Single Bubble Research Articles

Modeling frequency shifts of collective bubble resonances with the boundary element method.

Increasing the number of closely packed air bubbles immersed in water changes the frequency of the Minnaert resonance. The collective interactions between bubbles in a small ensemble are primarily in the same phase, causing them to radiate a spherically symmetric field that peaks at a frequency lower than the Minnaert resonance for a single bubble. In contrast, large periodic arrays include bubbles that are further apart than half of the wavelength such that collective resonances have bubbles oscillating in opposite phases, ultimately creating a fundamental resonance at a frequency higher than the single-bubble Minnaert resonance. This work investigates the transition in resonance behavior using a modal analysis of a mass-spring system and a boundary element method. The computational complexity of the full-wave solver is significantly reduced to a linear dependence on the number of bubbles in a rectangular array. The simulated acoustic fields confirm the initial downshift in resonance frequency and the strong influence of collective resonances when the array has hundreds of bubbles covering more than half of the wavelength. These results are essential in understanding the low-frequency resonance characteristics of bubble ensembles, which have important applications in diverse fields such as underwater acoustics, quantum physics, and metamaterial design.

Acoustically driven translation of a single bubble in pulsed traveling ultrasonic waves

The acoustic radiation force has been proven as an effective mechanism for displacing particles and bubbles, but it has been mainly applied in a standing wave mode in microfluidics. Alternatively, the use of pulsed traveling acoustic waves could enable new options, but its transient dynamic, which entails the additional complexities of pulse timing, reflections, and the type of waveform, has not yet been fully investigated. To better understand these transient effects, a transient numerical solution and an experimental testbed were developed to gain insights into the displacement of microbubbles when exposed to on- and off-periods of pulsed traveling waves. In this study, a practical sinusoid tone burst excitation at a driving frequency of 0.5 MHz is investigated. Our numerical and experimental results were found to be in good agreement, with only a 13% deviation in the acoustically driven velocity. With greater detail from the numerical solution at a sampling rate of 1 GHz, the fundamental mechanism for the bubble translation was revealed. It was found that the added mass force, gained through the on-period of the pulse, continued to drive the bubble throughout the off-period, enabling a large total displacement, even in the case of low duty-cycle (2%) pulsing. In addition, the results showed greater translational velocity is possible with a lower number of cycles for the same input acoustic energy (constant duty cycle and acoustic pressure amplitude). Overall, this study proposes a new, practical, and scalable approach for the acoustic manipulation of microbubbles for scientific, biomedical, and industrial applications.

Modeling of a Single Bubble Dynamics at Boiling by Lattice Boltzmann Method

Modeling of a Single Bubble Dynamics at Boiling by Lattice Boltzmann Method

A Review of Drag Coefficient Models in Gas‐Liquid Two‐Phase Flow

AbstractAlthough great efforts have been made in modeling the drag force in gas‐liquid two‐phase flow, the research about that in both theory and method is at the stage of development due to its diversity and complexity, and previous summary work about drag is usually based on a certain aspect. In this review, a unified framework that guides the drag coefficient model in gas‐liquid two‐phase flow is provided. From simple to complex, this paper introduces the drag coefficient of solid particles, single bubbles, bubble swarms, and bubbles in turbulence moving in liquid in turn. The variables affecting the drag coefficient in each of the above situations and the relationship between the drag coefficient and these variables are mentioned.

Influencing mechanisms of gas bubbles on propagation characteristics of leakage acoustic waves in gas-liquid two-phase flow

Propagation speed of acoustic waves in liquid can be significantly degraded when gas bubbles exist. To reveal the influence of gas bubbles on propagation characteristics of leakage acoustic waves in liquid pipelines, numerical simulation is utilized in the present paper. It can be divided into three stages when leakage acoustic waves propagate through a single gas bubble and the influence of each stage on propagation characteristics of acoustic waves is discussed. In gas-liquid two-phase flow, there are two basic mechanisms of gas resistance on wave propagation: elastic resistance effect and drag resistance effect. The results show that the influence of elastic resistance effect on sound speed is much greater than that of drag resistance effect. When propagating through a long gas bubble with the radius of 2 mm and the length of 7 mm, the elastic resistance effect causes a time delay of 0.00038 s while the drag resistance effect only causes a time delay of 0.00002 s. The results of this paper contribute to better understanding of the differences in acoustic wave propagation characteristics between different flow patterns in gas-liquid two-phase flow, and lay a foundation for the utilization of acoustic leakage detection methods in gas-liquid two-phase flow pipelines.

Bubbles in biomass fluidized bed gasifiers: A phenomenological probabilistic predictive model

Bubble properties in fluidized beds including size, velocity, and path, vary randomly. This article proposes a new PPPM (Phenomenological Probabilistic Predictive Model) l, that allows one to establish a vrb-BAC prediction band, to describe bubble data, obtained in a lab scale biomass-sand fluidized bed, by using CREC Optiprobes. The PPPM, represents a significant improvement from an earlier Probabilistic Predictive Model (PPM) reported by Torres and de Lasa in 2021, with the new PPPM being based on a balance of forces including gravity, drag, buoyancy, and minimum fluidization excess velocity. The resulting PPPM bubble rise velocity (vrb) is obtained as a function of the bubble axial chord (BAC) and is specifically evaluated by studying bubbles in a high-density sand (above 2500 kg/m3) fluidized bed. The PPPM leads to a behavioral band showing a normal bubble frequency distribution that becomes increasingly skewed as the gas superficial velocity increases. The proposed PPPM is shown to be applicable to single bubbles in a sand bed at incipient fluidization and to multiple bubbles in a biomass-sand bubbling bed. The PPPM is validated in the present study, by comparing it against 46,000 bubbles, under different gas superficial velocities and biomass loadings. By using the PPPM, it is shown 91% of all bubbles studied fall within the PPPM prediction band. Given the demonstrated ability of the PPPM, it is anticipated that this model will significantly contribute to the development of large-scale multiphase biomass gasifier models.

Mechanism study of bubble dynamics under the buoyancy effects

The motion of a single bubble in a 2-D vertical channel filled with stagnant or moving fluid is simulated for various sets of conditions using the computational fluid dynamics(CFD) method. The volume of fluid (VOF) model is applied to track the interface of the bubble. Corresponding results are compared with experimental and theoretical studies, and good agreement is achieved. Two-phase flows composed of various fluids are simulated to check the impact of physical properties on bubble dynamics, and buoyancy is found to have a key influence on the bubble rising behavior, including both the trajectory and the terminal rising velocity. The dimensionless number Bu is introduced to characterize this effect, and a larger Bu leads to a larger bubble rising velocity. Three other dimensionless numbers Eo, We, and Mo are introduced to study the bubble deformation which can be characterized by aspect ratio E, and an approximately linear relationship is found between E, Eo, and bubble size. Inertial force is proved to influence the bubble motion significantly in moving fluid, whose velocity dominates the bubble terminal speed. The simulation of motion for two bubbles is also performed and investigated detailedly.

Revisiting secondary CMB distortions due to kinetic Sunyaev–Zel’dovich effect from quasar bubbles before reionization

ABSTRACT We discuss the secondary cosmic microwave background (CMB) anisotropy due to kinetic Sunyaev–Zel’dovich (kSZ) effect from ionized bubbles around individual quasars prior to the reionization of the Universe. The bubbles create local ionization modulations which move with the large-scale structure linear bulk flow and act as sources for kSZ. We improve upon previous calculations of this effect, using a halo model based description of quasar abundance, and find that the kSZ distortion power spectrum, Cℓ, from the bubbles to be sub-dominant to kSZ from patchy reionization driven by galaxies. However, the shape of the two Cℓ’s are very different with the quasar bubble Cℓ having a peak at ℓ ≈ 500–700 whereas the Cℓ due to patchy reionization flattening out at ℓ > 1000 thus making it plausible to separate the two using Cℓ template-fitting in a future survey like CMB-HD. Next, we look at the imprint of a single quasar bubble on the CMB and show that it can be detected in a high-resolution, ambitious effort like CMB-HD. A detection of a high redshift quasar bubble in the CMB would carry complimentary information to its detection in H i or Lyman-α and a joint analysis can be used to break parameter degeneracies.

Assessing the Mass Transfer Coefficient in Jet Bioreactors with Classical Computer Vision Methods and Neural Networks Algorithms

Development of energy-efficient and high-performance bioreactors requires progress in methods for assessing the key parameters of the biosynthesis process. With a wide variety of approaches and methods for determining the phase contact area in gas–liquid flows, the question of obtaining its accurate quantitative estimation remains open. Particularly challenging are the issues of getting information about the mass transfer coefficients instantly, as well as the development of predictive capabilities for the implementation of effective flow control in continuous fermentation both on the laboratory and industrial scales. Motivated by the opportunity to explore the possibility of applying classical and non-classical computer vision methods to the results of high-precision video records of bubble flows obtained during the experiment in the bioreactor vessel, we obtained a number of results presented in the paper. Characteristics of the bioreactor’s bubble flow were estimated first by classical computer vision (CCV) methods including an elliptic regression approach for single bubble boundaries selection and clustering, image transformation through a set of filters and developing an algorithm for separation of the overlapping bubbles. The application of the developed method for the entire video filming makes it possible to obtain parameter distributions and set dropout thresholds in order to obtain better estimates due to averaging. The developed CCV methodology was also tested and verified on a collected and labeled manual dataset. An onwards deep neural network (NN) approach was also applied, for instance the segmentation task, and has demonstrated certain advantages in terms of high segmentation resolution, while the classical one tends to be more speedy. Thus, in the current manuscript both advantages and disadvantages of the classical computer vision method (CCV) and neural network approach (NN) are discussed based on evaluation of bubbles’ number and their area defined. An approach to mass transfer coefficient estimation methodology in virtue of obtained results is also represented.

An ammonia flash break-up model based on bubble dynamics with force and energy analysis on droplet

Ammonia flash break-up model was developed using bubble dynamics based on force analysis of surface tension and pressure forces in this study. The initial bubble radius was calculated by modifying bubble number density equation considering the superheat degree with assuming a single bubble in the droplet. The Rayleigh–Plesset equation with compressibility factor was employed to calculate bubble growth in the liquid ammonia droplet. Droplet disintegration was predicted by force analysis. The velocity change by flash break-up was assumed to be a product of the surplus energy between the surface-energy change and the pressure work, and the bubble growth rate. The simulation results were compared to results in a previous experimental study of ammonia spray behavior. The time constant of the thermodynamic breakup model was added to simulate the flash boiling condition that induces rapid spray changes. In this study, the time constant 12 is used through the verification process. Compared with previous experimental results of ammonia flash boiling spray, the proposed flash breakup model was superior in predicting radial spray development by the flash boiling compared to the conventional aerodynamic breakup model.

Three-dimensional dynamics of a single bubble rising near a vertical wall: Paths and wakes

In order to clarify the migration mechanism and wake behavior of a single bubble rising near a vertical wall, three-dimensional direct numerical simulations are implemented based on the open-source software Basilisk and various types of migration paths like linear, zigzag and spiral are investigated. The volume of fluid (VOF) method is used to capture the bubble interface at a small scale, while the gas-liquid interface and high-velocity-gradient regions in the flow field are encrypted with the adaptive mesh refinement technology. The results show that the vertical wall has an obstructive effect on the diffusion of the vortex boundary layer on the surface of the bubble migrating in a straight line, and the resulting reaction force tends to push the bubbles away from the wall surface. For the zigzag or spiral movement of a bubble in the x-y plane, the perpendicular wall is an unstable factor, but on the contrary, the motion in the z-y plane is stabilized.

Разработка математической модели акустического источника, сопровождающего распад кавитационной каверны на схлопывающиеся пузырьки

Object and purpose of research. This paper is intended to develop a mathematical model of cavitation void fragmentation into separate collapsing bubbles as an acoustic source for further implementation in Logos software package. The study was performed on propeller models in cavitating environment. Subject matter and methods. Volume and quantity of bubbles appearing after fragmentation of a cavitation void on propellers, as well as amplitude and frequency properties of a single bubble collapse are studied as per CFD methods. Viscous flow properties are found from finite-volume (FVM) solution to unsteady Reynolds equations (RANS) closed by a biparametric semi-empirical turbulence model. The coefficients in the mathematical model of acoustic source thus obtained were calibrated through validation that included noise measurements at KSRC Cavitation Tunnel. Main results. This work included numerical simulation of collapse dynamics for a single cavitation bubble at different initial conditions, with approximation of the pressure impact created by bubble collapse in the infinite fluid and near a solid wall. The study estimated volume and quantity of the bubbles created by the fragmentation of cavitation void on propellers (3 propellers of different shape operating at different advance ratios and cavitation numbers). The mathematical model representing above-mentioned process could be further implemented in Logos software as a finite-volume algorithm with k-ω SST turbulence model. The study also created a validation base for further testing and calibration of the mathematical model thus developed. Conclusion. The study was performed as part of project Mathematical simulation on exa- and zetaflops class supercomputers launched by National Centre for Physics and Mathematics (Russia). The analysis of obtained results has shown that the mathematical model suggested in this paper does have practical potential, but it needs additional empirical data for greater flexibility and more accurate estimates. Without this model, these practical tasks still could be handled but at a cost of considerable and, most importantly, unnecessary increase in required hardware resources.

An AMR-Based Liquid Film Simulation with Surfactant Transport Using PLIC-HF Method

In this study, an AMR-PLIC-HF method is proposed and implemented by GPU parallel computing based on CUDA programming language and NVIDIA GPU. The present method improves the computation efficiency without compromising the accuracy and conservation of the volume. To satisfy the requirements of stencil points of the PLIC-HF method, an extended stencil computation method based on the tree-based AMR method is proposed and implemented. The Weakly Compressible Scheme (WCS) is used in the present work as a fluid solver. An evolving pressure projection method is adopted to suppress the oscillation induced by the reflection of acoustic waves. The Langmuir model is introduced into the solver to calculate surfactant transport and the Marangoni effect caused by the gradient of the interface concentration of the surfactant. The single vortex flow results verify the accuracy of the AMR-PLIC method. A single bubble rising problem with two different physical property settings is simulated. The results show good agreement with the results given by incompressible solvers. This verifies the accuracy of the two-phase flow solver including the AMR-PLIC-HF method and the WCS. The generation and rupture of liquid film by a single bubble freely rising to an interface is simulated by the present solver with a 1024×2048 AMR grid as the finest resolution. This simulation successfully calculates surfactant transport and the Marangoni effect.

The effect of bulk viscosity on single bubble dynamics and sonoluminescence

In our previous paper, we derived a new single bubble model including the effect of bulk viscosity. To confront it to experiments, single bubble dynamics was measured here in 30% (v/v) glycerol-water mixture under different acoustic amplitudes and compared to models including or not the effect of bulk viscosity. The results showed that calculated bubble dynamics were not significantly affected by the bulk viscosity within the experimental conditions used in this study. However, there was a noticeable delay for the first rebound when bulk viscosity was considered. The corresponding sonoluminescence intensities were collected and compared with theoretical predictions. The results did not allow to discriminate between the two models (one includes the effect of bulk viscosity, the other does not), confirming the negligible effect of bulk viscosity in this condition (30% (v/v) glycerol-water mixture). Due to the instability of a single bubble in higher viscosity solutions, we could not implement experiments that can discriminate between the two models.

Cavitation bubble dynamics and microjet atomization near tissue-mimicking materials

In recent years, considerable interest has been devoted to the interactions between cavitation bubbles and tissue-mimicking materials due to their promising applications in medicine and biomedical sciences. The strong fluid–structure interaction between a cavitation bubble and these elastic surfaces triggers unique collapse dynamics, characterized by bubble splitting and subsequent microjetting phenomena that can damage adjacent boundaries. In this work, we investigate how the elasticity of the boundary and the distance between the bubble and the elastic surface affect the bubble dynamics and the velocity of its microjet. To this end, we generate single laser-induced cavitation bubbles in the vicinity of agarose hydrogels with different degrees of elasticity and follow the bubble dynamics using high-speed imaging techniques, with a special focus on the formation and evolution of the microjets. We provide a time-resolved evidence of the atomization of the liquid microjet within the bubble, which precedes the establishment of a fully liquid microjet. The atomized portion of the microjet can reach supersonic velocities of up to 2000 ms−1, while the ensuing fully developed liquid microjet travels at averaged speeds of up to 1000 ms−1. To gain further insight into the bubble dynamics leading to the formation of these very fast microjets, we also propose a numerical model based on the boundary integral method and observe a remarkable agreement between the numerical simulations and the experimental observations.

Interaction of a single bubble and an elastic plate: Influence of the standoff distance

The objective of this study was to investigate the coupled dynamics of a collapsing bubble and the motion of a nearby elastic plate at different initial distances. This was achieved using a combination of experimental and computational models. In the experiments, high-speed photography was used to record the temporal and spatial evolution of the collapse of a single bubble near an elastic boundary under normalized standoff distances γ ranging from 1.0 to 3.3. Digital image correlation was used to synchronously record the motion of the elastic plate. For the numerical simulations, taking the fluid compressibility and boundary motion into account, the immersed-boundary method was introduced to simulate the interaction between the elastic plate and bubble collapse. The results show that, with different initial distances, the dynamic behaviors of the bubble, including oscillation time, impact mode, and energy conversion, are different, and this is caused by the elastic rebound of the plate. In addition, the direction and amplitude of the deformation of the elastic plate are also influenced by the impact effects during bubble oscillation and rebound. The combined form of these impact behaviors changes with initial distance, and there are three typical impact patterns: the shock-wave effect, jet-effect, and hybrid shock-wave and jet-effect modes. In particular, when γ < 1.5, the jet effect and hybrid impact forms, which are dominated by the high-speed jet, can result in asymmetric deformation and cause greater local damage to the elastic plate. Finally, we summarize the combined mechanisms that govern the impact of a collapsing bubble on an elastic plate.

Daisy-shaped liquid bridges in foam-filled granular packings

HypothesisMany applications of liquid foams use them to fill the porosity of various granular media. How is the liquid distributed in such foam-filled systems, in which the geometry of the bubble assembly can be strongly constrained by pore confinement? ExperimentsWe study how the liquid is distributed in a grain packing filled with liquid foam, as a function of both liquid content and bubble-to-grain size ratio. Moreover, Surface Evolver simulations are carried out at the scale of a single bubble confined into a tetrahedral pore. FindingsWe reveal that foam-filled granular assemblies exhibit a robust pendular-like regime, which is reminiscent of the pendular regime in unsaturated media. The main difference is that here the liquid bridges are daisy-shaped, i.e. with a liquid core bounded by bubbly petals. A simple theoretical model is proposed to describe the foam liquid bridges between contacting grains. In the case of large bubbles, the model is compared with the Surface Evolver simulation. The model is also applied to the case of wall liquid bridge, which is compared with the experimental observation. Beyond their geometrical characteristics, the presence of these liquid bridges, which can represent almost 25% of the liquid contained in the porosity, makes it possible to imagine a new approach (binder foam-based) to bind granular assemblies and turn them to solid materials.

Numerical simulation of bubbly flows by the improved lattice Boltzmann method for incompressible two-phase flows

Bubbly flow problems are simulated to verify the effectiveness of the improved lattice Boltzmann method for incompressible two-phase flows. In this method, it is possible to compute two-phase fluid flows with high density ratios accurately and efficiently compared with the previous method. Firstly, we simulate a stationary bubble to investigate the accuracy of the interfacial tension. As a result, the calculated pressure differences are in good agreement with the theoretical predictions, and the relative errors of the pressure difference are less than 5%. Secondly, we simulate a single bubble rising in a liquid under gravity. It is found that the terminal bubble shapes and Reynolds numbers are in good agreement with available numerical and experimental data. Thirdly, we simulate two bubbles rising in a liquid under gravity for different initial arrangements. It is found that the bubble shapes and transient Reynolds numbers during the coalescence process are generally in agreement with the available numerical results. Finally, we simulate typical slug and churn flows in a square duct. It is found that transition from slug flow to churn flow occurs when the pressure difference between inlet and outlet of the duct is increased. In addition, it is found that square ducts with larger width tend to generate churn flows. These results demonstrate that the present method is applicable to complicated bubbly flow problems.

Numerical Studies of Bubbles in Swirling Channel Flows

Abstract The motion of bubbles in upflow in a vertical rotating closed channel is examined numerically, using a front tracking/finite volume method. The flow is driven upward by a constant pressure gradient. The Reynolds number is low enough so that the flow remains laminar and the Eötvös number is sufficiently low so the bubbles remain nearly spherical. A bubble is placed between the centerline and the walls and for low rotation rate the bubble moves to a wall, due to the lift force and the fluid shear near the walls, but for higher rotation rate the bubble moves to the center of the channel, due to the radial pressure gradient established by the rotation. For intermediate rotation rates, we find bubbles where the lift force and the pressure gradient balance and the bubbles remain between the centerline and the walls. We also examine the collective motion of a few bubbles and show that their dynamics are similar to what is observed for a single bubble.

Impact-driven cavitation bubble dynamics

The dynamics of a single cavitation bubble exposed to a transient acceleration is studied experimentally. A single cavitation bubble is seeded with a pulsed laser in a free-falling and impacting water-filled test tube. After impact, a pressure wave containing compression and rarefaction phases is generated and interacts with the bubble. The bubble dynamics is studied with high-speed imaging and compared to numerical simulations using the Keller–Miksis model. The timing of bubble seeding with respect to the pressure wave is varied, and a regime of enhanced collapse strength is found.