Dynamics of a bubble cluster in an acoustic field

A mathematical model describing the dynamics of clustered gas bubbles under the effect of an acoustic field is presented. The proposed model is used as the basis for an analytical study of small bubble oscillations in monodisperse and polydisperse clusters and for a numerical study of nonlinear bubble oscillations under high-amplitude external pressures. The following effects are found to occur in a polydisperse cluster: a synchronization of the collapse phases of bubbles with different radii and a collapse intensification for bubbles of one size in the presence of bubbles of another size. These effects are explained by the interaction between bubbles of different radii in the cluster.     

A combined resonance-Doppler technique for studying bubble evolution in liquids

Gas bubbles in liquids have been studied for decades with a variety of optical and acoustic techniques. The evolution of a bubble consists of several stages, including formation and growth at a nozzle, detachment and resonance, and rise towards terminal velocity. Most existing techniques can monitor only a single aspect of the bubble behaviour. This work describes an acoustic technique to monitor all stages of an air bubble's evolution. The technique uses a combination of passive acoustic listening and active ultrasonic Doppler observation to study millimetre-sized air bubbles in liquid. A hollow cylindrical piezoelectric transducer, located around the nozzle used to produce the bubbles, detects the resonance of the bubble following its detachment. An ultrasonic Doppler system, positioned several centimetres above the nozzle, monitors both the growth and the rise of the bubble, including shape oscillations and the terminal velocity through the use of joint time-frequency analysis. Because all aspects of the bubble evolution are affected by the properties of the liquid, by monitoring the bubble evolution with this technique the rising bubble can potentially be used as a tool to characterize the liquid.     

不同管口浸没方式下气泡运动特性实验研究

为了对比研究不同管口浸没方式下气泡的运动特性,通过可视化实验揭示了顶部、侧部和底部三种管口浸没方式下的气泡上升运动过程,得到了气泡形状、等效直径、位移、速度以及高宽比的变化规律,通过获得相邻气泡质心间垂直距离定量表征了气泡在上升过程中的紊乱程度.研究结果表明,顶部管口浸没方式下的气泡形态明显区别于侧部和底部管口浸没方式...     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

The acoustic emissions of cavitation bubbles in stretched vortices

Pairs of unequal strength, counter-rotating vortices were produced in order to examine the inception, dynamics, and acoustic emission of cavitation bubbles in rapidly stretching vortices. The acoustic signatures of these cavitation bubbles were characterized during their inception, growth, and collapse. Growing and collapsing bubbles often produced a sharp, broadband, pop sound. The spectrum of these bubbles, and the peak resonant frequency can generally be related to quiescent flow bubble dynamics and corresponding resonant frequencies. However, some elongated cavitation bubbles produced a short tonal burst, or chirp, with frequencies on the order of a few kilohertz. Theses frequencies are too low to be related to resonant frequencies of a bubble in a quiescent flow. Instead, the frequency content of the acoustic signal during bubble inception and growth is related to the volumetric oscillations of the bubble while it interacted with vortical flow that surrounds the bubble (i.e., the resonant frequency of the vortex-bubble system). A relationship was determined between the observed peak frequency of the oscillations, the highly stretched vortex properties, and the water nuclei content. It was found that different cavitation spectra could relate to different flow and fluid properties and therefore would not scale in the same manner.     

Enhancement of oscillation amplitude of cavitation bubble due to acoustic wake effect in multibubble environment

Acoustic cavitation occurs in ultrasonic treatment causing various phenomena such as chemical synthesis, chemical decomposition, and emulsification. Nonlinear oscillations of cavitation bubbles are assumed to be responsible for these phenomena, and the neighboring bubbles may interact each other. In the present study, we numerically investigated the dynamic behavior of cavitation bubbles in multi-bubble systems. The results reveal that the oscillation amplitude of a cavitation bubble surrounded by other bubbles in a multi-bubble system becomes larger compared with that in the single-bubble case. It is found that this is caused by an acoustic wake effect, which reduces the pressure near a bubble surrounded by other bubbles and increases the time delay between the bubble contraction/expansion cycles and sound pressure oscillations. A new parameter, called “cover ratio” is introduced to quantitatively evaluate the variation in the bubble oscillation amplitude, the time delay, and the maximum bubble radius.     

Low frequency resonant dispersion of sound in bubble media

Presented is a theory of a new type of resonant dispersion of sound in a gas-liquid bubble media based on the use of effective dynamic density. We show that because of spheroidal-translational oscillations of the bubbles the dynamic density of the gas-liquid media has a resonance dependence on the frequency, which is manifested in wave process as a low-frequency resonant dispersion of sound. This dispersion is significantly different from the known high-frequency resonant dispersion, which is due to resonance in the volume oscillations of the bubbles. The results of the experiments confirming the existence of the resonant dispersion of sound at a frequency equal to half the natural frequency of the spheroidal oscillations of bubbles are provided.     

三维格子Boltzmann方法研究上升双气泡的运动特性

应用格子Boltzmann三维模型，对双气泡在静水中的运动进行数值研究.采用八点差分和十八点差分格式分别求解一阶▽φ和二阶▽²φ可以有效避免气液密度比过大造成的数值不稳定问题.结果表明：当两个相同直径的气泡在上升时，位置靠上的气泡形状变化像单气泡上升一样，而位置靠下的气泡会受到前一个气泡尾迹的影响，并有很明显的形状变化.当两个气泡直径不同时，不管初始位置如何，大气泡总会对小气泡造成强烈的影响.     

Natural frequencies of two bubbles in a compliant tube: analytical, simulation, and experimental results

Motivated by various clinical applications of ultrasound contrast agents within blood vessels, the natural frequencies of two bubbles in a compliant tube are studied analytically, numerically, and experimentally. A lumped parameter model for a five degree of freedom system was developed, accounting for the compliance of the tube and coupled response of the two bubbles. The results were compared to those produced by two different simulation methods: (1) an axisymmetric coupled boundary element and finite element code previously used to investigate the response of a single bubble in a compliant tube and (2) finite element models developed in comsol Multiphysics. For the simplified case of two bubbles in a rigid tube, the lumped parameter model predicts two frequencies for in- and out-of-phase oscillations, in good agreement with both numerical simulation and experimental results. For two bubbles in a compliant tube, the lumped parameter model predicts four nonzero frequencies, each asymptotically converging to expected values in the rigid and compliant limits of the tube material.     

The characterization of acoustic cavitation bubbles - an overview

Acoustic cavitation, in simple terms, is the growth and collapse of preexisting microbubbles under the influence of an ultrasonic field in liquids. The cavitation bubbles can be characterized by the dynamics of oscillations and the maximum temperatures and pressures reached when they collapse. These aspects can be studied both experimentally and theoretically for a single bubble system. However, in a multibubble system, the formation of bubble streamers and clusters makes it difficult to characterize the cumulative properties of these bubbles. In this overview, some recently developed experimental procedures for the characterization of acoustic cavitation bubbles have been discussed.     

Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method

The rise of bubbles in viscous liquids is not only a very common process in many industrial applications, but also an important fundamental problem in fluid physics. An improved numerical algorithm based on the front tracking method, originally proposed by Tryggvason and his co-workers, has been validated against experiments over a wide range of intermediate Reynolds and Bond numbers using an axisymmetric model [J. Hua, J. Lou, Numerical simulation of bubble rising in viscous liquid, J. Comput. Phys. 22 (2007) 769–795]. In the current paper, this numerical algorithm is further extended to simulate 3D bubbles rising in viscous liquids with high Reynolds and Bond numbers and with large density and viscosity ratios representative of the common air–water two-phase flow system. To facilitate the 3D front tracking simulation, mesh adaptation is implemented for both the front mesh on the bubble surface and the background mesh. On the latter mesh, the governing Navier–Stokes equations for incompressible, Newtonian flow are solved in a moving reference frame attached to the rising bubble. Specifically, the equations are solved using a finite volume scheme based on the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm, and it appears to be robust even for high Reynolds numbers and high density and viscosity ratios. The 3D bubble surface is tracked explicitly using an adaptive, unstructured triangular mesh. The numerical model is integrated with the software package PARAMESH, a block-based adaptive mesh refinement (AMR) tool developed for parallel computing. PARAMESH allows background mesh adaptation as well as the solution of the governing equations in parallel on a supercomputer. Further, Peskin distribution function is applied to interpolate the variable values between the front and the background meshes. Detailed sensitivity analysis about the numerical modeling algorithm has been performed. The current model has also been applied to simulate a number of cases of 3D gas bubbles rising in viscous liquids, e.g. air bubbles rising in water. Simulation results are compared with experimental observations both in aspect of terminal bubble shapes and terminal bubble velocities. In addition, we applied this model to simulate the interaction between two bubbles rising in a liquid, which illustrated the model’s capability in predicting the interaction dynamics of rising bubbles.     

Regimes of bubble volume oscillations in a pipe

The effect of an acoustically driven bubble on the acoustics of a liquid-filled pipe is theoretically analyzed and the dimensionless groups of the problem are identified. The different regimes of bubble volume oscillations are predicted theoretically with these dimensionless groups. Three main regimes can be identified: (1) For small bubbles and weak driving, the effect of the bubble oscillations on the acoustic field can be neglected. (2) For larger bubbles and still small driving, the bubble affects the acoustic field, but due to the small driving, a linear theory is sufficient. (3) For large bubbles and large driving, the two-way coupling between the bubble and the flow dynamics requires the solution of the full nonlinear problem. The developed theory is then applied to an air bubble in a channel of an inkjet printhead. A numerical model is developed to test the predictions of the theoretical analysis. The Rayleigh-Plesset equation is extended to include the influence of the bubble volume oscillations on the acoustic field and vice versa. This modified Rayleigh-Plesset equation is coupled to a channel acoustics calculation and a Navier-Stokes solver for the flow in the nozzle. The numerical simulations indeed confirm the predictions of the theoretical analysis.     

The effects of coupling and bubble size on the dynamical-systems behaviour of a small cluster of microbubbles

This study endeavours to apply a theoretical model for predicting the dynamics of a bubble cluster of various sizes, within which each bubble may assume different initial conditions from other bubbles in the cluster. The resulting system of coupled Keller-Miksis-Parlitz equations are solved numerically, and the effects of coupling and bubble size on bubble cluster dynamics are examined for a given set of ultrasound parameters. It has been found that the effects of coupling are significant, and a bubble cluster's bifurcation characteristics and route to chaos can be altered by inter-bubble interactions. This gives rise to the possibility of suppressing the chaotic oscillations of microbubbles by varying bubble cluster size. Small equilibrium radii bubbles have little influence on the dynamics of neighbouring bubbles in a cluster via coupling. Furthermore, a bubble system consisting of smaller-sized bubbles transitions from order to chaos at lower driving pressure amplitudes.     

Numerical modeling of ultrasonic cavitation by dividing coated microbubbles into groups

Homogeneous cavitation models usually use an average radius to predict the dynamics of all bubbles. However, bubbles with different sizes may have quite different dynamic characteristics. In this study, the bubbles are divided into several groups by size, and the volume-weighted average radius is used to separately calculate the dynamics of each group using a modified bubble dynamics equation. In the validation part, the oscillations of bubbles with two sizes are simulated by dividing them into 2 groups. Comparing with the predictions by the Volume of Fluid (VOF) method, the bubble dynamics of each size are precisely predicted by the proposed model. Then coated microbubbles with numerous sizes are divided into several groups in equal quantity, and the influence of the group number is analyzed. For bubble oscillations at f = 0.1 MHz and 1 MHz without ruptures, the oscillation amplitude is obviously under-estimated by the 1-group model, while they are close to each other after the group number increases to 9. For bubble ruptures triggered by Gaussian pulses, the predictions are close to each other when more than 5 groups are used.     

Bubble phenomena in sould fields: part two

Large-amplitude radial oscillations of gas bubbles are briefly illustrated with the aid of numerical examples. The origin and possible effects of pressure-radiation forces are considered and an estimate of the coalescence time under their action is given. Non-spherical oscillations, the related problem of the fragmentation of oscillating bubbles by instability of the spherical shape, and sound propagation in bubbly liquids conclude the review.     

Modeling non-spherical oscillations and stability of acoustically driven shelled microbubbles

The oscillation and destruction of microbubbles under ultrasound excitation form the basis of contrast enhanced ultrasound imaging and microbubble assisted drug and gene delivery. A typical microbubble has a size of a few micrometers and consists of a gas core encapsulated by a shell. These bubbles can be driven into surface mode oscillations, which not only contribute to the measured acoustic signal but can lead to bubble destruction. Existing models of surface model oscillations have not considered the effects of a bubble shell. In this study a model was developed to study the surface mode oscillations in shelled bubbles. The effects of shell viscosity and elasticity on the surface mode oscillations were modeled using a Boussinesq-Scriven approach. Simulation was conducted using the model with various bubble sizes and driving acoustic pressures. The occurrence of surface modes and the number of ultrasound cycles needed for the occurrence were calculated. The simulation results show a significant difference between shelled bubbles and shell free bubbles. The shelled bubbles have reduced surface mode amplitudes and a narrower bubble size range within which these modes develop compared to shell free bubbles. The clinical implications were also discussed.     

Dynamics of three cavitation bubbles with pulsation and symmetric deformation

A new system of dynamical equations was obtained by using the perturbation and potential flow theory to couple the pulsation and surface deformation of the second-order Legendre polynomials (P₂) of three bubbles in a line. The feasibility and effectiveness of the model were verified by simulating the radial oscillations, surface deformation with P₂, and shape evolution of three bubbles. The spherical radial pulsation and surface deformation of the three bubbles exhibit periodic behavior. The maximum secondary Bjerknes forces (SBFs) on the three bubbles are found not to depend on the system’s resonance frequency. Within a stable region, the SBFs of the three bubbles increase with increasing sound pressure amplitude but decrease with increasing distance between the bubbles. The primary Bjerknes force (PBF) on a bubble is significantly higher than the SBF on it.     

Influence of magnetic fields on the behavior of bubbles in liquid metals

The paper reviews numerical and experimental investigations concerned with the physics of rising bubbles in conducting liquid metals under the action of a magnetic field. Different situations, characterized by different void fractions ranging from single bubbles to bubble swarms, are considered. The impact of the geometrical arrangement is addressed covering large containers with bubbles far from the walls and narrow containers with bubbles interacting with the walls. It is demonstrated that magnetic fields offer a convenient means to influence bubble dynamics, which makes them interesting for technological applications.     

Buckling resistance of solid shell bubbles under ultrasound

Thin solid shell contrast agents bubbles are expected to undergo different volume oscillating behaviors when the acoustic power is increased: small oscillations when the shell remains spherical, and large oscillations when the shell buckles. Contrary to bubbles covered with thin lipidic monolayers that buckle as soon as compressed: the solid shell bubbles resist compression, making the buckling transition abrupt. Numerical simulations that explicitly incorporate a shell bending modulus give the critical buckling pressure and post-buckling shape, and show the appearance of a finite number of wrinkles. These findings are incorporated in a model based on the concept of effective surface tension. This model compares favorably to experiments when adjusting two main parameters: the buckling tension and the rupture shell tension. The buckling tension provides a direct estimation of the acoustic pressure threshold at which buckling occurs.     

A two-frequency acoustic technique for bubble resonant oscillation studies

A two-frequency acoustic apparatus has been developed to study the dynamics of a single gas or vapor bubble in water. An advantage of the apparatus is its capability of trapping a bubble by an ultrasonic standing wave while independently driving it into oscillations by a second lower frequency acoustic wave. For a preliminary application, the apparatus is used to study resonant oscillations. First, near-resonant coupling between the volume and the n = 3 shape oscillation modes of air bubbles at room temperature is studied, where n is the mode number. The stability boundary, amplitude versus frequency, of the volume oscillation forms a wedge centered at the resonant frequency, which qualitatively agrees with a theoretical prediction based on a phase-space analysis. Next, the resonant volume oscillations of vapor bubbles are studied. The resonant radius of vapor bubbles at 80 degrees C driven at 1682 Hz is determined to be 0.7 mm, in agreement with a prediction obtained by numerical simulation.