Nearby Bubbles Research Articles

Modeling the chaotic dynamics of bubble growth under hydrodynamic interactions in pool boiling

This study seeks to understand the origins of intermittency in quantities of interest in pool boiling, such as bubble departure diameter and growth time. The intermittency of nucleation site activity due to hydrodynamic and thermal interactions with nearby nucleation sites is well-established; however, few mechanistic models have been developed that predict such intermittency. Here we assume a fluctuating pressure field at a nucleation site due to an adjacent bubble which alters bubble growth depending on the phase of the pressure oscillation with respect to the instant of bubble nucleation. The results suggest that even when a single departure frequency is assumed for nearby bubbles, its effect on the nucleation site being considered causes aperiodicity and intermittency in bubble departure quantities. The effects of pressure field phase angle, degree of superheat, and choice of force balance model on the bubble departure quantities are examined. The phase angle is shown to play a major role in determining bubble departure diameter and growth time. The departure diameter is observed to have a broad distribution, belying the assumption of a unique value. Period doubling of the ebullition cycle is observed for some conditions, a phenomenon documented by other investigators. A multifractal analysis of the time series of departure events indicates the presence of long term temporal correlations, which become weaker with increasing superheat. The second order Hurst exponent of the structure functions of departure events appears to have a universal behavior with Jakob number, independent of the choice of liquid. The Hurst exponent rises from zero to a value close to 0.5 at large superheats, suggesting a continuous transition from an ordered state to a disordered state along the boiling curve.

Simulation of bubble oscillations in cavitation-induced acoustic fields

Understanding bubble oscillations is critical in science, engineering and medicine. An important aspect of bubble dynamics is the transition from spherical to non-spherical oscillations when the bubble is subjected to external stimuli like time-dependent pressure fields. The mechanisms underpinning this process are not well understood for the complex pressure fields encountered in most applications. Here, we perform high-fidelity numerical simulations of the oscillations of a non-condensable gas bubble induced by the acoustic field generated by the collapse of a nearby cavitation bubble. We compare our simulation results with controlled laboratory experiments and demonstrate that our computational approach predicts spatial and temporal bubble oscillation patterns. This work opens new opportunities to understand the oscillation of bubbles induced by complex acoustic fields.

Cleaning effects due to shape oscillation of bubbles over a rigid boundary

Recent experiments have revealed the interesting cleaning effects that take place due to the shape mode oscillation of bubbles over a rigid boundary. While a microbubble was undertaking shape oscillation moving over a bacterial biofilm, it removed the contaminants from the boundary and created a clean path through the biofilm. This demonstrated much higher cleaning efficiency than that associated with the volume oscillation of cavitation bubbles; however, the mechanism is unknown. Here, we study this phenomenon using the boundary integral method with the viscous effects modeled using the viscous potential flow theory and the compressible effects using the weakly compressible theory. The viscous stress at the rigid boundary is approximated using the boundary layer theory. We observed that the natural frequencies of shape mode oscillation decrease significantly due to the presence of the boundary. The shear stress at the boundary due to the shape oscillation of a nearby bubble is at least 20 times higher than that due to volume oscillation with the same energy and is significant only within the area directly beneath the bubble. This is explained by the notably faster decay for higher shape modes of the kinetic energy in the fluid as the distance to the center of the bubble r increases with the induced velocity of mode k decaying at a rate of O(r−(k+2)) away from the bubble. These results achieve excellent agreement with the intriguing cleaning effects first observed in the experiment and explain the mechanism behind this new highly efficient method of cleaning.

Numerical investigation on boiling heat transfer in a rectangular channel under sub-atmospheric environment

Water evaporators are often used as heat sinks in spacecraft. The aim of this study is to investigate the heat transfer characteristics and the spatial and temporal characteristics of bubble formation in an airborne water evaporator at an absolute pressure of 7 KPa. In order to achieve this, a rectangular single-channel model based on the structure of the water evaporator is established. Since the temperature change of the glycol in the water evaporator is not obvious when it flows through the rectangular single-channel, the inner wall surface is set to be 333.15 K in order to reduce the computational cost in the simulation. In this paper, a VOF method is adopted to numerically investigate the heat transfer characteristics of the boiling in the upper pool of the rectangular channel under a low-pressure(7 kPa) environment. Good agreement was obtained by comparing the numerical results with the experimental data with the error within 6 %. The numerical results show that bubbles rise along the wall, combine with nearby small bubbles, grow and attach to the wall, and slide along the wall until they are discharged from the top of the wall. The perturbations generated by the bubbles cause the heat transfer coefficient and wall temperature to fluctuate, with the maximum fluctuation of the wall temperature being around 5 K. In addition, the effects of different rectangular channel structure sizes (0.5 mm, 1.5 mm, and 2.5 mm) on the boiling heat transfer and bubble characteristics were investigated. A channel size of 0.5 mm leads to severe bubble coalescence, which increases the wall temperature and deteriorates the heat transfer performance. When the channel spacing is increased, bubble coalescence is improved, but a channel spacing of 2.5 mm results in less bubble turbulence and weaker heat transfer performance.

Experimental study on the effect of the sawtooth nozzle structure on bubble behaviors

The initial formation of bubbles has a significant impact on bubble dynamics and acoustics. Meanwhile, the bubble initial shape is affected by the nozzle boundary. In this study, the processes of bubble generated from sawtooth nozzles have been investigated by means of controlled experiments. A three-dimensional visualization imaging system is used to study bubble behaviors. The morphology and the time-frequency spectrum of the sound pressure signal are analyzed synchronously. Moreover, the effects on bubble trajectory are also studied. Results show that sawtooth nozzle is not conducive to bubble detachment, resulting in larger bubble diameters than the circular nozzle. With the gas flow rate increasing, bubble diameter increases. When the gas flow rate reaches a certain critical value, the surface tension is not sufficient to support the continued development of bubble size. Due to effect of the sawtooth structure, bubbles tend to break in the necking stage, accompanying by small bubbles. The generation of accompanying bubbles lead to the irregular generation of nearby bubbles. This study aims to reveal the effect of sawtooth nozzle structure on the initial formation of bubbles, so as to predict the flow patterns and sound signal characteristics of the bubbles.

Numerical Investigation on Influence of Number of Bubbles on Laser-Induced Microjet

In this study, the impact of the number of bubbles on the velocity of laser-induced microjet is numerically investigated, focusing on the pressure wave propagation generated by multiple laser-induced bubbles. First, we show that the microjet velocity increases with the increasing impulse of the pressure wave propagating to the meniscus direction. This result indicates that it is possible to study the structure of the pressure field generated from bubbles to investigate the effect on microjet generation. In addition, it is found that the microjet is weakened with the increase in the number of bubbles. Next, we show that the propagation of the pressure waves has two types. The first type is propagating from a bubble to a meniscus. The second type is propagating round trip between nearby bubbles or by the bubble itself. Finally, we explain the reason for the decrease in the microjet velocity with the increasing number of bubbles by an expansion history of the bubbles, which depends on their interaction with the pressure waves. These results could help to design not only laser-induced microjet generation but also devices that use laser-induced bubbles generated in a microchannel.

Cavitation bubble interaction with compliant structures on a microscale: A contribution to the understanding of bacterial cell lysis by cavitation treatment

Numerous studies have already shown that the process of cavitation can be successfully used for water treatment and eradication of bacteria. However, most of the relevant studies are being conducted on a macro scale, so the understanding of the processes at a fundamental level remains poor. In attempt to further elucidate the process of cavitation-assisted water treatment on a scale of a single bubble, the present paper numerically addresses interaction between a collapsing microbubble and a nearby compliant structure, that mechanically and structurally resembles a bacterial cell. A fluid–structure interaction methodology is employed, where compressible multiphase flow is considered and the bacterial cell wall is modeled as a multi-layered shell structure. Simulations are performed for two selected model structures, each resembling the main structural features of Gram-negative and Gram-positive bacterial cell envelopes. The contribution of two independent dimensionless geometric parameters is investigated, namely the bubble-cell distance δ and their size ratio ς. Three characteristic modes of bubble collapse dynamics and four modes of spatiotemporal occurrence of peak local stresses in the bacterial cell membrane are identified throughout the parameter space considered. The former range from the development of a weak and thin jet away from the cell to spherical bubble collapses. The results show that local stresses arising from bubble-induced loads can exceed poration thresholds of cell membranes and that bacterial cell damage could be explained solely by mechanical effects in absence of thermal and chemical ones. Based on this, the damage potential of a single microbubble for bacteria eradication is estimated, showing a higher resistance of the Gram-positive model organism to the nearby bubble collapse. Microstreaming is identified as the primary mechanical mechanism of bacterial cell damage, which in certain cases may be enhanced by the occurrence of shock waves during bubble collapse. The results are also discussed in the scope of bacteria eradication by cavitation treatment on a macro scale, where processes of hydrodynamic and ultrasonic cavitation are being employed.

Effects of adjacent bubble on spatiotemporal evolutions of mechanical stresses surrounding bubbles oscillating in tissues

The cavitation dynamics and mechanical stress in viscoelastic tissues, as the primary mechanisms of some ultrasound therapies, are extremely complex due to the interactions of cavitation bubble with adjacent bubbles and surrounding tissues. Therefore, the cavitation dynamics and resultant mechanical stress of two-interacting bubbles in the viscoelastic tissues are numerically investigated, especially focusing on the effects of the adjacent bubble. The results demonstrate that the mechanical stress is highly dependent on the bubble dynamics. The compressive stress and tensile stress are generated at the stage of bubble expansion and collapse stage, respectively. Furthermore, within the initial parameters examined in this paper, the effects of the adjacent bubble will distinctly suppress the radial expansion of the small bubble and consequently lead its associated stresses to decrease. Owing to the superimposition of two stress fields, the mechanical stresses surrounding the small bubble in the direction of the neighboring bubble are smaller than those in other directions. For two interacting cavitation bubbles, the suppression effects of the nearby bubble on both the cavitation dynamics and the stresses surrounding the small bubble increase as the ultrasound amplitude and the initial radius of the large bubble increase, whereas they decrease with the inter-bubble distance increasing. Moreover, increasing the tissue viscoelasticity will reduce the suppression effects of the nearby bubble, except in instances where the compressive stress and tensile stress first increase and then decrease with the tissue elasticity and viscosity increasing respectively. This study can provide a further understanding of the mechanisms of cavitation-associated mechanical damage to the adjacent tissues or cells.

Influence of rigid wall on the nonlinear pulsation of nearby bubble

This paper mainly focuses on the nonlinear pulsation of a bubble near the rigid wall. Dynamics of near-wall bubble and free bubble are discussed and compared in details. Investigation reveals as the driving acoustic pressure amplitude increases, nonlinear pulsation of bubble becomes intense gradually. Besides, decreasing the viscosity of host liquid is advantageous for the nonlinear pulsation of bubble. Bifurcation diagrams of bubble radius show acoustic reflection of the rigid wall makes the initial bifurcation appear at low driving acoustic amplitude and on bubble with small ambient radius, and makes the bifurcation still exist for bubble in high-viscosity liquids. That indicates the rigid wall will produce enhancement on the nonlinearity of nearby bubble. As the bubble approaches the wall, the enhancement becomes strong. Moreover, research on the influence of driving frequency shows the rigid wall makes the frequency band corresponding to chaos around the resonant frequency of free bubble shift downward.

Investigating the resonance response of a system of two ultrasound-driven lipid encapsulated microbubbles

Ultrasound-stimulated microbubbles are clinical imaging agents and being developed for therapeutic applications. Here, we aim to understand the behaviour of two individual phospholipid-encapsulated microbubbles in close proximity to each other, typically the case given clinical doses. We developed a finite element model to study the radial resonance response of each microbubble within a two-microbubble system from 1–8 MHz with bubble diameters ranging from 2 to 4 μm, bubble center-to-center distances h = 8–24 μm, and peak-negative pressures of 30–45 kPa. For two identical microbubbles, our results show the frequency of maximum response (fMR) decreases (7%–10%) and the amplitude of maximum response (AMR) increases (9%–11%) as the microbubbles approach one another. For a two-bubble system of different microbubble sizes, the larger microbubble shows no change in fMR and a slight shift of AMR (2–3%). However, the smaller microbubble exhibits an increase in fMR (7–11%) and a significant decrease of AMR (38–52%). Furthermore, when in very close proximity (h = 8 μm), smaller bubbles exhibit a secondary resonance peak corresponding to the fMR of the larger bubble with amplitudes comparable to its primary resonance peak. Our work suggests that microbubble resonance behaviour is greatly affected by the presence of nearby bubbles, which has implications in imaging and therapy.

Fluid–structure modelling for material deformation during cavitation bubble collapse

The dynamics of cavitation bubbles and their interaction with solids has been studied for long, mostly on the macro-scale of sheet and vortex cavitation. Erosion takes place on small, concentrated areas of solid walls exposed to cavitation. One-way fluid structure interaction (FSI), in which the feedback of material deformation on the fluid is not considered, provides an adequate understanding of the underlying mechanism. However, in practical applications the solid material motion and deformation can significantly affect the bubble dynamics. This will, in principle, alter the structural loading, stresses and erosion in the solid. In this paper, we will report comparisons of one-way and two-way coupled FSI modelling using our finite volume based fluid solver YALES211http://yales2.coria-cfd.fr. and finite element based solid solver Cast3M.22http://www-cast3m.cea.fr. In two-way FSI coupling, the feedback of the solid wall deformation is considered in the fluid domain. To do so, we develop a compressible fluid solver with Arbitrary Lagrangian–Eulerian formulation to equip it with moving mesh capabilities in order to maintain a continuous fluid–solid domain. We present results using a step-wise coupling approach for two-way FSI and analyse the effects due to structural response on bubble dynamics and damping of impact pressures by different materials. Finally, we discuss our understanding on the need for one-way and two-way FSI modelling based on structural characteristics which can significantly affect the material erosion by nearby cavitation bubbles.

Experimental study of the motion characteristics of a bubble near a flexible structure with an attached air bubble

The strong coupling effect between an air bubble attached to a flexible plate and a nearby spark-generated bubble is investigated experimentally while also considering the structural deformation of the plate. Numerous interesting and complex bubble behaviors that depend strongly on the attached air bubble and deformation effect of the structure are observed with a high-speed camera. A multitude of bubble jet behaviors are observed during the two bubble pulsations, such as bubble splitting, jets away from the plate, jets toward the plate, upward and downward movement after splitting, and splitting after the coalescence of the two bubbles. Moreover, the attached air bubble can appear hemispherical, mushroom-shaped, or cup-shaped. To gain a better understanding of the interaction between the bubble and the flexible boundary, the displacement time history curves at the center point of the flexible structure and at the top and bottom vertices of the bubble are obtained. The motion response mode of the flexible plate under bubble loading is explored to summarize the deformation pattern of the flexible structure and the motion characteristics of the bubble. An air bubble attached to the flexible structure can change the motion characteristics of the spark-generated bubble to some extent.

High-speed photography and image analysis of orbital motion of gas bubbles in ultrasonic field

Bubbles in the fluid have a great influence on the macroscopic physical properties and flow state of the fluid. The study of bubble motion in fluid is of great significance to ultrasonic cleaning, sonochemistry, flood discharge and energy dissipation, aeration and cavitation reduction. Bubbles in the fluid may also exhibit a special translational motion in an ultrasonic field—orbital motion. The orbital motions of gas bubbles attached to a boundary in ultrasonic field are investigated experimentally by high-speed photography and image analysis. The present study focuses on the trajectories of wandering bubbles, the arrangement of gas bubble array, the source of gas bubbles and the surface fluctuation details of gas bubbles. It is found that the circular trajectory of the wandering gas bubble is unstable, irregular and unsmooth. The holding gas bubbles in the bubble array originate from wandering bubbles. The transformation of wandering bubbles into array bubbles is mainly realized by merging and increasing the volume, thereby reducing the Bjerknes force. The wandering bubbles are produced by the merging of a large number of cavitation bubbles in the ALF (acoustic lichtenberg figure) structure, which makes the radial vibration bubbles gradually transform into the surface fluctuating bubbles. Under the action of Bjerknes force, the array bubbles show regular surface fluctuations, while the smaller ones are completely unstable, showing extremely irregular morphology, and have an influence on the surface fluctuation of nearby array bubbles. The array bubbles show a very regular arrangement, and the adjacent array bubbles have opposite vibration phases and repel each other. The orbital motion of gas bubbles attached to a boundary is significantly different from that of the bubbles suspended in liquid. First of all, the attached bubbles move along the solid wall, while the suspended bubbles move completely away from the vessel wall in the liquid. Secondly, the attached bubbles move around a regular array of bubbles, while the suspended bubbles move orbitally alone. In addition, the attached bubble is nearly hemispherical, and its surface fluctuates violently, and its motion track is extremely unsmooth, which is different from the circular motion of spherical suspended bubble. Finally, there is a strong interaction between the attached wandering bubble and the array bubble, which has a great influence on the vibration and trajectory of the attached bubble. In contrast, the circular motion of the suspended bubble does not have such a complex effect.

Corrigendum and Addendum: Helium flux effects on bubble growth and surface morphology in plasma-facing tungsten from large-scale molecular dynamics simulations (2019 Nucl. Fusion 59 066035)

Two of the simulations discussed in a prior article (Hammond et al 2019 Nucl. Fusion 59 066035) were affected by a simulation glitch. We repeated the affected calculations and discuss them here. The overall conclusions are essentially unchanged, though the details are different. In particular, observations that we referred to as ‘concerted bursting’ were caused primarily by non-physical heating and cooling applied by the thermostat after most atoms’ velocities were deleted (for reasons that are not known for certain). The phenomenon of one bubble bursting and causing another nearby bubble to burst does exist, though its effects are much less spectacular in the absence of non-physical driving forces. The observation of an interconnected network of sub-surface cavities formed by burst bubbles is real, and the observation of holes on the surface 1–2 nm in diameter is also confirmed.

Simulation study of helium bubble coalescence in tungsten at various temperatures relevant to fusion conditions

Molecular dynamics (MD) methods are used to study nanosized helium (He) bubble coalescence process in tungsten (W) at various temperatures relevant to fusion conditions, on an atomistic scale. Bubble coalescence in W is observed at a higher temperature and He/V ratio, while the calculated internal bubble pressure due to virial stress increases with the increase in the He/V ratio; bubble coalescence is significantly dependent on the bubble distance. In these MD simulations, coalescence occurs, only when the surface distance between the two bubbles is equal to 1a0, where a0 denotes the lattice constant and is approximately 0.317 nm at 2100 K. On the other hand, a bubble diameter between 1a0 and 3a0 may have relatively limited effect on the coalescence, although larger-sized bubbles may have higher migration energy. Local stress profile calculated indicates that initial bubbles can interact with each other, which may enhance the He atoms diffusion between bubbles and their coalescence. Physical contact at the initial stage of coalescence may occur between two nearby bubbles accompanied by W lattice distortion because of the limited displacement of W atoms near the bubbles and rapid migration of He atoms within the two bubbles. These results are beneficial for understanding the evolution of He bubbles in bulk W.

A Clustering-Based Bubble Method for Generating High-Quality Tetrahedral Meshes of Geological Models

High-quality mesh generation is critical in the finite element analysis of displacements and stabilities of geological bodies. In this paper, we propose a clustering-based bubble method for generating high-quality tetrahedral meshes of geological models. The proposed bubble method is conducted based on the spatial distribution of the point set of given surface meshes using the clustering method. First, the inputted geological models consisting of triangulated surface meshes are divided into several parts based on spatial distribution of point set, which can be used for the determination of the positions and radii of initial bubbles. Second, a procedure based on distance of nearby bubbles is used to obtain the initial size of bubbles. Third, by enforcing the forces acting on bubbles, all bubbles inside the 3D domain reach an equilibrium state by the motion control equations. Finally, the center nodes of the bubbles can form a high-quality node distribution in the domain, and then the required tetrahedral mesh is generated. Comparative benchmarks are presented to demonstrate that the proposed method is capable of generating highly well-shaped tetrahedral meshes of geological models.

Modulation of the secondary Bjerknes force in multi-bubble systems.

The behaviours of insonated bubble clusters are regulated by the secondary Bjerknes force between bubble pairs. While the force has been investigated extensively for two-bubble systems, the modulation of the force by nearby bubbles remains unclear. This problem is investigated in this paper by theoretical analyses and numerical simulations of a three bubble system. For weak oscillations, the third bubble is found to have strong effects when its radius is close to the resonant radius. The equilibrium distance between the bubble pair is reduced when the radius of the third bubble is smaller than the resonant threshold, and increased when it is larger. For strong oscillations of bubbles with radii of a few microns, the third bubble reduces the magnitude of the force, hence increasing the equilibrium distance. The modulation effects depend strongly on the relative sizes of the bubbles. Stronger effects can be produced when the third bubble is placed closer to the smaller bubble in the bubble pair. The findings highlight the need for a more accurate parametrization of the secondary Bjerknes force in the simulation and manipulation of bubble clusters.

Photon number conservation and the large-scale 21 cm power spectrum in seminumerical models of reionization

Seminumerical models of the reionization of neutral hydrogen (HI) based on the excursion set (ES) approach are known to violate photon number conservation at the few per cent level. In this work, we highlight a more severe, previously unrecognized shortcoming of ES models: the large-scale 21 cm power spectrum (equivalently, H i bias |$b_{\rm H\, \small {I}}$|⁠) is a relatively strong function of the spatial resolution used to generate ES ionization maps. We trace this problem to the fact that photon non-conservation in these models arises from a resolution-dependent mixture of spatially resolved, photon non-conserving bubbles, and partially ionized grid cells which are perfectly photon conserving (PC) by construction. We argue that this inevitably leads to a resolution dependence of |$b_{\rm H\, \small {I}}$|⁠, with the correct, converged value only emerging at very coarse resolution. Quantitatively, we find that |$b_{\rm H\,{\small I}}$| can be non-converged by as much as ∼20–|$25{{\ \rm per\ cent}}$| in conservative ES implementations with grid sizes Δx = 5–10h−1cMpc, even when photon non-conservation is as small as ∼3–|$4{{\ \rm per\ cent}}$|⁠. Thus, although numerically efficient, ES ionization maps coarse enough to produce a converged H i bias would wash out all topological features of the ionization field at scales |$k\gtrsim 0.05\, h{^{-1}}$|cMpc. We therefore present a new, explicitlyPC seminumerical algorithm which distributes photons isotropically around sources while also accounting for anisotropic overlaps between nearby bubbles. Our PC algorithm predicts a resolution-independent value of |$b_{\rm H\,{\small I}}$| consistent with the result of low-resolution ES maps, thus serving as a useful compromise between standard ES implementations and more expensive radiative transfer simulations.

Dynamics and Stability of Air Bubbles in a Porous Medium

A numerical method is developed for reliably computing the evolution of the boundary of a multiply connected water-saturated domain with air bubbles in the case when the pressure inside them depends on the bubble volume. It is assumed that the distance between the gas bubbles is comparable with their size. Gas bubbles can be near an extended phase transition boundary separating a porous medium flow and a domain saturated with a mixture of air and water vapor. The numerical method is verified by comparing the numerical solution of a test problem with its analytical solution. Caused by finite-amplitude perturbations of the phase interface, the deformation of an air bubble in an extended horizontal water-saturated porous layer with a constant pressure gradient is studied. It is shown that the instability of the bubble boundary with respect to finite perturbations leads to the splitting of the bubble. An analysis of the numerical solution shows that, although all circular bubbles move at the same velocity irrespective of their size, nevertheless, due to instability, a portion of the bubble boundary where the air displaces the fluid moves faster than an opposite portion where the fluid displaces the air. As a result, nearby bubbles are capable of merging before splitting.

STUDYING THE INTERSTELLAR MEDIUM AND THE INNER REGION OF NPS/LOOP 1 WITH SHADOW OBSERVATIONS TOWARD MBM36

ABSTRACT We analyzed data from a shadow observation of the high density molecular cloud MBM36 (l ∼ 4°, b ∼ 35°) with Suzaku. MBM36 is located in a region that emits relatively weakly in the 3/4 keV band compared to the surrounding North Polar Spur (NPS)/Loop 1 structure and the Galactic Bulge (GB). The contrast between high and low density targets in the MBM36 area allows one to separate the local and distant contributors to the soft diffuse X-ray background, providing a much better characterization of the individual components compared to single pointing observations. We identify two non-local thermal components, one at kT ≈ 0.12 keV and one at kT ≈ 0.29 keV. The colder component matches well with models of emission from the higher latitude region of the GB. The emission of the warmer component is in agreement with models predicting that the NPS is due to a hypershell from the center of the Milky Way. Geometrical and pressure calculations rule out a nearby bubble as responsible for the emission associated with the NPS. Any Galactic Halo/circumgalactic halo emission, if present, is outshined by the other components. We also report an excess emission around 0.9 keV, likely due to an overabundance of Ne ix.