Bubble Collisions Research Articles

Cosmological Implications of Electroweak Monopole

In this talk we review the basic features of the electroweak monopole, and estimate the remnant electroweak monopole density of the standard model in the present universe. We show that, although the electroweak phase transition is of the first order, the monopole production comes from the thermal fluctuations of the Higgs field after the phase transition, not the vacuum bubble collisions during the phase transition. Moreover, most of the monopoles produced initially are annihilated as soon as created, and this annihilation continues very long time, longer than the muon pair annihilation time. As the result the remnant monopole density at present universe becomes very small, of 10-11 of the critical density, too small to be the dark matter. We discuss the physical implications of our results on the ongoing monopole detection experiments.

Cosmological Implication of Electroweak Monopole

We estimate the remnant electroweak monopole density of the standard model in the present universe. We show that, although the electroweak phase transition is of the first order, the monopole production comes from the thermal fluctuations of the Higgs field after the phase transition, not the vacuum bubble collisions during the phase transition. Moreover, most of the monopoles produced initially are annihilated as soon as created, and this annihilation continues very long time, longer than the muon pair annihilation time. As the result the remnant monopole density at present universe becomes very small, of 10-11 of the critical density, too small to be the dark matter. We discuss the physical implications of our results on the ongoing monopole detection experiments.

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.

Gravitational waves from first-order phase transitions: towards model separation by bubble nucleation rate

We study gravitational-wave production from bubble collisions in a cosmic first-order phase transition, focusing on the possibility of model separation by the bubble nucleation rate dependence of the resulting gravitational-wave spectrum. By using the method of relating the spectrum with the two-point correlator of the energy-momentum tensor < T(x)T(y) >, we first write down analytic expressions for the spectrum with a Gaussian correction to the commonly used nucleation rate, Γ ∝ eβ tarrow eβ t−γ2t2, under the thin-wall and envelope approximations. Then we quantitatively investigate how the spectrum changes with the size of the Gaussian correction. It is found that the spectral shape shows \U0001d4aa(10)% deviation from Γ ∝ eβ t case for some physically motivated scenarios. We also briefly discuss detector sensitivities required to distinguish different spectral shapes.

A deterministic and viable coalescence model for Euler–Lagrange simulations of turbulent microbubble-laden flows

The topic of the paper is the development of an enhanced film drainage model for the prediction of bubble coalescence in the context of the Euler–Lagrange approach relying on large-eddy simulations. The starting point is the coalescence model by Jeelani and Hartland (1991), which compared to other often used models has several benefits: (1) A temporally evolving contact surface is considered avoiding the strong simplification of a constant contact area. (2) For contaminated bubbles an initially inertia-dominated process followed by a viscous-controlled regime are distinguished. (3) The contact time of the bubbles results as a side product of the modeling assumptions and thus is consistent with the film drainage concept. The main reason why this improved coalescence model was not applied in the past is the specific circumstance that the implicit equation for the determination of the transition time between the two phases (inertial and viscous) cannot be determined analytically. This problem is eliminated in the present study by numerically solving this equation. However, to avoid a time-consuming procedure for each individual bubble collision, a regression function is set up for a pre-defined range of bubble diameters and relative collision velocities. This renders the coalescence model feasible for flows with a huge number of bubbles. In a first step, the new coalescence model is validated against the experiments of single bubble coalescence with a free surface by Zawala and Malysa (2011) and Kosior et al. (2014). For the different cases considered the coalescence model yields reasonable agreement with the experiments. Furthermore, it is demonstrated that the results are improved compared to more popular but simpler models available in the literature. Afterwards, the coalescence model is applied to four-way coupled Euler–Lagrange simulations of a bubble column with clean and contaminated bubbles considering two different sizes. Significant deviations are found between the different cases, which can be traced back to varying collision frequencies and the different coalescence mechanisms in effect. Thus, it is shown that on the one hand the enhanced coalescence model leads to reasonable results and on the other hand is highly efficient allowing to take a huge number of bubble collisions deterministically into account.

Gravitational waves from a supercooled electroweak phase transition and their detection with pulsar timing arrays

We investigate the properties of a stochastic gravitational wave background produced by a first-order electroweak phase transition in the regime of extreme supercooling. We study a scenario whereby the percolation temperature that signifies the completion of the transition, T_mathrm{p}, is as low as a few MeV (nucleosynthesis temperature), while most of the true vacuum bubbles are formed much earlier at the nucleation temperature, T_mathrm{n}sim 50 GeV. This implies that the gravitational wave spectrum is mainly produced by the collisions of large bubbles and characterised by a large amplitude and a peak frequency as low as f sim 10^{-9}{-}10^{-7} Hz. We show that such a scenario can occur in (but not limited to) a model based on a non-linear realisation of the electroweak gauge group, so that the Higgs vacuum configuration is altered by a cubic coupling. In order to carefully quantify the evolution of the phase transition of this model over such a wide temperature range we go beyond the usual fast transition approximation, taking into account the expansion of the Universe as well as the behaviour of the nucleation probability at low temperatures. Our computation shows that there exists a range of parameters for which the gravitational wave spectrum lies at the edge between the exclusion limits of current pulsar timing array experiments and the detection band of the future Square Kilometre Array observatory.

Effect of surfactant on bubble collisions on a free surface

An investigation of the coefficient of restitution of bubble collision on a free surface in the presence of surfactants is presented. A reduced rebound velocity in the surfactant solution is observed and quantified using the Langmuir number, the ratio between absorption and desorption rates.

CFD simulation of multiphase (liquid–solid–gas) flow in an airlift column photobioreactor

A 2D computational fluid dynamics simulation was carried out using a multiphase flow model with an Eulerian–Eulerian approach for a microalgae culture in an airlift column photobioreactor. Simulation was performed for a $$0.0625\,l/l_{\mathrm{culture}}\cdot \hbox {min}$$ inlet airflow. Air, water and microalgae velocity contours showed less gas phase present in the downcomer than in the riser, suggesting the necessity of vigorous mixing in the ascendant portion if homogeneous water and solid flow is to be achieved. Air velocity is smaller in the downcomer (shorter velocity vectors) than in the riser. Water velocity vectors point always in the expected direction, down in the downcomer and up in the riser. Microalgae paths, perhaps due to the small size of the microorganisms, follow the water velocity vectors. As there are fewer hydraulic restrictions to the liquid phase in the riser, a large amount of energy is dissipated by gas–liquid interactions. In the downcomer region, the gas phase is almost nonexistent, and bubble collisions are almost nonexistent as well. A quasi-stagnation zone was found at the lower section of the downcomer, showing that the design requires improvement. Finally, the turbulent kinetic energy is larger at the top and middle region of the riser; meanwhile, it is lower at the downcomer. Similar results were observed for the energy dissipation rate.

Evaluation of gas–liquid mass transfer in gas‐induced stirred tank reactor using electrical resistance tomography

AbstractBACKGROUNDA gas‐entrainment impeller is attractive for multiphase reactive systems such as Fischer–Tropsch reaction and deep liquid‐phase oxidation of organics with the possibility of low gas conversion per pass, enhancement of mixing performance and better inter‐phase mass transfer compared with conventional impellers.RESULTSTomograms obtained from ERT measurement reveal that the conductivity of a gas–water system changes as a function of impeller Reynolds number, ReI. The global gas holdup profile behaviour with ReI exhibited a sigmoid character which was adequately captured by ϵG = ϵG,0 + ϵG,max(1 − exp(−τglReI)). The parity plot showed strong linearity between model predicted and experimental data. The radial gas holdup profiles showed an upward parabolic trend with higher gas holdup values for gas‐entrainment impeller systems than the conventional 4‐blade impeller. To assess the efficiency of power consumption, the mass transfer coefficient, kLa, for a gas–liquid system in a stirred tank reactor was correlated as a function of dimensionless combination of power number and gas holdup; where α is the bubble collision frequency (s−1) and β is the gas‐inducing enhancement factor.CONCLUSIONThree different regimes of volumetric mass transfer coefficient were identified in the stirred tank reactor for each case. Overall, the combination of qualitative and quantitative analyses of ERT along with dissolved oxygen concentration permitted an insightful analysis of the self‐gas inducing impeller as a superior mixing technology for potential industrial applications involving gas–liquid operations. © 2017 Society of Chemical Industry

Bubble-induced noise and vibration in cylindrical shell filled with liquid nitrogen

Bubble-induced vibration is a very crucial aspect in some critical systems like laser interferometer gravitational-wave observatory. Recently, laser interferometer gravitational-wave observatory detected the gravitational wave produced due to the merger of two black holes. To detect the other universe collision event due to other binary pairs like neutron stars, black holes or combination, the sensitivity of the detector should be very high. The sensitivity depends on the reduction of the noise present in the detector system / components. Liquid nitrogen cryopump is also one of the sources for the noise. This noise has been produced due to the bubble structure interaction. The present work analyzes the bubble generated noise spectrum level and its acoustic effect due to induced vibration. The spectrum levels considering force, acceleration, velocity, and displacement effect have been studied in detail for a thin annular fluid (LN2) filled cylindrical shell. It is assumed that the structure of cylindrical shell is homogeneous as well as isotropic. The noise level generated due to radial force excitation resulting from bubble collision has been found to be in the range of −85 dB to −45 dB at a lower resonance frequency.

A simple collision model for small bubbles

In this work, a model for the interaction force between a small bubble and a wall or another bubble is presented. The formulation is especially designed for Lagrangian calculations of bubble or soft sphere trajectories, with or without resolution of the continuous fluid. The force only relies on position and velocity of the bubble. The model does not include any empirical parameter that would have to be calibrated. Therefore, this force model is easy to implement. The formulation of the force is explicit, which means low computational effort. The collision of a small bubble with an inclined top wall is investigated numerically and experimentally. The computational results achieved with the new collision model show good agreement with the experiment.

Gravitational waves at aLIGO and vacuum stability with a scalar singlet extension of the standard model

A new gauge singlet scalar field can undergo a strongly first-order phase transition (PT) leading to gravitational waves (GW) potentially observable at aLIGO and simultaneously stabilize the electroweak vacuum. aLIGO (O5) is potentially sensitive to cosmological PTs at $10^7$-$10^8$ GeV, which coincides with the requirement that the singlet scale is less than the Standard Model (SM) vacuum instability scale, which is between $10^8$ GeV and $10^{14}$ GeV. After sampling its parameter space, we identify three benchmark points with a PT at about $T\approx 10^7$ GeV in a gauge singlet extension of the SM. We calculate the nucleation temperature, order parameter, characteristic timescale, and peak amplitude and frequency of GW from bubble collisions during the PT for the benchmarks and find that, in an optimistic scenario, GW from such a PT may be in reach of aLIGO (O5). We confirm that the singlet stabilizes the electroweak vacuum whilst remaining consistent with zero-temperature phenomenology as well. Thus, this scenario presents an intriguing possibility that aLIGO may detect traces of fundamental physics motivated by vacuum stability at an energy scale that is well above the reach of any other experiment.

Simultaneous High-Speed Recording of Sonoluminescence and Bubble Dynamics in Multibubble Fields.

Multibubble sonoluminescence (MBSL) is the emission of light from imploding cavitation bubbles in dense ensembles or clouds. We demonstrate a technique of high-speed recording that allows imaging of bubble oscillations and motion together with emitted light flashes in a nonstationary multibubble environment. Hereby a definite experimental identification of light emitting individual bubbles, as well as details of their collapse dynamics can be obtained. For the extremely bright MBSL of acoustic cavitation in xenon saturated phosphoric acid, we are able to explore effects of bubble translation, deformation, and interaction on MBSL activity. The recordings with up to 0.5million frames per second show that few and only the largest bubbles in the fields are flashing brightly, and that emission often occurs repetitively. Bubble collisions can lead to coalescence and the start or intensification of the emission, but also to its termination via instabilities and splitting. Bubbles that develop a liquid jet during collapse can flash intensely, but stronger jetting gradually reduces the emissions. Estimates of MBSL collapse temperature peaks are possible by numerical fits of transient bubble dynamics, in one case yielding 38 000K.

Gravitational waves from bubble collisions: An analytic derivation

We consider gravitational wave production by bubble collisions during a cosmological first-order phase transition. In the literature, such spectra have been estimated by simulating the bubble dynamics, under so-called thin-wall and envelope approximations in a flat background metric. However, we show that, within these assumptions, the gravitational wave spectrum can be estimated in an analytic way. Our estimation is based on the observation that the two-point correlator of the energy-momentum tensor $\langle T(x)T(y)\rangle$ can be expressed analytically under these assumptions. Though the final expressions for the spectrum contain a few integrations that cannot be calculated explicitly, we can easily estimate it numerically. As a result, it is found that the most of the contributions to the spectrum come from single-bubble contribution to the correlator, and in addition the fall-off of the spectrum at high frequencies is found to be proportional to $f^{-1}$. We also provide fitting formulae for the spectrum.

Gravitational waves and Higgs boson couplings for exploring first order phase transition in the model with a singlet scalar field

We calculate the spectrum of gravitational waves originated from strongly first order electroweak phase transition in the extended Higgs model with a real singlet field. In order to calculate the bubble nucleation rate, we perform a two-field analysis to evaluate bounce solutions connecting the true and the false vacua using the one-loop effective potential at finite temperatures. Imposing the Sakharov condition of the departure from thermal equilibrium for baryogenesis, we survey allowed regions of parameters of the model. We then investigate the gravitational waves produced at electroweak bubble collisions in the early Universe, such as the sound wave, the bubble wall collision and the plasma turbulence. We find that the strength at the peak frequency can be large enough to be detected at future space-based gravitational interferometers such as eLISA, DECIGO and BBO. Predicted deviations in the various Higgs boson couplings are also evaluated at the zero temperature, and are shown to be large enough too. Therefore, in this model strongly first order electroweak phase transition can be tested by the combination of the precision study of various Higgs boson couplings at LHC, the measurement of the triple Higgs boson coupling at future lepton colliders and the shape of the spectrum of gravitational wave detectable at future gravitational interferometers.

Influences of wake-effects on bubble dynamics by utilizing micro-pin-finned surfaces under microgravity

The influences of wake on bubble dynamics under various heat fluxes have been studied in microgravity. Nucleate pool boiling experiments of FC-72 on silicon chips fabricated with micro-pin-fins were conducted in 10−3 gravitational acceleration for 3.6s. Experimental results indicated that wake field had little influence on bubble dynamics at low heat flux, q=12.53W/cm2, but its effects on bubble dynamics became very great at moderate heat flux, q=27.89W/cm2, and high heat flux, q=39.54W/cm2. More importantly, wake-effects appeared even more significant in microgravity. In the wake field, the horizontal flow of the liquid on micro-pin-finned silicon chips promoted the collision, coalescence and movement of bubbles, and the vertical flow of liquid phase exerted an upward force on bubbles, which can effectively shorten the growth cycle and decrease the departure radius of bubbles. Furthermore, fresh liquid could easily be inhaled into the micro-pin-finned structure owning to the negative pressure in wake region, which can supply sufficient liquid for the growth of bubble, avoiding film boiling. The interaction between the micro-pin-finned structure and the wake effect promoted the process of bubble coalescence and departure effectively, so the process of heat transfer was significantly improved on micro-pin-finned surface. In addition, the flow field and bubble behavior in wake region were also briefly analyzed based on some reasonable simplifications and hypotheses. The theoretical analyses showed that the durations of wake-effects lasted longer than the time periods of the bubble in next generation, and the bubble diameters were also smaller than the thickness of wake region. Therefore, the dominant bubble of next generation was influenced by the wake field during its ebullition cycle, which is consistent with the experimental phenomenon.

Stability and convergence of computational eulerian two-fluid model for a bubble plume

The Eulerian two-fluid model (TFM) of Ishii (1975) is used to analyze the dynamics of an air-water bubble plume. The focus is on the effect of the linear stability, in particular the ill-posed condition, on the nonlinear stability of the TFM. It is well-known that the TFM for bubbly flows is ill-posed as an initial value problem in the absence of short wavelength physics for non-zero slip velocities. It is also known that the 1-D TFM can be made conditionally well-posed (for void fraction <26%) by adding momentum transfer due to interfacial pressure difference and virtual mass. However, there is still the possibility of a TFM being ill-posed in regions of higher void fractions (void fraction >26%). Physically, as the void fraction increases, the bubbles tend to undergo collisions, and the momentum transfer due to this mechanism may become significant. In the current study a bubble collision model adapted from the work of Alajbegovic et al. (1999) is used for CFD TFM calculations for bubbly flows using an LES approach. It is shown by linear stability analysis and non-linear simulations that the collision term makes the TFM unconditionally well-posed and stable in a non-linear sense.Secondly, computational grid convergence tests are performed with the well-posed CFD TFM. It is observed that the coarse grid solution exhibits an unphysical limit cycle behavior that is inconsistent with turbulence, but as the mesh is refined the solution becomes chaotic. CFD TFM simulations commonly employ a grid restriction to avoid ill-posed behavior. However, this is unnecessary with a well-posed Eulerian TFM derived from first principles using the continuum assumption. Once the restriction is removed by adding appropriate short-wavelength physics, i.e., interfacial pressure difference and collision mechanism, convergence may be approached in a statistical sense consistent with a turbulent CFD model.

Surface-wettability-induced sliding bubble dynamics and its effects on convective heat transfer

To explore the effects of wettability on heat transfer in sliding bubble dynamics, we investigated how the dynamics of sliding bubbles and heat transfer over a heated surface depend on the degree of wettability. We used volume-of-fluid scheme to track the interface of the dispersed phase via the local volume fraction. The results of the numerical model used in this study were consistent with those of experimental studies. After bubble collision, the bubble was found to adhere to a heated hydrophobic surface, as the bubble impinged upon the surface. The heat-transfer coefficient increased significantly in the region of the hydrophobic surface where the adhered bubble passed. The bubble completely adhered to the surface, as the adhesion force continuously increased. When the contact angle increased in the surface-contact regime (above 110°), the bubble spread out over the surface. The average Nusselt number in the surface-contact regime was found to be greater than that in other regimes (below 110°); thus, the surface more strongly affected heat transfer.

Baryogenesis and gravitational waves from runaway bubble collisions

We propose a novel mechanism for production of baryonic asymmetry in the early Universe. The mechanism takes advantage of the strong first order phase transition that produces runaway bubbles in the hidden sector that propagate almost without friction with ultra-relativistic velocities. Collisions of such bubbles can non-thermally produce heavy particles that further decay out-of-equilibrium into the SM and produce the observed baryonic asymmetry. This process can proceed at the very low temperatures, providing a new mechanism of post-sphaleron baryogenesis. In this paper we present a fully calculable model which produces the baryonic asymmetry along these lines as well as evades all the existing cosmological constraints. We emphasize that the Gravitational Waves signal from the first order phase transition is completely generic and can potentially be detected by the future eLISA interferometer. We also discuss other potential signals, which are more model dependent, and point out the unresolved theoretical questions related to our proposal.

Effect of Collision Force on Well-Posedness and Stability of the Two-Fluid Model for Vertical Bubbly Flows

It is well-known that an incomplete two-fluid model (TFM) leads to imaginary roots of the characteristic polynomial, thus rendering the model ill-posed. A common approach to fix this problem has been to introduce sufficient numerical/artificial diffusion or nonphysical hyperbolizing terms to stabilize the model. The disadvantage of this approach is that the physical instabilities that can be accurately predicted by the TFM either get severely dampened or disappear entirely. The preferred alternative is to introduce appropriate physics that may stabilize the TFM at short wavelengths while preserving the physical long-wavelength instabilities. For instance, in near-horizontal stratified flows, the appropriate physical mechanism is surface tension. However, it is not apparent what such a mechanism should be in dispersed bubbly flows.Researchers in the past have demonstrated that the inclusion of the momentum transfer due to interfacial pressure along with virtual mass force makes the model conditionally well-posed up to a gas volume fraction of 26%. However, in practice, one may observe bubbly flows having gas concentrations beyond this theoretical limit. Hence, it is important to make the behavior of the TFM well-posed for the entire range of gas volume fractions that is physically permissible. In this paper, the often-neglected phenomenon of bubble collisions is considered. The colliding bubbles generate a dispersed-phase pressure that is resistive to increased compaction. The inclusion of bubble pressure in the TFM renders the model well-posed up to the maximum packing limit. Furthermore, it is also shown that the collision force is necessary to predict the wave propagation velocities for bubbly flows over the entire range of void fractions observed in reality. Comparisons are made with the data, and a reasonable agreement is seen. Finally, it is demonstrated with computational fluid dynamics calculations that the addition of appropriate physical mechanisms (i.e., interfacial pressure and collision) makes the multidimensional TFM well-posed.