Minimum Bubble Radius Research Articles

Repetitive shock waves generated by a single long pulse underwater arc discharge

The electrohydraulic effect induced by underwater arc discharge is an efficient way to generate controllable, high-intensity shock waves. However, the development process of underwater arc discharge involves the complex coupling of plasma arc, gas bubble, and liquid medium, of which the evolution mechanism is not well understood. In this paper, the underwater arc discharge process at a millisecond pulse (>50 ms) was investigated by high-speed shadow imaging and colorimetric temperature measurement, and a simulation model of bubble pulsation was proposed to quantitatively estimate the state variation and energy transfer of the gas bubble. The results indicate that the whole arc discharge process can be categorized into three successive stages: short-period oscillation, long-period oscillation, and quasi-steady state. The vapor inside the bubble can reach a supercritical state (827 K and 140 MPa) at the minimum bubble radius. The simulation shows that the light radiation absorption and the heat conduct loss through metal electrodes are the two dominant factors influencing the pulsation of the bubble, and further analysis indicates that the dynamic evolution of the arc determines the bubble pulsation mode. Our findings demonstrate why and how repetitive electrohydraulic shock waves can be generated by a single long pulse underwater arc discharge, providing a low-cost way of shock wave generator based on an AC/DC high-voltage power source.

Dynamics of a Laser-Induced Cavitation Bubble near a Cone: An Experimental and Numerical Study

A bubble’s motion is strongly influenced by the boundaries of tip structures, which correspond to the bubble’s size. In the present study, the dynamic behaviors of a cavitation bubble near a conical tip structure are investigated experimentally and numerically. A series of experiments were carried out to analyze the bubble’s shape at different relative cone distances quantitatively. Due to the crucial influence of the phase change on the cavitation bubble’s dynamics over multiple cycles, a compressible two-phase model taking into account the phase change and heat transfer implemented in OpenFOAM was employed in this study. The simulation results regarding the bubble’s radius and shape were validated with corresponding experimental photos, and a good agreement was achieved. The bubble’s primary physical features (e.g., shock waves, liquid jets, high-pressure zones) were well reproduced, which helps us understand the underlying mechanisms. Meanwhile, the latent damage was quantified by the pressure load at the cone apex. The effects of the relative distance γ and cone angle θ on the maximum temperature, pressure peaks, and bubble position are discussed and summarized. The results show that the pressure peaks during the bubble’s collapse increase with the decrease in γ. For a larger γ, the first minimum bubble radius increases while the maximum temperature decreases as θ increases; the pressure peak at the second final collapse is first less than that at the first final collapse and then much greater than that one. For a smaller γ, the pressure peaks at different θ values do not vary very much.

Study on the effect of bubble number on the collapse of a multi-bubble system near the rigid wall

The mechanism of multi-bubble collapse is one of the key technologies that need to be overcome in the development of large submersibles, which is urgently needed to study and explore. The VOF method is used to study the collapse process of a multi-bubble system near the rigid wall. The bubble collapse process is analyzed under three different bubble numbers and four different initial bubble wall distances. The influence of the number of bubbles and initial bubble wall distance on the bubble collapse process is obtained, and the mechanism of multi-bubble collapsing near the rigid wall is revealed. The results indicate that in a multi-bubble system, as the number of bubbles increases, the duration of bubble collapse increases, the minimum bubble radius decreases, and the maximum central pressure increases. The closer the bubble is to the rigid wall, the longer the duration of bubble collapse, which also lead to fluctuations in the maximum center pressure and maximum interface velocity of a multi-bubble system. The results of this study are expected to provide a theoretical basis and technical support for the design and performance optimization of deep submersible mechanical seals.

Thermodynamic effects on single cavitation bubble dynamics under various ambient temperature conditions

Thermodynamic characteristics and their effects on single cavitation bubble dynamics are important to elucidate the physical behaviors of cavitation phenomena. In this study, experimental and numerical methods were utilized to explore the thermodynamic effects on single cavitation bubble dynamics under various ambient temperature conditions. A series of experiments was performed to generate a single cavitation bubble at ambient temperatures between 20 and 80 °C using a laser-induced method and a high-speed camera to observe the dynamic behaviors of bubbles. By increasing the ambient temperature, a nonspherical bubble shape with a jet flow at the bubble rebound stage was observed. Next, the numerical simulation results in terms of the bubble radius and bubble shape were validated with the corresponding experimental data. Generally, the results exhibited reasonable agreement, particularly at the later collapse and rebound stages. Critical hydrodynamic and thermodynamic mechanisms over multiple oscillation stages at different ambient temperatures were analyzed. The bubble behaviors and their intensities were numerically quantified with respect to the bubble radius, collapsing time, internal pressure, internal temperature, and phase transition rate parameters. The results showed that the maximum bubble radius, first minimum bubble radius, and collapsing time increased with an increase in the ambient temperature. Nevertheless, the peak values of the internal pressure and internal temperature decreased with an increase in the ambient temperature. Generally, the bubble collapsed less violently at high temperatures than at low temperatures.

Comparative Investigation of the Spherical Acoustic Microbubble Models in an Unbounded Liquid.

Microbubble oscillating associated with many applications in biomedical and engineering sectors. The spherical oscillations of a single microbubble submerged in a quiescent liquid exerted by an acoustic force can be governed either by the Rayleigh-Plesset (RP) equation or by the Keller-Miksis (KM) equation under different physical assumptions. In this paper, both models were numerically and analytically analyzed, and the systematic parametric study was performed. The viscosity and compressibility effects and linearization in both models were investigated with the aids of MATLAB and Maple tools.  In KM, the effects of the linear and nonlinear equations of states (EOS) compared for updating density with time. At the minimum bubble radius, the liquid viscosity surrounding bubble surface expected to be decreased due to rising in temperature. This leads to effects the maximum bubble radius for upcoming cycles.

Influence of the nonequilibrium phase transition on the collapse of inertia nonspherical bubbles in a compressible liquid

In this work, we investigate the shock wave–inertial vapor bubble interactions by taking the nonequilibrium phase transition at the interface, fluid compressibility, and axisymmetric bubble deformations including jet penetration into account. We use the level set method (Sussman et al., 1994) and the ghost fluid method (Fedkiw et al., 1999), which were improved so as to consider the nonequilibrium phase transition (Jinbo & Takahira, 2012). The numerical treatments for heat and mass fluxes through interfaces due to the phase transition are implemented, satisfying the conservation laws of mass, momentum, and energy at the interface and preventing the interface from becoming diffused. The influence of surface tension is also considered in the method. The improved method is applied to the shock–bubble interaction under the experimental conditions by Sankin et al. (2005). The pressure waveform of the incident shock wave is comprised of a leading compressive wave with a peak pressure of 39MPa and a pulse duration of around 1μs, followed by a trailing tensile wave of −8MPa in peak pressure with a pulse duration of around 2μs which is determined from the experiment. The liquid-jet formation and the generation of shock waves from the collapsing nonspherical bubble are simulated successfully by taking the nonequilibrium phase transition and surface tension into account. The validity of the simulation is shown by comparing the numerical results (e.g. the intensity of the shock wave generated by the bubble collapse and displacement of the bubble centroid) with those obtained from the experiments (Sankin et al., 2005; Klaseboer et al., 2007). We investigate the effects of the phase of bubble oscillations when the incident shock wave impinges on the spherically-shrinking bubble, on the shock wave radiated from the bubble collapse. It is also shown that when the nonequilibrium phase transition at the interface of nonspherically collapsing bubbles is considered, the minimum bubble radius and the maximum space-averaged pressure value inside the bubble reached during its collapse decreases and increases, respectively, compared with those in the case without the phase transition.

Bubble size distribution in acoustic droplet vaporization via dissolution using an ultrasound wide-beam method

Performance and efficiency of numerous cavitation enhanced applications in a wide range of areas depend on the cavitation bubble size distribution. Therefore, cavitation bubble size estimation would be beneficial for biological and industrial applications that rely on cavitation. In this study, an acoustic method using a wide beam with low pressure is proposed to acquire the time intensity curve of the dissolution process for the cavitation bubble population and then determine the bubble size distribution. Dissolution of the cavitation bubbles in saline and in phase-shift nanodroplet emulsion diluted with undegassed or degassed saline was obtained to quantify the effects of pulse duration (PD) and acoustic power (AP) or peak negative pressure (PNP) of focused ultrasound on the size distribution of induced cavitation bubbles. It was found that an increase of PD will induce large bubbles while AP had only a little effect on the mean bubble size in saline. It was also recognized that longer PD and higher PNP increases the proportions of large and small bubbles, respectively, in suspensions of phase-shift nanodroplet emulsions. Moreover, degassing of the suspension tended to bring about smaller mean bubble size than the undegassed suspension. In addition, condensation of cavitation bubble produced in diluted suspension of phase-shift nanodroplet emulsion was involved in the calculation to discuss the effect of bubble condensation in the bubble size estimation in acoustic droplet vaporization. It was shown that calculation without considering the condensation might underestimate the mean bubble size and the calculation with considering the condensation might have more influence over the size distribution of small bubbles, but less effect on that of large bubbles. Without or with considering bubble condensation, the accessible minimum bubble radius was 0.4 or 1.7μm and the step size was 0.3μm. This acoustic technique provides an approach to estimate the size distribution of cavitation bubble population in opaque media and might be a promising tool for applications where it is desirable to tune the ultrasound parameters to control the size distribution of cavitation bubbles.

Energy Balance for a Sonoluminescence Bubble Yields a Measure of Ionization Potential Lowering

Application of energy conservation between input sound and the microplasma which forms at the moment of sonoluminescence places bounds on the process, whereby the gas is ionized. Detailed pulsed Mie scattering measurements of the radius versus time for a xenon bubble in sulfuric acid provide a complete characterization of the hydrodynamics and minimum radius. For a range of emission intensities, the blackbody spectrum emitted during collapse matches the minimum bubble radius, implying opaque conditions are attained. This requires a degree of ionization >36%. Analysis reveals only 2.1±0.6 eV/atom of energy available during light emission. In order to unbind enough charge, collective processes must therefore reduce the ionization potential by at least 75%. We interpret this as evidence that a phase transition to a highly ionized plasma is occurring during sonoluminescence.

Numerical Simulation on Collapse of Vapor Bubble Using Particle Method

In this paper, the collapse of a void bubble filled with vapor content is numerically investigated using a novel moving particle semi-implicit with meshless advection by flow-directional local grid (MPS-MAFL) method. The interfacial velocity, collapse time, bubble shape variation, peak pressure, rebound bubble radius, and other interesting parameters were obtained and are discussed profoundly. The vapor bubble undergoes several cycles of oscillation with reduced amplitude during the whole collapse process, which is similar to cavitation bubble collapse. The computational results show that the bubble collapse time is linearly proportional to the initial bubble size, which agrees with the Rayleigh equation. The minimum rebound bubble radius ratio is less affected by initial bubble size for a large bubble. Comparison work was also conducted against experimental data by Board and Kimpton. The comparison revealed that the MPS method supplied with an adiabatic compression assumption for vapor content is more suitable to evaluate the collapse behaviors of a low-pressure vapor bubble. This work is helpful for further application of the moving particle semi-implicit with meshless advection using flow-directional local grid (MPS-MAFL) method to solving complicated bubble dynamics.

Oscillation characteristics of a laser-induced cavitation bubble in water at different temperatures

Comprehensive numerical and experimental analyses of the effect of temperature on cavitation oscillations are performed. In the experimental study, the oscillation of a laser-generated single cavitation bubble near a rigid boundary is obtained using a fiber-optic diagnostic technique based on optical beam detection (OBD). The maximum and minimum bubble radii as well as the oscillation times for each oscillation cycle are determined according to the characteristic signals. And cavitation bubble tests are performed using water at different temperatures, and its temperature ranges from freezing point (0 °C) to near boiling. Furthermore, a modified Rayleigh–Plesset equation is derived for calculating the temporal development of the bubble radius at different temperatures. Both the experimental and the numerical results show that the maximum bubble radius and bubble lifetime both increase as temperature increases. The mechanism behind it has also been discussed.

The collapse and rebound of gas–vapor cavity on metal surface

The oscillation property of a gas–vapor cavity near a solid boundary is investigated by a sensitive fiber-optic sensor based on optical beam deflection principle when a high-intensity laser pulse is focused on an aluminum surface in water. The temporal and spatial evolutions of the bubble wall during the expansion and collapse are traced according to sequence waveforms induced by the bubble motion. Both the maximum and minimum bubble radii at each oscillating cycle are determined by experiment. Further, in combination with the spherical bubble theory, the variation of the gas content remaining in the cavity during each pulsation is estimated by the method of fitting curve. The results show that about half of the gas content is dissolved into the surrounding water during the whole process. The less gas content in the cavity makes the bubble contract more violently. The corresponding minimum radius and the collapsing duration become smaller and shorter.

New suggestion concerning the origin of sonoluminescence

We suggest a new mechanism where sonoluminescence is produced by the tremendously large adiabatic pressure pulse (shock wave) generated by the close to supersonic (or above) impact of the fluid on the hard core bubble. The light flash is mostly emitted by the fluid surrounding the bubble. More generally, the emission spectrum of any material submitted to a large adiabatic compression is (roughly) globally dilated by some Grüneisen coefficient γ ̄ . Temperature simultaneously increases by the same factor, which increases the power of the emitted radiation by a factor γ ̄ 4 . A rigorous lower bound for the sound velocity in the compressed region at impact is obtained with purely kinematic arguments only assuming the existence of a non-negative Van der Waals volume for the fluid. For supersonic impacts, the increase of the sound velocity reaches at least one order of magnitude (and, with reasonable assumptions, much more), which yields an estimation of the Grüneisen coefficient γ ̄ and indicates it may become very large. Then, during the pressure pulse, the thermal infrared (IR) radiation of the compressed fluid can be extended up to visible–ultraviolet (UV) simultaneously with an intense brightness. The dynamics of collapsing bubbles have been analyzed taking into account fluid compressibility. Shock waves are generated when the bubble, at a minimum radius, suddenly becomes almost incompressible. For impacts close to supersonic (or above), an intense pressure is briefly generated in a sphere which extends beyond the central bubble and which thus mostly contains surrounding fluid compacted to near its Van der Waals volume. This compacted fluid generates an intense emission of UV–visible light which suddenly disappears when the fluid expands from its Van der Waal volume. This situation occurs when the sphere of compacted fluid reaches a critical size of a few minimum bubble radii. Next, this pressure pulse radially propagates through the fluid, initially at highly supersonic velocities, which decay to the normal sound velocity as it simultaneously spreads out.

The collapse and rebound of laser-induced cavitation bubble in viscous fluid

The oscillation property of a laser-induced cavitation bubble in a viscous fluid is investigated by a sensitive fiber-optic sensor based on optical beam deflection. The temporal and spatial evolutions of the bubble wall during the expansion and collapse are traced according to sequential waveforms induced by the bubble oscillation. Both the maximum and minimum bubble radii at each oscillation cycle are determined by experiment. Further, in combination with the theoretical analysis and numerical calculation, the variation of the maximum and minimum radii during oscillation and life-time of the bubble in different viscous fluids is obtained. The experimental results indicate that the liquid viscosity has an obvious influence on the bubble oscillation; larger viscosity makes the bubble contract more slowly, and the corresponding minimum radius and the bubble life-time become larger and longer, while the maximum radius is smaller.

Cavitation under spherical focusing of acoustic pulses

The early stage of the dynamics of interacting cavitation bubbles in a transmitted spherically focused pulsed wave consisting of compression and rarefaction phases is studied. The cavitation is investigated away from the liquid boundaries for negative pressures up to −42 MPa with a decrease rate of −40 MPa/μs by high-speed microscopic filming (100 million frames per second and a spatial resolution of 5–50μm/pixel) and pressure measurements. It is demonstrated that, according to the kinematics of size variation, the bubbles are separated into two fractions: expanding and collapsing ones. Experimental data provide grounds to assume that the formation of a two-fraction bubble cluster occurs on account of different threshold values of pressure in the rarefaction wave for two characteristic sizes of nuclei, namely, micronuclei (d I < 10μm) and nanonuclei (“bubstons,” d II ∼ 1 nm), which become detectable only when the rarefaction wave amplitude exceeds the critical one. Pulsed compression of small bubbles in the process of transformation of a rarefaction wave into a compression wave occurs under the effect of a cluster’s internal pressure up to 20 MPa and proceeds with the conservation of the spherical shape of the second-fraction bubbles. It is demonstrated that the velocity of the center of mass of a bubble reaches its peak value close to the moment of bubble collapse. The translational and radial dynamics of a bubble are studied in a numerical experiment using the Rayleigh-Plesset equation and taking into account the viscous force and the pressure gradient. The results of measuring the translational shift may be useful for estimating the minimum bubble radius by comparing the numerical results with the experiment.

What are the limits of energy focusing in sonoluminescence?

Sonoluminescence (‘‘SL’’) is an amazing marker for the extraordinary degree of acoustic energy focusing achieved in a cavitating bubble. Local energy dissipation exceeds Kirchhoff’s law by 1015 and the ambient acoustic energy density concentrates by 12 orders of magnitude to create picosecond flashes of broadband ultraviolet light. For single bubbles driven at 30 kHz, SL is nature’s smallest blackbody. Therefore the bubble’s interior is such a dense plasma that the photon-matter mean-free path is shorter than the wavelength of light. Excitation of a vertical column of fluid (∼50 Hz), so as to create a water hammer, upscales flash energy by a factor over one million, achieving peak powers approach 1 W. At 1 MHz the spectrum resembles Bremsstrahlung from a transparant plasma with a temperature ∼1 MK. At 10 MHz the collapsed size of the SL bubble approaches 10 nm, which raises the possibility that the SL parameter space may extend to the domain of quantum mechanics. At 30 MHz experiments are under way to excite sonoluminescence with sound fields in excess of 3000 atm. The strongest cavitation collapses may be realized with Greenspan’s ultrasonic resonators that reach fields in excess of 20 atm without cavitating. When bubbles are seeded with an external laser a massive cavitation event ensues.

Shock-wave propagation and cavitation bubble oscillation by Nd:YAG laser ablation of a metal in water.

A highly sensitive fiber-optic sensor based on optical beam deflection is applied for investigating the propagation of a laser-induced plasma shock wave, the oscillation of a cavitation bubble diameter, and the development of a bubble-collapse-induced shock wave when a Nd:YAG laser pulse is focused upon an aluminum surface in water. By the sequence of experimental waveforms detected at different distances, the attenuation properties of the plasma shock wave and of the bubble-collapse-induced shock wave are obtained. Besides, based on characteristic signals, both the maximum and the minimum bubble radii at each oscillation cycle are determined, as are the corresponding oscillating periods.

What are the limits of energy focusing in sonoluminescence?

Sonoluminescence [SL] is amazing for the extraordinary degree by which ultrasonic energy can be focused by a cavitating bubble. Local energy dissipation exceeds Kirkhoff’s law by 1E15 and the acoustic energy density concentrates by 12 orders of magnitude to create picosecond flashes of broadband ultraviolet light. At the minimum bubble radius, the acceleration exceeds 1E11 g and a megabar level shock wave is emitted into the surrounding fluid. For single bubbles driven at 30 KHz, SL is nature’s smallest blackbody. This implies that the bubble’s interior is such a dense plasma that the photon-matter mean free path is shorter than the wavelength of light, and suggests that SL originates in an unusual state of matter. Excitation of a vertical column of fluid [∼10 Hz] so as to create a water hammer leads to the upscaling of SL and generation of flashes of light with 3E8 photons and peak powers approaching 1 W. At 1 MHz, the spectrum resembles bremsstrahlung from a transparent plasma with a temperature ∼1 MK. At 10 MHz the collapsed size of the SL bubble approaches 10 nm, which raises the possibility that the SL parameter space may extend to the domain of quantum mechanics. [Research supported by DARPA and DOE.]

Dynamics of laser-induced cavitation bubbles

Single cavitation bubble luminescence induced by laser in contrast to single bubble sonoluminescence has no need in a sound field for a strong collapse and for light emission. The cavitation bubbles are produced by focused laser light and make the single strong collapse. As shown experimentally, the number of emitted photons from cavitation luminescence is much greater than it was observed in sonoluminescence due to the large bubble size during the final stage of collapse. To describe the process of laser-induced bubble collapse a mathematical model is used, which is based upon the spherically symmetric motion including compressibility, heat and mass transfer effects. The basic results of the numerical solution are presented for the bubbles with maximum radii of about 1 mm. According to the observed results the minimum bubble radius in collapse is about 15 μm, and the mass decreases up to 5% of the initial value. Calculations with a small amounts of noncondensable gas inside the bubble predict its strong influence on the dynamics. As shown numerically the theoretical model gives a good agreement with experimental measurements.

Observation of bubble dynamics within luminescent cavitation clouds: Sonoluminescence at the nano-scale.

Measurements of acoustically driven cavitation luminescence indicate that this phenomenon is robust over a huge parameter space ranging from 10 kHz to >10 MHz. The minimum bubble radius achieved is an upper bound for the size of the light-emitting region and ranges from about 1 microm at 15 kHz to tens of nm at 11 MHz. Although lines can be discerned in the spectra of some cavitation clouds, they sit on top of a broadband continuum which can have greater spectral density in the ultraviolet than is observed for resonantly driven sonoluminescence from a single bubble.

Mie scattering from a sonoluminescing bubble with high spatial and temporal resolution

The dynamics of a single-air bubble trapped in a resonant sound field in water has been characterized by Mie scattering and a Streak camera with high spatial and temporal resolution. The streak images show that in the endphase of the cavitation collapse the scattered light intensity is no function of the bubble radius anymore. In the last nanoseconds around minimum bubble radius most of the light is scattered at the highly compressed water surrounding the bubble and not at the bubble wall. This leads to a minimum in the scattered light intensity about 700 ps before the sonoluminescence pulse is emitted. And neglecting this changes leads to a strong overestimation of the bubble-wall velocity. In the reexpansion phase the high spatial resolution of the streak camera allows one to distinguish between the light scattered at the bubble wall and the light scattered at the outgoing shock wave.