, positionally and spherically stable bubbles, is calculated in the parameter space of the bubble radius at rest and sound pressure amplitude for different sound field frequencies, static pressures, and gas concentrations of the liquid. The bubble habitat grows with static pressure and shrinks with sound field frequency. The range of diffusionally stable bubble oscillations, found at positive slopes of the habitat-diffusion border, can be increased substantially with static pressure.

Influence of liquid density on the parametric shape instability of sonoluminescence bubbles in water and sulfuric acid

Parametric shape instability of sonoluminescing argon bubbles in water and aqueous H(2)SO(4) was numerically analyzed considering gas and liquid density variations. The employed model couples Gilmore, Tait (liquid) and van der Waals (gas) equations to simulate radial dynamics and density changes, respectively. Shape stability-instability zones in the P(a)-R(0) space resulted from a linear stability analysis. For the argon-water and argon-water-acid systems, numerical results indicate a rapid rise in both gas and liquid densities during final stages of bubble implosion which result in a stabilizing effect on the parametric instability.