A strict formulation of a nonlinear Helmholtz equation for the propagation of sound in bubbly liquids. Part I: Theory and validation at low acoustic pressure amplitudes

Enhancing sonothrombolysis outcomes with dual-frequency ultrasound: Insights from an in silico microbubble dynamics study

Sonothrombolysis is a technique that employs the ultrasound waves to break down the clot. Recent studies have demonstrated significant improvement in the treatment efficacy when combining two ultrasound waves of different frequencies. Nevertheless, the findings remain conflicted on the ideal frequency pairing that leads to an optimal treatment outcome. Existing experimental studies are constrained by the limited range of frequencies that can be investigated, while numerical studies are typically confined to spherical microbubble dynamics, thereby restricting the scope of the analysis. To overcome this, the present study investigated the microbubble dynamics caused by the different combinations of ultrasound frequencies. This was carried out using computational modelling as it enables the visualisation of the microbubble behaviour, which is difficult in experimental studies due to the opacity of blood. The results showed that the pairings of two ultrasound waves with low frequencies generally produced stronger cavitation and higher flow-induced shear stress on the clot surface. However, one should avoid the frequency pairings that are integer multipliers of each other, i.e., frequency ratio of 1/3, 1/2 and 2, as they led to resultant wave with low pressure amplitude that weakened the cavitation. At 0.5 + 0.85 MHz, the microbubble caused the highest shear stress of 60.5 kPa, due to its large translational distance towards the clot. Although the pressure threshold for inertial cavitation was reduced using dual-frequency ultrasound, the impact of the high-speed jet can only be realised when the microbubble travelled close to the clot. The results obtained from the present study provide groundwork for deeper understanding on the microbubble dynamics during dual-frequency sonothrombolysis, which is of paramount importance for its optimisations and the subsequent clinical translation.

Coffee brewing sonoreactor for reducing the time of cold brew from several hours to minutes while maintaining sensory attributes

This research designed and developed an ultrasonic reactor for a fast and on demand production of cold brew coffee, remarkably reducing the brewing time from 24 h to less than 3 min. The technology was engineered by utilizing resonance to induce ultrasonic waves around the walls of the brewing basket of an espresso machine. The sound transmission system comprised a transducer, a horn and a brewing basket. This arrangement transformed the coffee basket into an effective sonoreactor that injected sound waves at multiple points through its walls, thereby generating multiple regions for acoustic cavitation within the reactor. Furthermore, acoustic streaming induced greater mixing and enhanced mass transfer during brewing. The design was accomplished by modeling the transmission of sound, and acoustic cavitation. Brew characterization and chemical composition analysis was performed, considering factors such as pH, acidity, color, and the composition of caffeine, fatty acids, and volatiles. The efficiency of the extraction increased by decreasing the basket loading percentage (BLP). For instance, sonicating at 100 W doubled the extraction yield and caffeine concentration, from 15.05 % to 33.44 % at BLP = 33 %, and from 0.91 mg/mL to 1.84 mg/mL at BLP = 67 %, respectively. The total fatty acids increased from 1.16 mg/mL to 9.20 mg/mL, representing an eightfold increase, at BLP = 33 %. Finally, a sensory analysis was conducted to evaluate appearance, aroma, texture, flavor, and aftertaste, which demonstrated that coffee brewed for 1 and 3 min in the sonoreactor exhibited almost undistinguishable properties compared to a standard 24 h brewing without ultrasound.

In-situ observation of phase separation dynamics for immiscible aqueous solution within ultrasonic field

A high-speed imaging technique was used to observe the phase separation process of water (H2O)-20 %succinonitrile (SCN) immiscible solution within ultrasound field. Combining with numerical simulation, the effects of ultrasonic cavitation and acoustic streaming on the fragmentation and migration of secondary droplets were revealed. It was found that the previously spherical or near-spherical secondary H2O-rich droplets formed under static condition were dynamically transformed into several novel forms, such as tadpole-like, string-beads, gourd-like, and threadlike patterns. The calculated results showed that the cavitation could fragment micron-scale H2O-rich droplets because of the produced higher shock wave pressure than the droplets' Laplace pressure, and the subsequent droplet morphology evolution mainly depended on the liquid ejection volume determined by the distance between the droplets and the collapsing bubbles. Meanwhile, acoustic streaming, which generated shear force exceeding the surface tension of H2O-rich phase, stretched, split and finally fractured millimeter-sized or even larger secondary droplets into several smaller spherical sub-droplets. In comparison, the observed secondary droplet distribution characteristics in H2O-20 %SCN solution were similar to the Bi-rich particles in the ultrasonic solidification microstructures of Al-30 %Bi immiscible alloy, confirming that this work provided a deep understanding of the liquid phase separation mechanism within ultrasonic field.

A computational framework for the multiphysics simulation of microbubble-mediated sonothrombolysis using a forward-viewing intravascular transducer

Sonothrombolysis is a technique that utilises ultrasound waves to excite microbubbles surrounding a clot. Clot lysis is achieved through mechanical damage induced by acoustic cavitation and through local clot displacement induced by acoustic radiation force (ARF). Despite the potential of microbubble-mediated sonothrombolysis, the selection of the optimal ultrasound and microbubble parameters remains a challenge. Existing experimental studies are not able to provide a complete picture of how ultrasound and microbubble characteristics influence the outcome of sonothrombolysis. Likewise, computational studies have not been applied in detail in the context of sonothrombolysis. Hence, the effect of interaction between the bubble dynamics and acoustic propagation on the acoustic streaming and clot deformation remains unclear. In the present study, we report for the first time the computational framework that couples the bubble dynamic phenomena with the acoustic propagation in a bubbly medium to simulate microbubble-mediated sonothrombolysis using a forward-viewing transducer. The computational framework was used to investigate the effects of ultrasound properties (pressure and frequency) and microbubble characteristics (radius and concentration) on the outcome of sonothrombolysis. Four major findings were obtained from the simulation results: (i) ultrasound pressure plays the most dominant role over all the other parameters in affecting the bubble dynamics, acoustic attenuation, ARF, acoustic streaming, and clot displacement, (ii) smaller microbubbles could contribute to a more violent oscillation and improve the ARF simultaneously when they are stimulated at higher ultrasound pressure, (iii) higher microbubbles concentration increases the ARF, and (iv) the effect of ultrasound frequency on acoustic attenuation is dependent on the ultrasound pressure. These results may provide fundamental insight that is crucial in bringing sonothrombolysis closer to clinical implementation.

Probing the pressure dependence of sound speed and attenuation in bubbly media: Experimental observations, a theoretical model and numerical calculations

The problem of attenuation and sound speed of bubbly media has remained partially unsolved. Comprehensive data regarding pressure-dependent changes of the attenuation and sound speed of a bubbly medium are not available. Our theoretical understanding of the problem is limited to linear or semi-linear theoretical models, which are not accurate in the regime of large amplitude bubble oscillations. Here, by controlling the size of the lipid coated bubbles (mean diameter of ≈5.4μm), we report the first time observation and characterization of the simultaneous pressure dependence of sound speed and attenuation in bubbly water below, at and above microbubbles resonance (frequency range between 1-3 MHz). With increasing acoustic pressure (between 12.5-100 kPa), the frequency of the peak attenuation and sound speed decreases while maximum and minimum amplitudes of the sound speed increase. We propose a nonlinear model for the estimation of the pressure dependent sound speed and attenuation with good agreement with the experiments. The model calculations are validated by comparing with the linear and semi-linear models predictions. One of the major challenges of the previously developed models is the significant overestimation of the attenuation at the bubble resonance at higher void fractions (e.g. 0.005). We addressed this problem by incorporating bubble-bubble interactions and comparing the results to experiments. Influence of the bubble-bubble interactions increases with increasing pressure. Within the examined exposure parameters, we numerically show that, even for low void fractions (e.g. 5.1×10-6) with increasing pressure the sound speed may become 4 times higher than the sound speed in the non-bubbly medium.

Simulations of a full sonoreactor accounting for cavitation

In spite of the increasing interest in ultrasound processing applications, industrial scale-up remains limited, in particular by the unavailability of predictive computer tools. In this study, using a previously published model of cavitating liquids implementable as a non-linear Helmholtz equation, it is shown that a full sonoreactor can be modelled and simulated. The model includes the full transducer and the vibrations of the vessel walls, using the physics of elastic solids and piezo-electricity. The control-loop used by the generator to set the optimal frequency is also accounted for. Apart from the geometry, the unique input of the model is the current feeding the transducer whereas the dissipated electrical power, transducer complex impedance and working frequency are available as outputs. The model is put to the test against experiments realized in different geometries, varying either the input current or the transducer immersion depth. Despite the overestimation of the power dissipated in the liquid, the evolution of the acoustic load in both cases is reasonably well reproduced by simulation, which partially validates the method used.

Identification approach of acoustic cavitation via frequency spectrum of sound pressure wave signals in numerical simulation

In a sono-reactor, complex ultrasound pressure wave signal can be detected, containing multiple information related to acoustic cavitation. In this present study, acoustic cavitation in a cylinder is investigated numerically. Via Fast Fourier Transfer (FFT), the sound pressure signals from sonotrode emitting surface are separated into harmonics, sub/ultra-harmonics and cavitation white noise: (1) the appearance of harmonics proved the non-linear propagation of ultrasound, (2) at the vibratory amplitude from 5∼20μm, only harmonics exists in the frequency spectra, corresponding to expansion and compression of non-condensable gas (NCG), (3) at the vibratory amplitude range of 30∼50μm, the occurrence of sub/ultra-harmonics demonstrated gaseous cavitation occurred, and (4) at the vibratory amplitude higher than 55μm, cavitation white noise arose, pointing out the initiation of vaporous cavitation. Based on the combination of frequency spectra and cavitation zones distribution, the acoustic cavitation state in water liquid is determined.

Comparison of frequency domain and time domain methods for the numerical simulation of contactless ultrasonic cavitation

The use of a top-mounted electromagnetic induction coil has been demonstrated as a contactless alternative to traditional ultrasonic treatment (UST) techniques that use an immersed mechanical sonotrode for the treatment of metals in the liquid state. This method offers similar benefits to existing UST approaches, including degassing, grain refinement, and dispersion of nanoparticles, while also preventing contact contamination due to erosion of the sonotrode. Contactless treatment potentially extends UST to high temperature or reactive melts. Generally, the method relies on acoustic resonance to reach pressure levels suitable for inertial cavitation and as a result the active cavitation volume tends to lie deep in the melt rather than in the small volume surrounding the immersed sonotrode probe. Consequently, (i) with suitable tuning of the coil supply frequency for resonance, the treatment volume can be made arbitrarily large, (ii) the problem of shielding and pressure wave attenuation suffered by the immersed sonotrode is avoided. However, relying on acoustic resonance presents problems: (i) the emergence of bubbles alters the speed of sound, resonance is momentarily lost, and cavitation becomes intermittent, (ii) as sound waves travel through and reflect on all the materials surrounding the melt, the sound characteristics of the crucible and supporting structures need to be carefully considered. The physics of cavitation coupled with this intermittent behaviour poses a challenge to sonotrode modelling orthodoxy, a problem we are trying to address in this publication. Two alternative approaches will be discussed, one of which is in the time domain and one in the frequency domain, which couple the solution of a bubble dynamics solver with that of an acoustics solver, to give an accurate prediction of the acoustic pressure generated by the induction coil. The time domain solver uses a novel algorithm to improve simulation time, by detecting an imminent bubble collapse and prescribing its subsequent behaviour, rather than directly solving a region that would normally require extremely small time steps. This way, it is shown to predict intermittent cavitation. The frequency domain solver for the first time couples the nonlinear Helmholtz model used for studying cavitation, with a background source term for the contribution of Lorentz forces. It predicts comparable RMS pressures to the time domain solver, but not the intermittent behaviour due to the underlying harmonic assumption. As further validation, the frequency domain method is also used to compare the generated acoustic pressure with that of traditional UST using a mechanical sonotrode.

Multi-frequency sonoreactor characterisation in the frequency domain using a semi-empirical bubbly liquid model

Recently, multi-frequency systems were reported to improve performance in power ultrasound applications. In line with this, digital prototyping of multi-frequency sonoreactors also started gaining interest. However, the conventional method of simulating multi-frequency acoustic pressure fields in the time-domain led to many challenges and limitations. In this study, a multi-frequency sonoreactor was characterised using frequency domain simulations in 2-D. The studied system consists of a hexagonal sonoreactor capable of operating at 28, 40 and 70 kHz. Four frequency combinations were studied: 28-40, 28-70, 40-70 and 28-40-70 kHz. A semi-empirical, modified Commander and Prosperetti model was used to describe the bubbly-liquid effects in the sonoreactor. The root-mean-squared acoustic pressure was compared against experimental validation results using sonochemiluminescence (SCL) images and was noted to show good qualitative agreement with SCL results in terms of antinode predictions. The empirical phase speed calculated from SCL measurements was found to be important to circumvent uncertainties in bubble parameter specifications which reduces error in the simulations. Additionally, simulation results also highlighted the importance of geometry in the context of optimising the standing wave magnitudes for each working frequency due to the effects of constructive and destructive interference.

Multiphysics Modelling of Ultrasonic Melt Treatment in the Hot-Top and Launder during Direct-Chill Casting: Path to Indirect Microstructure Simulation

This study concerns the numerical simulation of two competing ultrasonic treatment (UST) strategies for microstructure refinement in the direct-chill (DC) casting of aluminium alloys. In the first, more conventional, case, the sonotrode vibrating at 17.3 kHz is immersed in the hop-top to treat the sump melt pool, in the second case, the sonotrode is inserted between baffles in the launder. It is known that microstructure refinement depends on the intensity of acoustic cavitation and the residence time of the treated fluid in the cavitation zone. The geometry, acoustic field intensity, induced flow velocities, and local temperature are factors which affect this treatment. The mathematical model developed in this work couples flow velocity, acoustics modified by cavitation, heat transfer, and solidification at the macroscale, with Lagrangian refiner particles, used to determine: (a) their residence time in the active zones, and (b) their eventual distribution in the sump as a function of the velocity field. This is the first attempt at using particle models as an efficient, though indirect, alternative to microstructure simulation, and the results indicate that UST in the launder, assisted with baffle separators, yields a more uniform distribution of refining particles, avoiding the strong acoustic streaming jet that, otherwise, accompanies hot-top treatment, and may lead to the strong segregation of refining particles. Experiments conducted in parallel to the numerical studies in this work appeared to support the results obtained in the simulation.

Modeling the thermal behavior of an acoustically driven gas bubble

Numerical simulation of an acoustically driven gas bubble is usually achieved by solving a Rayleigh-Plesset-type equation, in which the time-dependent pressure of the gas inside the bubble needs to be appropriately modeled. This is done in most existing methods by assuming a polytropic relation between the gas pressure and the bubble volume, which sometimes oversimplifies the thermal interaction between the bubble and the ambient liquid. In this paper, a model is developed aiming to perform an accurate and efficient calculation of the pressure variation in the bubble. The approach is different from that in the recent paper by the author and his collaborator which used a combination of an integral and a collocation method to solve the energy equation in the gas [Zhou and Prosperetti (2020). J. Fluid Mech. 901, R3]. The starting point of the proposed method in this paper is the gas continuity equation which is manipulated to lead to three ordinary differential equations. In this way, the thermal behavior of an oscillating gas bubble is captured at a modest coding and computational cost.

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.

A strict formulation of a nonlinear Helmholtz equation for the propagation of sound in bubbly liquids. Part II: Application to ultrasonic cavitation

This paper addresses one of the greatest challenges in sonochemistry that has impaired scaling up ultrasonic processes, which is the lack of models capable of predicting the pressure distribution in sonoreactors. This work studies the effect of acoustic pressure on the transmission of sound thought cavitating bubbly liquids by utilizing the nonlinear Helmholtz equation that was demonstrated on the paper part I. The model showed that the wave number and the attenuation can be estimated from the bubble dynamics of inertial bubbles and the local bubble density. The linear model of Commander and Prosperetti is encompassed by the nonlinear model. The model was employed to predict the pressure distribution below an ultrasonic horn tip achieving a relatively close prediction of the experimental data and certainly an accurate qualitative description of the distribution of the pressure field in spite of the simplifications of the model and the assumptions of unknown variables such as the bubble density, bubble distribution and the vessel boundary conditions.

Acoustic resonance for contactless ultrasonic cavitation in alloy melts

Contactless ultrasound is a novel, easily implemented, technique for the Ultrasonic Treatment (UST) of liquid metals. Instead of using a vibrating sonotrode probe inside the melt, which leads to contamination, we consider a high AC frequency electromagnetic coil placed close to the metal free surface. The coil induces a rapidly changing Lorentz force, which in turn excites sound waves. To reach the necessary pressure amplitude for cavitation with the minimum electrical energy use, it was found necessary to achieve acoustic resonance in the liquid volume, by finely tuning the coil AC supply frequency. The appearance of cavitation was then detected experimentally with an externally placed ultrasonic microphone and confirmed by the reduction in grain size of the solidified metal. To predict the appearance of various resonant modes numerically, the exact dimensions of the melt volume, the holding crucible, surrounding structures and their sound properties are required. As cavitation progresses the speed of sound in the melt changes, which in practice means resonance becomes intermittent. Given the complexity of the situation, two competing numerical models are used to compute the soundfield. A high order time-domain method focusing on a particular forcing frequency and a Helmholtz frequency domain method scanning the full frequency range of the power supply. A good agreement is achieved between the two methods and experiments which means the optimal setup for the process can be predicted with some accuracy.

Numerical Modelling of the Ultrasonic Treatment of Aluminium Melts: An Overview of Recent Advances

The prediction of the acoustic pressure field and associated streaming is of paramount importance to ultrasonic melt processing. Hence, the last decade has witnessed the emergence of various numerical models for predicting acoustic pressures and velocity fields in liquid metals subject to ultrasonic excitation at large amplitudes. This paper summarizes recent research, arguably the state of the art, and suggests best practice guidelines in acoustic cavitation modelling as applied to aluminium melts. We also present the remaining challenges that are to be addressed to pave the way for a reliable and complete working numerical package that can assist in scaling up this promising technology.

Ultrasonic liquid metal processing: The essential role of cavitation bubbles in controlling acoustic streaming

The acoustic streaming behaviour below an ultrasonic sonotrode in water was predicted by numerical simulation and validated by experimental studies. The flow was calculated by solving the transient Reynolds-Averaged Navier-Stokes equations with a source term representing ultrasonic excitation implemented from the predictions of a nonlinear acoustic model. Comparisons with the measured flow field from Particle Image Velocimetry (PIV) water experiments revealed good agreement in both velocity magnitude and direction at two power settings, supporting the validity of the model for acoustic streaming in the presence of cavitating bubbles. Turbulent features measured by PIV were also recovered by the model. The model was then applied to the technologically important area of ultrasonic treatment of liquid aluminium, to achieve the prediction of acoustic streaming for the very first time that accounts for nonlinear pressure propagation in the presence of acoustic cavitation in the melt. Simulations show a strong dependence of the acoustic streaming flow direction on the cavitating bubble volume fraction, reflecting PIV observations. This has implications for the technological use of ultrasound in liquid metal processing.

Numerical modelling of acoustic streaming during the ultrasonic melt treatment of direct-chill (DC) casting

Acoustic streaming and its attendant effects in the sump of a direct-chill (DC) casting process are successfully predicted under ultrasonic treatment for the first time. The proposed numerical model couples acoustic cavitation, fluid flow, heat and species transfer, and solidification to predict the flow pattern, acoustic pressure, and temperature fields in the sump. The model is numerically stable with time steps of the order of 0.01 s and therefore computationally attractive for optimization studies necessitating simulation times of the order of a minute. The sump profile is altered by acoustic streaming, with the slurry region depressed along the centreline of the billet by a strong central jet. The temperature gradient in the transition zone is increased, potentially interfering with grain refinement. The cooling rate in the sump is also altered, thereby modifying the dendrite arm spacing of the as-cast billet. The relative position of the sonotrode affects the sump profile, with the sump depth decreased by around 5 mm when the sonotrode is moved above the graphite ring level by 100 mm. The acoustic streaming jet penetrates into the slurry zone and, as a result, the growth direction of dendritic grains in the off-centre position is altered.

Low-intensity ultrasound induced cavitation and streaming in oxygen-supersaturated water: Role of cavitation bubbles as physical cleaning agents

A number of acoustic and fluid-dynamic phenomena appear in ultrasonic cleaning baths and contribute to physical cleaning of immersed surfaces. Propagation and repeated reflection of ultrasound within cleaning baths build standing-wave-like acoustic fields; when an ultrasound intensity gradient appears in the acoustic fields, it can in principle induce steady streaming flow. When the ultrasound intensity is sufficiently large, cavitation occurs and oscillating cavitation bubbles are either trapped in the acoustic fields or advected in the flow. These phenomena are believed to produce mechanical action to remove contaminant particles attached at material surfaces. Recent studies suggest that the mechanical action of cavitation bubbles is the dominant factor of particle removal in ultrasonic cleaning, but the bubble collapse resulting from high-intensity ultrasound may be violent enough to give rise to surface erosion. In this paper, we aim to carefully examine the role of cavitation bubbles from ultrasonic cleaning tests with varying dissolved gas concentration in water. In our cleaning tests using 28-kHz ultrasound, oxygen-supersaturated water is produced by oxygen-microbubble aeration and used as a cleaning solution, and glass slides spin-coated with silica particles of micron/submicron sizes are used to define cleaning efficiency. High-speed camera recordings and Particle Image Velocimetry analysis with a pressure oscillation amplitude of 1.4 atm at the pressure antinode show that the population of cavitation bubbles increases and streaming flow inside the bath is promoted, as the dissolved oxygen supersaturation increases. The particle removal is found to be achieved mainly by the action of cavitation bubbles, but there exists optimal gas supersaturation to maximize the removal efficiency. Our finding suggests that low-intensity ultrasound irradiation under the optimal gas supersaturation in cleaning solutions allows for having mild bubble dynamics without violent collapse and thus cleaning surfaces without cavitation erosion. Finally, observations of individual bubble dynamics and the resulting particle removal are reported to further support the role of cavitation bubbles as cleaning agents.

Fundamental studies of ultrasonic melt processing

Ultrasonic (cavitation) melt processing attracts considerable interest from both academic and industrial communities as a promising route to provide clean, environment friendly and energy efficient solutions for some of the core issues of the metal casting industry, such as improving melt quality and providing structure refinement. In the last 5 years, the authors undertook an extensive research programme into fundamental mechanisms of cavitation melt processing using state-of-the-art and unique facilities and methodologies. This overview summarises the recent results on the evaluation of acoustic pressure and melt flows in the treated melt, direct observations and quantitative analysis of cavitation in liquid aluminium alloys, in-situ and ex-situ studies of the nucleation, growth and fragmentation of intermetallics, and de-agglomeration of particles. These results provide valuable new insights and knowledge that are essential for upscaling ultrasonic melt processing to industrial level.