Resonance Frequency Of Bubble Research Articles

Sound in a bubbly hybrid neutron star

Increasingly precise astrophysical observations of the last decade in combination with intense theoretical studies allow for drawing a conclusion about potential quark matter presence in neutron stars’ interiors. Quark matter may form the neutron star inner core or be immersed in the form of bubbles, or droplets. We consider the second scenario and demonstrate that even a small fraction of quark matter bubbles can lead to a high nonlinearity of the sound wave. Below the bubble resonant frequency the sound speed is lower than the ambient value. At the resonance it sharply grows. The peak is constrained by viscous dissipation. Above the resonance the speed exceeds the pure neutron star matter value. The dispersion equation for the bubbly neutron star compressibility is derived. Published by the American Physical Society 2024

Rupture of membranous microbubbles induced by pulsed acoustic wave

Encapsulated microbubbles serve as suitable drug carriers in medicine. This paper proposes corrections for the resonance frequency of lipid-coated bubbles under various acoustic pressure levels and the critical pressure for bubble rupture based on the Marmottant model. The suggestion to induce the rupture of lipid-coated bubbles using acoustic waves leans toward utilizing pulse waves rather than continuous waves. Corresponding experiments validate the accuracy of these corrections and the rationale behind the suggestion, aligning closely with theoretical predictions. This study offers a more precise predictive framework for the behavior of lipid-coated bubbles under acoustic waves.

Fractional derivative-based approximation of acoustic waveform dispersion measured in bubbly water beyond resonance frequency.

Acoustic pulses transmitted across air bubbles in water are usually analyzed in terms of attenuation coefficient and phase velocity in the frequency domain. The present work expresses an analytical approximation of the acoustic waveform in the time domain. It is introduced by experiments performed with a Gaussian derivative source wavelet, S0(t), with a derivative order, β0 = 4, and a peak frequency, νp0, much larger than the bubble resonance frequency. The measurements highlight a significant shape variability of the waveform Bx(t), measured at x≤ 0.74 m and characterized by a peak frequency νpx≃νp0. The results are in good agreement with the approximation Bx(t)∝(dγx/dtγx)S0(δxt - T), where γx is an additional fractional-derivative order determined by an optimization procedure and T is related to the travel time. The time-scale parameter, δx=β0/(β0+γx), becomes a free parameter for more general source signals. The correlation coefficient between Bx(t) and the approximated waveform is used to identify the applicability of the method for a wide range of bubbly waters. The results may be of potential interest in characterizing gas bubbles in the ocean water column and, more generally, in modeling wave propagation in dispersive media with fractional-derivative orders in the time domain.

Investigation of interaction effects on dual-frequency driven cavitation dynamics in a two-bubble system

The cavitation dynamics of a two-bubble system in viscoelastic media excited by dual-frequency ultrasound is studied numerically with a focus on the effects of inter-bubble interactions. Compared to the isolated bubble cases, the enhancement or suppression effects can be exerted on the amplitude and nonlinearity of the bubble oscillations to different degrees. Moreover, the interaction effects are found to be highly sensitive to multiple paramount parameters related to the two-bubble system, the dual-frequency ultrasound and the medium viscoelasticity. Specifically, the larger bubble of a two-bubble system shows a stronger effect on the smaller one, and this effect becomes more pronounced when the larger bubble undergoes harmonic and/or subharmonic resonances as well as the two bubbles get closer (e.g., d0 < 100 μm). For the influences of the dual-frequency excitation, the results show that the bubbles can achieve enhanced harmonic and/or subharmonic oscillations as the frequency combinations with small frequency differences (e.g., Δf < 0.2 MHz) close to the corresponding resonance frequencies of bubbles, and the interaction effects are consequently intensified. Similarly, the bubble oscillations and the interaction effects can also be enhanced as the acoustic pressure amplitude of each frequency component is equal and the pressure amplitude pA increases. Above a pressure threshold (pA = 215 kPa), a larger bubble undergoes period 2 (P2) oscillations, which can force a smaller bubble to change its oscillation pattern from period 1 (P1) into P2 oscillations. In addition, it is found that the medium viscosity dampens the bubble oscillations while the medium elasticity affects the bubble resonances, accordingly exhibiting stronger interaction effects at smaller viscosities (e.g., μ < 4 mPa·s) or certain elasticities (approximately G = 70–120 kPa, G = 160–200 kPa and G = 640–780 kPa) at which the bubble resonances occur. The study can contribute to a better understanding of the complex dynamic behaviors of interacting cavitation bubbles in viscoelastic tissues for high efficient cavitation-mediated biomedical applications using dual-frequency ultrasound.

Characterization of sonicated gluten protein and subsequent rheological properties of model dough and noodles.

The present study aimed to investigate the effects of the thermo-mechanical and rheological properties of a wheat gluten-sonicated model dough and noodles, as well as the effects of ultrasonic frequency (20, 28, 40, 68 and 80 kHz) on the functional properties and structural features of gluten. Water absorption, stability and developmental time, and viscoelastic behavior of gluten-sonicated model dough were all found to be improved. Water absorption, tensile resistance and stretching distance of noodles increased markedly, whereas cooking loss decreased. Ultrasonication at different frequencies also significantly affected gluten structure, including its surface hydrophobicity, micro-network structure, and secondary and tertiary structures. These alterations then caused changes in its functional characteristics. Compared to untreated gluten, sonicated gluten exhibited significantly increased oil and water capacities (8.75-15.26% and 100.65-127.71% higher than the untreated gluten, respectively), foaming and emulsifying properties, and increased solubility (63.46-98.83% higher than control). In addition, these findings indicated that 40 kHz was the likely resonance frequency of the cavitation bubble in the gluten solution. However, sodium dodecyl sulfate-polyacrylamide gel electrophoresis electropherograms revealed that such treatments did not affect the molecular weight of gluten, which was also consistent with its unchanged disulfide bond content. The present study clarified the impact of frequency on the properties of gluten and model dough. The best frequency for modification of gluten was 40 kHz. Collectively, these findings suggest that ultrasonic technology has the potential for use in modifying wheat gluten and commercial noodle processing. © 2022 Society of Chemical Industry.

Interaction between bubble and particle in spherical liquid cavity surround by an elastic medium

A theory is developed to model the dynamic of bubble and particle inside a spherical liquid-filled cavity surrounded by an elastic medium. The aim of this work is to study how the outer elastic medium affects the interaction between bubble and particle. Starting from the theory of velocity potential distribution, combined with Lagrangian equations, the motion equations of bubbles and particles in the cavity are obtained. The resonance frequency of the bubbles and influence of the interaction between particle and bubble on the translational behavior under the action of sound waves are analyzed. The results show that the properties of medium elasticity and density can change the resonance frequency of the bubble in the cavity. As the radius of the spherical cavity increases, the resonance frequency of the bubble has a tendency to first decrease and then increase, and gradually tends to the resonance frequency of a single bubble in an unbounded liquid. The translation of bubble and particle in the spherical liquid cavity is affected by factors such as acoustic field parameters, the characteristics of the outer elastic medium, and the characteristics of the bubble and particle themselves. The overall characteristic is that the particle has a tendency to move to the cavity wall, and the translation of bubble is closely related to the interaction characteristics between bubble and particle.

Study on Bubble Cavitation in Liquids for Bubbles Arranged in a Columnar Bubble Group

In liquids, bubbles usually exist in the form of bubble groups. Due to their interaction with other bubbles, the resonance frequency of bubbles decreases. In this paper, the resonance frequency of bubbles in a columnar bubble group is obtained by linear simplification of the bubbles’ dynamic equation. The correction coefficient between the resonance frequency of the bubbles in the columnar bubble group and the Minnaert frequency of a single bubble is given. The results show that the resonance frequency of bubbles in the bubble group is affected by many parameters such as the initial radius of bubbles, the number of bubbles in the bubble group, and the distance between bubbles. The initial radius of the bubbles and the distance between bubbles are found to have more significant influence on the resonance frequency of the bubbles. When the distance between bubbles increases to 20 times the bubbles’ initial radius, the coupling effect between bubbles can be ignored, and after that the bubbles’ resonance frequency in the bubble group tends to the resonance frequency of a single bubble’s resonance frequency. Fluent software is used to simulate the bubble growth, shrinkage, and collapse of five and seven bubbles under an ultrasonic field. The simulation results show that when the bubble breaks, the two bubbles at the outer field first begin to break and form a micro-jet along the axis line of the bubbles. Our methods and conclusions will provide a reference for further simulations and indicate the significance of the prevention or utilization of cavitation.

Acoustic Characteristics of Biosynthetic Bubbles for Ultrasound Contrast Imaging.

Biosynthetic bubbles produced by floating microorganisms, such as bacteria and algae, have recently attracted wide attention as novel ultrasound contrast agents owing to their significant potential in ultrasound imaging and acoustic reporter gene-based imaging. However, the acoustics properties of these bubbles are unclear. In this study, we developed a finite-element model to describe the oscillation of nonspherical biosynthetic bubbles composed of a gas core encapsulated in a protein shell. In this model, the elastic properties of the bubble shells were characterized in terms of the density, thickness, Young's modulus, and Poisson's ratio. Theoretical calculations were performed for a single bubble and an assembly of randomly oriented bubbles. Our results demonstrate that (1) there are many types of surface oscillation modes for nonspherical biosynthetic bubbles, and a systematic relationship exists between the surface modes and the resonance frequencies; (2) the bubble shell shape has a significant effect on the acoustic behavior; (3) the resonance frequency of an ellipsoidal bubble decreases with the decrease in its polar radius-to-equatorial axis ratio; and (4) the acoustic scattering of a randomly oriented suspension is isotropic at and below the first resonance frequency. Our findings provide physical insight into the biomedical applications of biosynthetic bubbles and can be used to optimize the acoustics properties of such bubbles.

Subwavelength resonances of encapsulated bubbles

The aim of this paper is to derive an original formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance frequency, as a perturbation away from the resonance of the uncoated bubble, in terms of the thickness of the coating. The formula is numerically verified in the case of circular bubbles, where the resonance can be efficiently computed using the multipole method. The approach involves the use of a pole-pencil decomposition of the leading order term in the asymptotic expansion of some integral operator in terms of the thickness of the coating, followed by the application of the generalized argument principle to find the characteristic value. This approach is quite general and can be applied to other subwavelength resonators such as coated plasmonic nanoparticles.

Coupled resonance of bubbles in spherical cavitation clouds

The interaction between bubbles in bubble group mainly acts on the other bubble through radiation sound pressure between the bubbles. In this paper, based on the bubble dynamics equation in bubble clouds, the equation of bubble wall motion is linearly reduced, the expression of bubble resonance frequency in spherical bubble group is obtained and the correction coefficient of bubble resonance frequency and single bubble are given. Furthermore, the effects of the initial radius, the number of bubbles and the distance between bubbles on the resonance frequency are discussed. The results show that the phase of bubbles is taken into account. Considering the interaction between bubbles, the resonance frequency of bubbles in spherical bubble group is obviously less than that of single bubble. With the decrease of the number of bubbles in bubble group, the distance between bubbles increases, the interaction between bubbles in bubble group decreases, and the resonance frequency of bubbles returns to the resonance frequency of Minnaert single bubble. At the same time, the resonance frequency of bubbles in bubble group changes gradient with the increase of the distance between bubbles and the number of bubbles. However, when the number of bubbles increases a certain value, the resonant frequency of the bubble is almost constant. When the bubble group has a certain radius, the more the number of bubbles, the smaller the resonance frequency of the bubble is, but there exists a critical value. It is also found that a smaller correction coefficient is held by the bubble group with larger initial radius, which indicates the same number of bubble groups. Under the same bubble spacing, the interaction of small bubbles with smaller bubbles is more significant, and the resonance frequency of the bubble is obviously affected. Because the frequency and amplitude of driving sound pressure can only be given values in ultrasonic cavitation, the resonant frequency of cavitation bubbles will be reduced by properly injecting air bubbles into liquid, which makes most of cavitation bubbles undergo intense non-linear oscillating steady-state cavitation. Therefore, the occurrence of cavitation can be effectively suppressed.

Analysis of dynamic interactions in a bubble-particle system in presence of an acoustic field

Use of an acoustic field in flotation is known to improve mineral recovery. However, studies in this area are rather limited and in general there is a lack of a mechanistic description of the collision and collection efficiency of particles in presence of an external acoustic field. This study aims to contribute to this knowledge gap by developing a simplified 3D numerical model of single bubble-particle interactions based on a discrete element method (DEM) based approach. Volume mode oscillatory behaviour of the bubble was modelled within the theoretical spherical shape limit (0.1 ≤ Bo ≤ 0.5) using 1D Rayleigh-Plesset equation in a quiescent liquid medium and one-way coupled to particle motion obtained through DEM. Interaction dynamics were simulated for various operating conditions involving three parameters, namely oscillation amplitude ratio (ε ≤ 0.1), excitation frequency (below and above resonance frequency) and bubble-particle surface-to-surface distance (∼1.0 to 10.6% of bubble radius). Regime maps were constructed to establish suitable combinations of these three operating parameters to represent the collision and attachment behaviour of a particle with the oscillating bubble. While conventional flotation models predict particle collision efficiency based on the nearest streamline adjacent to the bubble surface, application of an acoustic field on a bubble was shown to incur collision with a particle in the far field away from the interface due to oscillatory motion. It was noted that although such collisions occurred in the below-resonance-frequency regime (∼35 to 79 Hz), particle attachment did not occur due to weakening of the attractive capillary force. In the above-resonance-frequency regime (3.61–14.4 kHz), however, particle attachment was predicted and attachment probability increased in the vicinity of the bubble resonance frequency.

Improved Anderson–Hampton acoustic velocity model for marine sandy gas-bearing sediments

Anderson & Hampton model is an important theoretical foundation for detection of marine shallow gas and identification of gas-bearing sediments. In the acoustic test of sandy gas-bearing sediments, it was found that if the excitation frequency is lower than the bubble resonance frequency, this model overestimates the attenuation of compressional wave velocity of the sediments, and it is difficult to accurately determine the original occurrence status of gas in the sediments by back analysis. The main reason is that the Gassmann equation in Anderson-Hampton model does not accurately describe the modulus parameters of sandy gassy sand sediments. Based on the occurrence characteristics of marine sandy gas-bearing sediments, an improved Anderson-Hampton acoustic velocity model was established by introducing saturation Sr and an attenuation factor reflecting the decay speed of wave speed. The advantage of the new model was pointed out and the sensitivity of parameter was analyzed simultaneously.

Effect of viscosity on propagation properties of acoustic waves in liquids with bubbles

In this paper, propagation properties of linear acoustic waves in viscous liquids with bubbles are studied by using the effective medium theory. The attenuation coefficient and the phase velocity of waves are investigated. The influence of the viscosity on the wave equation and the vibration equation of bubble is considered. Research results show the resonance absorption of acoustic waves is caused by the resonance of bubble and influenced by the interaction of bubbles. The interaction results in the difference between the resonance absorption frequency of waves and the resonance frequency of bubble, and makes the frequency width of resonance absorption regions of waves become large. In non-resonance regions, the influence of the viscosity and the volume fraction of gas on low-frequency acoustic waves is investigated. The viscosity can influence acoustic waves through the wave equation and the vibration equation of bubble. We analyze the effect of the two ways, and give conditions for some approximation theories.

Research into resonance phenomena in gas-vapor bubbles

In order to calculate resonating gas bubbles, the mathematical model was supplemented by taking into account phase-transition processes on the surface of a bubble in gas-vapor media, as well as the thermal effects at gas dissolution in fluid. A series of calculations of the resonance mode for bubbles of dimensions of 0.5‒3 mm in water at temperatures from +1 to +99 °C and atmospheric pressure was performed. As a result of mathematical modeling, the possibility of resonance in gas-vapor bubbles in water in the frequency range of 0.5–5 kHz was established. It was shown that in the resonance mode the amplitude of oscillations of the wall of a bubble first increases rapidly and then is stabilized at the level of 30‒50 % of the radius. It was established that motion velocity of the walls of a bubble under resonance conditions can exceed 6 m/s. It was shown that in the compression mode internal pressure of a bubble can increase by three times or decrease by two times compared with ambient pressure. Dependence of approximation resonance frequency of air bubbles in water on their diameter was established. It was found that in the resonance mode, temperature of gas-vapor medium of a bubble periodically decreases by 6 °C and increases by 12 °C in comparison with the original one. In this case, the temperature of the surface of a bubble decreases by 1 °C and increases by 7 °C. It was shown that favorable conditions for water vapor condensation (fog formation) are created at the stage of the growth of a bubble. The schematic of the research setup and the results of field observations of gas-vapor bubbles under condition of the influence of sound waves was presented. The existence of resonance of bubbles at calculation frequencies was proved and formation of bubbles was established experimentally. The phenomena of a bubble division and its explosion were illustrated. It was found that addition of surface active substances extends the frequency range of formation of multi-bubbles by five times and contributes to an increase in the number of small bubbles inside a large one. The research results can be applied to intensification of various technological processes related to heat and mass exchange in gas-vapor systems.

Multiple scattering of an ultrasonic shock wave in bubbly media.

This experimental study deals with the propagation of an ultrasonic shock wave in a random heterogeneous medium, constituted of identical 75μm radius bubbles, trapped in a yield-stress fluid. The fundamental frequency of the incident wave (in the MHz range) was much larger than the resonance frequency of bubbles (38kHz). A well-expanded coda, resulting from the multiple scattering of the incident shock wave through the heterogeneous medium, was experimentally measured in transmission. Despite the significant amplitude of the shock wave (90kPa), no sign of nonlinear response of the bubbles was detected. Both the coherent and incoherent fields were successfully described by linear theories. Using a shock wave presents the advantage of characterizing the medium over a large frequency range (1.5-15MHz).

The detailed acoustic signature of a micro-confined cavitation bubble.

Numerous scenarios exist for a cavitation bubble growing in a liquid. We focus here on cavitation phenomena within water under static tension in a confined environment. Drawing inspiration from the natural materials in plants, we design a novel experimental setup where a micrometric volume of water is confined by a hydrogel-based material. We show that, submerging the sample in a hypertonic solution, the water within the cavity is placed under tension and the acoustic emission produced by the resulting bubble nucleation is precisely detected. This new experimental procedure is able to strongly reduce the acoustic reflections occurring at the hydrogel/air interface with more classical techniques. We also propose a mathematical model to characterise the pressure wave emitted in order to correctly take into account the dissipation effect induced by the visco-elastic behaviour of the confining hydrogel. Both bubble resonant frequency and damping are captured by the model and quantitatively match the values found in the experiments.

The acoustic characteristics of bubbly liquids near the individual bubble resonance frequency

In biomedical, naval and oceanographic arenas, the acoustic characteristics of bubbly liquids have simultaneously confounded and been exploited by acoustic tools used in the respective fields. The work of Carstensen and Foldy [J. Acoust. Soc. Am. 19, 481-501 (1947)] served as a cornerstone of the post-World War II understanding of this system, but at high bubble concentrations near the individual bubble resonance frequency (IBRF), the quantitative prediction and measurement of bubbly liquid sound speed and attenuation remains an open topic. In 1989, Commander and Prosperetti [J. Acoust. Soc. Am. 85 732-746 (1989)] advanced the field with a rigorous model valid at the IBRF but it was limited to low void fractions. The data available in 1989 did not corroborate their model at IBRF, but at the time, it was unclear whether this was due to model or experimental deficiencies. This paper reviews an impedance tube measurement [J. Acoust. Soc. Am. 117, 1895-1910 (2005)] that did validate the model for bubble volume fractions up to about 10-4, and also reviews more recent work associated with an industrial underwater noise mitigation system, that validates their model up to void fractions exceeding 10-2, significantly higher than expected.

Effect of gas bubble volume fraction on low-frequency acoustic characteristic of sandy sediment

Owing to the decomposition of organic material and other reasons, the actual marine sediment contains gas bubbles, and the existence of gas bubbles will significantly affect the low-frequency acoustic characteristics of sediment. Therefore, it is significant to investigate the effect of gas bubbles on the low-frequency sound velocity in the sediment. Considering the uncontrollable environmental factors of field experiment, an experiment platform for obtaining acoustic characteristics of a large-scale gas-bearing unsaturated sandy sediment is constructed in the indoor water tank. Considering the long wavelength of low-frequency acoustic wave and the multipath interference in water tank, the transmitted acoustic signals are received by hydrophones which are buried in the unsaturated sediment. The sound velocity data (79-142 m/s) in the gas-bearing unsaturated sediment are acquired by using a multi-hydrophone inversion method in the bounded space for the first time in a 300-3000 Hz range, and the sound velocity data (112-121 m/s) are also acquired by using a double-hydrophone method in the same frequency range. The refraction experiments at different horizontal distances between the source and the hydrophones are conducted, which verifies the reliability of sound velocity data acquired by using the multi-hydrophone inversion method and the double-hydrophone method. At the acoustic frequency well below the resonance frequency of the largest bubble in the sediment, the pore water and the gas bubbles are regarded as an effective uniform fluid based on effective medium theory. On this basis, the density and the bulk elastic modulus of pore water in the effective density fluid model are replaced by the effective density and the effective bulk modulus of the effective uniform fluid, then a corrected effective density fluid model is proposed in gas-bearing unsaturated sediment. The numerical analysis indicates that when the gas bubble volume fraction is small (1%), a small increase in the gas bubble will cause a significant decrease in the effective bulk elastic modulus of sediment, but the density of pore water is much greater than the density of gas bubbles, the presence of a small number of gas bubbles hardly changes the density of pore fluid and certainly does not change the density of sediment, which results in a significant decrease at a low-frequency sound velocity in the gas-bearing unsaturated sediment. Furthermore, with the increase of gas bubble volume fraction, the sound velocity predicted by the corrected model gradually decreases, and the decreasing trend gradually becomes gentle. The corrected model reveals the effect of gas bubbles on the low-frequency acoustic characteristic of sediment. By analyzing the sensitivity of the predicted sound velocity to parameters of the model, the gas bubble volume fractions (1.07%-2.81%) of different areas are acquired by inversion according to the measured sound velocity distribution and the corrected model. In the future, it will provide a new method of obtaining the volume fraction and the distribution of gas bubbles in the sediment.

Lamb-type waves generated by a cylindrical bubble oscillating between two planar elastic walls

The volume oscillation of a cylindrical bubble in a microfluidic channel with planar elastic walls is studied. Analytical solutions are found for the bulk scattered wave propagating in the fluid gap and the surface waves of Lamb-type propagating at the fluid-solid interfaces. This type of surface wave has not yet been described theoretically. A dispersion equation for the Lamb-type waves is derived, which allows one to evaluate the wave speed for different values of the channel height h. It is shown that for h<λt, where λt is the wavelength of the transverse wave in the walls, the speed of the Lamb-type waves decreases with decreasing h, while for h on the order of or greater than λt, their speed tends to the Scholte wave speed. The solutions for the wave fields in the elastic walls and in the fluid are derived using the Hankel transforms. Numerical simulations are carried out to study the effect of the surface waves on the dynamics of a bubble confined between two elastic walls. It is shown that its resonance frequency can be up to 50% higher than the resonance frequency of a similar bubble confined between two rigid walls.

Noise reduction by the application of an air-bubble curtain in offshore pile driving

Underwater noise pollution is a by-product of marine industrial operations. In particular, the noise generated when a foundation pile is driven into the soil with an impact hammer is considered to be harmful for the aquatic species. In an attempt to reduce the ecological footprint, several noise mitigation techniques have been investigated. Among the various solutions proposed, the air-bubble curtain is often applied due to its efficacy in noise reduction. In this paper, a model is proposed for the investigation of the sound reduction during marine piling when an air-bubble curtain is placed around the pile. The model consists of the pile, the surrounding water and soil media, and the air-bubble curtain which is positioned at a certain distance from the pile surface. The solution approach is semi-analytical and is based on the dynamic sub-structuring technique and the modal decomposition method. Two main results of the paper can be distinguished. First, a new model is proposed that can be used for predictions of the noise levels in a computationally efficient manner. Second, an analysis is presented of the principal mechanisms that are responsible for the noise reduction due to the application of the air-bubble curtain in marine piling. The understanding of these mechanisms turns to be crucial for the exploitation of the maximum efficiency of the system. It is shown that the principal mechanism of noise reduction depends strongly on the frequency content of the radiated sound and the characteristics of the bubbly medium. For piles of large diameter which radiate most of the acoustic energy at relatively low frequencies, the noise reduction is mainly attributed to the mismatch of the acoustic impedances between the seawater and the bubbly layer. On the contrary, for smaller piles and when the radiated acoustic energy is concentrated at frequencies close to, or higher than, the resonance frequency of the air bubbles, the sound absorption within the bubbly layer becomes critical.