Bubble Vibration Research Articles

Effect of micro-clearance structure on the collapse of individual liquid hydrogen bubbles

Cavitation occurs in the micro-clearance of liquid-hydrogen-lubricated bearings owing to the pressure drop caused by high-speed shearing. The pressure undulation caused by cavitation collapse results in bearing surface erosion and significantly affects the bearing performance. In this study, a modified Z-G-B cavitation model was used to study the crushing process of a single liquid hydrogen bubble in a shear micro-clearance. Fast Fourier transform (FFT) and wavelet transform (WT) were applied to study the frequency characteristics of the pressure, mass transfer rate, and vapor mass fraction during bubble rupture in shearing micro-clearance. To obtain a deeper insight into the details of the effect of the shear micro-clearance structure on bubble collapse, the relationship between the flow field energy, attenuation rate, and frequency was investigated. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods were used to analyze the energy of each order mode of the flow field. The analysis results of the bubble vibration intensity with respect to time and frequency provide a theoretical basis for the optimization of the bearing structure.

Flow pulsation characteristics of variable displacement piston pump considering coupling effects cavitation bubble and swash plate inclination angle vibration

Variable-displacement piston pumps, in comparison with quantitative pumps, offer high volumetric efficiency, energy savings, and variable displacement advantages. The outlet flow pulsation of these pumps is influenced by several factors, including swash plate inclination angle vibration, cavitation bubbles, flow distribution structure, and valve control structure. This complexity poses challenges in accurately predicting the flow pulsation at the outlet of variable-displacement piston pumps. In response to this challenge, a novel outlet flow pulsation model for variable-displacement piston pumps is proposed, taking into account the coupling effects of cavitation bubbles and swash plate inclination angle vibration, building upon an existing model. Initially, the effects of cavitation bubbles and swash plate inclination vibrations on flow pulsation were analyzed. Subsequently, a comprehensive flow pulsation model for variable-displacement piston pumps was developed, considering the coupling effects of cavitation bubbles and swash plate inclination angle vibrations. This model was compared with three other existing flow pulsation models. The accuracy of the results was validated using a constructed test bench, with an accuracy improvement of approximately 12% compared to traditional theoretical models. Finally, an optimization model for outlet flow pulsation was proposed. The structural parameters of the valve plate, aimed at minimizing flow pulsation, were determined using the multi-agent particle swarm optimization algorithm. These findings underscore the importance of considering the coupled effects of cavitation bubble and swash plate inclination angle vibration in the design optimization process for reducing low-flow pulsation. This study provides a theoretical foundation for the design of variable-displacement piston pumps with minimized vibration and noise levels.

A new model for bubble cluster dynamics in a viscoelastic media

Bubble cluster dynamics in viscoelastic media is instructive for ultrasound diagnosis and therapy. In this paper, we propose a statistical model for bubble cluster dynamics in viscoelastic media considering the radius distribution of bubble nuclei. By investigating and comparing the response for a bubble in three conditions: single bubble; multi-bubble with the same radius; multi-bubble with different radius, the following rules are found: The promotion or suppression of the bubble cluster on the bubble vibration is not monotonous with the increase of the number of bubbles. The promotion or suppression of the bubble cluster on the bubble vibration varies alternately with the frequency. The effect of bubble cluster on bubble vibration is mostly suppressed when the driving acoustic pressure amplitude pa is high (5000 kPa). Usually, the bubble cluster promotes the vibration of the large bubbles (R0 = 10 μm) more, or suppresses it less.

Theoretical analysis of linear oscillations of bubbles in a polydisperse cluster

The dynamics of a single air bubble in an unbounded liquid are significantly different from the dynamics of an individual bubble in clusters due to the hydrodynamic interaction between the bubbles. Studying the mechanism of this interaction is one of the important aspects in the study of the fundamental nature of acoustic and hydrodynamic cavitation. In this work, to analyze small oscillations of bubbles in a spherical cluster near a stable equilibrium position, the mathematical theory of a linear conservative system with several degrees of freedom is applied to explain the mechanism of interaction between bubbles of different sizes. Using this theory, in the general case, it has been proven that the number of resonance frequencies in a polydisperse cluster coincides with the number of fractions. It is shown that in the regions of the main resonance (at low frequencies) bubbles of different fractions oscillate in phase, and in the regions of secondary resonances (at high frequencies) the phases successively change to the opposite, starting with the fraction containing bubbles of the largest radius, and further changing in order of decreasing. Using the example of a two-fraction cluster, it was found that there is an inertial connection between the bubbles, but there is no force connection; when the number of bubbles of one of the fractions is small, the connection between them and the bubbles of the other fraction is weak, while the interaction between them can be strong. An analysis of the energy transfer between bubbles of different fractions showed that the change in the nature of bubbles oscillations in the fraction with a small radius, while the nature of vibration of bubbles in the other fraction does not change, is the result of dynamic damping.

Quantitative estimation of phospholipid molecules desorbed from a microbubble surface under ultrasound irradiation

Microbubbles have potential applications as drug and gene carriers, and drug release can be triggered by externally applied ultrasound irradiation while inside blood vessels. Desorption of molecules forming the microbubble shell can be observed under ultrasound irradiation of a single isolated microbubble, and the volume of desorbed molecules can be quantitatively estimated from the contact angle between the bubble and a glass plate. Microbubbles composed of a 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) shell and a poorly-soluble gas are created. When the microbubbles are exposed to a pulsed ultrasound, the contact angles increase dramatically; the percentage of DMPC molecules desorbed from the bubble surface reaches 70%. Vibration of a single bubble in the radial direction is measured using a laser Doppler vibrometer. The relationship between the vibrational characteristics and the amount of molecular desorption reveals that a larger vibrational amplitude of the bubble around the resonance size induces a larger amount of molecular desorption. These results support the possibility of controlling molecular desorption with pulsed ultrasound.

Introducing realistic distributions of gas bubble size and inclusion aspect ratio to model the coexistence of gas hydrate and free gas

The coexisting free gas within the hydrate stability zone is recognized by laboratory and field studies. The conventional resistivity method fails to obtain hydrate saturation in the sediment with gas hydrate and free gas because both of them are electrical insulators. Hydrate saturation can be obtained from a velocity log based on a certain rock physics model. However, few studies of rock physics have been conducted on gas and hydrate coexistence. In this study, a more realistic distribution of gas bubble size and inclusion aspect ratio was introduced into an effective medium model to elucidate how such coexistence affects velocity and attenuation at a broad-band frequency. The modeling results obtained indicate that such coexistence decreases P-wave velocity at low frequencies, while increases P- and S-wave velocities at high frequencies. The velocity decrease of P-wave at low frequencies is attributed to the overwhelming effect of gas bubble vibration, while it seems not to affect P-wave velocity at high frequencies significantly. Moreover, coexisting gas hydrate and free gas may strengthen P-wave attenuation at the broad-band frequency range. It is found that the damping of oscillating gas bubbles dominates P-wave attenuation at low frequencies, while squirt flow in the porous hydrate is more likely to contribute to P-wave attenuation at high frequencies. Hydrate morphology is also a significant factor affecting P-wave velocity and attenuation at high frequencies. This research reveals that rock physics modeling can provide insight into how to characterize the coexisting gas hydrate and free gas as referring to the acoustic velocity and attenuation at seismic, sonic, and ultrasonic frequencies.

Definition of Bubbly Liquids Parameters for the Optimization of Their Nonlinear Effects on Ultrasound

The aim of this paper is to optimize the generation of frequencies obtained nonlinearly from the propagation of ultrasound in a bubbly liquid. A study is presented for which the number and size of the gas bubbles in the liquid are varied to determine the optimal medium, which is the one that allows the highest amplitude for these frequency components. We use a previously developed numerical software that tracks the nonlinear behavior of both ultrasound and bubble vibrations in time to carry out several simulations. We focus our attention on two one-dimensional configurations, a resonator of length set at a quarter of the wavelength with a free-wall condition and a cavity of length set at sixteen wavelengths with open-field condition. In each case, we analyze the generation of the 2nd, 3rd, and 4th harmonics of the source frequency. Our results show that, in both cases, the use of higher source amplitudes and lower source frequencies is more useful to increase the harmonic amplitudes. Moreover, smaller bubbles are more adequate when the void fraction is kept constant for this purpose in the first configuration, whereas the modification of void fraction has no influence in the second configuration, for which given a void fraction value, bubble sizes whose ratio are f0/f≈5, f0/f≈7, and f0/f≈9 maximize the 2nd, 3rd, and 4th harmonics, respectively. These conclusions could be of interest for some applications.

Microbubble Delivery Platform for Ultrasound-Mediated Therapy in Brain Cancers.

The blood-brain barrier (BBB) is one of the most selective endothelial barriers that protect the brain and maintains homeostasis in neural microenvironments. This barrier restricts the passage of molecules into the brain, except for gaseous or extremely small hydrophobic molecules. Thus, the BBB hinders the delivery of drugs with large molecular weights for the treatment of brain cancers. Various methods have been used to deliver drugs to the brain by circumventing the BBB; however, they have limitations such as drug diversity and low delivery efficiency. To overcome this challenge, microbubbles (MBs)-based drug delivery systems have garnered a lot of interest in recent years. MBs are widely used as contrast agents and are recently being researched as a vehicle for delivering drugs, proteins, and gene complexes. The MBs are 1-10 μm in size and consist of a gas core and an organic shell, which cause physical changes, such as bubble expansion, contraction, vibration, and collapse, in response to ultrasound. The physical changes in the MBs and the resulting energy lead to biological changes in the BBB and cause the drug to penetrate it, thus enhancing the therapeutic effect. Particularly, this review describes a state-of-the-art strategy for fabricating MB-based delivery platforms and their use with ultrasound in brain cancer therapy.

Theoretical prediction of the scattering of spherical bubble clusters under ultrasonic excitation

Due to the nonlinear vibration of ultrasound contrast agent bubbles, a nonlinear scattered sound field will be generated when bubbles are driven by ultrasound. A bubble cluster consists of numerous bubbles gathering in a spherical space. It has been noted that the forward scattering of a bubble cluster is larger than its backscattering, and some studies have experimentally found the angular dependence of a bubble cluster’s scattering signal. In this paper, a theory is proposed to explain the difference of acoustic scattering at different directions of a bubble cluster when it is driven by ultrasound, and predicts the angular distribution of scattered acoustic pressure under different parameters. The theory is proved to be correct under circumstances of small clusters and weak interactions by comparing theoretical results with numerical simulations. This theory not only sheds light on the physics of bubble cluster scattering, but also may contribute to the improvement of ultrasound imaging technology, including ultrasonic harmonic imaging and contrast-enhanced ultrasonography.

Cell angle control by rotating flow using bubble vibration

Cell angle control by rotating flow using bubble vibration

Mapping of laminar separation bubble and bubble-induced vibrations over a turbine blade at low Reynolds numbers

A detailed experimental investigation on the mapping of the LSB formation over a turbine blade with different airfoils, and their vibration effects were considered first in this study. Wind tunnel experiments were performed on FX 84-W-150, SD7062, Clark-Y and WASP airfoils at Re = 3.5 × 104, Re = 7 × 104 and various angles of attack. Experimental arrangements consisted of detailed instantaneous and time-dependent flow visualizations, quasi-wall shear stress measurements by means of a hot-film sensor, aerodynamic force measurements with an external force balance system. It was observed that there was a strong correlation between voltage signals obtained from the hot-film sensor and the smoke-wire results. Fluctuation amplitude started to increase within the LSB especially at the aft portion due to the transition induced trapped roll-up vortices. Then, fluctuations peaked upstream of the reattachment point. It was observed that the airfoil with different thickness and camber caused the LSB (either short or long) to form, resulting in variation of aerodynamic forces with the time. This could trigger the stochastic vibrations such as flap-wise and edge-wise vibrations at the blade, causing the stochastic fatigue loads and limiting the lifespan of turbine blades.

Acoustic signatures and bubble entrainment mechanisms of a drop impacting a water surface with surfactant

The acoustics of a water drop impact on a bath of water and sodium dodecyl sulfate (SDS) is studied close to the irregular entrainment regime. In particular, acoustic events, corresponding to bubble vibration, are observed for several SDS concentrations. These acoustic events are induced by five different kinds of hydrodynamic events, including four different bubble entrainment mechanisms and one bubble excitation mechanism. These families of events appear to have their own acoustic signature. The different mechanisms are described in detail and typical signals belonging to these families are presented. Their main features are highlighted and linked to the hydrodynamics of the corresponding event.

Circular motion of submillimeter-sized acoustic bubbles attached to a boundary by high-speed image analysis

The circular motion of submillimeter-sized bubbles attached to a boundary in an 18.5 kHz ultrasonic field are investigated experimentally by high-speed photography and image analysis. It is found that the vibration of gas bubbles with diameters of 0.2–0.4 mm is between spherical radial vibration and regular surface fluctuation. Different from the circular motion of suspended bubbles in water, the circular motion of gas bubbles attached to a boundary presents some new characteristics. These bubbles attached to a boundary (wandering bubbles) will rotate around a fixed bubble array (holding bubbles). Both the wondering bubbles and holding bubbles are “degas” bubbles. The primary Bjerknes force acting on wandering bubbles in the acoustic wave field and the secondary Bjerknes force between the wandering bubbles and the holding bubbles strongly affects the circular motion. The circling and residence behavior of gas bubbles is described and analyzed in detail, which is helpful to understand and improve industrial applications such as ultrasonic cleaning, sonochemical treatment, aeration and cavitation reduction.

Numerical simulation of the interaction of wave phase conjugation with bubble clouds

The interaction of the Wave Phase Conjugation (WPC) process with bubble cloud dynamics is investigated via numerical modeling in application to bubble size measurements. The WPC simulator by Modarreszadeh and Timofeev (Computers and Fluids 197, 104353) is used as a starting point. In the simulator, a modified version of the high-order Nodal Discontinuous Galerkin method is used for modeling of acoustic wave propagation in the active WPC conjugator and the surrounding linear or non-linear fluid in 2D/axisymmetric domains. The effects of bubble dynamics are incorporated with the help of induced volume fractions. The modified Keller–Miksis model is employed to simulate vibrations of bubbles subjected to acoustic waves. After thorough verification and validation of the numerical scheme and the physical model, the interaction of various bubble clouds, including poly-disperse ones, with the WPC process is examined with the help of some existing and newly suggested descriptive indicators, e.g., the amplification factor and the absolute and relative signal intensities. The results show that signals scattered from bubble-plane clouds, in which the bubbles are non-physically synced, are strong enough to affect the modulation process if the stimulation frequency is close to the natural frequency of bubbles. For more realistic bubble clouds, the modulation process is almost intact. However, conjugate waves do carry some signatures of bubble-cloud dynamics, e.g., signals with frequencies higher than the natural frequency of bubbles are significantly diminished. The study demonstrates that WPC-based techniques have a promising potential to be used for measuring bubble dimensions.

Polyhedral Bubble Vibrations.

Underwater bubbles are extremely good acoustic resonators, but are freely evolving and dissolving. Recently it was found that bubbles can be stabilized in frames, but the influence of the frame shape is still undocumented. Here we first explore the vibration of polyhedral bubbles with a low number of faces, shaped as the five Platonic solids. Their resonance frequency is well approximated by the formula for spherical bubbles with the same volume. Then we extend these results to shapes with a larger number of faces using fullerenes, paving the way to obtain arbitrary large resonant bubbles.

Dynamics of bubbles in spherical liquid cavity wrapped by elastic medium

The cavitation effects occur in the ultrasound therapy technology. With the development of ultrasound therapy technology, cavitation effect in biological tissues has attracted more and more attention. The aim of the present study is to discuss the factors affecting cavitation nucleation and dynamics in tissues, and to provide a theoretical reference for the application of cavitation effects to ultrasound therapy. A model is developed for the cavitation inception in a spherical liquid cavity wrapped by an elastic medium. The Blake threshold value and the critical radius of the liquid cavity for the generation of spherical bubbles are obtained by the pressure equilibrium relationship. The effects of the excitation frequency, the volume modulus of the medium and the volume of the liquid in the cavity on the bubble vibration behavior are analyzed by deriving a bubble dynamic equation that consider the elastic effect of the medium outside the cavity using Lagrange equation. It is shown that the volume modulus, initial radius of bubble nucleus and surface tension can affect the Blake threshold pressure and bubble size, and those form a parameter reference for the control conditions that trigger or inhibit cavitation. The gas core can rapidly grow to a new equilibrium radius and oscillate under the action of an acoustic wave, and the bubble equilibrium radius is independent of the external field, but it can affect the bubble dynamic behavior. When the frequency of the ultrasonic signal is equal to the natural oscillation frequency of the bubble, the bubble collapses after several periods of intense vibration, and the pressure fluctuation in the liquid in the cavity is obvious. The response of bubbles under high frequency ultrasonic driving is relatively weak, and the oscillations of bubbles are dominated by free oscillation.

The Nonlinear Scattering Characteristics of Sound Waves by a Bubble

The scattering characteristics of sound waves by bubbles have been widely applied to ship tracking, wake-homing torpedo and reverberation suppression. To explore the nonlinear scattering characteristics of sound waves by bubbles, the Keller-Miksis equation of bubble vibration was adopted and a numerical solution to the nonlinear equation is presented. Then, the characteristics of nonlinear scattering, including the intensity of the scattered waves, the frequency and radius selection under pulse excitation and the scattered wave duration, are studied. The nonlinear scattered waves by a bubble are too small to be detected when the intensity of the excitation source is small. As the intensity of the excitation source increases, so does that of scattered harmonics by the bubble. If the intensity of the excitation source is further increased to a certain extent, the scattered waves by the bubble occurs dispersion phenomenon, emitting broadband noise. It may be the reason why a broadband noise will be produced by the cavitation of bubbles.

Nonlinear propagation and anomalous absorption of ultrasound in liquid

Recent work has rendered possible the formulation for the nonlinear propagation of pressure waves in liquids by using the generalized Navier - Stokes equations and the modified equations of state, with the heat transfer and fluid viscidity taken into consideration. And the nonlinear approximation solution of the second order term is obtained. The conclusion concerns the acoustic pressure, phase speed, attenuation, and velocity distribution function. When the amplitude of driving acoustic pressure is higher than the cavitation threshold of the host liquid, the cavitation occurs. The cavitation bubbles will prevent the sound field from spreading in the liquid, and the acoustic energy accumulates near the cavitation zone. So when studying the transmission characteristics of acoustic wave in the liquid, the cavitation attenuation must be considered. Note that the particularity of cavitation bubble movement, cavitation bubble vibration and viscous force are simulated under the initial driving sound. Through the analysis, it is found that the transmission of sound is influenced by the viscosity of the fluid, heat transfer, driving sound pressure (amplitude, frequency, duration) and cavitation bubble in liquid. The physical mechanism is that the higher driving pressure causes the cavitation to turn stronger, the acoustic loss to be faster, the sound propagation distance to be smalletr and the vibration of bubbles to transfer energy from the fundamental wave to harmonics. As a result, the stronger absorption from the liquid causes abnormal phenomena, and the output sound is lower finally. It shows that the nonlinear radial motion of cavitation bubble is mainly responsible for the sound intensity attenuation.

Axially-distributed bubble-bubble interaction under a coustic excitation in pipeline

Acoustically-excited bubble dynamics is the foundation of pipeline bubble detection based on acoustic technology. Due to the existence of multiple bubbles in pipeline flow, the Bjerknes forces among arbitrary bubbles under acoustic excitation may enforce bubble-bubble interaction and then change the features of bubble dynamics. Based on traditional free bubble’s Rayleigh-Plesset (R-P) model, this paper tries to establish bubble-bubble interaction model in consideration of the second Bjerknes force and bubble distribution in the pipeline axial direction. Meanwhile, the influence of finite wave speed in compressible fluid is considered. The proposed model is numerically calculated by the fourth-order Runge-Kutta method. Firstly, the differences in bubble feature between the free bubble’s R-P model and bubble-bubble interaction model are compared under excitation with different frequencies and amplitudes. Results show that the differences in bubble dynamics are minor when the bubble’s distance is large enough. When the bubble’s distance is fixed, the differences are significant on condition that the frequency of acoustic excitation is nearly the resonant frequency of bubbles. Secondly, through establishing compressible model and incompressible fluid model, we compare the differences between the two models. Numerical calculations show that the second Bjerknes force under the compressible assumption acts as an external force and forces the bubble to vibrate. On the other hand, the second Bjerknes force under the incompressible assumption changes the dynamics of bubble-bubble interaction as well as the resonant features. Finally, we study the effect of bubble-bubble distance and bubble’s axial position on bubble vibration characteristics. The bubble-bubble distance affects the second Bjerknes force and may lead the bubbles to vibrate nonlinearly. The bubble’s axial position changes the phase of external acoustic force and leads to the difference in initial vibration feature. When this difference is coupled with the second Bjerknes force, the bubble-bubble interaction may be changed even into nonlinear vibration, leading the bubble’s oscillation spectrum to differ from linear vibrations significantly. These results demonstrate that the resonant state of a small bubble may be converted into nonlinear vibration state if the second Bjerknes force is present. On the other hand, the resonant state of a large bubble can keep linear vibration when the second Bjerknes force is not obvious.

Procedure for calculating the thermoacoustic pressure fluctuations at boiling subcooled liquid

This paper reports a study of the thermoacoustic phenomena in steam-generating channels of the cooling system of heat-loaded devices. The examined cooling modes are characterized by surface boiling of the heat carrier, which occurs due to high heat flows at the cooled surface and large underheating of the flow core to the saturation temperature. Under such conditions, high-frequency pulsations of acoustic pressure may occur in cooling channels. It has been established that the emergence of thermoacoustic oscillations could lead to the formation of a standing wave in the channel, one of the conditions for whose formation is the presence of a wave reflection boundary. We have proposed a mathematical model describing the generation of thermoacoustic vibrations in a cooling channel. It was assumed that fluctuations with a high amplitude arise due to the resonance observed when the frequency of forced vibrations of steam bubbles coincides with the vapor-liquid column's natural frequency of vibrations or their harmonics. To calculate the amplitude of pressure fluctuations in the channel, the dependence has been derived, which takes into consideration the viscous dissipation of energy and energy losses at the ends of the channel. It has been shown that when approaching the resonance, the contribution of volumetric viscosity to the viscosity absorption factor increases. It has been established that for the examined conditions the losses of energy on the walls of the channel and losses in the boundary layer could be neglected. We have calculated the amplitude of thermoacoustic pressure fluctuations for conditions corresponding to actual processes in surface-boiling cooling channels. The reported procedure is proposed to be used in the design of liquid cooling systems for heat-loaded devices for which cooling modes imply a significant underheating of the heat carrier to a saturation temperature, as well as surface boiling