Identical Bubbles Research Articles

The velocity fields around aspherical bubbles

Abstract This paper studies the simplest system, which can possess the left-right symmetrical and asymmetrical surroundings, three bubbles in a line. Assuming that the deformations are small, the surfaces of bubbles are described by a combination of the first three Legendre polynomials, that is, spherical symmetrical mode P0, antisymmetrical mode P1 and symmetrical mode P2. Based on the dynamics of three-bubble system, this paper further studies the velocity fields distribution around them. It can be seen from the contour distribution of the velocity field that the velocity component always decreases with the increase of the distance r. When three identical bubbles are separated uniformly, the velocity field around the central bubble is always in a symmetric, while there are asymmetric velocity fields around two side bubbles.

Passive acoustic measurement of bubble size and number from a bubble chain

Experiments and matching simulations are presented on the passive-acoustic emissions of a chain of bubbles, with the aim of deducing both the bubble size and number of bubbles from the emitted sound. It is well known that bubble-acoustic interactions cause shifts in frequency from those predicted for single bubbles, complicating the goal of measuring bubble size by measuring frequency, and also affecting the collective resonances of bubbles driven by ultrasound. A horizontal line of identical bubbles was held fixed in space, eliminating uncertainties in earlier studies due to the variable shape and location of freely rising bubbles. At one end of the line, a first, identical bubble naturally emitted a pulse of sound on formation from an underwater nozzle, exciting the rest of the bubbles into a coupled acoustic emission. It was found that a theoretically predicted relation between frequency and the number of bubbles, which can be derived from the coupled equations of motion, permitted an accurate fit to the data. Measurements of two independent spectral peaks unambiguously determined the two unknowns of bubble size and bubble number. However, experiments diverge from theory and simulations for greater than six bubbles, which are speculated may be explicable by network theory.

Short-range repulsive force model for near-contact interactions of bubbles.

We introduce a short-range repulsive force model to tackle near-contact interactions when the collision occurs between bubbles. In contrast to the previous numerical method adopting the adaptive mesh refinement technique, such a mesoscale model can be applied to a relatively coarse mesh, which can prevent the nonphysical coalescence between bubbles without excessive mesh refinement. We assume that the repulsive force is inversely proportional to the third power of distance, as a reasonable approximation to the short-range phase interactions. The model is validated against two different experiments. In both experiments, two identical bubbles rising side by side were considered. First, the experiment performed in a water-glycerol mixture helps determine the model parameter K. Second, three typical combinations of bubble size and initial separation distance are simulated, presenting different types of interactions, i.e., coalescence, bouncing coalescence, and bouncing separation, agreeing well with the second experiment, which was performed in pure water. Owing to its simplicity, this model can be easily implemented into existing codes, and it can be extended to the case with multiple bubbles or droplets.

The influence of inter-bubble spacing on the resonance response of ultrasound contrast agent microbubbles

Ultrasound-driven microbubbles, typically between 1 and 8 µm in diameter, are resonant scatterers that are employed as diagnostic contrast agents and emerging as potentiators of targeted therapies. Microbubbles are administered in populations whereby their radial dynamics – key to their effectiveness - are greatly affected by intrinsic (e.g. bubble size) and extrinsic (e.g. boundaries) factors. In this work, we aim to understand how two neighbouring microbubbles influence each other. We developed a finite element model of a system of two individual phospholipid-encapsulated microbubbles vibrating in proximity to each other to study the effect of inter-bubble distance on microbubble radial resonance response. For the case of two equal-sized and identical bubbles, each bubble exhibits a decrease between 7 and 10% in the frequency of maximum response (fMR) and an increase in amplitude of maximum response (AMR) by 9–11% as compared to its isolated response in free-space, depending on the bubble size examined. For a system of two unequal-sized microbubbles, the large bubble shows no significant change, however the smaller microbubble shows an increase in fMR by 7–11% and a significant decrease in AMR by 38–52%. Furthermore, in very close proximity the small bubble shows a secondary off-resonance peak at the corresponding fMR of its larger companion microbubble. Our work suggests that frequency-dependent microbubble response is greatly affected by the presence of another bubble, which has implications in both imaging and therapy applications. Furthermore, our work suggests a mechanism by which nanobubbles show significant off-resonance vibrations in the clinical frequency range, a behaviour that has been observed experimentally but heretofore unexplained.

The left-right symmetrical and asymmetrical deformations in a three-bubble system

This paper studies the simplest system that can possess left-right symmetrical and asymmetrical surroundings, three bubbles in a line. Assuming that the deformations are small, the surfaces of bubbles are described by a combination of the first three Legendre polynomials, that is, spherical symmetrical mode P0, L-R antisymmetrical mode P1, and symmetrical mode P2. A dynamical model is built to describe aspherical oscillations of central and two side bubbles. It is found that when three identical bubbles are separated uniformly, the central bubble only has a P2 component and P1 component tends to zero, while two side bubbles have both P1 and P2 components. When three identical bubbles are separated by different distances, they can be degenerated into a two-bubble system and a free bubble. The bubble deformations contain both P1 and P2 components in the two-bubble system, while both aspherical components P1 and P2 of the free bubble tend to zero. If side bubbles are different in ambient radii but located symmetrically on the left and right of the central bubble, the side bubble pulsated more strongly plays an important role on the deformation of the central one.

Dynamics of double bubbles under the driving of burst ultrasound

This paper investigates the pulsations and translation of bubbles in a double-bubble system driven by burst ultrasound. Results illustrate that for two identical bubbles, decreasing the frequency of burst or increasing its amplitude can enhance the pulsations and improve the translation velocities of bubbles. In a certain scope, large bubble brings about fast translation velocity, but the velocity will fall down for too large bubble, such as the bubble with ambient radius over about its resonance radius. When the ambient radii of two bubbles are different, translation of the large bubble is smaller than that of the small bubble. In addition, the effect of initial distance between bubbles is described as well. If burst serials are used, shortening the time interval between each burst and improving the acoustic amplitude of bursts are beneficial for the translations of bubbles.

Measurement of forced convection subcooled boiling flow through a vertical annular channel with high-speed video cameras and image reconstruction

ABSTRACT In order to develop models regarding subcooled boiling flow and its heat transfer, we conducted subcooled boiling experiments to investigate subcooled bubble formation and measured development process of the bubbles using a test loop with a vertical annulus flow path under atmospheric conditions. Two-phase flow parameters regarding subcooled boiling, such as instantaneous bubble velocity, turbulent velocity components, void fraction, onset of nucleate boiling (ONB) and onset of significant void (OSV), were obtained with two high-speed video cameras in high resolution in temporally and spatially. The identical bubbles were identified from the two video images taken by the high-speed video cameras, and the trajectories were reconstructed in three-dimensional. The instantaneous bubble velocities and turbulence velocity components regarding bubble transport were quantified with the trajectory data. It was observed that the bubbles were rising along the surface of the heater rod moved largely in the circumferential direction, and it was found from the result that velocity component for circumferential direction was enough large compared with that for radial direction.

An experimental study of two identical air bubbles rising side-by-side in water

We experimentally study the dynamics of two identical air bubbles rising side-by-side in water by varying two parameters, namely, the radius of the bubble and center to center distance between them. The bubbles follow a three-dimensional spiraling motion, and their path and shape oscillations are observed in both the front and top views by using a high speed camera with a back-lit illumination and a mirror arrangement. Bubbles of different sizes are created by using a dumping cup mechanism, and the center to center distance between the two bubbles is varied by using telescopic joints. The dynamics of the two side-by-side bubbles is compared and contrasted with that of a single rising bubble. We found that the bubbles act independent of each other, like a single bubble, when the center to center distance is greater than seven times the radius of the bubbles. For similar separation distances, increasing the size of the bubbles results in a smaller terminal velocity and also lesser deviation from a spiral path due to high inertia.

Bubbling transition as a mechanism of destruction of synchronous oscillations of identical microbubble contrast agents.

We study the process of the destruction of synchronous oscillations in a model of two interacting microbubble contrast agents exposed to an external ultrasound field. Completely synchronous oscillations in this model are possible in the case of identical bubbles when the governing system of equations possess a symmetry leading to the existence of a synchronization manifold. Such synchronous oscillations can be destructed without breaking the corresponding symmetry of the governing dynamical system. Here, we describe the phenomenological mechanism responsible for such destruction of synchronization and demonstrate its implementation in the studied model. We show that the appearance and expansion of transversally unstable areas in the synchronization manifold leads to the transformation of a synchronous chaotic attractor into a hyperchaotic one. We also demonstrate that this bifurcation sequence is stable with respect to symmetry breaking perturbations.

Synchronous oscillations and symmetry breaking in a model of two interacting ultrasound contrast agents

We study nonlinear dynamics in a system of two coupled oscillators, describing the motion of two interacting microbubble contrast agents. In the case of identical bubbles, the corresponding symmetry of the governing system of equations leads to the possibility of existence of asymptotically stable synchronous oscillations. However, it may be difficult to create absolutely identical bubbles and, moreover, one can observe in experiments regimes that are unstable with respect to perturbations of equilibrium radii of bubbles. Therefore, we investigate the stability of various synchronous and asynchronous dynamical regimes with respect to the breaking of this symmetry. We show that the main factors determining stability or instability of a synchronous attractor are the presence/absence and the type of an asynchronous attractor coexisting with the synchronous attractor. On the other hand, asynchronous hyperchaotic attractors are stable with respect to the symmetry breaking in all the situations we have studied. Therefore, they are likely to be observed in physically realistic scenarios and can be beneficial for suitable applications when chaotic behavior is desirable.

Numerical analysis of the interaction of two underwater explosion bubbles using the compressible Eulerian finite-element method

This paper presents numerical investigations of the nonlinear interactions between two underwater explosion (UNDEX) bubbles using the compressible Eulerian finite-element method (EFEM). The volume of fluid method is applied to capture the multi-fluid interface. In this model, the high-temperature and high-pressure gaseous products inside the UNDEX bubble are described by the equation of state for Jones–Wilkins–Lee, which allows us to consecutively simulate the propagation of the primary explosion shock wave and multi-period bubble pulsations. To verify the efficiency and accuracy of the present model, comparisons with experimental data are performed, showing that both the dynamic behaviors of oscillating bubbles and the pressure profiles of primary shock waves, bubble pulsations, and jetting loads are highly consistent. In addition, it is found that the EFEM model can satisfactorily reproduce the complex characteristics of interacting bubbles, such as the coalescence and splitting that occur during later pulsating cycles in bubbles. On this basis, the effects of the initial bubble–bubble distance γbb and buoyancy parameter δ on the features of bubble interactions and the corresponding pressure loads in the flow field are analyzed and discussed. In particular, the pressure induced by two identical UNDEX bubbles (each generated by detonation of an explosive with weight W) is compared to that induced by a single bubble generated by an explosive with weight W or 2W to provide the basic technical support and reference for the design of multiple-weapon attacks in military engineering applications.

Oscillating endoskeletal antibubbles

An antibubble is a gas bubble with a liquid droplet inside. Antibubbles have a potential role in ultrasonic imaging, ultrasound-guided drug delivery, and hydrocarbon leakage detection. The liquid core droplets inside antibubbles can be stabilised with a process called Pickering stability. Other systems proposed include spoke crystals to suspend the droplet or endoskeletal structures. In this study, the oscillatory response of microscopic endoskeletal antibubbles to ultrasound has been investigated, primarily to determine whether the presence of an endoskeleton attenuates the oscillation amplitude of the antibubble. Three emulsions containing (anti)bubbles were prepared for evaluation. Each emulsion was pipetted into the observation chamber of a high-speed microscopic observation system. A high-speed camera, operating at 10 million frames per second, was couples to the microscope. During camera recording, the materials were subjected to ultrasound pulses from a laboratory-assembled single-element transducer. The presence of an endoskeleton with droplets hampers the oscillation of antibubbles as compared to identical bubbles without endoskeleton and droplet content.

Double-negative acoustic metamaterials

The aim of this paper is to provide a mathematical theory for understanding the mechanism behind the double-negative refractive index phenomenon in bubbly fluids. The design of double-negative metamaterials generally requires the use of two different kinds of subwavelength resonators, which may limits the applicability of double-negative metamaterials. Herein we rely on media that consists of only a single type of resonant element, and show how to turn the acoustic metamaterial with a single negative effective property obtained in [H. Ammari and H. Zhang, Effective medium theory for acoustic waves in bubbly fluids near Minnaert resonant frequency. SIAM J. Math. Anal., 49 (2017), 3252--3276.] into a negative refractive index metamaterial, which refracts waves negatively, hence acting as a superlens. Using bubble dimers made of two identical bubbles, it is proved that both the effective mass density and the bulk modulus of the bubbly fluid can be negative near the anti-resonance of the two hybridized Minnaert resonances for a single constituent bubble dimer. A rigorous justification of the Minnaert resonance hybridization, in the case of a bubble dimer in a homogeneous medium, is established. The acoustic properties of a single bubble dimer are analyzed. Asymptotic formulas for the two hybridized Minnaert resonances are derived. Moreover, it is proved that the bubble dimer can be approximated by a point scatterer with monopole and dipole modes. For an appropriate volume fraction of bubble dimers with certain conditions on their configuration, a double-negative effective medium when the frequency is near the anti-resonance of the hybridized Minnaert resonances can be obtained.

Numerical investigation on the collapse of a bubble cluster near a solid wall.

This paper studies numerically the collapse of a cluster of cavitation bubbles (as a primitive model for a bubble cloud) near a solid wall. The homogeneous two-phase mixture model is used, with the liquid-vapor interface resolved by volume of fluid method. The liquid is treated as compressible, allowing the propagation of pressure waves at the speeds determined by a state equation. This cluster consists of 27 identical bubbles, evenly distributed in a cubic region, with various bubble-wall and bubble-bubble distances considered. Our simulations suggest that the bubble-wall distance plays a more significant role. The maximum impulsive pressure of 41MPa is achieved when the cluster is very close to the wall. The inward progress of collapse is observed by examining the evolutions of bubble shapes and flow fields, with two distinctly different sequences of collapse identified between the small and large bubble-wall distances. At a large bubble distance, the centermost bubble is the last to collapse, while at a small bubble distance, it is the central bubble nearest to the wall which collapses lastly. This difference can also explain the more intensive impulsive pressure for the smaller bubble-wall distances. The proposed numerical approach is of special interest because it can resolve the details of bubble-bubble and bubble-wall interactions, which are significant to the study of the collapse of a cavitation cloud, and its potential damage to hydraulic systems.

Resonant acoustic scattering by two spherical bubbles.

The mutual interaction between two close bubbles in an acoustic field is studied. This interaction is modeled in the linear framework of the multiple scattering theory using spherical harmonics expansions and the addition theorem. In order to deal with small as well as large bubbles, viscous dissipation in the liquid, thermal dissipation in the gas, and surface tension are taken into account in the calculations of the scattering coefficients of a unique bubble. Under the assumption of the long wavelengths, the scattering coefficient of the monopolar mode is linked to the one obtained by using the Rayleigh-Plesset equation. The exact characteristic equation providing the symmetric and antisymmetric resonances of the two bubbles is established. Numerical results show that a great number of modes of vibration is required to describe the acoustic field around the bubbles. Moreover, whatever the spacing between two identical bubbles, the scattering cross section has a maximum value at the frequency of the symmetric mode while the antisymmetric mode is not detected. However, the strengthening of the scattering observed close to the symmetric resonance frequency is clearly due to the presence of the antisymmetric mode.

Resonant solitons in a polydisperse bubble medium

The effect of polydispersity of bubbles on formation of the spatial structure of the wave field, consisting of a sound forerunner, resonant solitons and trace, is investigated. It is shown that in a polydisperse medium the general structure of the wave field is the same as in the medium with identical bubbles, but the energy and spectral characteristics of all wave field components vary substantially.

Influence of spatial position of gas bubbles in liquid on their joint dynamics

The influence of the mutual arrangement of initially identical spherical equidistant gas bubbles in liquid on their dynamics at the antinode pressure of an ultrasonic standing wave is studied. A mathematical model is used, in which small deformations of bubbles are taken into account. Two configurations of their relative position are considered: linear and planar. The first configuration is composed from three bubbles with their centers on one straight line, the second configuration is composed from five bubbles with their centers on two mutually orthogonal straight lines. It is shown that the magnitude of the deformations of the central bubbles in the linear and planar configurations is approximately the same.

Harmonic response from microscopic antibubbles

An antibubble is a gas bubble containing a liquid droplet core. Both the droplet and the gas bubble are typically surrounded by stabilising shells. Owing to electrostatic forces exerted by these shells, core droplets of micrometer diameter do not readily coalesce with the surrounding liquid medium. Owing to the incompressibility of the liquid droplet core, antibubbles will oscillate asymmetrically, i.e., the radial excursion amplitude of the surface is greater during expansion than during contraction, when subjected to diagnostic ultrasound. Consequently, the harmonic content of the ultrasound signal radiated from antibubbles must be higher than that from identical bubbles without a liquid core. Whether the harmonic signal component generated by physical antibubbles is higher than the harmonic component of identical bubbles without a core has been studied here. We subjected prefabricated antibubbles and identical bubbles without core droplets to 1-MHz ultrasound and to a commercial ultrasound system, and recorded the spectra with a broadband transducer oriented perpendicularly to the transmitter. Normalised by the acoustic response from the medium, the antibubble signal shows stronger higher harmonics than the reference signal, and negligible fundamental response. In conclusion, antibubbles are suitable candidates for harmonic imaging. The generation of higher harmonics without fundamental has been attributed to asymmetric antibubble expansion.

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 effect of cell boundary on 2D foam

We have studied the effect of cell boundary on 2D foam, with particular attention to perfect arrays of identical bubbles, and those containing only a single defect with time. We have also examined the effect of the wetness of the foam, observing the stability of two-dimensional foam comprising bubble rafts constrained to a fixed area of liquid surface. Perfectly six-fold coordinated foam appear to be unstable against loss of cohesion, but the lifetime to breakage of the perfect foam increases systematically with changing the cell boundaries. Foams containing a single defect are stable against such breakage due to the elastic stress fields around it.