Bubble Collapse Time Research Articles

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.

A cavitation detector for microbubble therapy based on the Stockwell transform

Quantification of the wideband signal associated with bubble collapse is desirable to measure cavitation dosage during microbubble therapy. We have developed a cavitation detection algorithm based on time-frequency analysis with the Stockwell transform. This transform is ideal since it isolates cavitation transients in time and frequency at much higher resolution than other time-frequency methods. In this study, we acquired simultaneous high-speed images and acoustic signals from bubbles undergoing oscillation during acoustic pulses commonly used for permeability enhancement (Transmit: 1.5 MHz, 10-cycle, peak negative pressure range 150–500 kPa, Receive: 15 MHz cavitation detector). Above 200 kPa, linescan vs time images showed relative bubble expansion greater than 2 and echoes contained a wideband signal that coincided with bubble collapse. The Stockwell transform of detected echoes revealed wideband spectrums localized to the time of bubble collapse. After filtering below 4 MHz to reject linear echoes, the root mean square (RMS) of the spectral amplitude was obtained from the time-frequency decomposition, yielding peaks at cavitation transients. The magnitude of the Fourier transform of the RMS signal at 1.5 MHz provided a sensitive indicator for bubble collapse and differed significantly across pressures where cavitation occurred (p < 0.05,t-test). The proposed measurement provides a sensitive metric for cavitation activity during microbubble therapy.

Reduction of Bubble Cavitation by Modifying the Diffraction Wave from a Lithotripter Aperture

A new method was devised to suppress the bubble cavitation in the lithotripter focal zone to reduce the propensity of shockwave-induced renal injury. An edge extender was designed and fabricated to fit on the outside of the ellipsoidal reflector of an electrohydraulic lithotripter to disturb the generation of diffraction wave at the aperture, but with little effect on the acoustic field inside the reflector. Although the peak negative pressures at the lithotripter focus using the edge extender at 20 kV were similar to that of the original configuration (-11.1 ± 0.9 vs -10.6 ± 0.7 MPa), the duration of the tensile wave was shortened significantly (3.2 ± 0.54 vs 5.83 ± 0.56 μs, P<0.01). There is no difference, however, in both the amplitude and duration of the compressive shockwaves between these two configurations as well as the -6 dB beam width in the focal plane. The significant suppression effect of bubble cavitation was confirmed by the measured bubble collapse time using passive cavitation detection. At the lithotripter focus, while only about 30 shocks were needed to rupture a blood vessel phantom using the original HM-3 reflector at 20 kV, no damage could be produced after 300 shocks using the edge extender. Meanwhile, the original HM-3 lithotripter at 20 kV can achieve a stone comminution efficiency of 50.4 ± 2.0% on plaster-of-Paris stone phantom after 200 shocks, which is comparable to that of using the edge extender (46.8 ± 4.1%, P=0.005). Modifying the diffraction wave at the lithotripter aperture can suppress the shockwave-induced bubble cavitation with significant reduced damage potential on the vessel phantom but satisfactory stone comminution ability.

The acoustics of cavitation in spool valve with U-notches

Spiral cavity produced by the swirling flow is observed in spool valve with U-notches. Individual bubbles with similar grown-up size appear in the wake of the fixed cavity. Consecutive bubble collapse produces frequency peak in the spectra, which decreases with the cavitation number. Vortex shedding occurs by the ‘break-off’ of the tail of the spiral cavity, the collapse of which affects significantly to those accompanied individual bubbles dynamics and acoustics. Rayleigh prediction to the bubble collapse time is taken, which is a bit smaller than the experimental result. The considerable viscidity effect of the oil medium is assumed as the predominant reason.

The collapse of a bubble against infinite and finite rigid boundaries for underwater laser propulsion

In order to investigate the influence of a bubble on underwater laser propulsion, the analytical formula of the bubble collapse time near rigid boundary is deduced from Rayleigh collapse time and Rattray prolongation factor. Experiments and numerical simulations are employed to validate the collapse time formula. The collapsing features of a bubble, including the maximum bubble radius Rmax, the collapse time of the bubble TCR, the shock wave and liquid jet emitted during the bubble collapse, are obtained near infinite and finite rigid boundaries. The theoretical, numerical and experimental results for the dimensionless distance γ &amp;gt; 1 all illuminate that TCR increases with Rmax near the rigid boundary. Rmax and TCR increase with the laser energy first, then begin to level out as the laser energy continues to increase, thus it is impossible to increase the propelling force just through increasing the laser pulse energy continuously. In addition, TCR is smaller, and the shock wave pressure and the liquid jet velocity are larger near the finite rigid boundary than that near the infinite rigid boundary, which means that the bubble collapses fiercer in the former case, in other words the finite rigid boundary gets more propelling force.

A Data Acquisition System to Detect Bubble Collapse Time and Pressure Losses in Water Cavitation

This paper presents a data acquisition system oriented to detect bubble collapse time and pressure losses in water cavitation in an internal orifice. An experimental campaign on a cavitating flow of water through an orifice has been performed to analyze the flow behavior at different pressures and temperatures. The experiments were based on visual observations and pressure fluctuations frequency analysis. Comparing the visual observations and the spectral analysis of the pressure signals, it is evident that the behavior of the different cavitating flows can be correlated to the frequency spectrum of the upstream, downstream and differential pressure fluctuations. The further reduction of the cavitation number and the consequent increase in the width of the cavitating area are related to a corresponding significant increase of the amplitude of typical frequency components. The spectrogram analysis of the pressure signals leads to the evaluation of the bubble collapse time, also compared with the numerical results calculated by the Rayleigh–Plesset equation.

Numerical Solution on Spherical Vacuum Bubble Collapse Using MPS Method

Single vacuum bubble collapse in subcooled water has been simulated using the moving particle semi-implicit (MPS) method in the present study. The liquid is described using moving particles, and the bubble-liquid interface was set to be the vacuum pressure boundary without interfacial heat mass transfer. The topological shape of the vacuum bubble is determined according to the location of interfacial particles. The time dependent bubble diameter, interfacial velocity, and bubble collapse time were obtained within a wide parametric range. Comparison with Rayleigh’s prediction indicates a good consistency, which validates the applicability and accuracy of the MPS method. The potential void-induced water hammer pressure pulse was also evaluated, which is instructive for the cavitation erosion study. The present paper discovers fundamental characteristics of vacuum bubble hydrodynamics, and it is also instructive for further applications of the MPS method to complicated bubble dynamics.

Numerical simulation on void bubble dynamics using moving particle semi-implicit method

In present study, the collapse of void bubble in liquid has been simulated using moving particle semi-implicit (MPS) code. The liquid is described using moving particles and the bubble–liquid interface was set to be vacuum pressure boundary without interfacial heat mass transfer. The topological shape of bubble can be traced according to the motion and location of interfacial particles. The time dependent bubble diameter, interfacial velocity and bubble collapse time were obtained under wide parametric range. The comparison with Rayleigh and Zababakhin's prediction showed a good agreement which validates the applicability and accuracy on MPS method in solving present momentum problems. The potential void induced water hammer pressure pulse was also evaluated which is instructive for further material erosion study. The bubble collapse with non-condensable gas has been further simulated and the rebound phenomenon was successfully captured which is similar with vapor-filled cavitation phenomenon. The present study exhibits some fundamental characteristics of void bubble hydrodynamics and it is also expected to be instructive for further applications of MPS method to complicated bubble dynamics problems.

Experimental investigation of the collapse of laser-generated cavitation bubbles near a solid boundary

The oscillation of a laser-generated single cavitation bubble near a solid boundary is investigated by a fiber-optic diagnostic technique based on optical beam deflection (OBD). The maximum bubble radii and collapse time for each oscillation cycle are determined from a sequence of bubble oscillations. Furthermore, by combining the revised Rayleigh theory, the prolongation factor κ at different dimensionless parameter γ ( γ = L / R max , where R max is the maximum bubble radius and L is the distance of a cavity inception point from a boundary) is obtained. In addition, the prolongation factor of the collapse time versus laser energy is also derived, which are valuable in the fields of hydraulic cavitation, laser lithotripsy and laser ophthalmology.

Formation of nano-and microspherules of minerals in ore deposits depending on depth of host rock occurrence

The cavitation and cavitation-ablation mechanisms of formation of mineral nano-and microspherules in hydrothermal fluids are considered. The formation conditions of nano-and microspherules were studied with regard to the depth of host rock occurrence on the basis of the theory describing the cavitation mechanism. It is shown that the temperature and pressure of hydrothermal fluid as functions of the depth of host rock occurrence may markedly affect the dimensions of cavitation bubbles, the temperature within them at the moment of greatest compression, and the time of bubble collapse in the fluid. the dimensions of nano-and microspherules produced by cavitation depend only slightly on the depth of host rock occurrence and are mainly controlled by the thermophysical properties of their constituents. Characteristic dimensions of nanospherules formed as a result of ablation from the surface of overheated material have been obtained.

Simulations of pressure pulse–bubble interaction using boundary element method

We propose a methodology based on the boundary element method (BEM) to simulate pressure pulse–bubble interaction. The pulse resembles a shock wave and is in the form of a step pulse function incorporated into the Bernoulli equation. Compressibility effects of the water surrounding the bubble are neglected, and the dynamic response of the bubble to the impinging pulse is assumed to be mainly inertia controlled. The interaction induces the formation of a high-speed jet that penetrates the bubble. Results show that bubble shape, collapse time and jet velocity are in good agreement with other numerical models and experiments, and the method is more computationally efficient.

A Three‐Regime Model of Speculative Behaviour: Modelling the Evolution of the S&amp;P 500 Composite Index

We examine whether a three‐regime model that allows for dormant, explosive and collapsing speculative behaviour can explain the dynamics of the S&P 500. We extend existing models of speculative behaviour by including a third regime that allows a bubble to grow at a steady rate, and propose abnormal volume as an indicator of the probable time of bubble collapse. We also examine the financial usefulness of the three‐regime model by studying a trading rule formed using inferences from it, whose use leads to higher Sharpe ratios and end of period wealth than from employing existing models or a buy‐and‐hold strategy.

The influence of the laser spot size and the pulse number on laser-induced backside wet etching

The laser-induced backside wet etching (LIBWE) of transparent solids at the interface to absorbing liquid is a new promising method for laser microstructuring. The influence of the laser spot size and the applied pulse number to the etch rate were investigated in detail for fused silica and two different liquids. Additional to the significant rise of the etch rate with increasing spot size considerable incubation effects have been observed at low laser fluences and pulse numbers. Based on the bubble formation during LIBWE processing, a relation between the bubble collapse time and the etch rate was ascertained. This relation fits the etch rate dependence on the spot size well. It is assumed that the deposition of decomposition products from the bubble accounts for the spot size influence the etch rate.

Surface tension effects on the behavior of a cavity growing, collapsing, and rebounding near a rigid wall

Surface tension effects on the behavior of a pure vapor cavity or a cavity containing some noncondensible contents, which is growing, collapsing, and rebounding axisymmetrically near a rigid wall, are investigated numerically by the boundary integral method for different values of dimensionless stand-off parameter gamma, buoyancy parameter delta, and surface tension parameter beta. It is found that at the late stage of the collapse, if the resultant action of the Bjerknes force and the buoyancy force is not small, surface tension will not have significant effects on bubble behavior except that the bubble collapse time is shortened and the liquid jet becomes wider. If the resultant action of the two force is small enough, surface tension will have significant and in some cases substantial effects on bubble behavior, such as changing the direction of the liquid jet, making a new liquid jet appear, in some cases preventing the bubble from rebound before jet impact, and in other cases causing the bubble to rebound or even recollapse before jet impact. The mechanism of surface tension effects on the collapsing behavior of a cavity has been analyzed. The mechanisms of some complicated phenomena induced by surface tension effects are illustrated by analysis of the computed velocity fields and pressure contours of the liquid flow outside the bubble at different stages of the bubble evolution.

Reduction of tissue injury in shock-wave lithotripsy by using an acoustic diode

An acoustic diode (AD) was constructed of two acoustic transparent membranes with good initial contact to allow the transmission of the positive pressure of lithotripter shock wave at an almost unaltered level, yet attenuate significantly its negative pressure, was fabricated. It was evaluated systematically on a Dornier HM-3 lithotripter to assess its application potential to reduce vascular injury without compromising stone fragmentation efficiency during shock-wave lithotripsy. By inserting the AD, the maximum compressive pressure, maximum tensile pressure and tensile duration of the lithotripter shock wave were formed to drop from 49.7 to 47.8 MPa, −7.5 to −7.0 MPa and 6.0 to 5.1 μs, respectively. Damage of a 0.2-mm inner diameter vessel phantom (cellulose hollow fiber) was reduced from rupture after 31 ± 11 shocks to no rupture after 100 shocks. Maximum bubble size in free-field, maximum dilation of the vessel phantom wall and bubble collapse time became smaller with the use of the AD. However, stone fragmentation showed similar results without a statistically significant difference between the case with and without the AD. All these evidences suggest that the use of an acoustic diode may be a feasible approach to reduce tissue injury without compromising stone comminution in shock-wave lithotripsy. (E-mail: slzhu@duke.edu)

Dependence on liquid temperature and purity of light emission characteristics in single cavitation bubble luminescence

We produced single bubbles in water using a visible pulsed laser and studied the characteristics of the light emitted during the bubble collapse time as a function of the water temperature for different water purity values. The water temperature ranged from freezing point (0 °C) to near boiling. We measured the luminescence pulse for the mentioned temperature range at various purity values. We also obtained the average bubble lifetime and the average luminescence pulse emitted as a function of water temperature. The main conclusion was that the luminescence can be modified by the water quality and by the water temperature. Maximum luminescence was obtained near the water freezing point.

Effects of an acoustic diode on the pressure waveform and cavitation bubble dynamics produced by a piezoelectric shock wave generator

High-speed schlieren imaging, combined with fiber optical probe hydrophone (FOPH) and passive cavitation detection (PCD) were used to access the effects of an acoustic diode (AD) on the pressure waveform and associated cavitation activities produced by a piezoelectric shock wave (PSW) generator. Without the AD, a typical pressure waveform at the focus of the PSW generator consists of a leading shock wave, followed by a tensile wave and several oscillation waves (OWs) of gradually reduced amplitudes. When the AD was placed 30 mm in front of the focus, the amplitude of the tensile wave was reduced and the subsequent OWs were removed. The pulse intensity integral of the tensile wave was reduced by 58%, and subsequently, PSW-induced bubble dynamics were altered significantly. Based on PCD data, the collapse time of cavitation bubble(s) was reduced by about 11%. Although intensive collapse of microbubbles was observed in about 10 μs following the shock front of the original PSW, the forced collapse of microbubbles was not observed when the AD was used, presumably due to the removal of the OWs. Theoretical calculation based on the Gilmore model confirmed these experimental observations. [Work supported by the Whitaker Foundation and NIH.]

Optimal resonant stimulation of sonoluminescence

In single-bubble sonoluminescence, a bubble is levitated and forced to oscillate by a standing sound wave. Once per cycle, at the maximum compression of the bubble volume, the emission of a pulse of visible light is observed; due to the strong bubble collapse, a shock wave is emitted in the liquid also. It was found that these shock waves can be visualized by the means of a schlieren method. Using a stroboscopic illumination of the bubble, its dynamical behavior and the shocks can be recorded in slow motion by a video camera. Experimentally measured velocities of the shock waves were compared with numerical calculations. Further, the recorded shock waves contain information about the bubble position and collapse time. In the regime of instable sonoluminescence, sudden changes in bubble position depending on bubble size were observed. The phenomenon in the context of interactions of the bubble with the complex sound field is discussed. [Work supported by the DFG (SFB 185).]

A new shock pressure waveform to amplify transient cavitation effect

Shock-wave-induced tissue damage and/or stone disintegration are greatly dependent on cavitation effect. In order to control this effect in tissue, a new piezocomposite shock-wave generator (200 mm in diameter and focused at 190 mm) has been developed with the capability of producing two different kinds of shock pressure-time waveform at its focus (type 1: a tensile wave followed by a compressive wave, and type 2: a compressive wave followed by a tensile wave). The cavitation effects produced by these two pressure waveforms were compared in the following experiments: (1) measurement of cavitation bubble collapse time (defined as the time difference between the shock wave arrival and the main bubble collapse), (2) study of cavitation-induced destructive effects in the agar gel, (3) study of disintegration rate on plaster balls (a kidney stone-mimicking material), and (4) study of cavitation-induced destructive effects on rabbit liver in vivo. All of these experiments revealed the amplified effect of transient cavitation produced by the type 1 pressure-time waveform. Comparisons with a computed simulation using the Gilmore Akulichef model, taking into account the rectified diffusion, confirm the experimental results. It is concluded that the temporal characteristics of the shock pressure waveform have a major influence on transient cavitation.

Use of two pulses to control cavitation in lithotripsy

In lithotripsy acoustic cavitation appears to play a role in both comminution of kidney stones and damage to tissue. To investigate the role of cavitation, we used a pair of confocal electrohydraulic lithotripters (ellipsoidal reflectors). A delay in firing of Δt modified the cavitation field without altering the peak positive and negative pressures. Bubble collapse time tc, measured by passively detecting acoustic emissions generated by the bubble, was used as a measure of cavitation activity. A two-pulse sequence from the source shortened tc relative to the single pulse value tc1. Collapse times calculated by using the Gilmore equation agreed well with measurements. Relative intensity of bubble collapse was determined by depth of pits created in aluminium foil. For pulse delays Δt&amp;lt;0.3tc1 the pit size decreased, a result that implies the second pulse stifled the collapse. Conversely, for delays in the range 0.5tc1&amp;lt;Δt&amp;lt;tc1, cavitation apparently intensified, since pit depth increased by a factor of up to 2. Pit depth correlates well with (calculated) pressure radiated by the bubble. When the two reflectors were pointed at each other and fired simultaneously, pitting was localized to a spot less than 1 cm in diameter. [Work supported by ONR, ARL:UT IR &amp; D, and NIH PO1-DK43881.]