Numerical modelling of acoustic cavitation threshold in water with non-condensable bubble nuclei

Numerical modelling of acoustic cavitation threshold in water is presented taking into account non-condensable bubble nuclei, which are composed of water vapor and non-condensable air. The cavitation bubble growth and collapse dynamics are modeled by solving the Rayleigh-Plesset or Keller-Miksis equation, which is combined with the energy equations for both the bubble and liquid domains, and directly evaluating the phase-change rate from the liquid and bubble side temperature gradients. The present work focuses on elucidating acoustic cavitation in water with a wide range of cavitation thresholds (0.02–30 MPa) reported in the literature. Computations for different nucleus sizes and acoustic frequencies are performed to investigate their effects on bubble growth and cavitation threshold. The numerical predictions are observed to be comparable to the experimental data in the previous works and show that the cavitation threshold in water has a wide range depending on the bubble nucleus size.     

Cavitation resistance of cryogenic liquids: Incubation time criterion

Experimental data on acoustic cavitation in cryogenic liquids are analyzed using a criterion based on the incubation time concept. An analogous approach was successfully used earlier for analyzing the cavitation resistance of degassed and sea water at constant temperature. The proposed criterion takes into account the change in the static cavitation threshold and incubation time upon an increase in temperature.     

Comparison between maximum radial expansion of ultrasound contrast agents and experimental postexcitation signal results

Experimental postexcitation signal data of collapsing Definity microbubbles are compared with the Marmottant theoretical model for large amplitude oscillations of ultrasound contrast agents (UCAs). After taking into account the insonifying pulse characteristics and size distribution of the population of UCAs, a good comparison between simulated results and previously measured experimental data is obtained by determining a threshold maximum radial expansion (Rmax) to indicate the onset of postexcitation. This threshold Rmax is found to range from 3.4 to 8.0 times the initial bubble radius, R0, depending on insonification frequency. These values are well above the typical free bubble inertial cavitation threshold commonly chosen at 2R0. The close agreement between the experiment and models suggests that lipid-shelled UCAs behave as unshelled bubbles during most of a large amplitude cavitation cycle, as proposed in the Marmottant equation.     

Monitoring of transient cavitation induced by ultrasound and intense pulsed light in presence of gold nanoparticles

One of the most important challenges in medical treatment is invention of a minimally invasive approach in order to induce lethal damages to cancer cells. Application of high intensity focused ultrasound can be beneficial to achieve this goal via the cavitation process. Existence of the particles and vapor in a liquid decreases the ultrasonic intensity threshold required for cavitation onset. In this study, synergism of intense pulsed light (IPL) and gold nanoparticles (GNPs) has been investigated as a means of providing nucleation sites for acoustic cavitation. Several approaches have been reported with the aim of cavitation monitoring. We conducted the experiments on the basis of sonochemiluminescence (SCL) and chemical dosimetric methods. The acoustic cavitation activity was investigated by determining the integrated SCL signal acquired over polyacrylamide gel phantoms containing luminol in the presence and absence of GNPs in the wavelength range of 400–500 nm using a spectrometer equipped with cooled charged coupled devices (CCD) during irradiation by different intensities of 1 MHz ultrasound and IPL pulses. In order to confirm these results, the terephthalic acid chemical dosimeter was utilized as well. The SCL signal recorded in the gel phantoms containing GNPs at different intensities of ultrasound in the presence of intense pulsed light was higher than the gel phantoms without GNPs. These results have been confirmed by the obtained data from the chemical dosimetry method. Acoustic cavitation in the presence of GNPs and intense pulsed light has been suggested as a new approach designed for decreasing threshold intensity of acoustic cavitation and improving targeted therapeutic effects.     

An equivalent method of jet impact loading from collapsing near-wall acoustic bubbles: A preliminary study

Cavitation damage is a micro, high-speed, multi-phase complex phenomenon caused by the near-wall bubble group collapse. The current numerical simulation method of cavitation mainly focuses on the collapse impact of a single cavitation bubble. The large-scale simulation of the cavitation bubble group collapse is difficult to perform and has not been studied, to the best of our knowledge. In this study, the equivalent model of impact loading of acoustic bubble collapse micro-jets is proposed to study the cavitation erosion damage of materials. Based on the theory of the micro-jet and the water hammer effect of the liquid–solid impact, an equivalent model of impact loading of a single acoustic bubble collapse micro-jet is established under the principle of deformation equivalence. Since the acoustic bubbles can be considered uniformly distributed in a small enough area, an equivalent model of impact loading of multiple acoustic bubble collapse micro-jets in a micro-segment can be derived based on the equivalent results of impact loading of a single acoustic bubble collapse micro-jet. In fact, the equivalent methods of cavitation damage loading for single and multiple near-wall acoustic bubble collapse micro-jets are formed. The verification results show the law of cavitation deformation of concrete using equivalent loading is consistent with that of a micro-jet simulation, and the average relative errors and the mean square errors are insignificant. The equivalent method of impact loading proposed in this paper has high accuracy and can greatly improve the calculation efficiency, which provides technical support for numerical simulation of concrete cavitation.     

Quantitative observations of cavitation activity in a viscoelastic medium

Quantitative experimental observations of single-bubble cavitation in viscoelastic media that would enable validation of existing models are presently lacking. In the present work, single bubble cavitation is induced in an agar gel using a 1.15 MHz high intensity focused ultrasound transducer, and observed using a focused single-element passive cavitation detection (PCD) transducer. To enable quantitative observations, a full receive calibration is carried out of a spherically focused PCD system by a bistatic scattering substitution technique that uses an embedded spherical scatterer and a hydrophone. Adjusting the simulated pressure received by the PCD by the transfer function on receive and the frequency-dependent attenuation of agar gel enables direct comparison of the measured acoustic emissions with those predicted by numerical modeling of single-bubble cavitation using a modified Keller-Miksis approach that accounts for viscoelasticity of the surrounding medium. At an incident peak rarefactional pressure near the cavitation threshold, period multiplying is observed in both experiment and numerical model. By comparing the two sets of results, an estimate of the equilibrium bubble radius in the experimental observations can be made, with potential for extension to material parameter estimation. Use of these estimates yields good agreement between model and experiment.     

Electromechanical,acoustical and thermodynamical characterization of a low-frequency sonotrode-type transducer in a small sonoreactor at different excitation levels and loading conditions

The paper reports and compares the results of the electromechanical, acoustical and thermodynamical characterization of a low-frequency sonotrode-type ultrasonic device inside a small sonoreactor, immersed in three different loading media, namely, water, juice and milk, excited at different excitation levels, both below and above the cavitation threshold. The electroacoustic efficiency factor determined at system resonance through electromechanical characterization in degassed water as the reference medium is 88.7% for the device in question. This efficiency can be reduced up to three times due to the existence of a complex sound field in the reactor in linear driving conditions below the cavitation threshold. The behaviour of the system is more stable at higher excitation levels than in linear operating conditions.During acoustical characterization, acoustic pressure is spatially averaged, both below and above the cavitation threshold. The standing wave patterns inside the sonoreactor have a stronger influence on the variation of the spatially distributed RMS pressure in linear operating conditions. For these conditions, the variation of ±1.7 dB was obtained, compared to ±1.4 dB obtained in highly nonlinear regime. The acoustic power in the sonoreactor was estimated from the magnitude of the averaged RMS pressure, and from the reverberation time of the sonoreactor as the representation of the losses. The electroacoustic efficiency factors obtained through acoustical and electromechanical characterization are in a very good agreement at low excitation levels. The irradiated acoustic power estimated in nonlinear conditions differs from the dissipated acoustic power determined with the calorimetric method by several orders of magnitude.The number of negative pressure peaks that represent transient cavitation decreases over time during longer treatments of a medium with high-power ultrasound. The number of negative peaks decreases faster when the medium and the vessel are allowed to heat up.     

Thresholds for cavitation produced in water by pulsed ultrasound

The threshold for transient cavitation produced in water by pulsed ultrasound was measured as a function of pulse duration and pulse repetition frequency at both 0.98 and 2.30 MHz. The cavitation events were detected with a passive acoustic technique which relies upon the scattering of the irradiation field by the bubble clouds associated with the events. The results indicate that the threshold is independent of pulse duration and acoustic frequency for pulses longer than approximately 10 acoustic cycles. The threshold increases for shorter pulses. The cavitation events are likely to be associated with bubble clouds rather than single bubbles.     

The design of a high power ultrasonic test cell using finite element modelling techniques

This paper will describe the application of a finite element (FE) code to design a test cell, in which a single transducer is used to generate acoustic cavitation. The FE model comprises a 2-D slice through the centre of the test cell and was used to evaluate the generated pressure fields as a function of frequency. Importantly, the pressure fields predicted by FE modelling are used to indicate the position of pressure peaks, or 'hot-spots', and nulls enabling the systems design engineer to visualise both the potential cavitation areas, corresponding to the 'hot-spots', and areas of low acoustic pressure. Through this design process, a rectangular test cell was constructed from perspex for use with a 40 kHz Tonpilz transducer. A series of experimental measurements was conducted to evaluate the cavitation threshold as a function of temperature and viscosity/surface tension, for different fluid load media. The results indicate the potential of the FE design approach and assist the design engineer in understanding the influence of the fluid load medium on the cell's ability to produce a strong cavitation field.     

Applying spectrum analysis and cepstrum analysis to examine the cavitation threshold in water and in salt solution

The paper presents the way of determining the cavitation threshold by means of classical spectral analysis and proposes the usage of cepstrum analysis in examining the cavitation phenomenon. Cepstrum analysis enables a more lucid interpretation of signals generated in the cavitation process than the universally used Fourier analysis. This refers above all to evaluating the relationship between particular frequencies as well as frequency groups. The research conducted allowed us to observe the changes of spectrum near the cavitation threshold in water, in water partly degassed and in salt solution in the free field and in the standing wave field. Differences of spectrum structure for particular cases were noted, especially for the third harmonic and the first subharmonic. The measurements done in the standing wave field showed differences in spectrum, depending on whether the measurements were done in the loop or in the node of the wave. In particular, what was not observed was the occurrence of subharmonics with a frequency two times lower than the basic frequency which were typical of the free field. Other characteristic spectrum elements that could unmistakably point to reaching the cavitation threshold were not noticed either. The cepstrum analysis proved the existence of irregularities, hardly visible in the classical Fourier spectrum. This refers especially the range below the signal's basic frequency.     

The effect of static pressure on the inertial cavitation threshold

The amplitude of the acoustic pressure required to nucleate a gas or vapor bubble in a fluid, and to have that bubble undergo an inertial collapse, is termed the inertial cavitation threshold. The magnitude of the inertial cavitation threshold is typically limited by mechanisms other than homogeneous nucleation such that the theoretical maximum is never achieved. However, the onset of inertial cavitation can be suppressed by increasing the static pressure of the fluid. The inertial cavitation threshold was measured in ultrapure water at static pressures up to 30?MPa (300 bars) by exciting a radially symmetric standing wave field in a spherical resonator driven at a resonant frequency of 25.5 kHz. The threshold was found to increase linearly with the static pressure; an exponentially decaying temperature dependence was also found. The nature and properties of the nucleating mechanisms were investigated by comparing the measured thresholds to an independent analysis of the particulate content and available models for nucleation.     

Scale-up of vortex based hydrodynamic cavitation devices: A case of degradation of di-chloro aniline in water

Hydrodynamic cavitation (HC) is being increasingly used in a wide range of applications. Unlike ultrasonic cavitation, HC is scalable and has been used at large scale industrial applications. However, no information about influence of scale on performance of HC is available in the open literature. In this work, we present for the first time, experimental data on use of HC for degradation of complex organic pollutants in water on four different scales (~200 times scale-up in terms of capacity). Vortex based HC devices offer various advantages like early inception, high cavitational yield and significantly lower propensity to clogging and erosion. We have used vortex based HC devices in this work. 2,4 dichloroaniline (DCA) – an aromatic compound with multiple functional groups was considered as a model pollutant. Degradation of DCA in water was performed using vortex-based HC devices with characteristic throat dimension, d_t as 3, 6, 12 and 38 mm with scale-up of almost 200 time based on the flow rates (1.3 to 247 LPM). Considering the experimental constraints on operating the largest scale HC device, the experimental data is presented here at only one value of pressure drop across HC device (280 kPa). A previously used per-pass degradation model was extended to describe the experimental data for the pollutant used in this study and a generalised form is presented. The degradation performance was found to decrease with increase in the scale and then plateaus. Appropriate correlation was developed based on the experimental data. The developed approach and presented results provide a sound basis and a data set for further development of comprehensive multi-scale modelling of HC devices.     

Physical and chemical characterization of shock-induced cavitation

A strong impact on a water surface induces a shock wave propagation with a significant pressure variation leading to cavitation bubble formation. A new shock induced cavitation reactor described in this work was characterized by physical and chemical techniques. Water hammer model verification with Joukowsky approach allowed to determine the wave speed propagation and gas fraction in water submitted to shock. These values were used for frequency analysis and compared with direct bubble visualization in order to estimate the influence of the experimental parameters on the shock-induced cavitation. Thereby, the shock wave contains a broad spectrum as decomposed into frequencies. This multi-frequency nature induces heterogeneous bubbles with calculated radii of 0.01 to 3.5 mm and observed radii of 0.01 to 2.8 mm depending on experimental conditions (initial pressure, impact height, gas atmosphere). For the first time, the formation of hydroxyl radicals was proven under impact-induced cavitation. The concentration of radicals increases with increasing number of successive impacts, reaching ca. 1.3 µmol.L⁻¹ after 500 impacts in the presence of 20% O₂-Ar as saturating gas. Radical generation seems to be relatively independent of the impact height but strongly depend on the type of gas saturating water, being substantially lower in the presence of air. Moreover, radical generation increases when decreasing the initial pressure and depends on the frequency at which water is impacted by the piston. Nevertheless, yield of OH radicals during shock-induced cavitation remains much lower than that produced by power ultrasound.     

Cavitation threshold measurements for microsecond length pulses of ultrasound

The acoustic cavitation threshold of an aqueous solution has been measured at megahertz frequencies as a function of pulse width and pulse repetition frequency for various combinations of these quantities. The fluid tested was a 0.1M KOH-H3BO3 buffer solution with pH 10.9, which contained luminol, was saturated with argon, and filtered to 25 mu. The presence of cavitation was detected by a photomultiplier tube that required the emission of visible light that was both larger in magnitude and longer in duration than a preset criterion. It was observed that the cavitation threshold of water under pulse conditions decreases both when the pulse width is fixed and the pulse repetition frequency is increased, and when the pulse repetition frequency is fixed and the pulse width is increased. Acoustic cavitation thresholds measured in aqueous solutions are significantly less than those acoustic pressures associated with instruments that are currently in widespread use in medicine.     

Thermodynamic and kinetic considerations of nucleation and stabilization of acoustic cavitation bubbles in water

Qualitative explanation for a homogeneous nucleation of acoustic cavitation bubbles in the incompressible liquid water with simple phenomenological approach has been provided via the concept of the desorbtion of the dissolved gas and the vaporization of local liquid molecules. The liquid medium has been viewed as an ensemble of lattice structures. Validity of the lattice structure approach against the Brownian motion of molecules in the liquid state has been discussed. Criterion based on probability for nucleus formation has been defined for the vaporization of local liquid molecules. Energy need for the enthalpy of vaporization has been considered as an energy criterion for the formation of a vaporous nucleus. Sound energy, thermal energy of the liquid bulk (Joule-Thomson effect) and free energy of activation, which is associated with water molecules in the liquid state (Brownian motion) as per the modified Eyring's kinetic theory of liquid are considered as possible sources for the enthalpy of vaporization of water molecules forming a single unit lattice. The classical nucleation theory has then been considered for expressing further growth of the vaporous nucleus against the surface energy barrier. Effect of liquid property (temperature), and effect of an acoustic parameter (frequency) on an acoustic cavitation threshold pressure have been discussed. Kinetics of nucleation has been considered.     

An acoustic backscattering technique for the detection of transient cavitation produced by microsecond pulses of ultrasound

An acoustic backscattering technique for detecting transient cavitation produced by 10-microseconds-long pulses of 757-kHz ultrasound is described. The system employs 10-microseconds-long, 30-MHz center frequency tone bursts that scatter from cavitation microbubbles. Experiments were performed with suspensions of hydrophobic polystyrene spheres in ultraclean water. Transient cavitation threshold pressures measured with the active cavitation detector (ACD) were always less than or equal to those measured using a passive acoustic detection scheme. The measured cavitation thresholds decreased with increasing dissolved gas content and increasing suspended particle concentration. Results also show that ultrasonic irradiation of the polystyrene sphere suspensions by the ACD lowered the threshold pressure measured with the passive detector. A possible mechanism through which suspensions of hydrophobic particles might nucleate bubbles is presented.