A reduced-order, single-bubble cavitation model with applications to therapeutic ultrasound

Rayleigh-Taylor instability of collapsing bubbles in cryogenic liquids

In order to predict the maximum cavitation damage to hydraulic machinery in cryogenic engineering such as turbopumps in liquid rockets, it is essential to know the achievable intensity of bubble collapse. Rayleigh-Taylor instability imposes an extinction threshold for collapsing bubbles and determines the upper limit for the strongest collapse possible. In this study, we numerically investigate this information for collapsing bubbles in liquid oxygen. Our results reveal two distinct features of bubble instability in cryogenic liquids compared with that in water. First, high-order surface distortions are preferably developed on the bubble surface. Second, the bubble is most unstable when it collapses moderately, whereas it is stabilized as the collapse intensity is strengthened. A mechanistic study links these intriguing phenomena to the relatively slow bubble dynamics in cryogenic liquids. In that context, the growth time of the distortions emerges as a pivotal factor for the instability development. Together with the amplification rate, it controls the ultimate mode and amplitude of the instability.

Mass and heat transfer in audible sound driven bubbles

Most research on sonoluminescence and sonochemistry has been conducted at acoustic frequencies above ∼20 kHz. Consequently, mathematical models for the dynamics of acoustically-driven bubbles have hardly been examined in the audible frequency spectrum. Here, we develop a new hybrid modelling approach that combines the rigour of the advection-diffusion model whilst retaining the simplicity of a reduced-order boundary layer model to predict phase-change, mass and heat transfer in an inertially collapsing bubble excited by audible sound. Differences in these approaches are explored through a thorough validation against experimental data obtained from ultra-high speed videos of bubble dynamics at 17.8 kHz. Our results indicate that, while the boundary layer model agrees well with the advection-diffusion model at high driving frequencies, there are significant deviations at lower frequencies, where the boundary layer model overpredicts parameters such as bubble size and quantity of trapped vapour while underpredicting others such as temperature and pressure. These deviations at lower frequencies is caused by an inaccurate estimation of the boundary layer thickness originating from the time-scale competition between diffusion and fast bubble wall motion. Our work questions the suitability of existing reduced-order models developed for ultrasonic frequencies when applied to the audible range, reinforcing that further research in the audible range is needed.

Ultrasonic viscosity-reduction vacuum residue oil

With the rapid development of economy, the demand for energy is increasing rapidly. And the output and processing amount of vacuum residue oil are also increasing year by year. The processing of vacuum residue oil is always a difficult problem in petrochemical industry. The high viscosity is the significant characteristic of vacuum residue oil. It is easy to cause serious influence in residue oil processing, such as reactor blockage. With the development of ultrasonic technology, ultrasonic viscosity reduction has become the focus of research. Its potential role in petrochemical industry has attracted more and more attention. Ultrasonic viscosity reducing vacuum residue oil is a new viscosity reducing process. Compared with the traditional viscosity reduction method, it has good viscosity reduction effect. The research progress of ultrasonic viscosity reducing vacuum residue oil is reviewed. In this paper, the mechanism of ultrasonic action, physical and chemical effects, ultrasonic viscosity reduction treatment conditions, viscosity reduction residue oil system influence and viscosity recovery, ultrasonic sound field simulation are reviewed and analyzed. In addition, ultrasound has a synergistic effect. Ultrasonic synergistic physicochemical methods (microwave; hydrogen donor) also has remarkable effects. Ultrasonic treatment technology is adopted on the basis of traditional microwave viscosity reduction and residue oil hydrogenation donor. This kind of ultrasonic collaborative method has excellent application prospect. But there are problems with this technology. The research direction of ultrasonic viscosity reduction residue oil in the future is also suggested. It can provide reference for related research.

Ultrasound cavitation induced nucleation in metal solidification: An analytical model and validation by real-time experiments

Microstructural refinement of metallic alloys via ultrasonic melt processing (USMP) is an environmentally friendly and promising method. However, so far there has been no report in open literature on how to predict the solidified microstructures and grain size based on the ultrasound processing parameters.In this paper, an analytical model is developed to calculate the cavitation enhanced undercooling and the USMP refined solidification microstructure and grain size for Al-Cu alloys. Ultrafast synchrotron X-ray imaging and tomography techniques were used to collect the real-time experimental data for validating the model and the calculated results. The comparison between modeling and experiments reveal that there exists an effective ultrasound input power intensity for maximizing the grain refinement effects for the Al-Cu alloys, which is in the range of 20-45 MW/m2. In addition, a monotonous increase in temperature during USMP has negative effect on producing new nuclei, deteriorating the benefit of microstructure refinement due to the application of ultrasound.

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.

Non-linear Acoustic Emissions from Therapeutically Driven Contrast Agent Microbubbles

Non-linear emissions from microbubbles introduced to the vasculature for exposure to focused ultrasound are routinely monitored for assessment of therapy and avoidance of irreversible tissue damage. Yet the bubble-based mechanistic source for these emissions, under subresonant driving at typical therapeutic pressure amplitudes, may not be well understood. In the study described here, dual-perspective high-speed imaging at 210,000 frames per second (fps), and shadowgraphically at 10 Mfps, was used to observe cavitation from microbubbles flowing through a 500-µm polycarbonate capillary exposed to focused ultrasound of 692 kHz at therapeutically relevant pressure amplitudes. The acoustic emissions were simultaneously collected via a broadband calibrated needle hydrophone system. The observations indicate that periodic bubble-collapse shock waves can dominate the non-linear acoustic emissions, including subharmonics at higher driving amplitudes. Contributions to broadband emissions through variance in shock wave amplitude and emission timings are also identified. Possible implications for in vivo microbubble cavitation detection, mechanisms of therapy and the conventional classification of cavitation activity as stable or inertial are discussed.

Effects of Nonlinear Propagation of Focused Ultrasound on the Stable Cavitation of a Single Bubble

Many biomedical applications such as ultrasonic targeted drug delivery, gene therapy, and molecular imaging entail the problems of manipulating microbubbles by means of a high-intensity focused ultrasound (HIFU) pressure field; namely stable cavitation. In high-intensity acoustic field, bubbles demonstrate translational instability, the well-known erratic dancing motion, which is caused by shape oscillations of the bubbles that are excited by their volume oscillations. The literature of bubble dynamics in the HIFU field is mainly centered on experiments, lacking a systematic study to determine the threshold for shape oscillations and translational motion. In this work, we extend the existing multiphysics mathematical modeling platform on bubble dynamics for taking account of (1) the liquid compressibility which allows us to apply a high-intensity acoustic field; (2) the mutual interactions of volume pulsation, shape modes, and translational motion; as well as (3) the effects of nonlinearity, diffraction, and absorption of HIFU to incorporate the acoustic nonlinearity due to wave kinematics or medium—all in one model. The effects of acoustic nonlinearity on the radial pulsations, axisymmetric modes of shape oscillations, and translational motion of a bubble, subjected to resonance and off-resonance excitation and various acoustic pressure, are examined. The results reveal the importance of considering all the involved harmonics and wave distortion in the bubble dynamics, to accurately predict the oscillations, translational trajectories, and the threshold for inertial (unstable) cavitation. This result is of interest for understanding the bubble dynamical behaviors observed experimentally in the HIFU field.

The influence of gas diffusion on bubble persistence in shock-scattering histotripsy

Bubble cloud persistence reduces the efficacy of mechanical liquefaction with shock-scattering histotripsy. In this study, the contribution of gas transfer to bubble longevity was investigated in silico by solving the equations for bubble oscillations and diffusion in parallel. The bubble gas content increased more than 5 orders of magnitude during the expansion phase, arresting the inertial collapse. The residual gas bubble required more than 15 ms for passive dissolution post excitation, consistent with experimental observation. These results demonstrate gas diffusion is an important factor in the persistence of histotripsy-induced cavitation.

Multiscale modeling of plasmonic enhanced energy transfer and cavitation around laser-excited nanoparticles

Nanoscale bubbles generated around laser-excited metallic nanoparticles are promising candidates for targeted drug and gene delivery in living cells. The development of new nanomaterials for efficient nanobubble-based therapy is however limited by the lack of reliable computational approaches for the prediction of their size and dynamics, due to the wide range of time and space scales involved. In this work, we present a multiscale modeling framework that segregates the various channels of plasmon de-excitation and energy transfer to describe the generation and dynamics of plasmonic nanobubbles. Detailed comparison with time-resolved shadowgraph imaging and spectroscopy data demonstrates that the bubble size, dynamics, and formation threshold can be quantitatively predicted for various types of nanostructures and irradiation parameters, with an error smaller than the experimental uncertainty. Our model in addition provides crucial physical insights into non-linear interactions in the near-field that should guide the experimental design of nanoplasmonic materials for nanobubble-based applications in nanomedicine.

The effects of heat and mass diffusion on freely oscillating bubbles in a viscoelastic, tissue-like medium

In certain cavitation-based ultrasound techniques, the relative importance of thermally vs mechanically induced damage is unclear. As a first step to investigate this matter, a numerical model for bubble dynamics in tissue-like, viscoelastic media is presented in which full thermal effects are included inside and outside the bubble, as well as interdiffusion of vapor and non-condensible gas inside the bubble. Soft tissue is assumed to behave according to a Kelvin-Voigt model in which viscous and elastic contributions are additive. A neo-Hookean formulation, appropriate for finite-strain elasticity, accounts for the large deformations produced by cavitation. Numerical solutions to problems of relevance to therapeutic ultrasound are examined, and linear analysis is used to explain the underlying mechanisms. The dependence between the surrounding medium's elasticity (shear modulus) and the extent to which the effects of heat and mass transfer influence bubble dynamics is quantified. In particular, the oscillation properties are related to the eigenvalues determined from linear theory. Regimes under which a polytropic relation describes the heat transfer to sufficient accuracy are identified, for which the complexity and computational expense associated with solving full partial differential equations can be avoided.

Deconvolution of acoustically detected bubble-collapse shock waves

The shock wave emitted by the collapse of a laser-induced bubble is detected at propagation distances of 30, 40and50mm, using a PVdF needle hydrophone, with a non-flat end-of-cable frequency response, calibrated for magnitude and phase, from 125kHz to 20MHz. High-speed shadowgraphic imaging at 5×10⁶ frames per second, 10nstemporal resolution and 256 frames per sequence, records the bubble deflation from maximum to minimum radius, the collapse and shock wave generation, and the subsequent rebound in unprecedented detail, for a single sequence of an individual bubble. The Gilmore equation for bubble oscillation is solved according to the resolved bubble collapse, and simulated shock wave profiles deduced from the acoustic emissions, for comparison to the hydrophone recordings. The effects of single-frequency calibration, magnitude-only and full waveform deconvolution of the experimental data are presented, in both time and frequency domains. Magnitude-only deconvolution increases the peak pressure amplitude of the measured shock wave by approximately 9%, from single-frequency calibration, with full waveform deconvolution increasing it by a further 3%. Full waveform deconvolution generates a shock wave profile that is in agreement with the simulated profile, filtered according to the calibration bandwidth. Implications for the detection and monitoring of acoustic cavitation, where the role of periodic bubble collapse shock waves has recently been realised, are discussed.

An analysis of the acoustic cavitation noise spectrum: The role of periodic shock waves

Research on applications of acoustic cavitation is often reported in terms of the features within the spectrum of the emissions gathered during cavitation occurrence. There is, however, limited understanding as to the contribution of specific bubble activity to spectral features, beyond a binary interpretation of stable versus inertial cavitation. In this work, laser-nucleation is used to initiate cavitation within a few millimeters of the tip of a needle hydrophone, calibrated for magnitude and phase from 125 kHz to 20 MHz. The bubble activity, acoustically driven at f₀ = 692 kHz, is resolved with high-speed shadowgraphic imaging at 5 × 10⁶ frames per second. A synthetic spectrum is constructed from component signals based on the hydrophone data, deconvolved within the calibration bandwidth, in the time domain. Cross correlation coefficients between the experimental and synthetic spectra of 0.97 for the f₀/2 and f₀/3 regimes indicate that periodic shock waves and scattered driving field predominantly account for all spectral features, including the sub-harmonics and their over-harmonics, and harmonics of f₀.

Theoretical model of ice nucleation induced by acoustic cavitation. Part 1: Pressure and temperature profiles around a single bubble

This paper deals with the inertial cavitation of a single gas bubble in a liquid submitted to an ultrasonic wave. The aim was to calculate accurately the pressure and temperature at the bubble wall and in the liquid adjacent to the wall just before and just after the collapse. Two different approaches were proposed for modeling the heat transfer between the ambient liquid and the gas: the simplified approach (A) with liquid acting as perfect heat sink, the rigorous approach (B) with liquid acting as a normal heat conducting medium. The time profiles of the bubble radius, gas temperature, interface temperature and pressure corresponding to the above models were compared and important differences were observed excepted for the bubble size. The exact pressure and temperature distributions in the liquid corresponding to the second model (B) were also presented. These profiles are necessary for the prediction of any physical phenomena occurring around the cavitation bubble, with possible applications to sono-crystallization.

A theoretical study of inertial cavitation from acoustic radiation force impulse imaging and implications for the mechanical index

The mechanical index (MI) attempts to quantify the likelihood that exposure to diagnostic ultrasound will produce an adverse biological effect by a non-thermal mechanism. The current formulation of the MI implicitly assumes that the acoustic field is generated using the short pulse durations appropriate to B-mode imaging. However, acoustic radiation force impulse (ARFI) imaging employs high-intensity pulses up to several hundred acoustic periods long. The effect of increased pulse durations on the thresholds for inertial cavitation was studied computationally in water, urine, blood, cardiac and skeletal muscle, brain, kidney, liver and skin. The results indicate that, although the effect of pulse duration on cavitation thresholds in the three liquids can be considerable, reducing them by, for example, 6%-24% at 1 MHz, the effect on tissue is minor. More importantly, the frequency dependence of the MI appears to be unnecessarily conservative; that is, the magnitude of the exponent on frequency could be increased to 0.75. Comparison of these theoretical results with experimental measurements suggests that some tissues do not contain the pre-existing, optimally sized bubbles assumed for the MI. This means that in these tissues, the MI is not necessarily a strong predictor of the probability of an adverse biological effect.

Microbubble behavior in an ultrasound field for high intensity focused ultrasound therapy enhancement

The enhancement of heating due to inertial cavitation has been focused to reduce the long treatment time of conventional high-intensity focused ultrasound (HIFU) therapy. The influences of the physical properties of surrounding tissues, initial void fraction, and spatial distribution of bubbles on microbubble-enhanced HIFU are examined. A bubble dynamics equation based on the Keller-Miksis equation is employed in consideration of the elasticity of surrounding tissue. The mixture phase and bubbles are coupled by the Euler-Lagrange method to take into account the interaction between ultrasound and bubbles. As a result, the temperature around the target increases with the initial void fraction. But at the high void fraction of 10(-5), ultrasound is too attenuated to heat the target, and the heating region moves to the transducer side. On the other hand, both the viscosity and shear elasticity of the surrounding media reduce the attenuation of ultrasound propagation through the bubbly mixture. Numerical results show that localized heating is induced with increasing viscosity or shear elasticity, though it depends on the pressure amplitudes. In addition, it was numerically confirmed that the localization of the microbubble distribution is important to obtain efficient localized heating.

Rectified growth of histotripsy bubbles

Histotripsy treatments use high-amplitude shock waves to fractionate tissue. Such treatments have been demonstrated using both cavitation bubbles excited with microsecond-long pulses and boiling bubbles excited for milliseconds. A common feature of both approaches is the need for bubble growth, where at 1 MHz cavitation bubbles reach maximum radii on the order of 100 microns and boiling bubbles grow to about 1 mm. To explore how histotripsy bubbles grow, a model of a single, spherical bubble that accounts for heat and mass transport was used to simulate the bubble dynamics. Results suggest that the asymmetry inherent in nonlinearly distorted waveforms can lead to rectified bubble growth, which is enhanced at elevated temperatures. Moreover, the rate of this growth is sensitive to the waveform shape, in particular the transition from the peak negative pressure to the shock front. Current efforts are focused on elucidating this behavior by obtaining an improved calibration of measured histotripsy waveforms with a fiber-optic hydrophone, using a nonlinear propagation model to assess the impact on the focal waveform of higher harmonics present at the source's surface, and photographically observing bubble growth rates.

Observations of the collapses and rebounds of millimeter-sized lithotripsy bubbles

Bubbles excited by lithotripter shock waves undergo a prolonged growth followed by an inertial collapse and rebounds. In addition to the relevance for clinical lithotripsy treatments, such bubbles can be used to study the mechanics of inertial collapses. In particular, both phase change and diffusion among vapor and noncondensable gas molecules inside the bubble are known to alter the collapse dynamics of individual bubbles. Accordingly, the role of heat and mass transport during inertial collapses is explored by experimentally observing the collapses and rebounds of lithotripsy bubbles for water temperatures ranging from 20 to 60 °C and dissolved gas concentrations from 10 to 85% of saturation. Bubble responses were characterized through high-speed photography and acoustic measurements that identified the timing of individual bubble collapses. Maximum bubble diameters before and after collapse were estimated and the corresponding ratio of volumes was used to estimate the fraction of energy retained by the bubble through collapse. The rebounds demonstrated statistically significant dependencies on both dissolved gas concentration and temperature. In many observations, liquid jets indicating asymmetric bubble collapses were visible. Bubble rebounds were sensitive to these asymmetries primarily for water conditions corresponding to the most dissipative collapses.