Bubble Vibration Research Articles

Single microbubbles vibrations measured with an “acoustical camera"

Measuring and understanding the nonlinear vibrations of contrast agent microbubbles in response to an ultrasound wave is essential to optimize the technique employed by an ultrasound scanner to distinguish microbubbles from tissue. In this context, an acoustical method was developed to retrieve the radial response of single microbubbles to a pressure wave by means of a low-amplitude probing wave. If the frequency of the latter is much higher than the spherical resonance frequency of the microbubble (typically between 1 and 10 MHz), the relative amplitude modulation (induced by a pressure wave) in the signal scattered in response to the probing wave is quasi-equal to the radial strain (i.e., relative variation in radius) induced by the pressure wave. A reference response to the probing wave acquired before and after the transmission of the pressure wave allows us to reveal asymmetry in microbubble oscillations. Although efficient nonlinear wave interaction is well known in bubbly liquids, we demonstrated that such an “acoustical camera” can extract quantitative information (the radius as function of time) on single bubble vibrations by analyzing the nonlinear coupling between two ultrasound waves.

Modeling of Particle Migration inside Vibration Bubbles in Bubble-Stretching Dispersion Method

Bubble-stretching based dispersion method can be used to prevent the agglomeration of nanoparticles during the process of preparing nanocomposites, whereas its effectiveness is restricted by the practically low migration ratio of particles onto the bubble wall. Theoretical models for bubble vibration and particle migration have been presented, followed by numerically study on effects of different parameters on migration ratio of particles on to the bubble wall. The numerical results have shown that bubble initial radius, bubble initial pressure and particle diameters impact the particle migration ratio obviously and it is found that the particle migration ratio can be improved effectively through the optimal control of the vibration parameters of the bubble happed in the dispersion process. Therefore, this article provides a theoretical basis for the efforts on increasing the particles migration ratio and thus the dispersion effectiveness of nanoparticles in polymer melt.

Gaseous bubble dynamics in a pulsational viscous flow

The paper is devoted to the investigation of gaseous bubble dynamics in a pulsational viscous flow. Behaviour of the bubble suspended in a viscous liquid of different density and located near the rigid wall of oscillating container is studied. The effect of the bubble and host liquid characteristics and vibration parameters on the interaction force is examined.

Vibration of the bubble in bubbly liquids

The vibration of bubbles in bubbly liquids has been studied when the driving sound field is fixed. The radius of the bubble will change when the bubble is driven by a driving acoustic field for a short time. This small change of radius is then fed back to the scattering process of the bubbles driven by the driving acoustic field. Thus the compound acoustic field including the scattered field of the bubble can be obtained. Then the bubble is again driven into vibration for a short time. By repeating the same procedure, the bubble vibration and its radius variation are simulated by a numerical method. It is shown that in the case of numerous bubbles in the liquid the vibration of a bubble is different from the case of only a single bubble in it. Because numerous bubbles will show interactions between one another, the radius of the bubble will change in different manner. For different size and content of bubbles, the radius of the bubble changes according to the following rules. The radius will oscillate in the vicinity of the equilibrium position; the radius oscillation shows a periodic cavitation process; the radius will vibrate during one cycle of cavitation; then, the radius will increase and oscillate in the vicinity of a certain value. Therefore, it is necessary that the bubble content should be considered in analyzing the vibration of the bubble in a bubbly liquid under a driving sound field.

Numerical Simulation of the Micromixing Induced by Ultrasonic Vibration of Sidewall-Trapped Microbubbles

It exist several strategies to mix two fluids in a micro channel. The way micro bubble vibrations influence the mixing flow is still unknown. This paper presents numerical simulations of the mixing within the micro device with and without micro bubble vibrations. A simplified model of the microchannel has been successfully employed, via using moving panels instead of sidewall-trapped bubbles oscillation. The simulation method, which exerted sinusoidal movements on the panels to approximately represent the ultrasonic vibrations of microbubbles, has been used to fully solve the Navier-Stokes equations. The comparison between simulations and previously reported experiments, in terms of flow pattern and the mixing performance within micro channel, exhibits a very good agreement. When ultrasonic vibrations of a frequency of 80 kHz and amplitude of 8 μm were applied, the mixing flow patterns have been reproduced and with a little differences comparing to the experimental results. All of these studies have revealed the mix mechanism under the micrometer scale in a certain way.

Acoustical Properties of Individual Liposome-Loaded Microbubbles

A comparison between phospholipid-coated microbubbles with and without liposomes attached to the microbubble surface was performed using the ultra-high-speed imaging camera (Brandaris 128). We investigated 73 liposome-loaded microbubbles (loaded microbubbles) and 41 microbubbles without liposome loading (unloaded microbubbles) with a diameter ranging from 3–10 μm at frequencies ranging from 0.6–3.8 MHz and acoustic pressures ranging from 5–100 kPa. The experimental data showed nearly the same shell elasticity for the loaded and unloaded bubbles, but the shell viscosity was higher for loaded bubbles compared with unloaded bubbles. For loaded bubbles, a higher pressure threshold for the bubble vibrations was noticed. In addition, an “expansion-only” behavior was observed for up to 69% of the investigated loaded bubbles, which mostly occurred at low acoustic pressures (≤30 kPa). Finally, fluorescence imaging showed heterogeneity of liposome distributions of the loaded bubbles.

Existence of global solutions to the 1D Abstract Bubble Vibration model

The Abstract Bubble Vibration model ($\mathrm{ABV}$) is a system of two PDEs consisting of a transport equation and a Poisson equation. It has been derived in order to provide a better understanding of hyperbolic-elliptic couplings which are involved in low Mach number models. While a local existence theorem has already been proven in any dimension for the ($\mathrm{ABV}$) model, we get interested in this paper in the one-dimensional case, where we prove the existence of global-in-time solutions no matter how smooth the data. We also provide explicit expressions of these solutions thanks to the method of characteristics that we apply to the transport equation taking advantage of the coupling with the Poisson equation. We then illustrate numerically these results using two different schemes depending on the smoothness of data.

Theoretical Study of an Abstract Bubble Vibration Model

We present the theoretical study of a hyperbolic-elliptic system of equations called the Abstract Bubble Vibration (Abv) model. This simplified system is derived from a model describing a diphasic low Mach number flow. It is thus aimed at providing mathematical properties of the coupling between the hyperbolic transport equation and the elliptic Poisson equation. We prove an existence and uniqueness result including the approximation of the time interval of existence for any smooth initial condition. In particular, we obtain a global-in-time existence result for small parameters. We then focus on properties of solutions (depending of their smoothness) such as maximum principle or evenness. In particular, an explicit formula of the mean value of solutions is given.

Insights into explosive activity at closely-spaced eruptive vents using infrasound signals: Example of Mt. Etna 2008 eruption

On 13 May 2008 an eruptive fissure opened on Mount Etna's eastern flank feeding both explosive activity and lava effusion from multiple vents for about 14 months. During the investigated May-September 2008 eruptive period, infrasound recordings from a 4 station-sparse network allowed tracking of the explosive activity in terms of location and dynamics. In order to focus on activity from the eruptive fissure, the infrasonic events generated by the summit craters were selected by using both spectral features and time delays between pairs of stations and excluded from our analysis. Then, to accurately locate events from the fissure, we used a composite method, based on the semblance and brightness functions. This enabled the study of the co-existence of more than one infrasound source and/or its migration along the eruptive fissure. Hence, results permitted us to discriminate the number of active vents and their location along the fissure even when, due to poor weather conditions, it was not possible to access the vents or carry out direct observations. The eruptive activity was characterised by variations in the number of active vents according to the overall intensity of the eruptive event. Variability of the infrasound waveforms highlighted either that distinct vents produced signals with different waveforms, or that single vents generated different events during distinct periods of time, or finally both the previous phenomena. We applied the strombolian bubble vibration model to model waveform differences and attributed the signal variations to bubble radius changes.

Measurement of the Resonant Characteristics of a Single Bubble Vibration by Using a Laser Doppler Vibrometer

We constructed the experimental system with a laser Doppler vibrometer (LDV) for measuring the vibration of a single microbubble. It was demonstrated that the system enabled the capture of the vibration with an amplitude of nanometer order. We attempted to experimentally measure the resonant characteristics of a bubble attached to a wall by using the system. As a result, we succeeded in measuring the characteristics and evaluating the Q factor and the resonant radius at a driving frequency of 27.8 kHz, although these values are different from those predicted on the basis of the theory for a single free bubble. The LDV measurement system is expected to an effective tool for evaluating bubble vibrations with very small displacement amplitudes, such as the vibration of a microcapsule.

Measurement of the Resonant Characteristics of a Single Bubble Vibration by Using a Laser Doppler Vibrometer

Measurement of the Resonant Characteristics of a Single Bubble Vibration by Using a Laser Doppler Vibrometer

Vibration of a single microcapsule with a hard plastic shell in an acoustic standing wave field

Observation techniques for measuring the small vibration of a single microcapsule of tens of nanometers in an acoustic standing wave field are discussed. First, simultaneous optical observation of a microbubble vibration by two methods is investigated, using a high-speed video camera, which permits two-dimensional observation of the bubble vibration, and a laser Doppler vibrometer (LDV), which can observe small bubble vibration amplitudes at high frequency. Bubbles of tens of micrometers size were trapped at the antinode of an acoustic standing wave generated in an observational cell. Bubble vibration at 27 kHz could be observed and the experimental results for the two methods showed good agreement. The radial vibration of microcapsules with a hard plastic shell was observed using the LDV and the measurement of the capsule vibration with radial oscillation amplitude of tens of nanometers was successful. The acoustic radiation force acting on microcapsules in the acoustic standing wave was measured from the trapped position of the standing wave and the radial oscillation amplitude of the capsules was estimated from the theoretical equation of the acoustic radiation force, giving results in good agreement with the LDV measurements. The radial oscillation amplitude of a capsule was found to be proportional to the amplitude of the driving sound pressure. A larger expansion ratio was observed for capsules closer to the resonance condition under the same driving sound pressure and frequency.

Excitation of airwaves caused by bubble bursting in a cylindrical conduit: Experiments and a model

Strombolian eruptions are considered to be a consequence of the bursting of a large bubble. In order to understand the relation between the style of bubble bursting and the resulting airwave, we perform experiments of bubble bursting at the top of the surface of viscous liquid contained in an acrylic pipe which acts as an air column and observe it visually and acoustically. We find that when the liquid viscosity is less than 1 Pa s, the bubble vibrates before bursting. The major source of the airwave during the sequence of the bubble bursting is the bubble vibration. On the other hand, when the liquid viscosity is greater than 1 Pa s, the bubble does not vibrate. During bubble bursting, an aperture appears on the bubble film. The aperture growth first accelerates and later decelerates before finally stopping. The major source of the airwave is the aperture growth. We calculate a synthetic waveform of the airwave generated by the aperture growth which explains the experimentally observed airwave well. When the frequency of the airwave generated by the aperture growth matches the eigenfrequency of the air column, resonance occurs. Applying this model to the Strombolian eruption, the characteristic low frequency (<20 Hz) is explained if the velocity of the aperture growth is several meters per second. The model also explains the asymmetrical initial rise of the airwave observed in the Strombolian eruptions as a result of the accelerating growth of the aperture.

Vibration of A Single Protein Bubble in Bingham Liquid

The vibration of a single protein bubble may take place under the action of high pressure difference. In this process, the bubble wall may experience a finite deformation. The equation describing the dynamics of the protein bubble with viscoelastic film in Bingham liquid is derived. A numerical solution to this equation is carried out to study the effect of liquid pressure, the characteristic parameters of Bingham liquid and the viscosity of the protein film on the finite deformation of the bubble. The results show that the vibration of the protein bubble wall is caused by the action of pressure difference, the elastic stress in finite deformation and the dissipation of viscosity of the protein film and Bingham liquid. The vibration is nonlinear. Decreasing the pressure difference between gas and Bingham liquid on both sides of the protein bubble will lead to a change of vibration performance. The frequency and amplitude are reduced, tegether with the speed of vibration damping. In addition, the deformation rate of the bubble is smaller when the amplitude of vibration is reduced, which means shorter time to reach a balance state. On the other side, the increase of the magnitude of viscosity of the protein film or the plastic viscosity of Bingham liquid can restrain the vibration of the protein bubble wall in the course of finite deformation, as a result, the load bearing capacity of bubble is enhanced.

Characterization and location of infrasonic sources in active volcanoes: Mount Etna, September–November 2007

The period September–November 2007 was characterized at Mount Etna by explosive activity and intense degassing. During this time interval, infrasonic signals were recorded by an infrasonic network. By a triggering procedure, about 1000 infrasonic events were found, characterized by very high signal‐to‐noise ratio and grouped into nine families. Successively, the spectral analysis allowed subdividing these nine families into three clusters based on the peak frequency and the quality factor of the events. Finally, by the location analysis a cluster (cluster 1) was related to the degassing activity of the northeast crater (NEC), while the other two (clusters 2 and 3) to the explosive activity of the southeast crater (SEC). The comparison between the stacked infrasonic waveforms, interpreted as generated by the vibration of large gas bubbles, and the synthetic ones, permitted to calculate radius, length of the bubble, and initial overpressure, by a genetic algorithm method. The higher overpressure values of cluster 3 compared to the cluster 2 values were in good agreement with the stronger intensity of the explosions accompanying the infrasonic events of cluster 3. The variation of both intensities and waveforms is tentatively attributed to the occasional accumulation of lithic clasts (due to moderate landslides?) on the explosive vent. Indeed, events belonging to cluster 3 were no longer observed once the landslides had ended. Finally, the daily emitted gas volume, related to the active degassing, was estimated for NEC and SEC by using the infrasonic data during the studied period.

Harmonic fluids

Fluid sounds, such as splashing and pouring, are ubiquitous and familiar but we lack physically based algorithms to synthesize them in computer animation or interactive virtual environments. We propose a practical method for automatic procedural synthesis of synchronized harmonic bubble-based sounds from 3D fluid animations. To avoid audio-rate time-stepping of compressible fluids, we acoustically augment existing incompressible fluid solvers with particle-based models for bubble creation, vibration, advection, and radiation. Sound radiation from harmonic fluid vibrations is modeled using a time-varying linear superposition of bubble oscillators. We weight each oscillator by its bubble-to-ear acoustic transfer function, which is modeled as a discrete Green's function of the Helmholtz equation. To solve potentially millions of 3D Helmholtz problems, we propose a fast dual-domain multipole boundary-integral solver, with cost linear in the complexity of the fluid domain's boundary. Enhancements are proposed for robust evaluation, noise elimination, acceleration, and parallelization. Examples are provided for water drops, pouring, babbling, and splashing phenomena, often with thousands of acoustic bubbles, and hundreds of thousands of transfer function solves.

3P5-14 Influences of low frequency ultrasound to cells cultured on gel : Mechanical effects of bubble vibrations(Poster Session)

3P5-14 Influences of low frequency ultrasound to cells cultured on gel : Mechanical effects of bubble vibrations(Poster Session)

P61 高粘性流体中の気泡の振動・破裂で発生する空振の実験的研究(ポスターセッション,日本火山学会2008年秋季大会)

P61 高粘性流体中の気泡の振動・破裂で発生する空振の実験的研究(ポスターセッション,日本火山学会2008年秋季大会)

Finite-amplitude vibration of a bubble in water

The numerical results obtained by Rayleigh–Plesset (R-P) equation failed to agree with the experimental Mie scattering data of a bubble in water without inappropriately increasing the shear viscosity and decreasing the surface tension coefficient. In this paper, a new equation proposed by the present authors (Qian and Xiao) is solved. Numerical solutions obtained by using the symbolic computation program from both the R-P equation and the Qian-Xiao (Q-X) equation clearly demonstrate that Q-X equation yields best results matching the experimental data (in expansion phase). The numerical solutions of R-P equation also demonstrate the oscillation of a bubble in water depends strongly upon the surface tension and the shear viscosity coefficients as well as the amplitude of driving pressure, so that the uniqueness of the numerical solutions may be suspected if they are varied arbitrarily in order to fit the experimental data. If the bubble's vibration accompanies an energy loss such as the light radiation during the contract phase, the mechanism of the energy loss has to be taken into account. We suggest that by use of the bubble's vibration to investigate the state equations of aqueous solutions seem to be possible. We also believe that if one uses this equation instead of R-P equation to deal with the relevant problems such as the ‘phase diagrams for sonoluminescing bubbles’, etc., some different results may be expected.

Experimental examination on the interactive force between two bubbles under ultrasound irradiation: Influence of the distance between two bubbles on bubble behavior

The interactive force called the secondary Bjerknes force works among multiple bubbles under ultrasound irradiation, which results in the complicated behaviors of bubbles. In this study, we have experimentally examined the direction of the interactive force depending on the distance between two bubbles. When two bubbles vibrate individually, the direction of the interactive force depends on the phase difference between vibrations of these bubbles. In addition to this theory, considering the influence of the radiated acoustic wave from a bubble vibration on the other bubble vibration, Ida has pointed that this influence induces a change in the direction of the interactive force [M. Ida et al., Phys. Rev. E 67, 056617 (2003)]. In order to examine this theoretical prediction, the behaviors of both a free bubble and a bubble adhered to the polymer were observed under ultrasound irradiation, using a high‐speed video camera. From the results, we found the reversal of the direction of the interactive force due to the variation in the distance between two bubbles. These innovative experimental results give an interesting point of view to understand the dynamics of multiple bubbles.