Subcritical Bubbles Research Articles

Hydrodynamic interaction of a bubble pair in viscoelastic shear-thinning fluids

We experimentally investigate the interaction between a pair of bubbles ascending in a stagnant viscoelastic shear-thinning fluid. In particular, we focus on the effect of bubble size, across the velocity discontinuity, on the bubble-bubble interaction. Compared to the drafting–kissing–tumbling (DKT) behavior in Newtonian fluids, bubbles in the viscoelastic shear-thinning fluid exhibit a drafting–kissing–dancing (DKD) phenomenon. In the dancing phase, the bubble pair repeatedly interchange their relative leading and trailing positions as they rise to the free surface. To gain further insights, the flow fields around the bubble pair interaction are obtained using particle image velocimetry (PIV). From the experimental results, we suggest that the elasticity, deformability, and negative wake are responsible for such an interaction between the bubble pair, thus revealing the fundamental physics of bubble clustering often observed in non-Newtonian fluids. • Strikingly different two bubble interactions in viscoelastic shear-thinning fluids. • At critical bubble volume, a discontinuity in the bubble velocity occurs. • For subcritical bubble pairs, the bubbles attract to form chains and coalesce. • Whereas, in supercritical bubble pairs, a ‘dancing’ oscillating behavior is observed. • Negative wake, deformability, and elasticity determine the type of interaction.

Hydrodynamic interaction and coalescence of two inline bubbles rising in a viscoelastic liquid

In this paper, direct numerical simulations (DNS) are performed to investigate the inline rise of a pair of three-dimensional (3D) air bubbles in a viscoelastic liquid using the volume-of-fluid approach with an adaptive mesh refinement technique. The exponential Phan-Thien–Tanner model is used as the non-linear viscoelastic constitutive equation for the liquid. The numerical model has been validated by comparison with previously published results, including the terminal velocity jump discontinuity of an isolated bubble rising in a viscoelastic fluid, when its volume exceeds a certain critical value. Focusing on the inline rising bubble pair in such a viscoelastic medium with different configurations, we found that the wake of the small leading bubble attracts a larger trailing bubble, whereas for a supercritical bubble in front of a subcritical bubble, they tend to further separate. Before reaching a critical volume, the two subcritical bubbles remain close to each other after approaching each other, forming a stable chain. For pairs containing a supercritical trailing bubble, however, a drafting–kissing scenario occurs before the bubble–bubble coalescence. The long-range repulsion and the short-range attraction due to fluid elasticity are critical to the aforementioned bubble pair interactions. Interestingly, the terminal rise velocities of the stable bubble chain and the coalesced bubble both increase with the initial spacing. The squeezing flow near the growing bubble neck seems to delay the coalescence process. The capillary wave propagating down to the coalesced bubble tip together with the extensional flow behind the stretched bubble determines the generation of satellite microdroplets along the tail of the coalesced bubble. To the best of our knowledge, this is the first 3D DNS on a bubble pair ascending in viscoelastic fluids.

Global electroweak symmetric vacuum

Although the Higgs potential in the Standard Model (SM) contains only a simple electroweak symmetry breaking vacuum in the small field region, additional metastable or global vacua could exist in models beyond the SM. In this paper, we study one intriguing scenario with an additional electroweak symmetric vacuum that could be the global one. For the thermal universe ending at the current metastable vacuum, the electroweak symmetry should stay non-restored at high temperatures. We realize the scenario in a model with Higgs-portal couplings to SM singlet scalars with approximately global O(N) symmetries with a large N. For a large portion of model parameter space, both the quantum and thermal tunneling rates are suppressed such that our current metastable vacuum is long-lived enough. Our scenario predicts order-one changes for the Higgs self-couplings and a large contribution to the signal of the off-shell Higgs invisible decay. It can be partly probed at the LHC Run 3 and well tested at the high luminosity LHC. We also discuss the subcritical (anti-de Sitter) bubbles from the thermal tunneling that could have a large population and interesting cosmological implications.

Dynamics of Electroweak Phase Transition in the 3-3-1-1 Model

The bubble nucleation in the framework of 3-3-1-1 model is studied. Previous studies show that first order electroweak phase transition occurs in two periods. In this paper we evaluate the bubble nucleation temperature throughout the parameter space. Using the stringent condition for bubble nucleation formation we find that in the first period, symmetry breaking from \(SU(3)\rightarrow SU(2)\), the bubble is formed at the nucleation temperature $T=150$ GeV and the lower bound of the scalar mass is 600 GeV. In the second period, symmetry breaking from \((SU(2)\rightarrow U(1)\), only subcritical bubbles are formed. This constraint eliminates the electroweak baryon genesis in the second period of the model.

Shear Thickening in Concentrated Soft Sphere Colloidal Suspensions: A Shear Induced Phase Transition

A model of shear thickening in dense suspensions of Brownian soft sphere colloidal particles is established. It suggests that shear thickening in soft sphere suspensions can be interpreted as a shear induced phase transition. Based on a Landau model of the coagulation transition of stabilized colloidal particles, taking the coupling between order parameter fluctuations and the local strain-field into account, the model suggests the occurrence of clusters of coagulated particles (subcritical bubbles) by applying a continuous shear perturbation. The critical shear stress of shear thickening in soft sphere suspensions is derived while reversible shear thickening and irreversible shear thickening have the same origin. The comparison of the theory with an experimental investigation of electrically stabilized colloidal suspensions confirms the presented approach.

Kinetics of the phase separation of a low-viscosity liquid supersaturated with gas at the intermediate and later stages

The separation kinetics of a low-viscosity liquid supersaturated with gas is studied. It is shown that the number of bubbles per unit volume at the intermediate stage of the process remains virtually constant, whereas the amount of the gas per unit volume of the solution significantly decreases, almost attaining the equilibrium value. At the later stage, small subcritical bubbles disappear due to gas transfer to large supercritical bubbles; as a result, the number of bubbles in the virtually equilibrium (as to the dissolved gas) liquid decreases. For all the stages, the kinetics of the changes in the bubble distribution function and in the amount of gas per unit volume of the solution is determined.

Effect of thermal fluctuations on the first order quark-hadron phase transition

We study the effects of thermal fluctuations on the dynamics of the quark-hadron phase transition assuming the phase transition to be of first order. These fluctuations give rise to a sizable fraction (up to 0.5) of the total volume occupied by the hadronic phase in the form of subcritical bubbles for temperatures near and below the critical temperature ${(T}_{c}).$ This suggests that the phase transition will not proceed through homogeneous bubble nucleation. We also discuss the possibility, if any, of percolation of subcritical hadron bubbles and its role in the phase transition.

On acoustic cavitation of slightly subcritical bubbles

The classical Blake threshold indicates the onset of quasistatic evolution leading to cavitation for gas bubbles in liquids. When the mean pressure in the liquid is reduced to a value below the vapor pressure, the Blake analysis identifies a critical radius which separates quasistatically stable bubbles from those which would cavitate. In this work, we analyze the cavitation threshold for radially symmetric bubbles whose radii are slightly less than the Blake critical radius, in the presence of time-periodic acoustic pressure fields. A distinguished limit equation is derived that predicts the threshold for cavitation for a wide range of liquid viscosities and forcing frequencies. This equation also yields frequency-amplitude response curves. Moreover, for fixed liquid viscosity, our study identifies the frequency that yields the minimal forcing amplitude sufficient to initiate cavitation. Numerical simulations of the full Rayleigh–Plesset equation confirm the accuracy of these predictions. Finally, the implications of these findings for acoustic pressure fields that consist of two frequencies will be discussed.

Surface Induced Phase Transition in Quark-Gluon Plasma Produced in the Laboratory

We discuss an outside-inside scenario for a first order quark-hadron transition in the quark-gluon plasma (QGP) expected to be produced in heavy ion collisions, wherein the entire QGP region itself becomes like a subcritical bubble, and starts shrinking. We argue that this shrinking QGP bubble will lead to concentration of baryon number in a narrow beamlike region in the center, which can be detected by Hanbury-Brown-Twiss (HBT) analysis, or as a raised plateau in the rapidity plot of baryon number.

Modeling thermal fluctuations: phase mixing and percolation

We consider the nonequilibrium dynamics of a a real scalar field in a degenerate double-well potential. The system is prepared in the lowest free energy state in one of the wells and the dynamics is driven by the coupling of the field to a thermal bath. Using a simple analytical model, based on the subcritical bubbles method, we compute the fraction of the total volume which fluctuates to the opposite phase as a function of the parameters of the potential. Furthermore, we show how complete phase mixing, {\em i.e.} symmetry restoration, is related to percolation, which is dynamically driven by domain instability. Our method describes quantitatively recent results obtained by numerical simulations, and is applicable to systems in the Ising universality class.

On acoustic cavitation of slightly subcritical bubbles

An analytic expression is obtained for the threshold acoustic pressure amplitude which causes gas bubbles that are slightly smaller than the critical size to undergo cavitation in a liquid. The derivation is based on the Rayleigh–Plesset equation which describes nonlinear bubble oscillations. In the limit where the steady part of the pressure field in the vicinity of the bubble is decreased to a value less than the vapor pressure inside the bubble, it is well known that there exists a critical bubble radius above which bubbles spontaneously cavitate. For bubbles which are below this critical size and would otherwise be stable, imposition of a time-harmonic acoustic pressure of the right frequency causes the bubbles to become unstable and undergo cavitation. The threshold value of this acoustic pressure is found by employing a nonlinear analysis which reduces the Rayleigh–Plesset equation to a damped and forced Mathieu equation for the case of such slightly subcritical bubbles.

On the use of classical configurations as subcritical bubbles

The role of classical configuration as subcritical bubbles in the physics of the early universe is analyzed. It is shown that the subcritical bubbles in the scalar background can only be viewed classical objects, i.e. they obey the classical equations of motion, if their amplitude is small, so that the change of the number of quanta is not too rapid. Also it is required that the number of quanta is large enough. In particular analyses with Gaussian bubbles of the size of the size of the correlation length and amplitude of the non-trivial minimum of the scalar potential seem not to be generally valid but should be done with more care.

Quantum Subcritical Bubbles

We quantize subcritical bubbles which are formed in the weakly first order phase transition. We find that the typical size of the thermal fluctuation reduces in the quantum-statistical physics. We estimate the typical size and the amplitude of thermal fluctuations near the critical temperature in the electroweak phase transition using quantum statistical average. Furthermore based on our study, we give implication on the dynamics of phase transition.

Small Thermal Fluctuations on a Large Domain

Weak first-order phase transitions proceed with percolation of new phase. The kinematics of this process is clarified from the point of view of subcritical bubbles. We examine the effect of small subcritical bubbles around a large domain of asymmetric phase by introducing an effective geometry. The percolation process can be understood as a perpetual growth of the large domain aided by the small subcritical bubbles.

ON THE NONEQUILIBRIUM EFFECTIVE POTENTIAL

Nonequilibrium phenomena of the phase transitions are studied. It is shown that due to finite relaxation time of the particle distributions, the use of scalar background dependent distribution functions is inconsistent. This observation may change the picture of rapid processes during the electroweak phase transition, like subcritical bubble formation and propagation of bubble walls.

A stochastic approach to thermal fluctuations during a first order electroweak phase transition

We investigate the role played by subcritical bubbles at the onset of the electroweak phase transition. Treating the configuration modelling the thermal fluctuations around the homogeneous zero configuration of the Higgs field as a stochastic variable, we describe its dynamics by a phenomenological Langevin equation. This approach allows to properly take into account both the effects of the thermal bath on the system: a systematic dissipative force, which tends to erase out any initial subcritical configuration, and a random stochastic force responsible for the fluctuations. We show that the contribution to the variance ≪ 2≫ ν in a given volume V from any initial subcritical configuration is quickly damped away and that, in the limit of long times, ≪ 2( t)≫ ν approaches its equilibrium value provided by the stochastic force and independent from the viscosity coefficient, as predicted by the fluctuation-dissipation theorem. In agreement with some recent claims, we conclude that thermal fluctuations do not affect the nucleation of critical bubbles at the onset of the electroweak phase transition making electroweak baryogenesis scenarios still a viable possibility to explain the primordial baryon asymmetry in the Universe.

Oscillons are not present during a first order electroweak phase transition

It has been recently argued that localized, unstable, but extremely long-lived configurations, called oscillons, could affect the dynamics of a first order electroweak phase transition in an appreciable way. Treating the amplitude and the size of subcritical bubbles as statistical degrees of freedom, we show that thermal fluctuations are not strong enough to generate subcritical configurations able to settle into a an oscillon long-lived regime.

Quantum Decoherence of Subcritical Bubble in Electroweak Phase Transition

In a weakly first order phase transition the typical scale of a subcritical bubble calculated in our previous papers turned out to be too small. At this scale quantum fluctuations may dominate and our previous classical result may be altered. So we examine the critical size of a subcritical bubble where quantum-to-classical transition occurs through quantum decoherence. We show that this critical size is almost equal to the typical scale which we previously obtained.

Do subcritical bubbles hinder first order phase transition?

We consider the role played by subcritical bubbles during the electroweak phase transition, estimate their average size, amplitude and formation rate taking into account the crucial role played by thermalization. We also study the influence of subcritical bubbles on the formation of critical bubbles in the thin wall regime and show that, contrary to some recent claims, subcritical bubbles do not affect the nucleation of critical bubbles in an appreciable way. From this fact we conclude that the electroweak baryogenesis scenarios associated with a first order electroweak phase transition still remain an attractive possibility.

Dynamics of Subcritical Bubbles in First Order Phase Transition

We derivate the Langevin and the Fokker-Planck equations for the radius of $O(3)$-symmetric subcritical bubbles as a phenomenological model to treat thermal fluctuation. The effect of thermal noise on subcritical bubbles is examined. We find that the fluctuation-dissipation relation holds and that in the high temperature phase the system settles down rapidly to the thermal equilibrium state even if it was in a nonequilibrium state initially. We then estimate the typical size of subcritical bubbles as well as the amplitude of fluctuations on that scale. We also discuss their implication to the electroweak phase transition.