Multiple Bubble Interactions Research Articles

Study of nucleate boiling growth regime on thin surfaces.

In a context of energy transition, heat exchanges are a key for energy sobriety. Among those exchanges, nucleate boiling is the preferred heat transfer method for high heat flux. Vaporisation plays an important role in the nuclear industry, but also in thermal machines such as cooling systems in data centers. In spite of decades studying boiling thermodynamics, modelling heat transfers in the nucleate boiling is still a major difficulty because of its numerous parameters. In the 1960s, scientists developed promising models called heat flux partitioning models. These models have been improved over the years, but they need closure laws about bubbles dynamics and nucleation site density. For the purpose of improving those models, we took part in an international collaboration (ANR TraThI) to study interface heat transfer. Project focuses on boiling with a controlled nucleation site density with a strong emphasis on studying isolated bubbles in water pool boiling, and later addressing multiple bubble interactions in pool and flow boiling. This work focuses on the bubble growth regimes on thin metallic foil observed in a water pool boiling experiment, with a distinction between microlayer and contact line growth regime. Pulsed nanosecond laser was used to create active nucleation site, while high-speed infrared thermography and shadowgraphy were implemented to record transient wall temperatures and bubble dynamics, respectively. This work shows that our experimental configuration induced two different bubble growth regimes, depending on the imposed heat flux and the recent past at the nucleation site and its vicinity. Study provides a framework for further in-depth investigations with different experimental configurations.

Interactions between a central bubble and a surrounding bubble cluster

The interaction of multiple bubbles is a complex physical problem. A simplified case of multiple bubbles is studied theoretically with a bubble located at the center of a circular bubble cluster. All bubbles in the cluster are equally spaced and own the same initial conditions as the central bubble. The unified theory for bubble dynamics [35] is applied to model the interaction between the central bubble and the circular bubble cluster. To account for the effect of the propagation time of pressure waves, the emission source of the wave is obtained by interpolating the physical information on the time axis. An underwater explosion experiment with two bubbles of different scales is used to validate the theoretical model. The effect of the bubble cluster with a variation in scale on the pulsation characteristics of the central bubble is studied.

The interaction of multiple bubbles in a Hele-Shaw channel

We study the dynamics of two air bubbles driven by the motion of a suspending viscous fluid in a Hele-Shaw channel with a small elevation along its centreline via physical experiment and numerical simulation of a depth-averaged model. For a single-bubble system we establish that, in general, the bubble propagation speed monotonically increases with bubble volume so that two bubbles of different sizes, in the absence of any hydrodynamic interactions, will either coalesce or separate in a finite time. However, our experiments indicate that the bubbles interact and that an unstable two-bubble state is responsible for the eventual dynamical outcome: coalescence or separation. These results motivate us to develop an edge-tracking routine and to calculate these weakly unstable two-bubble steady states from the governing equations. The steady states consist of pairs of ‘aligned’ bubbles that appear on the same side of the centreline with the larger bubble leading. We also discover, through time-dependent simulations and physical experiment, another class of two-bubble states that, surprisingly, are stable. In contrast to the ‘aligned’ steady states, these bubbles appear on either side of the centreline and are ‘offset’ from each other. We calculate the bifurcation structures of both classes of steady states as the flow rate and bubble volume ratio are varied. We find that they exhibit intriguing similarities to the single-bubble bifurcation structure, which has implications for the existence of $n$ -bubble steady states.

Impact-induced bubble interactions and coalescence in soft materials

Cavitation in soft materials attracts many attentions due to its importance for a range of biomedical problems and applications, such as cavitation-induced traumatic brain injury, high-intensity focused ultrasound lithotripsy, and the treatment of tumors. However, existing studies are mainly focused on the deformation behavior of a single bubble. The dynamic configuration and the failure process of multiple bubble interactions, which are significantly different from those of a single bubble, remain largely unknown. Here, we performed experimental and analytical studies to investigate the impact-induced interactions of bubbles in soft materials, where bubbles of controllable size and spacing were introduced with the aid of a highly efficient rheology modifier, namely carbomer. A drop tower system paired with a high-speed camera was utilized to conduct impact tests and concurrently visualize the evolution of the bubble configuration. A theoretical model containing pressure radiated by bubbles is proposed to predict the spherically symmetric deformation of multi-bubble interactions, as well as the inhibition between bubbles during deformation. A combination of energy-based strength theory and finite element analysis is used to reveal the squeeze and coalescence mechanisms of the bubbles. The failure of soft material is shown to depend on stress triaxiality; in particular, the material can rupture at unloading and under a stress lower than the historic maximum. A phase diagram was drawn to predict the critical impact loads for bubble coalescence at different conditions. Our work provides a promising clue to the understandings for the interactions and coalescence behavior of bubbles those ubiquitously exist in natural and artificial soft materials.

Pulsed ultrasound propagation through polydisperse contrast agent suspensions

Gas microbubbles stabilised by a surfactant or polymer coating are widely used in echocardiography and, increasingly, for quantitative studies of tissue perfusion. It is their highly nonlinear response to ultrasound excitation that makes them such effective contrast agents. It is this property also, however, that leads to image artefacts and difficulties in obtaining accurate quantitative information. There are few theoretical models describing the response of a contrast agent population that take into account both nonlinear behaviour and multiple bubble interactions. Computational complexity arises when the medium contains a polydisperse bubble population because a nonlinear ordinary differential equation (ODE) governing the bubble response must be computed for the current radius of each bubble size R0 present at each spatial location at every time step, which unfortunately makes the numerical model impractical for real-time clinical use. Further complexity occurs when near-resonant microbubbles shed their lipid coating drastically transforming the suspension’s acoustic response to subsequent pulses. In this work, we investigate approximations that can significantly reduce the computational complexity and demonstrate that, under certain parameter regimes, these approximations can simulate the nonlinear propagation of a repeated ultrasound pulses through a polydisperse contrast agent suspension to reasonably high accuracy.

Nonlinear dynamics of acoustic bubbles excited by their pressure-dependent subharmonic resonance frequency: influence of the pressure amplitude, frequency, encapsulation and multiple bubble interactions on oversaturation and enhancement of the subharmonic signal

Nonlinear behavior of bubbles, and most importantly $$\frac{1}{2}$$ -order subharmonics (SH), are used to increase the contrast-to-tissue ratio (CTR) in diagnostic ultrasound (US) and to monitor bubble-mediated therapeutic US. It is shown experimentally and numerically that when bubbles are sonicated with a frequency that is twice their resonance frequency ( $$f_\mathrm{r}$$ ), SHs at half the excitation frequency are generated at the minimum excitation pressure. Thus, $$f=2f_\mathrm{r}$$ is defined as the SH resonance frequency. SHs increase rapidly with pressure and reach an upper limit of the achievable SH signal strength. Numerous studies have investigated the pressure threshold of SH oscillations; however, conditions to enhance the saturation level of SHs have not been investigated. In this paper, nonlinear dynamics of bubbles excited at frequencies in the range of $$f_\mathrm{r}<f<2f_\mathrm{r}$$ is studied for different sizes of bubbles (400 nm–8 $$\upmu \mathrm{m}$$ ). In agreement with previous studies, we show that the SH resonance frequency is pressure dependent and decreases as pressure increases. When a bubble is sonicated with its pressure-dependent SH resonance frequency, oscillations undergo a saddle node bifurcation from a P1 or P2 regime to a P2 oscillation regime with higher amplitude. The saddle node bifurcation is concomitant with over-saturation of the SH and UH amplitude and eventual enhancement of the upper limit of SH and UH strength (e.g., $$\approx $$ 7 dB in UH amplitude). This can increase the CTR and signal-to-noise ratio in applications. Here, we show that the highest non-destructive SH amplitude occurs when $$f\approxeq 1.6-1.8f_\mathrm{r}$$ . In the case of interacting bubbles, $$f_\mathrm{r}$$ and pressure threshold of SH emissions decrease with increasing concentration, and supersaturation amplitude decreases above an upper limit of concentration.

Effect of solid surface in vicinity of multi-bubble array in cryogenic environment

Multiple bubble interactions in initially quiescent liquid are often accompanied by generation of jets, shockwaves and light. At cryogenic temperature (< 123 K) when certain materials (particularly bcc-type) become brittle, such afore-mentioned physical effects can be effective in disintegrating them to smaller fragments. CFD techniques based on direct numerical simulations can help to understand this phenomenon that may benefit nanotechnology-based industries and oil-gas exploration-firms working with air-gun arrays. In this paper, multiple bubble-pairs are simulated in a co-centric manner around a centrally located solid target (5 mm radius). The ambient fluid is liquid nitrogen (77 K) and the bubbles are gaseous nitrogen (87 K). 2D numerical simulation using the VOF method in compressible domain is carried out neglecting the effect of phase change and gravity. The stand-off distance between the solid target and bubble-pairs are varied systematically and its influence on the fluid-dynamic effects (e.g. pressure shockwave & jets) are compared. Initial calculations suggest that for stand-off distance of 0.93 mm, shockwaves measure above 10 times the ambient pressure and liquid jet speeds around 30 m/s in cryogenic environment, at multiple locations very close to the solid target. These consecutive physical impacts can foster ample liquid-hammer pressures, making it promising for solid wear at 77 K when juxtaposed against room-temperature cases.

Nonlinear dynamics of a cavitation bubble pair near a rigid boundary in a standing ultrasonic wave field

The dynamics of a micrometer-sized bubble pair in water near a rigid boundary under standing ultrasonic wave excitation is investigated in this study. The viscous effect in the boundary layer at the air-water interface is considered following the viscous correction model. The evolution of the bubble surface at the collapsing stage of the bubble pair is presented for different parameter sets. The field pressure near the rigid boundary, which is induced by the oscillating bubble pair, and the high-speed water jet at the collapse stage, form the main focus of the analysis. This reveals that a horizontal configuration of the bubble pair retards the strength of the bubble jet towards the boundary, whilst a vertical configuration, especially with differently-sized bubbles, can enhance the bubble collapse. This study may help to understand the interaction of multiple bubbles in an acoustic field and its application to surface cleaning.

Simulation of multiple cavitation bubbles interaction with single-component multiphase Lattice Boltzmann method

Understanding the behavior of multiple cavitation bubbles and their interactions is important for developing deeper insight into cavitation phenomena. Using a revised single-component multiphase Lattice Boltzmann method, the weak and strong interactions between two neighboring cavitation bubbles and the mutual interaction among a cluster of cavitation bubbles are simulated. The simulated bubble evolutions have satisfying agreement with previous experimental results. Details of the multiple bubble interactions (the pressure and velocity fields) are presented. In the case of two-bubble interactions, typical phenomena such as bubble toroidal deformation, micro-jets, the thinning of the liquid film, and bubble coalescence are successfully reproduced. The bubble radius changes under two-bubble weak interaction are adequately described by a revised 2-D Rayleigh-Plesset equation. The transition from the strong to weak interactions with increasing initial distance between the two bubbles is analyzed. The behaviors of a cluster of bubbles are also simulated, where the shield effect of outer layer bubbles and the micro-jets are accurately captured. The present multiphase Lattice Boltzmann method is a promising tool to investigate complex cavitation problems.

Analysis of bubble distribution in a multiphase rotodynamic pump

ABSTRACTRecent researches show that the pressure increment of a multiphase pump is affected by bubble size and distribution. In order to study the bubble distribution characteristics in such pumps, a novel approach describing the variable bubble size in the pump is proposed. The bubble number density equation, which has taken into account the phenomena of break-up and coalescence, is introduced into the flow simulation, and the drag coefficient is revised because of the interaction of multiple bubbles. The reliability of the approach is verified by comparison with the experiment. It was established that the bubbles move to the impeller hub due to the difference in centrifugal force between gas and liquid. Despite the high collision rate near the hub, bubble size changes little with the stirring action of the impeller. The mixture flows in a disorderly way and the bubble diameter increases due to the rotor–stator interaction. Owing to the increasing flow area in the diffuser, bubbles move to the mainstream region, and bubble size reaches its maximum owing to the flow separation near the hub. The distribution of bubbles is also analyzed under a different inlet gas volume fraction (IGVF) and inlet bubble diameter (d0). Bigger IGVF brings about a higher collision rate of bubbles, while smaller d0 makes the diffusion of bubbles easier.

Numerical investigation of single and multiple bubble condensing behaviors in subcooled flow boiling based on homogeneous mixture model

Numerical investigations of the condensing behaviors of a single bubble and multiple bubbles under different subcooled flows were conducted using the compressible homogeneous mixture method. The surface tension between the liquid and vapor phases was determined using the continuous surface force method. An implicit dual-time technique was applied to solve the two-phase compressible flow model. A sensitivity study of the empirical coefficients used to access the predictive capacity of the existing mass transfer models was conducted. The numerical simulation results were compared with experimental data. The obtained results agreed well with the experimental results. Additionally, the bubble condensation behavior was investigated for different initial subcooled temperatures, bubble diameters, and velocities. Subsequently, the effect of multiple bubble interactions on their condensation was studied. The condensation rate of the lower bubbles increased compared to the other bubbles as a result of induced random perturbation. When the gap between the bubbles was large, a negligible amount of condensation occurred between the bubbles.

Numerical investigation of multiple-bubble behaviour and induced pressure in a megasonic field

Clarifying the mechanism of particle removal by megasonic cleaning and multiple-bubble dynamics in megasonic fields is essential for removing contaminant particles during nanodevice cleaning without pattern damage. In particular, the effect of the interaction of multiple bubbles on bubble-collapse behaviour and impulsive pressure induced by bubble collapse should also be discussed. In this study, a compressible locally homogeneous model of a gas–liquid two-phase medium is used to numerically analyse the multiple-bubble behaviour in a megasonic field. The numerical results indicate that, for bubbles with the same equilibrium radius, the natural frequency of the bubble decreases, and bubbles with smaller equilibrium radii resonate with the megasonic wave as the number of bubbles increases. Therefore, the equilibrium radius of bubbles showing maximum wall pressure decreases with an increasing number of bubbles. The increase in bubble number also results in chain collapse, inducing high wall pressure. The effect of the configuration of bubbles is discussed, and the bubble–bubble interaction in the concentric distribution makes a greater contribution to the decrease in the natural frequency of bubbles than the interaction in the straight distribution.

Level-set simulations of buoyancy-driven motion of single and multiple bubbles

This paper presents a numerical study of buoyancy-driven motion of single and multiple bubbles by means of the conservative level-set method. First, an extensive study of the hydrodynamics of single bubbles rising in a quiescent liquid is performed, including its shape, terminal velocity, drag coefficients and wake patterns. These results are validated against experimental and numerical data well established in the scientific literature. Then, a further study on the interaction of two spherical and ellipsoidal bubbles is performed for different orientation angles. Finally, the interaction of multiple bubbles is explored in a periodic vertical channel. The results show that the conservative level-set approach can be used for accurate modelling of bubble dynamics. Moreover, it is demonstrated that the present method is numerically stable for a wide range of Morton and Reynolds numbers.

Computational study of the dynamics of two interacting bubbles in a megasonic field

Clarification of the mechanism of particle removal by megasonic cleaning and control of cavitation bubbles in the megasonic field are essential for cleaning of nanodevices without pattern damage. Multiple bubble interactions complicate the mechanism of particle removal. Therefore, it is important to understand multiple bubble dynamics to clarify the mechanism of particle removal by megasonic cleaning. In the present study, the dynamics of two bubbles in a megasonic field with several initial radii and initial separation distances were simulated by numerical analysis using a compressible locally homogeneous model of a gas–liquid two-phase medium. The present numerical method simulated the various complex behaviors of two bubbles, which are repulsive motion, coalescence, periodic and stable motion of the separation distance, and bubble breakup. The initial separation distance strongly affected the behavior of the two bubbles because the effect of the secondary pressure induced by the oscillation of one bubble on the other bubble depends on the separation distance. In particular, when the equilibrium radii are larger than the resonant radius and the radius of one or both bubbles is close to the resonant radius, the bubbles can show characteristic behaviors, such as periodic and stable motion of the separation distance.

Numerical Study of Dynamics of Bubbles Using Lattice Boltzmann Method

The dynamics of gaseous bubbles inside a tube filled with liquid has been modeled using the lattice Boltzmann method. The diffused interface concept has been used to capture the shape of the complex interface separating two phases having high density ratio. Hydrodynamics of rising bubble inside the tube is studied in detail. Properties like densities of the phases, viscosity of the liquid, and surface tension are varied to evaluate their effects on the final shape as well as on the terminal velocity of the bubble. The volume of the bubble and the diameter of tube are also varied over a wide range to establish the effect of initial conditions on shape and the terminal velocity. Further attempts have been made to study the interaction of multiple bubbles consisting of arrays in horizontal and vertical forms. Shape distortion of one bubble due to the influence of other and merging of two bubbles due to their different uprising velocities are numerically modeled. Finally, numerical simulation is made to model...

Direct observation of microbubble interactions with ex vivo microvessels.

The interaction between microbubbles with tissue is poorly understood. Experimental evidence, supported by numerical simulations, suggests that bubble dynamics is highly constrained within blood vessels. To investigate this further, a high-speed microimaging system was set up to study the effects of acoustically activated microbubbles on microvessels in ex vivo rat mesentery tissues. The microbubble-perfused tissues were placed under a microscope and insonified with MHz ultrasound. A variety of interactions was observed by a high-speed camera: arterioles, venules, and capillaries were all recorded to dilate and invaginate by activated microbubbles. For small diameter microvessels, dilation and invagination were nearly symmetric, and bubble-induced rupture of the vessel was observed at high pressure. For larger microvessels, the portion of the vessel nearest the bubble coupled the strongest to the bubble dynamics, and the extent of dilation was smaller than invagination. Tissue jetting toward the bubble was recorded in many cases. The interaction of multiple bubbles inside microvessels was also observed. Bubble oscillation, vessel wall velocity, and tissue jet velocity were quantitatively measured. Invagination of vessel walls, especially tissue jetting, may be the major mechanism for tissue injury by a bubble. [Work supported by NIH 5R01EB000350.]

Interactions of multiple spark-generated bubbles with phase differences

This paper aims to study the complex interaction between multiple bubbles, and to provide a summary and physical explanation of the phenomena observed during the interaction of two bubbles. High-speed photography is utilized to observe the experiments involving multiple spark-generated bubbles. Numerical simulations corresponding to the experiments are performed using the Boundary Element Method (BEM). The bubbles are typically between 3 and 5 mm in radius and are generated either in-phase (at the same time) or with phase differences. Complex phenomena are observed such as bubble splitting, and high-speed jetting inside a bubble caused by another collapsing bubble nearby (termed the ‘catapult’ effect). The two-bubble interactions are broadly classified in a graph according to two parameters: the relative inter-bubble distance and the phase difference (a new parameter introduced). The BEM simulations provide insight into the physics, such as bubble shape changes in detail, and jet velocities. Also presented in this paper are the experimental results of three bubble interactions. The interesting and complex observations of multiple bubble interaction are important for a better understanding of real life applications in medical ultrasonic treatment and ultrasonic cleaning. Many of the three bubble interactions can be explained by isolating bubble pairs and classifying their interaction according to the graph for the two bubble case. This graph can be a useful tool to predict the behavior of multiple bubble interactions.

The dynamics of bubbles

The fluid is assumed to be inviscid and incompressible and the flow irrotational. The three_dimensional numerical model is established to simulate the interaction of multiple bubbles and the fast Fourier transform on multipoles (FFTM) method is combined with the higher order boundary method (BEM) to study the physics of multiple bubble dynamics. FFTM method is employed to speedup the solution of the boundary integral equation while achieving the same order of accuracy, enabling to simulate the dynamics of multiple bubbles in a reasonable time. Elastic mesh technique (EMT), which is a new mesh regulation technique, is applied to maintain the regularity of the triangular element mesh used to discretize the dynamic boundary surface during the evolution of bubbles. All these measures make the present approach viable and robust, which is validated by computations of several bubble dynamics problems. Numerical analysi was carried out for the interaction of multiple bubbles and the bubble dynamics. Some physical behaviors of the multiple bubbles are presented in this work. The factors affecting the expansion, collapse, moving of multiple bubbles and the jet formation are also discussed.

Numerical and Physical Modeling of Air Diffuser Plume

A drift‐flux formulation that accounts for multiple bubble interactions is applied to describe the mean water velocity, air fraction, and plume growth for a vertical air diffuser plume that is bound on one side. A coarse‐bubble line‐diffuser source in a rectangular mixing tank is considered. Physical velocity and plume width measurements are used to calibrate the numerical model. The model is shown to be sensitive to the initial plume width and the entrainment coefficient. A dimensionless equation for the ambient water velocity at the outer edge of the plume is developed from physical measurements. The water velocity and air fraction are assumed to be uniform over the plume width. Four ordinary differential equations are developed and solved simultaneously to obtain the changes in significant plume variables with fluid depth. To reproduce the observed plume characteristics, the entrainment coefficient was 30‐60% higher than the single‐phase jet entrainment coefficient. The effect of the wall friction was minor for depths less than 1 m.