Identical Bubbles Research Articles

Star formation in shells of colliding multi-SNe bubbles

Abstract It is believed that when bubbles formed by multiple supernovae explosions interact with one another, they stimulate star formation in overlapping shells. We consider the evolution of a shocked layer formed by the collision of two identical bubbles each of which originated from OB clusters of ∼ 50 members and ∼ 50 pc. The clusters are separated by 200-400 pc.We found that depending on evolutionary status of colliding bubbles the shocked layer can either be destroyed into diffuse lumps, or be fragmented into dense clumps: the former occurs in collisions of young bubbles with continuing supernovae explosions, and the latter occurs in older bubble interactions.We argue that fragmentation efficiency in shells depends on external heating: for a heating rate <∼ 1.7×10−24 erg s−1 the number of fragments formed in a collision of two old bubbles reaches several tens at t ∼ 4 Myr, while a heating rate >∼ 7 × 10−24 erg s−1 prevents fragmentation. The clumps formed in freely expanding parts of bubbles are gradually destroyed and disappear on t <∼ 1 Myr,whereas those formed in the overlapping shells survive much longer. Because of this the number of fragments in an isolated bubble begins to decrease after reaching a maximum, while in collision of two old bubbles it fluctuates around 60-70 until longer than t ∼ 5 Myr.

Study on the interactions between two identical oscillation bubbles and a free surface in a tank

A boundary element method based on the incompressible potential flow theory is adopted to investigate the interaction between two identical oscillating bubbles and a free surface in a tank. An axisymmetric numerical model is established, and certain numerical techniques are proposed to address coefficient matrix singularity and fluid-structure intersection. Experiments with spark-generated bubbles in a cylindrical tank recorded by a high-speed camera are conducted, and the numerical results are validated. On this basis, a typical case of bubbles interacting with a free surface in a tank with relatively small inter-bubble and bubble-free surface distances is carefully studied. A crown-shaped water column at the free surface is observed both numerically and experimentally. The maximum volume of the lower bubble is found to be much larger than that of the upper one. The effects of the inter-bubble and bubble-wall distances on bubble dynamics and free surface motion are analyzed. The results can provide a useful reference for underwater explosion experiments in the confined fluid field.

Effective Medium Theory for Acoustic Waves in Bubbly Fluids near Minnaert Resonant Frequency

We derive an effective medium theory for acoustic wave propagation in a bubbly fluid near the Minnaert resonant frequency. We start with a multiple scattering formulation of the scattering problem in which an incident wave impinges on a large number of identical and small bubbles in a homogeneous fluid. Under certain conditions on the configuration of the bubbles distribution, we justify the point interaction approximation and establish an effective medium theory for the bubbly fluid as the number of bubbles tends to infinity. The convergence rate is also derived. As a consequence, we show that near and below the Minnaert resonant frequency, the obtained effective media may be highly refractive, which can be used to explain the superfocusing experiment observed in [M. Lanoy et al., Phys. Rev. B, 91 (2015), 224202]. Moreover, above the Minnaert resonant frequency, the effective medium is dissipative, while at that frequency, effective medium theory does not hold. Our theory sheds light on the mechanism of the extraordinary wave properties of metamaterials, which include bubbly fluid as an example, near resonant frequencies.

Velocity measurement for two-phase flows based on ultrafast X-ray tomography

The ultrafast electron beam X-ray tomography scanner ROFEX is used for the investigation of multiphase flows. Its functional principle allows us to obtain sequences of cross-sectional flow images, which shows local attenuation properties of the flow. Hence, the X-ray CT images mainly reveal the shape and interfaces of flow constituents, such as gas, liquid and solids via their X-ray contrast. It is, however, more difficult to obtain velocity information from multiphase flows. In this article we discuss different methods to extract information on the velocities of particles or interfaces as well as for continuous phase. For disperse phase velocity measurement, e.g. in gas–liquid or gas–solids flows, we employ cross-correlation based techniques using two imaging planes. Apart from the standard cross-correlation technique we developed a method and algorithm, which is capable to identify identical bubbles in the two planes giving us a unique Lagrangian particle-related velocity information. Eventually we give an example of velocity measurement in the continuous liquid phase using an X-ray contrast agent.

Computational modelling of the interaction of shock waves with multiple gas-filled bubbles in a liquid

This study presents a computational investigation of the interactions of a single shock wave with multiple gas-filled bubbles in a liquid medium. This work illustrates how multiple bubbles may be used in shock-bubble interactions to intensify the process on a local level. A high resolution front-tracking approach is used, which enables explicit tracking of the gas-liquid interface. The collapse of two identical bubbles, one placed behind the other is investigated in detail, demonstrating that peak pressures in a two bubble arrangement can exceed those seen in single bubble collapse. Additionally, a parametric investigation into the effect of bubble separation is presented. It is found that the separation distance has a significant effect on both the shape and velocity of the main transverse jet of the second bubble. Extending this analysis to effects of relative bubble size, we show that if the first bubble is sufficiently small relative to the second, it may become entirely entrained in the second bubble main transverse jet. In contrast, if the first bubble is substantially larger than the second, it may offer it significant protection from the incident shock. This protection is utilised in the study of a triangular array of three bubbles, with the central bubble being significantly smaller than the outer bubbles. It is demonstrated that, through shielding of bubbles until later in the collapse process, pressures over five times higher than the maximum pressure observed in the single bubble case may be achieved. This corresponds to a peak pressure that is approximately 40 times more intense than the incident shock wave. This work has applications in a number of different fields, including cavitation erosion, explosives, targeted drug delivery/intensification, and shock wave lithotripsy.

Simulating the universe(s) II: phenomenology of cosmic bubble collisions in full general relativity

Observing the relics of collisions between bubble universes would provide direct evidence for the existence of an eternally inflating Multiverse; the non-observation of such events can also provide important constraints on inflationary physics. Realizing these prospects requires quantitative predictions for observables from the properties of the possible scalar field Lagrangians underlying eternal inflation. Building on previous work, we establish this connection in detail. We perform a fully relativistic numerical study of the phenomenology of bubble collisions in models with a single scalar field, computing the comoving curvature perturbation produced in a wide variety of models. We also construct a set of analytic predictions, allowing us to identify the phenomenologically relevant properties of the scalar field Lagrangian. The agreement between the analytic predictions and numerics in the relevant regions is excellent, and allows us to generalize our results beyond the models we adopt for the numerical studies. Specifically, the signature is completely determined by the spatial profile of the colliding bubble just before the collision, and the de Sitter invariant distance between the bubble centers. The analytic and numerical results support a power-law fit with an index 1< κ ≲ 2. For collisions between identical bubbles, we establish a lower-bound on the observed amplitude of collisions that is set by the present energy density in curvature.

Heuristic consequences of a load of oxygen in microtubules

The current cell oxygen paradigm shows some major gaps that have not yet been resolved. Something seems to be lacking for the comprehensive statement of the oxygen distribution in the cell, especially the low cytoplasmic oxygen level. The entrapment of oxygen in microtubules (MTs) resolves the latter observation, as well as the occurrence of an extensive cytoplasmic foam formation. It leads to a novel oxygen paradigm for cells. During the steady-state treadmilling, the mobile cavity would absorb oxygenated cytoplasm forward, entrap gas nuclei and concentrate them. A fluorescence method is described to confirm the in vitro load of oxygen in MTs during their periodic growths and shrinkages. The latter operating mechanism is called the gas dynamic instability (GDI) of MTs. Several known biosystems could rest on the GDI. (1) The GTP-cap is linked with the gas meniscus encountered in a tube filled with gas. The GTP hydrolysis is linked to the conformational change of the GTPase domain according to the bubble pressure, and to the shaking of protofilaments with gas particles (soliton-like waves). (2) The GDI provides a free energy water pump because water molecules have to escape from MT pores when foam concentrates within the MT. Beside ATP hydrolysis in motor proteins, the GDI provides an additional driving force in intracellular transport of cargo. The water streams flowing from the MT through slits organize themselves as water layers between the cargo and the MT surface, and break ionic bridges. It makes the cargo glide over a water rail. (3) The GDI provides a universal motor for chromosome segregation because the depolymerization of kinetochorial MTs is expected to generate a strong cytoplasmic foam. Chromosomes are sucked up according to the pressure difference (or density difference) applied to opposite sides of the kinetochore, which is in agreement with Archimedes' principle of buoyancy. Non-kinetochorial MTs reabsorb foam during GDI. Last, the mitotic spindle is imagined as a gas recycler. (4) The luminal particles within MTs (called MIPs) are imagined as a foam organizer, the luminal proteins being part of the borders and edges of identical bubbles. (5) Last, volatile anesthetics could destabilize MTs through anesthetic-induced bubble nucleation between protofilaments, and therefore causing shear stress and the opening of MT. The load of oxygen in MTs might provide a major advance in this area of research.

The Origins of Bosons and Fermions

This paper proposes that all Bosons and all Fermions originate from even more elementary constituents, which called Spin Angular Momentum Vacuum (SAMV). SAMV is filled with Primitive Spin Particles (PSP). The total square spin angular momentum of each PSP is negative, less than zero. Those PSP labeled by index of Casimir Operator, are called Vacuum Spin Particle (VSP), which could be contracted into so-called Vacuum Bubbles (VB). VB are identical bubbles, are sub-observable physical quantities. VB are paired up into Vacuum Bubble Pair VBP. VSP ωj(or ω+,ω-) results from Self-identical vacuum bubble interaction through the zero order Phase Transition PT. When the 1st, 2nd, 3rd,... order PT of VBP occur, then VBP turn into Bosons and Fermions, excited out of sea level of SAMV ocean.

Interaction of bubbles in an inviscid and low-viscosity shear flow

The pressure loads on two identical spherical bubbles impulsively introduced in an inviscid simple shear flow are calculated. The interaction force due to these pressure loads is employed to model the dynamics of air bubbles injected to a low-viscosity fluid sheared in a Couette device at the first shear flow instability where the bubbles are trapped inside the stable Taylor vortex. It was shown that the interaction between the bubbles in the primary shear flow drives them away from each other. The performed simulations revealed that in an inviscid flow the separation distances between equal size bubbles undergo complex periodic motion. The presence of low-viscosity results in a qualitative change of the interaction pattern: The bubbles either eventually assume an ordered string with equal separation distances between all neighbors or some of them collide. The first regime is qualitatively similar to the behavior of bubbles at low Reynolds number [Prakash et al., Phys. Rev. E 87, 043002 (2013)]. Furthermore, if the Reynolds number exceeds some critical value the temporal behavior of the separations becomes nonmonotonic and exhibits over- and undershooting of the equilibrium separations. The latter effects were observed in the experiments, but are not predicted by the low Reynolds number model of the process [Prakash et al., Phys. Rev. E 87, 043002 (2013)].

The velocity field around two interacting cavitation bubbles in an ultrasound field

A model is developed to calculate the distribution of first-order velocity field caused by the coupled bubbles in an ultrasound field. Using this model, numerical investigations of velocity field have been made when the two identical bubbles are driven well below resonance by an acoustic field with pressure amplitude exceeding cavitation threshold. Three representative kinestates of the coupled bubbles were chosen for analyzing the velocity distribution of surrounding liquid. The results show that the nonlinear oscillations of a bubble pair affect violently the radial velocity distribution of surrounding liquid, especially in the expanding phase. Symmetry of the tangential velocity distribution implies a possibility of attraction or repulsion of the bubble pairs.

Interaction of equal-size bubbles in shear flow

The inertia-induced forces on two identical spherical bubbles in a simple shear flow at small but finite Reynolds number, for the case when the bubbles are within each other's inner viscous region, are calculated making use of the reciprocal theorem. This interaction force is further employed to model the dynamics of air bubbles injected to a viscous fluid sheared in a Couette device at the first shear flow instability where the bubbles are trapped inside the stable Taylor vortex. It was shown that, during a long time scale, the inertial interaction between the bubbles in the primary shear flow drives them away from each other and, as a result, equal-size bubbles eventually assume an ordered string with equal separation distances between all neighbors. We report on experiments showing the dynamic evolution of various numbers of bubbles. The results of the theory are in good agreement with the experimental observations.

Numerical simulation of the interactions between three equal-interval parallel bubbles rising in non-Newtonian fluids

The motion and interactions of three equal-interval parallel bubbles in non-Newtonian fluids were numerically simulated by volume of fluid method (VOF), in which the continuous surface tension model and the power-law model were adopted to represent surface tension and rheological properties of non-Newtonian fluids, respectively. The computational method was validated by the comparison of the processes of coalescence of two in-line bubbles and rising of two parallel bubbles between experiment and simulation. This method was then applied to study the effect of initial bubble diameter, initial horizontal bubble interval and rheological properties of non-Newtonian fluids on lateral coalescence and rising of three parallel bubbles. The dimensionless critical horizontal interval of bubble coalescence was obtained under different physical property conditions. The critical horizontal interval of bubble coalescence decreases with the increase of initial bubble diameter and flow index of non-Newtonian fluids. When the initial horizontal bubble interval is less than the critical horizontal interval of bubble coalescence, three bubbles will coalesce into a bigger bubble. The coalescing bubble could breakup into two identical daughter bubbles when the initial bubble diameter was increased or the flow index of non-Newtonian fluids was decreased. Three parallel bubbles rising in non-Newtonian fluids will experience repulsive interactions once the initial horizontal bubble interval is greater than the critical horizontal interval of bubble coalescence, the horizontal bubble interval increased gradually owing to the repulsive effect, while the vertical distance between bubbles varied dramatically for spherical bubble and ellipsoidal bubble due to the differences of their flow field structures.

Ultrasonic field parameters of nonlinear dynamics of double-bubble

Started from the bubble dynamics, establish a double bubble in the external field under the action of the equations of motion of bubbles, the interaction was studied. Research results show that: considered the interaction between bubbles, bubble movement equation, resonance frequency, resonance when the radius of the changes was significantly associated with a single bubble is different, these parameters not only with their initial bubble radius, and sound intensity, liquid viscosity and other factors are also associated with the distance between them and the relative of another bubble initial radius. When the bubble radius is large, the mutual influence between them more strong. The result is that the effect of vibration reduction. Study finds: the bubble resonance frequency and the distance between them, with the increase of the distance between air bubbles, the resonant frequency in decreasing. But when the distance between them is increased to a certain value, the resonance frequency tends to a certain value. It can also be understood as when the bubble is relatively far from the interactions between them on its influence can be neglected, the resonant frequency of the resonant frequency for single bubble. For a harmonic oscillator are radius variation, between the two bubbles is the role of mutual inhibition, but the bubble radius is different, this inhibition of strong and weak, different. Bubble initial radius identical bubbles, mutual inhibition is weaker, numerical calculation shows the same radius of the resonance radius greater than the radius of the results.

Micromanipulation using cavitational microstreaming generated by acoustically oscillating twin bubbles

This paper describes a novel non-invasive micromanipulation technique that employs the cavitational microstreaming generated by acoustically oscillating twin bubbles. First, a single acoustically oscillating bubble was attached to the tip of a rod that was combined with a three-dimensional traverse system, and a fish egg (diameter: 1mm) was then manipulated in an aqueous medium. Although the microstreaming generated by the single oscillating bubble was sufficiently strong to push and move the fish egg, the manipulation direction was uncontrollable. Hence, to improve the manipulation controllability, identical twin bubbles with the same size and resonant frequency were employed. The identical gas bubbles were generated on a microfabricated chip comprising sharp tip-shaped electrodes by employing an electrochemical method, electrolysis, and controlling the applied voltage and time. Subsequently, the bubbles were sequentially transferred to the tips of a U-shaped rod coated with a hydrophobic layer to improve the surface adhesion. The force generated from the acoustically oscillating bubbles and its direction were analyzed under various acoustic excitation conditions by using high-speed images. Our results showed that the generated force was proportional to the bubble oscillation amplitude, whereas the direction of the force depended on the distance between a bubble and object. A steel ball (500μm diameter) was used for investigating the force direction. When a bubble (600μm diameter) was acoustically excited, the steel ball was pulled toward the oscillating bubble when the distance between the bubble and ball was short (<3mm), whereas the steel ball was pushed away from the oscillating bubble when the distance was long (>3mm). Finally, a fish egg (diameter: 1mm) and glass beads (diameter: 100μm) were experimentally manipulated using acoustically oscillating twin bubbles.

Numerical investigation on coalescence of bubble pairs rising in a stagnant liquid

In the present study, we preformed a two-dimensional numerical simulation of the motion and coalescence of bubble pairs rising in the stationary liquid pool, using the moving particle semi-implicit (MPS) method. Moving particles were used to describe the liquid phase and the vapor phase was evaluated using real vapor sate equation. The bubble–liquid interface was set to be a free surface boundary which could be captured according to the motion and location of interfacial particles. The behaviors of coalescence between two identical bubbles predicted by the MPS method were in good agreement with the experimental results reported in the literature. Numerical results indicated that the rising velocity of the trailing bubble was larger than that of the leading bubble. Both of the leading bubble and the trailing bubble rose faster than the isolated bubble. After coalescence, the coalesced bubble showed velocity and volume oscillations. The time of the volume oscillations increased with increasing initial bubble diameter. The wake flow and vortex would form behind the coalesced bubble.

Odds of observing the multiverse

Eternal inflation predicts our observable universe lies within a bubble (or pocket universe) embedded in a volume of inflating space. The interior of the bubble undergoes inflation and standard cosmology, while the bubble walls expand outward and collide with other neighboring bubbles. The collisions provide either an opportunity to make a direct observation of the multiverse or, if they produce unacceptable anisotropy, a threat to inflationary theory. The probability of an observer in our bubble detecting the effects of collisions has an absolute upper bound set by the odds of being in the part of our bubble that lies in the forward light-cone of a collision; in the case of collisions with bubbles of identical vacua, this bound given by the bubble nucleation rate times ($H_{\rm{O}}/H_{\rm{I}})^2$, where $H_{\rm{O}}$ is the Hubble scale outside the bubbles and $H_{\rm{I}}$ is the scale of the second round of inflation that occurs inside our bubble. Similar results were obtained by Freigovel \emph{et al.} using a different method for the case of collisions with bubbles of much larger cosmological constant; here it is shown to hold in the case of collisions with identical bubbles as well. A significant error in a previous draft was corrected in order to arrive at this result.

The problem of stability of the spherical shape of a bubble during its supercompression

Deviation of the bubble shape from the spherical one during supercompression of a bubble in liquid is considered. The main attention is focused on determining the law of the initial bubble nonsphericity distribution in the spherical harmonics. The most probable one is that with the amplitude reducing as the harmonics number increases. Such distribution is confirmed by the analysis of the bubble sphericity perturbation evolution at the bubble collapse near a solid wall and at coalesce of two identical bubbles. The influence of the bubble sphericity distortion during bubble compression on the deformation of a shock wave arising in the bubble and the dependence of the bubble nonsphericity evolution on the nonlinear interaction between the distortions in the form of different harmonics are also discussed.

Numerical investigation of the stability of bubble train flow in a square minichannel

The stability of a train of equally sized and variably spaced gas bubbles that move within a continuous wetting liquid phase through a straight square minichannel is investigated numerically by a volume-of-fluid method. The flow is laminar and cocurrent upward and driven by a pressure gradient and buoyancy. The simulations start from fluid at rest with two identical bubbles placed on the axis of the computational domain, the size of the bubbles being comparable to that of the channel. In vertical direction, periodic boundary conditions are used. These result in two liquid slugs of variable length, depending on the initial bubble-to-bubble distance. The time evolution of the length of both liquid slugs during the simulation indicates if the bubble train flow is “stable” (equal terminal length of both liquid slugs) or “unstable” (contact of both bubbles). Several cases are considered, which differ with respect to bubble size, domain size, initial bubble shape, and separation. All cases lead to axisymmetric bubbles with the capillary number in the range of 0.11–0.23. The results show that a recirculation pattern develops in the liquid slug when its length exceeds a critical value that is about 10%–20% of the channel width. If a recirculation pattern exists in both liquid slugs, then the bubble train flow is stable. When there is a recirculation pattern in one liquid slug and a bypass flow in the other, the bubble train flow may be stable or not depending on the local flow field in the liquid slugs close to the channel centerline. These results suggest that a general criterion for the stability of bubble train flow cannot be formulated in terms of the capillary and Reynolds number only, but must take into account the length of the liquid slug.

Mouvement relatif de deux bulles semblables qui évoluent dans un fluide au repos, à faibles nombres de Reynolds

By using an iterative approach close to the method of reflections, the relative motion of two identical bubbles rising in a fluid at rest is investigated theoretically. The classical phenomena concerning the motion of two bubbles rising in line, or the repulsion of two bubbles rising side by side are obviously recovered, but moreover, the relative motion of the two particles may be obtained whatever their initial positions, requiring that they satisfy the basis assumption made in this study. This result is therefore used in order to represent all the possible relative trajectories adopted by a particle interacting with an other one. To cite this article: F. Candelier, C. R. Mecanique 335 (2007).

The mechanism of pattern formation in the developing drosophila retina

The biological patterning of the Drosophila retina in vivo has striking resemblance to liquid bubbles, in which the surface mechanics due to N-cadherin within a sub-group of retina cells can be mimicked by surface tension. In this work, the aggregating patterns were reasonably simplified into 2D clusters consisting of 2-6 identical bubbles confined within a shrinking boundary. By using a hybrid fluid dynamics model proposed for liquid foams, the aggregating process of 2-6 retina cells was studied. Assuming the minimal perimeter for patterning cells to be the condition of stability patterns, the stable converged patterns we simulated in this work are the same as the experimental observations. More importantly, a new pattern of 6 cells was obtained which was found physically more stable than the other two reported by Hayashi and Carthew. Aggregating perimeters of cells, i.e. the surface energy, showed a good linear fit with the cell numbers.