Bubble Oscillations Research Articles

Contrast-specific imaging of histotripsy: Chirp-coded subharmonic imaging combined with Volterra Filtering

Histotripsy is a non-thermal focused ultrasound therapy under development to ablate tissue mechanically via bubble cloud activity. Real-time ultrasound imaging is used for treatment guidance. Bubble cloud hyperechogenicity is reduced in deep abdominal targets, making contrast-specific imaging an active area of research. Subharmonic imaging with chirp-coded excitation can improve bubble cloud detection, though the contrast-to-tissue ratio (CTR) was still limited to nearly 6 dB. Nonlinear components of a signal can be delineated with Volterra filtering, including those associated with bubble oscillations. In this study, we tested Volterra filtering as a means to enhance bubble cloud detection. Histotripsy bubble clouds were generated in scattering tissue-mimicking phantoms. Imaging of the bubble clouds was performed with a chirped pulse (1.9-μs duration, 7–12 MHz bandwidth). The scattered signals were processed with a subharmonic matched filter, followed by a tuned second-order Volterra filter. Volterra filtering improved the CTR for bubble cloud detection two-fold relative to matched filtering alone (12.5 dB vs 5.6 dB). Further improvement in bubble contrast was observed for third-order Volterra filtering (CTR of 20.3 dB) but at the cost of underestimating the bubble cloud area. Overall, these findings indicate the utility of Volterra filtering as a means to improve histotripsy image guidance.

Histotripsy Bubble Dynamics in Elastic, Anisotropic Tissue-Mimicking Phantoms.

Elastic, anisotropic tissue such as tendon has proven resistant to mechanical fractionation by histotripsy, a subset of focused ultrasound that uses the creation, oscillation and collapse of cavitation bubbles to fractionate tissue. Our objective was to fabricate an optically transparent hydrogel that mimics tendon for evaluation of histotripsy bubble dynamics. Ex vivo bovine deep digital flexor tendons were obtained (n=4), and varying formulations of polyacrylamide (PA), collagen and fibrin hydrogels (n=3 each) were fabricated. Axial sound speeds were measured at 1 MHz for calculation of anisotropy. All samples were treated with a 1.5-MHz focused ultrasound transducer with 10-ms pulses repeated at 1 Hz (p+=127 MPa, p-=35 MPa); treatments were monitored with passive cavitation imaging and high-speed photography. Dehydrated fibrin gels were found to be the most similar to tendon in cavitation emission energy (fibrin=0.69 ± 0.24, tendon=0.64 ± 0.19 [× 1010 V2]) and anisotropy (fibrin=3.16 ± 1.12, tendon=19.4). Bubble cloud area in dehydrated fibrin (0.79 ± 0.14 mm2) was significantly smaller than most other tested hydrogels. Finally, anisotropy was found to have moderately strong linear relationships with cavitation energy and bubble cloud size (r=-0.65 and -0.80, respectively). Dehydrated fibrin shows potential as a repeatable, transparent, tissue-mimicking hydrogel for evaluation of histotripsy bubble dynamics in elastic, anisotropic tissues.

Dynamics of an oscillating microbubble in a blood-like Carreau fluid.

A numerical model for cavitation in blood is developed based on the Keller-Miksis equation for spherical bubble dynamics with the Carreau model to represent the non-Newtonian behavior of blood. Three different pressure waveforms driving the bubble oscillations are considered: a single-cycle Gaussian waveform causing free growth and collapse, a sinusoidal waveform continuously driving the bubble, and a multi-cycle pulse relevant to contrast-enhanced ultrasound. Parameters in the Carreau model are fit to experimental measurements of blood viscosity. In the Carreau model, the relaxation time constant is 5-6 orders of magnitude larger than the Rayleigh collapse time. As a result, non-Newtonian effects do not significantly modify the bubble dynamics but do give rise to variations in the near-field stresses as non-Newtonian behavior is observed at distances 10-100 initial bubble radii away from the bubble wall. For sinusoidal forcing, a scaling relation is found for the maximum non-Newtonian length, as well as for the shear stress, which is 3 orders of magnitude larger than the maximum bubble radius.

Time-Dependent Numerical Modelling of Acoustic Cavitation in Liquid Metal Driven by Electromagnetic Induction

The numerically simulated method of using electromagnetic field from an alternating current is a patented method to create in liquid metal, under the conditions of resonance, acoustic waves of sufficient strength to cause cavitation and implosion of gas bubbles, leading to beneficial degassing and grain refinement. The modelling stages of electromagnetics are described below along with acoustics in liquids, bubble dynamics, and their interactions. Sample results are presented for a cylindrical container with liquid aluminium surrounded by an induction coil. The possibility of establishing acoustic resonance and sustaining the bubble oscillation at a useful level is demonstrated. Limitations of the time-dependent approach to this multi-physics modelling problem are also discussed.

Experimental investigation on condensation regimes and transition boundary during bubble condensation in narrow rectangular channel

Direct steam contact condensation in subcooled water is widely used in various industries because of high efficiency in heat and mass transfer. A visual experiment is carried out to investigate the condensation process of vapor bubble in narrow rectangular channel. The steam injection mass flux, subcooled water temperature and water mass flow are 0.43–40 kg/m2·s, 50–93 °C, and 0–200 kg/m2·s, respectively. In order to obtain more accurate parameters of vapor bubble in narrow rectangular channel, a new bubble volume model was developed and compared with existed models. A three-dimensional condensation regime map is developed with the coordinates of steam injection flux, water mass flow, and water temperature. Five condensation patterns such as chug, oscillatory bubble, growth bubble, transition region and oscillatory jet are determined based on the dynamic behavior of steam-water interface. The bubble equivalent diameter and aspect ratio during evolution process are calculated, and these two parameters in each pattern exhibit a significant periodicity, except for the oscillatory Jet. The true area of heat transfer interface between bubble and subcooled water is much larger than the actual measured value under high steam injection mass flux. A transition criterion from oscillatory bubble regime to oscillatory jet regime is proposed by the analysis of the bubble critical diameter and the condensation heat transfer of steam-water interface.

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.

Direct numerical simulation of heat transfer on a deformable vapor bubble rising in superheated liquid

Heat transfer on a vapor bubble rising in superheated liquid is investigated by direct numerical simulation. The vapor–liquid system is described by the one-fluid formulation with the level set method capturing the interface. The proportional-integral-derivative controller is employed to keep the bubble's location fixed and evaluate interfacial forces. The heat transfer performance featured by the Nusselt number is evaluated based on the energy balance. Simulations are carried out for the bubble Reynolds number ranging from 20 to 500 and Morton number from 1.10 × 10−10 to 3.80 × 10−4. The aim of this paper is to shed some light on the effect of bubble deformation and oscillation on interfacial heat transfer. The results show that the front part of the bubble contributes to the majority of the interfacial heat transfer, while the rear part mainly affects the oscillation amplitude of the total heat transfer. The interface stretch during bubble oscillation is considered as a key mechanism in enhancing the instantaneous Nusselt number. The potential flow solution of the averaged Nusselt number is corrected by considering the influence of the aspect ratio. This research provides additional insights into the mechanism of interfacial heat transfer, and the results apply equally to interfacial mass transfer.

Interaction of a single bubble and an elastic plate: Influence of the standoff distance

The objective of this study was to investigate the coupled dynamics of a collapsing bubble and the motion of a nearby elastic plate at different initial distances. This was achieved using a combination of experimental and computational models. In the experiments, high-speed photography was used to record the temporal and spatial evolution of the collapse of a single bubble near an elastic boundary under normalized standoff distances γ ranging from 1.0 to 3.3. Digital image correlation was used to synchronously record the motion of the elastic plate. For the numerical simulations, taking the fluid compressibility and boundary motion into account, the immersed-boundary method was introduced to simulate the interaction between the elastic plate and bubble collapse. The results show that, with different initial distances, the dynamic behaviors of the bubble, including oscillation time, impact mode, and energy conversion, are different, and this is caused by the elastic rebound of the plate. In addition, the direction and amplitude of the deformation of the elastic plate are also influenced by the impact effects during bubble oscillation and rebound. The combined form of these impact behaviors changes with initial distance, and there are three typical impact patterns: the shock-wave effect, jet-effect, and hybrid shock-wave and jet-effect modes. In particular, when γ < 1.5, the jet effect and hybrid impact forms, which are dominated by the high-speed jet, can result in asymmetric deformation and cause greater local damage to the elastic plate. Finally, we summarize the combined mechanisms that govern the impact of a collapsing bubble on an elastic plate.

Interferometric Fiber Optic Probe for Measurements of Cavitation Bubble Expansion Velocity and Bubble Oscillation Time.

Cavitation bubbles are used in medicine as a mechanism to generate shock waves. The study of cavitation bubble dynamics plays a crucial role in understanding and utilizing such phenomena for practical applications and purposes. Since the lifetime of cavitation bubbles is in the range of hundreds of microseconds and the radii are in the millimeter range, the observation of bubble dynamics requires complicated and expensive equipment. High-speed cameras or other optical techniques require transparent containers or at least a transparent optical window to access the region. Fiber optic probe tips are commonly used to monitor water pressure, density, and temperature, but no study has used a fiber tip sensor in an interferometric setup to measure cavitation bubble dynamics. We present how a fiber tip sensor system, originally intended as a hydrophone, can be used to track the expansion and contraction of cavitation bubbles. The measurement is based on interference between light reflected from the fiber tip surface and light reflected from the cavitation bubble itself. We used a continuous-wave laser to generate cavitation bubbles and a high-speed camera to validate our measurements. The shock wave resulting from the collapse of a bubble can also be measured with a delay in the order of 1 µs since the probe tip can be placed less than 1 mm away from the origin of the cavitation bubble. By combining the information on the bubble expansion velocity and the time of bubble collapse, the lifetime of a bubble can be estimated. The bubble expansion velocity is measured with a spatial resolution of 488 nm, half the wavelength of the measuring laser. Our results demonstrate an alternative method for monitoring bubble dynamics without the need for expensive equipment. The method is flexible and can be adapted to different environmental conditions, opening up new perspectives in many application areas.

A finite-difference ghost-point multigrid method for multi-scale modelling of sorption kinetics of a surfactant past an oscillating bubble

We propose a method for the numerical solution of a multiscale model describing sorption kinetics of a surfactant around an oscillating bubble. The evolution of the particles is governed by a convection-diffusion equation for the surfactant concentration c, with suitable boundary condition on the bubble surface, which models the action of the short range attractive-repulsive potential acting on them when they get sufficiently close to the surface [1]. In the domain occupied by the fluid, the particles are transported by the fluid motion generated by the bubble oscillations.The method adopted to solve the equation for c is based on a finite-difference scheme on a uniform Cartesian grid and implemented in 2D and 3D axisymmetric domains. We use a level-set function to define the region occupied by the bubble, while the boundary conditions are discretized by a ghost-point technique to guarantee second order accuracy at the curved boundary. The sparse linear system is finally solved with a geometric multigrid technique designed ad-hoc for this specific problem. Several accuracy tests are provided to prove second order accuracy in space and time.The fluid dynamics generated by the oscillating bubble is governed by the Stokes equation solved with a second order accurate method based on a monolithic approach, where the momentum and continuity equations are solved simultaneously. Since the amplitude of the bubble oscillations are very small, a simplified model is presented where the computational bubble is actually steady and its oscillations are represented purely with time-dependent boundary conditions. A numerical comparison with the moving domain model confirms that this simplification is perfectly reasonable for the class of problems investigated in this paper.

Analysis of suppressive effect of large bubbles on oscillation of cavitation bubble in cavitation field

In this work, the interaction among multiple bubbles in a cavitation field is investigated by combining the experimental observation of small bubbles hovering around large bubbles. A model composed of three bubbles is developed, and the dynamic behavior of cavitation bubble is analyzed. By considering the time delay effect of the interaction among bubbles and the nonspherical oscillation of large bubbles, the modified bubble dynamic equations are obtained. Numerical results show that the nonspherical effect of large bubbles has little effect on the oscillation of cavitation bubble. The suppressive effect of large bubble on cavitation bubble is closely related to the radius of the large bubble. The larger the size of the large bubble, the stronger the suppression is. When the size of large bubble approaches to the resonant radius, the oscillation of cavitation bubble presents coupled resonance response, and the maximum expansion radius of bubble shows a resonance peak. The distribution of the secondary Bjerknes force versus bubble radius and the separation distance is strongly influenced by driving frequencies or sound pressure. When the large bubble is on the order of submillimeter, the intensity of the secondary Bjerknes force and the acoustic response mode are different due to the different intensity of the nonlinear response of the cavitation bubble. As the distance decreases, when the acoustic pressure increases to a certain value, the secondary Bjerknes force on the cavitation bubble decreases due to abnormal acoustic absorption. The secondary Bjerknes force on cavitation bubble is likely to be repulsive at different separation distances. The theoretical results accord well with experimental phenomenon.

Theoretical investigation on resonance characteristics of a vapor bubble based on Laplace transform method

In the present paper, resonance characteristics of the vapor bubble oscillating in an acoustic field are investigated analytically. The analytical solution of the non-dimensional perturbation of the instantaneous bubble radius during the transient process in the initial oscillation stage is explicitly obtained and physically analyzed at the resonance situation based on the Laplace transform method. And the typical oscillation behaviors obtained from the analytical solution are thoroughly exhibited and analyzed in the time and frequency domains. In addition, the corresponding oscillation behaviors at the non-resonance situation are also investigated for the purpose of comparisons. Through our investigation, several essential conclusions can be drawn as follows: (1) The analytical solution of the non-dimensional perturbation of the instantaneous bubble radius can be divided into four terms according to the physical meaning. Among them, it is the term related to the acoustic field that causes the progressively violent bubble oscillation. (2) The vapor bubble with a smaller equilibrium radius could respond faster and more significantly to the acoustic field during the oscillation. (3) The bubble oscillation characteristics always exhibit significant differences at the resonance and non-resonance situations in both the time and frequency domains, even if the difference between the natural frequency of the oscillating vapor bubble and the angular frequency of the acoustic field is greatly small.

EXPERIMENTAL STUDY OF THE INTERACTION BETWEEN A BUBBLE AND A POROUS PLATE

This paper aims to experimentally investigate the interaction between a bubble and a plate with multiple holes. The bubble is generated under the plate by underwater electric discharge method, and the top surface of the plate is flush with the water-air interface. In order to reveal the bubble dynamics and the droplets formation caused by bubble oscillation, the interaction process is recorded by high-speed photography. Similar to the interaction between bubble and plate with a single hole, there exist two jets, the primary slow jet and the secondary fast jet, caused by bubble expansion and collapse, respectively. The former starts to be pumped out as liquid columns and breaks up into fine droplets over time, while the latter erupts directly as droplets with more instability. As the distance between bubble and porous plate decreases, the speed of droplets increases and the velocity difference in droplets through different holes becomes greater. Besides, with the longer oscillation time the bubble is less likely to detach from the plate, and its maximum volume will be larger than expected. The effects of plate thickness and hole diameter on bubble dynamics and droplets formation are also investigated. Increasing the plate thickness and decreasing the hole diameter make the porous plate have a similar effect as the rigid wall. In this case, the bubble tends to migrate to the plate and inside the bubble, a jet toward the solid boundary will be generated. The amount of liquid being squeezed out through holes is reduced and the liquid columns are more likely to break up into sprays. In contrast, decreasing the plate thickness and increasing the hole diameter enhance the effect of free liquid on the bubble dynamics. Also, the efficiency of the oscillating bubble to pump liquids has increased.

Synchrotron X-ray imaging of the onset of ultrasonic horn cavitation.

High-power ultrasonic horns operating at low frequency are known to generate a cone-shaped cavitation bubble cloud beneath them. The exact physical processes resulting in the conical structure are still unclear mainly due to challenges associated with their visualization. Herein, we address the onset of the cavitation cloud by exploiting high-speed X-ray phase contrast imaging. It reveals that the cone formation is not immediate but results from a three-step phenomenology: (i) inception and oscillation of single bubbles, (ii) individual cloud formation under splitting or lens effects, and (iii) cloud merging leading to the formation of a bubble layer and, eventually, to the cone structure due to the radial pressure gradient on the horn tip.

Simulations of Bubble Formation and Oscillation Behavior in Micro-Leakage Measurement System

In the process of measuring micro-leakage based on the bubble method, the physical parameters of the liquid phase have a great impact on the formation and movement of bubbles, thus affecting the measurement accuracy of the system. Therefore, it is of great significance to study the physical parameters of the liquid phase. At present, it is difficult to independently study the parameters of the liquid phase by experimental methods. In this paper, based on the Cahn-Hilliard phase field model, a gas-liquid two-phase flow model for the expression of leakage is established to independently study the influence of different physical parameters on the formation and movement of bubbles in the measuring system. Firstly, the effects of liquid medium density, dynamic viscosity coefficient and surface tension on the initial shape (aspect ratio), the generation period and the shape oscillation of bubbles after they leave the nozzle are analyzed. Then, an experimental platform for visualization of bubbles in two-phase flow based on machine vision is built, through which the morphological parameters of bubbles in the liquid phase can be obtained in real time. Finally, the results of visualization experiment and numerical simulation are compared. The results show that the initial aspect ratio error of bubbles obtained by visual experiment and numerical simulation is 1.8%, and the average oscillation period error is 12.3%. The results are basically consistent, which proves the rationality and correctness of the mathematical model established. It is found that the liquid with larger dynamic viscosity coefficient μ and density ρ and smaller surface tension σ can be selected as the liquid medium of the measurement system. It is more conducive to the accurate expression of micro-leakage in the measurement system, and the bubble shape can quickly reach a stable state. It provides theoretical support for improving the accuracy and stability of the micro-leakage measurement system.

A multigrid solver for the coupled pressure-temperature equations in an all-Mach solver with VoF

We present a generalisation of the all-Mach solver of Fuster and Popinet (2018) [1] to account for heat diffusion between two different compressible phases. By solving a two-way coupled system of equations for pressure and temperature, the current code is shown to increase the robustness and accuracy of the solver with respect to classical explicit discretization schemes. Different test cases are proposed to validate the implementation of the thermal effects: an Epstein-Plesset like problem for temperature is shown to compare well with a spectral method solution. The code also reproduces free small amplitude oscillations of a spherical bubble where analytical solutions capturing the transition between isothermal and adiabatic regimes are available. We show results of a single sonoluminescent bubble (SBSL) in standing waves, where the result of the DNS is compared with that of other methods in the literature. Moreover, the Rayleigh collapse problem is studied in order to evaluate the importance of thermal effects on the peak pressures reached during the collapse of spherical bubbles. Finally, the collapse of a bubble near a rigid boundary is studied reporting the change of heat flux as a function of the stand-off distance.

Modelling Radial Oscillations of a Bubble in a Spherical Liquid-Filled Elastic Solid

In this paper, equation of a spherical bubble oscillations in Newtonian and viscous fluid with considering compressible fluid flow in a spherical liquid-filled elastic solid was developed. The exact solution of the linearisation and the numerical solution of the equation have been derived and compared.  Then numerical calculations are performed to investigate the effects of compressibility parameter  for gas and acoustic bubbles. We conclude that the amplitude of bubble radius oscillations increases with  and the effects of  is accumulating. Further, the discrepancy between the exact and numerical solutions increases with time when . However, the difference was not changed when the  is smaller than . Dual frequency is also considered in the acoustic environment.

Modeling of water hammer effect during the single cavitating bubble oscillation

The paper presents the results of an analytical study of the vapor-gas bubble dynamics in cavitation processes, giving consideration to the liquid compressibility. The study is based on the concept that cavitation effects are directly related to the occurrence of hydraulic shock on the surface of an extremely compressed bubble. The purpose of this work is to study cavitation bubble dynamics accounting for the spherical water hammer effects. An equation for the bubble dynamics was obtained, which includes the coefficient of liquid adiabatic compressibility as a basic parameter that is directly related to the liquid compressibility. For this equation reduces to the classical Rayleigh-Plesset equation for incompressible liquids. The results of a computational experiment performed within the framework of the modified model are presented for which the behavior of a cavitation bubble both in compressible and in incompressible water was analyzed. Based on a detailed analysis of the results obtained, it is shown that over time .the compressed bubble is in the state of a supercritical fluid with temperature up to 2000 K and pressure of about 400 MPa. The potential energy of the compressed liquid, in the form of a powerful acoustic pulse, emitted by the bubble at the stage of its collapse, is irreversibly dissipated in the surrounding liquid.

Delay-induced vibrational resonance in the Rayleigh–Plesset bubble oscillator

We examine the impacts of time-delay and phase shift between two acoustic driving forces on vibrational resonance (VR) phenomena in the oscillations of a spherical gas bubble. Using the approximate method of direct separation of the motions, we obtain the equation of slow motion and the response amplitude, and we validate the theoretical predictions with numerical simulations. We find that the response amplitude of the system at the lower frequency varies periodically with respect to the phase shift. When the phase shift consists of an even number of periods, it can be optimized to enhance the system’s response in the relevant parameter space of the high-frequency driving force. In addition to the enhancement of the VR peak by variation of the phase shift, our results show that the time-delay also plays a significant role in the bubble’s response to dual-frequency acoustic driving fields. It and can be exploited either to suppress drastically, or to modulate, the resonance peaks, thereby controlling the resonances. Our analysis shows further that cooperation between the time-delay and the amplitude of the high-frequency component of the acoustic waves can induce multiple resonances. These results could potentially be exploited to control and enhance ultrasonic cleaning processes by varying the time-delay parameter in the presence of phase shifted dual-frequency acoustic waves. Moreover, it could be employed to achieve improved accuracy in ultrasonic biomedical diagnosis and tumour therapy, as well as for targeted delivery of reagents transported within bubbles.

Influence of water level on RC caisson subjected to underwater explosions

With the increasing significance of marine safety issues, the studies on the underwater blast-resistant performance of wharves, e.g., reinforced concrete (RC) caissons, has become an urgent demand. At present, the influence of water level on caisson subjected to underwater explosions was studied experimentally and numerically, e.g., underwater explosion loading characteristics and dynamic behaviors of caisson. Firstly, four shots of underwater explosion test were carried out both in free field and on a partially submerged caisson specimen, and the overpressure- and deflection-time histories, as well as the structural damage pattern were recorded. Then, the underwater explosion loading characteristics including the preceding blast wave and the succeeding bubble oscillations, the cut-off effect of the water surface, as well as the dynamic behaviors of caisson are comprehensively discussed. Furthermore, both the 1D and 3D finite element (FE) models were established, and by adopting Coupled Eulerian-Lagrangian method and remapping technology, the reliability of the FE models and analysis approach were validated by comparing with the test results. Finally, the influence of water level on the dynamic behaviors of caisson against underwater explosions were numerically examined. It derives that, the empirical formula derived based on spherical charge for underwater explosion peak overpressure is applicable to group charge, while the formula for impulse provides higher prediction on group charge; bubble oscillation has great influence on the impulse of underwater explosions; the unsubmerged part of hydraulic structures suffers slighter damage during underwater explosions than submerged part; the upper part of caisson is more sensitive to the change of water level; the partially submerged caisson shows better blast-resistant performance than fully submerged caisson. The present work could provide helpful reference for the studies on the underwater explosion loadings, as well as the blast-resistant assessment and design of hydraulic structures.