Analysis of the effect of impact of near-wall acoustic bubble collapse micro-jet on Al 1060

The bubble collapse near a wall will generate strong micro-jet in a liquid environment under ultrasonic field. To explore the effect of the impact of near-wall acoustic bubble collapse micro-jet on an aluminum 1060 sheet, the cavitation threshold formula and micro-jet velocity formula were first proposed. Then the Johnson-Cook rate correlation material constitutive model was considered, and a three-dimensional fluid-solid coupling model of micro-jet impact on a wall was established and analyzed. Finally, to validate the model, ultrasonic cavitation test and inversion analysis based on the theory of spherical indentation test were conducted. The results show that cavitation occurs significantly in the liquid under ultrasonic field, as the applied ultrasonic pressure amplitude is much larger than liquid cavitation threshold. Micro pits appear on the material surface under the impact of micro-jet. Pit depth is determined by both micro-jet velocity and micro-jet diameter, and increases with their increase. Pit diameter is mainly related to the micro-jet diameter and d_p/d_j ≈ 0.95–1.2, while pit’s diameter-to-depth ratio is mainly negatively correlated with the micro-jet velocity. Wall pressure distribution is mostly symmetric and its maximum appears on the edge of micro-jet impingement. Obviously, the greater the micro-jet velocity is, the greater the wall pressure is. Micro pits formed after the impact of micro-jet on aluminum 1060 surface were assessed by ultrasonic cavitation test. Inversion analysis results indicate that equivalent stress, equivalent strain of the pit and impact strength, and velocity of the micro-jet are closely related with pit’s diameter-to-depth ratio. For the pit’s diameter-to-depth ratio of 16–68, the corresponding micro-jet velocity calculated is 310–370 m/s.     

Study on fracture of tungsten wire induced by acoustic cavitation at different hydrostatic pressures and driving electric powers

The near-solid wall multi-bubble cavitation is an extremely complex phenomenon, and cavitation has strong erosiveness. The melting point (about 3410 °C) of tungsten is highest among all pure metals, and its hardness is also very high (its yield strength is greater than 1 GPa). What would happen to pure tungsten wire under extreme conditions caused by collapsing cavitation bubbles at high hydrostatic pressure? In this paper, we have studied the fracture process of pure tungsten wire with diameter of 0.2 mm mounted at the focus of a standing acoustic wave produced by a spherical cavity transducer with two open ends placed in a near spherical pressure container, and also studied the macro and micro morphological characteristics of the fracture and the surface damage at different fracture stages of tungsten wire under various hydrostatic pressures and driving electric powers. The results have shown that the fracture time of tungsten wire is inversely proportional to avitation intensity with hydrostatic pressure and driving electric power, the higher the acoustic pressure caused by higher electric power, the shorter the fracture time. The possible fracture mechanisms of tungsten wire in this situation we found mainly contributed to asymmetrically bubbles collapse near the surface of tungsten wire, leading to tearing the surface apart; consequently cracks along the radial and axial directions of a tungsten wire extend simultaneously, classified as trans-granular fracture and inter-granular fracture, respectively. With the increase of cavitation intensity, the cracks tend to extend more radially and the axial crack propagation path becomes shorter, that is, mainly for trans-granular fracture; with the decrease of cavitation intensity, intergranular fracture becomes more obvious. When the hydrostatic pressure was 10 MPa and the driving electric power was 2 kW, the fibers became softener due to the fracture of the tungsten wire. The fracture caused by acoustic cavitation was different from conventional mechanical fracture, such as tensile, shear, fatigue fracture, on macro and micro morphology.     

Sound field measurement in a double layer cavitation cluster by rugged miniature needle hydrophones

During multi-bubble cavitation the bubbles tend to organize themselves into clusters and thus the understanding of properties and dynamics of clustering is essential for controlling technical applications of cavitation. Sound field measurements are a potential technique to provide valuable experimental information about the status of cavitation clouds. Using purpose-made, rugged, wide band, and small-sized needle hydrophones, sound field measurements in bubble clusters were performed and time-dependent sound pressure waveforms were acquired and analyzed in the frequency domain up to 20 MHz. The cavitation clusters were synchronously observed by an electron multiplying charge-coupled device (EMCCD) camera and the relation between the sound field measurements and cluster behaviour was investigated. Depending on the driving power, three ranges could be identified and characteristic properties were assigned. At low power settings no transient and no or very low stable cavitation activity can be observed. The medium range is characterized by strong pressure peaks and various bubble cluster forms. At high power a stable double layer was observed which grew with further increasing power and became quite dynamic. The sound field was irregular and the fundamental at driving frequency decreased. Between the bubble clouds completely different sound field properties were found in comparison to those in the cloud where the cavitation activity is high. In between the sound field pressure amplitude was quite small and no collapses were detected.     

Incubation pit analysis and calculation of the hydrodynamic impact pressure from the implosion of an acoustic cavitation bubble

An experimental study to evaluate cavitation bubble dynamics is conducted. The aim is to predict the magnitude and statistical distribution of hydrodynamic impact pressure generated from the implosion of various individual acoustic cavitation bubbles near to a rigid boundary, considering geometrical features of the pitted area.A steel sample was subjected to cavitation impacts by an ultrasonic transducer with a 5 mm diameter probe. The pitted surface was then examined using high-precision 3D optical interferometer techniques. Only the incubation period where surface is plastically deformed without material loss is taken into account. The exposure time was adjusted in the range of 3–60 s to avoid pit overlapping and a special procedure for pit analysis and characterisation was then followed. Moreover, a high-speed camera device was deployed to capture the implosion mechanisms of cavitation bubbles near to the surface.The geometrical characteristics of single incubation pits as well as pit clusters were studied and their deformation patterns were compared. Consequently, a reverse engineering approach was applied in order the hydrodynamic impact pressure from the implosion of an individual cavitation bubble to be determined. The characteristic parameters of the cavitation implosion process such as hydrodynamic impact pressure and liquid micro-jet impact velocity as well as the hydrodynamic severity of the cavitation impacts were quantified. It was found that the length of the hypotenuse of the orthographic projections from the center of the pit, which basically represents the deformed area of the pit, increases with the hydrodynamic impact aggressiveness in a linear rate. Majority of the hydrodynamic impacts were in the range of 0.4–1 GPa while the corresponding micro-jet velocities were found to be in the range of 200–700 m/s. Outcomes of this study, contribute to further understanding the cavitation intensity from the implosion of acoustically generated bubbles and could certainly represent a significant step towards developing more accurate cavitation models.     

The interaction of shockwaves with a vapour bubble in boiling histotripsy: The shock scattering effect

Boiling histotripsy is a High Intensity Focused Ultrasound (HIFU) technique which uses a number of short pulses with high acoustic pressures at the HIFU focus to induce mechanical tissue fractionation. In boiling histotripsy, two different types of acoustic cavitation contribute towards mechanical tissue destruction: a boiling vapour bubble and cavitation clouds. An understanding of the mechanisms underpinning these phenomena and their dynamics is therefore paramount to predicting and controlling the overall size of a lesion produced for a given boiling histotripsy exposure condition. A number of studies have shown the effects of shockwave heating in generating a boiling bubble at the HIFU focus and have studied its dynamics under boiling histotripsy insonation. However, not much is known about the subsequent production of cavitation clouds that form between the HIFU transducer and the boiling bubble. The main objective of the present study is to examine what causes this bubble cluster formation after the generation of a boiling vapour bubble. A numerical simulation of 2D nonlinear wave propagation with the presence of a bubble at the focus of a HIFU field was performed using the k-Wave MATLAB toolbox for time domain ultrasound simulations, which numerically solves the generalised Westervelt equation. The numerical results clearly demonstrate the appearance of the constructive interference of a backscattered shockwave by a bubble with incoming incident shockwaves. This interaction (i.e., the reflected and inverted peak positive phase from the bubble with the incoming incident rarefactional phase) can eventually induce a greater peak negative pressure field compared to that without the bubble at the HIFU focus. In addition, the backscattered peak negative pressure magnitude gradually increased from 17.4 MPa to 31.6 MPa when increasing the bubble size from 0.2 mm to 1.5 mm. The latter value is above the intrinsic cavitation threshold of –28 MPa in soft tissue. Our results suggest that the formation of a cavitation cloud in boiling histotripsy is a threshold effect which primarily depends (a) the size and location of a boiling bubble, and (b) the sum of the incident field and that scattered by a bubble.     

Cavitation erosion by shockwave self-focusing of a single bubble

The ability of cavitation bubbles to effectively focus energy is made responsible for cavitation erosion, traumatic brain injury, and even for catalyse chemical reactions. Yet, the mechanism through which material is eroded remains vague, and the extremely fast and localized dynamics that lead to material damage has not been resolved. Here, we reveal the decisive mechanism that leads to energy focusing during the non-spherical collapse of cavitation bubbles and eventually results to the erosion of hardened metals. We show that a single cavitation bubble at ambient pressure close to a metal surface causes erosion only if a non-axisymmetric energy self-focusing is at play. The bubble during its collapse emits shockwaves that under certain conditions converge to a single point where the remaining gas phase is driven to a shockwave-intensified collapse. We resolve the conditions under which this self-focusing enhances the collapse and damages the solid. High-speed imaging of bubble and shock wave dynamics at sub-picosecond exposure times is correlated to the shockwaves recorded with large bandwidth hydrophones. The material damage from several metallic materials is detected in situ and quantified ex-situ via scanning electron microscopy and confocal profilometry. With this knowledge, approaches to mitigate cavitation erosion or to even enhance the energy focusing are within reach.     

Cavitation onset caused by a dynamic pressure wave in liquid pipelines

When liquids flow in the pipelines, the onset of cavitation can be characterized by a variant of the Euler number known as the cavitation number (CN), which is based on the velocity and denoted by C in this paper. Conventionally, cavitation is considered to be induced when C ~ 1. However, experimental observations and several pipe bursts indicate that the CN may incorrectly predict the onset of cavitation. For example, when leakage occurs in the pipeline or a valve in the pipeline is opened, the resultant pressure loss generates a dynamic pressure wave with a small amplitude, which may lead to bubble formation, even though C ~ 1 is not satisfied. Hence, this paper proposes another CN based on the amplitude of the generated dynamic pressure wave, rather than the velocity, for ascertaining the onset of cavitation. The validity of the proposed CN was verified through experiments and a case study. The results indicated that the proposed CN can be effectively used for cavitation prediction induced by pressure fluctuations and for investigating phenomena such as pressure fluctuation, leakage, and corrosion in liquid pipelines, tanks, and pressure vessels, as well as the safety design of liquefied natural gas tanks and tankers.     

Damage characteristics and surface description of near-wall materials subjected to ultrasonic cavitation

For the analysis of ultrasonic cavitation erosion on the surface of materials, the ultrasonic cavitation erosion experiments for AlCu4Mg1 and Ti6Al4V were carried out, and the changes of surface topography, surface roughness, and Vickers hardness were explored. Cavitation pits gradually expand and deepen with the increase of experiment time, and Ti6Al4V is more difficult to erode by cavitation than AlCu4Mg1. After experiments, the cavitation damage characteristics such as the single pit, the rainbow ring area, the fisheye pit, and some small pits were observed, which can be considered to be induced by a single micro-jet impact, ablation effect caused by the high temperature, micro-jet impingement with a sharp angle, and multibeam micro-jets coupling impact or negative pressure in the local area produced by micro-jet impact, respectively. The surface roughness and Vickers hardness of the material increase slowly after rapid growth at different points in time as the experiment time increases. With the increase of the ultrasonic amplitude, both of them first increase and then decrease after the ultrasonic amplitude is greater than 10.8 μm. The increases in surface roughness and Vickers hardness tend to decrease as the viscosity coefficient increases. Ultrasonic cavitation can cause submicron surface roughness and increase surface hardness by 20.36%, so it can be used as a surface treatment method.     

Ultrasonic cavitation at liquid/solid interface in a thin Ga–In liquid layer with free surface

Cavitation in thin layer of liquid metal has potential applications in chemical reaction, soldering, extraction, and therapeutic equipment. In this work, the cavitation characteristics and acoustic pressure of a thin liquid Ga–In alloy were studied by high speed photography, numerical simulation, and bubble dynamics calculation. A self-made ultrasonic system with a TC4 sonotrode, was operated at a frequency of 20 kHz and a max output power of 1000 W during the cavitation recording experiment. The pressure field characteristic inside the thin liquid layer and its influence on the intensity, types, dimensions, and life cycles of cavitation bubbles and on the cavitation evolution process against experimental parameters were systematically studied. The results showed that acoustic pressure inside the thin liquid layer presented alternating positive and negative characteristics within 1 acoustic period (T). Cavitation bubbles nucleated and grew during the negative-pressure stage and shrank and collapsed during the positive-pressure stage. A high bubble growth speed of 16.8 m/s was obtained and evidenced by bubble dynamics calculation. The maximum absolute pressure was obtained at the bottom of the thin liquid layer and resulted in the strongest cavitation. Cavitation was divided into violent and weak stages. The violent cavitation stage lasted several hundreds of acoustic periods and had higher bubble intensity than the weak cavitation stage. Cavitation cloud preferentially appeared during the violent cavitation stage and had a life of several acoustic periods. Tiny cavitation bubbles with life cycles shorter than 1 T dominated the cavitation field. High cavitation intensities were observed at high ultrasonication power and when Q235B alloy was used because such conditions lead to high amplitudes on the substrate and further high acoustic pressure inside the liquid.     

Numerical study of the synergistic effect of cavitation and micro-abrasive particles

In ultrasonic-assisted machining, the synergistic effect of the cavitation effect and micro-abrasive particles plays a crucial role. Studies have focused on the investigation of the micro-abrasive particles, cavitation micro-jets, and cavitation shock waves either individually or in pairs. To investigate the synergy of shock waves and micro-jets generated by cavitation with micro-abrasive particles in ultrasonic-assisted machining, the continuous control equations of a cavitation bubble, shock wave, micro-jet, and micro-abrasive particle influenced by the dimensionless amount (R/R₀), a particle size-velocity–pressure model of the micro-abrasive particle was established. The effects of ultrasonic frequency, sound pressure amplitude, and changes in particle size on micro-abrasive particle velocity and pressure were numerically simulated. At an ultrasonic frequency of 20 kHz and ultrasonic sound pressure of 0.1125 MPa, a smooth spherical SiO₂ micro-abrasive particle (size = 5 µm) was obtained, with a maximum velocity of 190.3–209.4 m/s and pressure of 79.69–89.41 MPa. The results show that in the range of 5–50 μm, smaller particle sizes of the micro-abrasive particles led to greater velocity and pressure. The shock waves, micro-jets, and micro-abrasive particles were all positively affected by the dimensionless amount (R/R₀) of cavitation bubble collapse, the larger the dimensionless quantity, the faster their velocity and the higher their pressure.     

A theoretical model for ice primary nucleation induced by acoustic cavitation

The modelling and simulation of ice nucleation triggered by acoustic cavitation was addressed in this study. The objective was to evaluate the number of nuclei generated by a single gas bubble and afterwards by a multi-bubble system as function of the acoustic pressure (ultrasound wave amplitude) and supercooling level (liquid temperature). According to our calculations, the nucleation could be initiated with moderated acoustic pressure amplitude (around one bar) even at low supercooling levels (around few degrees). These results may provide a sound basis for the control of ice crystal size and morphology which is a key issue in industrial freezing and freeze-drying processes.     

Dependence of wetting on cavitation during the spreading of a filler droplet on the ultrasonically agitated Al substrate

The cavitation characteristics during the spreading of a pure Sn liquid droplet subjected to ultrasonication were studied for the first time through high-speed photography to reveal the wetting mechanism. Ultrasonic vibration realized the spreading of Sn droplet on the nonwetting pure Al substrate. However, the oxide layer of the substrate at the spreading front is difficult to remove. The high-speed photography result shows that a noncavitation region consistently appears at the spreading front, because the acoustic pressure is below the cavitation threshold of 1.26 MPa. In particular, the width of the noncavitation region gradually increases as the size of the spreading area increases. Such a result accounts for the condition wherein the oxide layer at the spreading front is difficult to remove. Furthermore, the bubble density during spreading gradually decreases due to the decreased acoustic pressure of the thinned liquid. Finally, the bubble dynamics were calculated to verify the wetting mechanism.     

Cavitation characteristics of flowing low and high boiling-point perfluorocarbon phase-shift nanodroplets during focused ultrasound exposures

This work investigated and compared the dynamic cavitation characteristics between low and high boiling-point phase-shift nanodroplets (NDs) under physiologically relevant flow conditions during focused ultrasound (FUS) exposures at different peak rarefactional pressures. A passive cavitation detection (PCD) system was used to monitor cavitation activity during FUS exposure at various acoustic pressure levels. Root mean square (RMS) amplitudes of broadband noise, spectrograms of the passive cavitation detection signals, and normalized inertial cavitation dose (ICD) values were calculated. Cavitation activity of low-boiling-point perfluoropentane (PFP) NDs and high boiling-point perfluorohexane (PFH) NDs flowing at in vitro mean velocities of 0–15 cm/s were compared in a 4-mm diameter wall-less vessel in a transparent tissue-mimicking phantom. In the static state, both types of phase-shift NDs exhibit a sharp rise in cavitation intensity during initial FUS exposure. Under flow conditions, cavitation activity of the PFH NDs reached the steady state less rapidly compared to PFP NDs under the lower acoustic pressure (1.35 MPa); at the higher acoustic pressure (1.65 MPa), the RMS amplitude increased more sharply during the initial FUS exposure period. In particular, the RMS-time curves of the PFP NDs shifted upward as the mean flow velocity increased from 0 to 15 cm/s; the RMS amplitude of the PFH ND solution increased from 0 to 10 cm/s and decreased at 15 cm/s. Moreover, amplitudes of the echo signal for the low boiling-point PFP NDs were higher compared to the high boiling-point PFH NDs in the lower frequency range, whereas the inverse occurred in the higher frequency range. Both PFP and PFH NDs showed increased cavitation activity in the higher frequency under the flow condition compared to the static state, especially PFH NDs. At 1.65 MPa, normalized ICD values for PFH increased from 0.93 ± 0.03 to 0.96 ± 0.04 and from 0 to 10 cm/s, then decreased to 0.86 ± 0.05 at 15 cm/s. This work contributes to our further understanding of cavitation characteristics of phase-shift NDs under physiologically relevant flow conditions during FUS exposure. In addition, the results provide a reference for selecting suitable phase-shift NDs to enhance the efficiency of cavitation-mediated ultrasonic applications.     

Effect of surface tension on a liquid-jet produced by the collapse of a laser-induced bubble against a rigid boundary

The effect of surface tension on the behavior of a liquid-jet is investigated experimentally by means of a fiber-coupled optical beam deflection (OBD) technique. It is found that a target under water is impacted in turn by a laser-plasma ablation force and by a high-speed liquid-jet impulse induced by bubble collapse in the vicinity of a rigid boundary. The liquid-jet impact is found to be the main damage mechanism in cavitation erosion. Furthermore, the liquid-jet increases monotonously with surface tension, so cavitation erosion rises sharply with increasing surface tension. Surface tension also reduces bubble collapse duration. From the experimental results and the modified Rayleigh theory, the maximum bubble radius is obtained and it is found to reduce with increasing surface tension.     

Precise spatial control of cavitation erosion in a vessel phantom by using an ultrasonic standing wave

In atherosclerotic inducement in animal models, the conventionally used balloon injury is invasive, produces excessive vessel injuries at unpredictable locations and is inconvenient in arterioles. Fortunately, cavitation erosion, which plays an important role in therapeutic ultrasound in blood vessels, has the potential to induce atherosclerosis noninvasively at predictable sites. In this study, precise spatial control of cavitation erosion for superficial lesions in a vessel phantom was realised by using an ultrasonic standing wave (USW) with the participation of cavitation nuclei and medium-intensity ultrasound pulses. The superficial vessel erosions were restricted between adjacent pressure nodes, which were 0.87 mm apart in the USW field of 1 MHz. The erosion positions could be shifted along the vessel by nodal modulation under a submillimetre-scale accuracy without moving the ultrasound transducers. Moreover, the cavitation erosion of the proximal or distal wall could be determined by the types of cavitation nuclei and their corresponding cavitation pulses, i.e., phase-change microbubbles with cavitation pulses of 5 MHz and SonoVue microbubbles with cavitation pulses of 1 MHz. Effects of acoustic parameters of the cavitation pulses on the cavitation erosions were investigated. The flow conditions in the experiments were considered and discussed. Compared to only using travelling waves, the proposed method in this paper improves the controllability of the cavitation erosion and reduces the erosion depth, providing a more suitable approach for vessel endothelial injury while avoiding haemorrhage.     

Interpreting the influence of liquid temperature on cavitation collapse intensity through bubble dynamic analysis

The violent collapse of inertial bubbles generates high temperature inside and emits strong impulsive pressure. Previous tests on sonoluminescence and cavitation erosion showed that the influence of liquid temperature on these two parameters is different. In this paper, we conducted a bubble dynamic analysis to explore the mechanism of the temperature effect and account for the above difference. The results show that the increase of vapor at higher liquid temperatures changes both the external compression pressure and the internal cushion and is responsible for the variation of bubble collapse intensity. The different trends of the collapsing temperature and emitted sound pressure are caused by the energy distribution during the bubble collapse. Moreover, a series of simulations are conducted to establish the distribution map of the optimum liquid temperature where the collapse intensity is maximized. The relationship between the collapse intensity and the radial dynamics of the bubble is discussed and the reliable indicator is identified. This study provides a clear picture of how the thermodynamic process changes cavitation aggressiveness and enriches the understanding of this complex thermal-hydrodynamic phenomenon.     

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.     

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.     

Dependence of cavitation,chemical effect,and mechanical effect thresholds on ultrasonic frequency

Cavitation, chemical effect, and mechanical effect thresholds were investigated in wide frequency ranges from 22 to 4880 kHz. Each threshold was measured in terms of sound pressure at fundamental frequency. Broadband noise emitted from acoustic cavitation bubbles was detected by a hydrophone to determine the cavitation threshold. Potassium iodide oxidation caused by acoustic cavitation was used to quantify the chemical effect threshold. The ultrasonic erosion of aluminum foil was conducted to estimate the mechanical effect threshold. The cavitation, chemical effect, and mechanical effect thresholds increased with increasing frequency. The chemical effect threshold was close to the cavitation threshold for all frequencies. At low frequency below 98 kHz, the mechanical effect threshold was nearly equal to the cavitation threshold. However, the mechanical effect threshold was greatly higher than the cavitation threshold at high frequency. In addition, the thresholds of the second harmonic and the first ultraharmonic signals were measured to detect bubble occurrence. The threshold of the second harmonic approximated to the cavitation threshold below 1000 kHz. On the other hand, the threshold of the first ultraharmonic was higher than the cavitation threshold below 98 kHz and near to the cavitation threshold at high frequency.