Initial Bubble Size Research Articles

The Effect of Bubble-Induced Turbulence on the Interfacial Area Transport in Gas-Liquid Two-Phase Flow

In the present work, two common modelling concepts taking into account the influence of bubbles on the turbulence of the liquid phase with available models in open literature were implemented in the EAGLE (Elaborated Analysis of Gas-Liquid flow Evolution) code and assessed against experimental data of Hibiki et al. (2001). The EAGLE code has been developed at KAERI based on the two-fluid model for a multi-dimensional analysis of two-phase flow with the implementation of non-drag force, standard k-ε turbulence model, and the interfacial area transport equation. In order to investigate the bubble size effect on two-phase flow evolution and to provide a data set for developing the physical models to describe the bubble-induced turbulence effect and also for validating the EAGLE code, a series of local parameter measurements as well as visualization tests were conducted in air-water vertical-upward flow condition in which the initial bubble size is controlled by a specially designed bubble generator. The numerical results and experimental data were compared, analysed and discussed in this paper.

Fate of methane bubbles released by pockmarks in Lake Constance

In the eastern part of Lake Constance, the second largest pre-alpine lake in Europe, about five hundred pockmarks (morphological depressions on the lake floor) were recently discovered of which ~40 % release methane bubbles. The carbon isotopic composition of the escaping gas indicated that the methane is of biogenic origin. In our study, we investigated the fate of the released methane bubbles, i.e., the dissolution, oxidation or transport of the bubbles to the surface. At a littoral pockmark site (PM12, 12 m water depth) and a profundal pockmark (PM80, 80 m water depth), we analysed the dissolved methane concentrations and the methane isotopic carbon signature in the water column. At PM80, higher methane concentrations (up to 1,523 nM), compared to the control site and the surface waters (225 ± 72 nM), were recorded only on some occasions and only in the bottom water, despite the fact that the released bubbles were dissolving within the hypolimnion based on bubble modeling. The isotope data suggest that most of the dissolved methane is oxidized below 40 m water depth. The isotopic signature of the methane in the surface water at PM80, however, differed from that of the methane in the hypolimnion; therefore, the surface methane at this profundal site is most likely an export product from the littoral zone. Assuming an initial bubble diameter of 5 mm, we calculated that these small bubbles would reach the surface, but approximately 96 % of the methane would have dissolved from the bubble into the hypolimnion. At PM12, we observed higher concentrations of dissolved methane (312 ± 52 nM) with no significant differences between seasons or between control sites versus pockmark site. In the shallow water, divers estimated the bubble size to be 10–15 mm, which from a release depth of 12 m would barely dissolved into the water column. The isotopic signature also indicated that there had been almost no methane oxidation in the shallow water column. Thus, the water depth of bubble release as well as the initial bubble size determine whether the methane enters the atmosphere largely unhindered (shallow site) or if the released methane is incorporated into the profundal water column.

The effect of viscoelasticity on the dynamics of two gas bubbles near a rigid boundary

Multi-bubble dynamics is investigated in the presence of a rigid boundary. A simplified configuration is considered in which two bubbles, not necessarily of the same size, are positioned along an axis of symmetry. The problem is formulated in terms of a generalized Bernoulli equation for a velocity potential. A boundary element method is adopted to determine the normal velocity at the bubble surface. Viscoelastic effects are incorporated into the model through the normal stress balance across the bubble surface. The model predicts that bubble dynamics, and jet formation, in particular, is strongly influenced by the initial bubble sizes, the initial stand-off distances and on the fluid parameters. Viscoelastic effects are shown to be responsible for some interesting dynamics. Although inter-bubble interaction is shown to play an important role, it is not always dominant for viscoelastic fluids.

Simulation of transient fluid flow in mold region during steel continuous casting

A system of models has been developed to study transient flow during continuous casting and applied to simulate an event of multiple stopper-rod movements. It includes four sub-models to incorporate different aspects in this transient event. A three-dimensional (3-D) porous-flow model of the nozzle wall calculates the rate argon gas flow into the liquid steel, and the initial mean bubble size is estimated. Transient CFD models simulate multiphase flow of steel and gas bubbles in the Submerged Entry Nozzle (SEN) and mold and have been validated with experimental data from both nail dipping and Sub-meniscus Velocity Control (SVC) measurements. To obtain the transient inlet boundary conditions for the simulation, two semi-empirical models, a stopper-rod-position based model and a metal-level-based model, predict the liquid steel flow rate through the SEN based on recorded plant data. Finally the model system was applied to study the effects of stopper rod movements on SEN/mold flow patterns. Meniscus level fluctuations were calculated using a simple pressure method and compared well with plant measurements. Insights were gained from the simulation results to explain the cause of meniscus level fluctuations and the formation of sliver defects during stopper rod movements.

Numerical investigation of vapor bubble condensation characteristics of subcooled flow boiling in vertical rectangular channel

Abstract In this study, the behavior of condensing single vapor bubble in subcooled boiling flow within two different vertical rectangular channels has been numerically investigated by using the VOF (Volume Of Fluid) multiphase flow model. The mass and energy transfer model of bubble condensing process induced by the interfacial heat transfer was proposed to describe the interfacial transportation between the two phases. The results of VOF simulations show a good agreements with previous experimental data in the bubble size variation and lifetime. The bubble lifetime is almost proportional to bubble initial size and be prolonged at increasing system pressure. With the increasing of the subcooling, the bubble lifetime reduces significantly, and the effect of mass flux could be negligible. When the bubble size increased, the bubble shape tends to be changed in a large channel. The VOF simulation results of deformation have good agreement with those of Kamei’ experiment and the results of MPS (Moving Particle Semi-implicit) simulation in a larger channel. Furthermore, the initial bubble size, subcooling of liquid and system pressure play an important role to influence the bubble deformation behaviors significantly. The bubble could be deformed sharper with the increasing subcooling and initial diameter, or could breakup when the subcooling and the initial diameter reach a certain value at the last bubble stage. Nevertheless, the trends of bubble deformation will be weakening with the increasing system pressure.

Nonlinear response to ultrasound of encapsulated microbubbles

The acoustic backscatter of encapsulated gas-filled microbubbles immersed in a weak compressible liquid and irradiated by ultrasound fields of moderate to high pressure amplitudes is investigated theoretically. The problem is formulated by considering, for the viscoelastic shell of finite thickness, an isotropic hyperelastic neo-Hookean model for the elastic contribution in addition to a Newtonian viscous component. First and second harmonic scattering cross-sections have been evaluated and the quantitative influence of the driving pressure amplitude on the harmonic resonance frequencies for different initial equilibrium bubble sizes and for different encapsulating physical properties has been determined. Conditions for optimal second harmonic imaging have been also investigated and some regions in the parameters space where the second harmonic intensity is dominant over the fundamental have been identified. Results have been obtained for albumin, lipid and polymer encapsulating shells, respectively.

COMPUTATIONAL SIMULATION OF ALTITUDE CHANGE-INDUCED INTRAOCULAR PRESSURE ALTERATION IN PATIENTS WITH INTRAVITREAL GAS BUBBLES

To study the impact of altitude on the intraocular pressure (IOP) in an eye with an intravitreal gas bubble. A mathematical model was developed to simulate intravitreal gas bubble expansion caused by change in altitude. Mechanical deformation of the eye was simulated using a finite-element model. Intraocular pressure-driven changes in aqueous humor flow were also considered. Two cases were studied: 1) ascent from sea level to 3,000 ft followed by immediate return to sea level and 2) ascent to 3,000 ft followed by prolonged exposure to 3,000 ft. The effect of IOP-lowering medications was studied by changing the model parameters. The IOP increase was directly related to the initial bubble size when ascent to 3,000 ft was simulated. When prolonged exposure to high altitude was modeled, loss of aqueous humor led to a less elevated value of IOP. In a typical simulated case, when the outflow facility was increased, the predicted IOP rise was reduced by 28%. Theoretical modeling of an eye with an intravitreal gas bubble can help an ophthalmologist evaluate the impact of altitude-induced IOP changes. Our model suggests that IOP-lowering drugs could help manage altitude-induced IOP changes in the presence of intravitreal gas bubbles.

Calcium Alginate Foams Prepared by a Microfluidic T-Junction System: Stability and Food Applications

Highly porous alginate foams were prepared via a novel route in which highly viscous alginate solutions were bubbled using a microfluidic T-junction device. The relationship between bubble size and bubbling conditions such as air pressure and solution flow rate was studied, and the ability of the T-junction setup to generate monodisperse microbubbles (mean diameter, ∼154 μm) and produce porous foams was systematically investigated. The foams were characterised by optical and scanning electron microscopy. Foams of varying lengths (12–45 mm) were successfully prepared using this technique, with an average density of ∼235 kg/m3. The pore diameter within the foams was determined by microscopy to be in the range of 600 nm–200 μm with a mean diameter of ∼31 μm. It was concluded that porosity in the foam (>90%) can be varied depending on the initial bubble size. Thus, a possible production method of stable highly porous solid foams for exploitation in food and bioprocess technologies is presented by which products can be made to different sizes.

Study on the bubble transport mechanism in an acoustic standing wave field

The use of bubbles in applications such as surface chemistry, drug delivery, and ultrasonic cleaning etc. has been enormously popular in the past two decades. It has been recognized that acoustically-driven bubbles can be used to disturb the flow field near a boundary in order to accelerate physical or chemical reactions on the surface. The interactions between bubbles and a surface have been studied experimentally and analytically. However, most of the investigations focused on violently oscillating bubbles (also known as cavitation bubble), less attention has been given to understand the interactions between moderately oscillating bubbles and a boundary. Moreover, cavitation bubbles were normally generated in situ by a high intensity laser beam, little experimental work has been carried out to study the translational trajectory of a moderately oscillating bubble in an acoustic field and subsequent interactions with the surface. This paper describes the design of an ultrasonic test cell and explores the mechanism of bubble manipulation within the test cell. The test cell consists of a transducer, a liquid medium and a glass backing plate. The acoustic field within the multi-layered stack was designed in such a way that it was effectively one dimensional. This was then successfully simulated by a one dimensional network model. The model can accurately predict the impedance of the test cell as well as the mode shape (distribution of particle velocity and stress/pressure field) within the whole assembly. The mode shape of the stack was designed so that bubbles can be pushed from their injection point onto a backing glass plate. Bubble radial oscillation was simulated by a modified Keller–Miksis equation and bubble translational motion was derived from an equation obtained by applying Newton’s second law to a bubble in a liquid medium. Results indicated that the bubble trajectory depends on the acoustic pressure amplitude and initial bubble size: an increase of pressure amplitude or a decrease of bubble size forces bubbles larger than their resonant size to arrive at the target plate at lower heights, while the trajectories of smaller bubbles are less influenced by these factors. The test cell is also suitable for testing the effects of drag force on the bubble motion and for studying the bubble behavior near a surface.

A population balance approach considering heat and mass transfer—Experiments and CFD simulations

Bubble condensation in sub-cooled water is a complex process, to which various phenomena contribute. Since the condensation rate depends on the interfacial area density, bubble size distribution changes caused by breakup and coalescence play a crucial role. Experiments on steam bubble condensation in vertical co-current steam/water flows have been carried out in an 8 m long vertical DN200 pipe. Steam is injected into the pipe and the development of the bubbly flow is measured at different distances to the injection using a pair of wire mesh sensors. By varying the steam nozzle diameter the initial bubble size can be influenced. Larger bubbles come along with a lower interfacial area density and therefore condensate slower. Steam pressures between 1 and 6.5 MPa and sub-cooling temperatures from 2 to 12 K were applied. Due to the pressure drop along the pipe, the saturation temperature falls towards the upper pipe end. This affects the sub-cooling temperature and can even cause re-evaporation in the upper part of the test section. The experimental configurations are simulated with the CFD code CFX using an extended MUSIG approach, which includes the bubble shrinking or growth due to condensation or re-evaporation. The development of the vapour phase along the pipe with respect to vapour void fractions and bubble sizes is qualitatively well reproduced in the simulations. For a better quantitative reproduction, reliable models for the heat transfer at high Reynolds number as well as for bubble breakup and coalescence are needed.

Extension of the inhomogeneous MUSIG model for bubble condensation

Bubble condensation plays an important role, e.g. in sub-cooled boiling or steam injection into pools. Since the condensation rate is proportional to the interfacial area density, bubble size distributions have to be considered in an adequate modeling of the condensation process. The effect of bubble sizes was clearly shown in experimental investigations done previously at the TOPFLOW facility of FZD. Steam bubbles were injected into a sub-cooled upward pipe flow via orifices in the pipe wall located at different distances from measuring plane. 1 mm and 4 mm injection orifices were used to vary the initial bubble size distribution. Measurements were done using a wire-mesh sensor. Condensation is clearly faster in case of the injection via the smaller orifices, i.e. in case of smaller bubble sizes. Recently the Inhomogeneous MUSIG model was implemented into the CFD code CFX from ANSYS enabling the simulation of poly-dispersed flows including the effects of separation of small and large bubbles due to bubble size dependent lift force inversion. It allows to divide the dispersed phase into size classes regarding the mass as well as regarding the momentum balance. Up to now transfers between the classes in the mass balance can be considered only by bubble coalescence and breakup (population balance). Here an extension of the model is proposed to include the effects due to phase transfer. The paper focuses on the derivation of equations for the extension of the Inhomogeneous MUSIG model and presents some first results for verification and validation.

Numerical study on the shape oscillation of an encapsulated microbubble in ultrasound field

The shape oscillation of an encapsulated microbubble in an ultrasound field is numerically investigated. To predict the nonlinear process, the continuity equation and the Navier–Stokes equation are directly solved by means of a boundary-fitted finite-volume method on an orthogonal curvilinear coordinate system. The mechanics of neo-Hookean membrane is incorporated into the dynamic equilibrium at the bubble surface. The numerical results show that the membrane raises the natural frequency of an encapsulated bubble especially for small bubble, whereas this effect is attenuated as the initial bubble size grows. For a small encapsulated bubble of which the natural frequency is sufficiently higher than the driving frequency, the oscillation is stable, namely, the oscillatory amplitude is small; besides, the radial mode and shape modes are out of resonance so that no deformation emerges. As the bubble becomes larger, the natural frequencies of encapsulated and gas bubbles get closer, leading to the less apparent difference in oscillatory amplitude between them. Furthermore, shape modes of an encapsulated bubble are prone to be induced when twice of the higher-order natural frequency is approximately equal to the frequency of radial mode particularly when the bubble is at radial resonance for which the large-amplitude pulsation enhances the compressive stress developing in the membrane. In contrast, the shape oscillation is less likely to occur for a gas bubble with micrometer size since the surface tension suppresses the developments of nonspherical shape modes.

The stability and physical properties of egg white and whey protein foams explained based on microstructure and interfacial properties

The goal of this investigation was to determine if physical models, based on micro-scale (bubbles) and nano-scale (interface) properties, can be used to explain the macroscopic foaming properties of egg white protein (EWP) and whey protein isolate (WPI). Foam properties were altered by adding different amounts of sucrose (4.27–63.6 g/100 mL) and microstructures were observed using confocal laser scanning microscopy and bubbles were quantitatively measured using image analysis. Addition of sucrose decreased the initial bubble size, corresponding to higher foam stability and lower air phase fraction. EWP foams were composed of smaller bubbles and lower air phase fractions than WPI foams. Increased sucrose concentration caused a decreased liquid drainage rate due to a higher continuous phase viscosity and smaller bubble sizes. WPI foams had faster rates for liquid drainage and bubble coarsening than EWP foams. The differences were attributed to faster bubble disproportionation in WPI foams, caused by lower interfacial elasticity and lower liquid phase fractions. The experimentally fitted parameters for foam yield stress did not follow universal trends and were protein type dependent. EWP foams had higher yield stress than WPI foams due to smaller bubble sizes and higher interfacial elasticity. The yield stress of WPI foams increased slightly with addition of sucrose and cannot be accounted for based solely on model parameters. It appears that changes in stability of EWP and WPI foams can be explained based on physical models while unaccounted for protein-specific effects remain regarding foam yield stress.

Dissolution of carbon dioxide bubbles and microfluidic multiphase flows

We experimentally study the dissolution of carbon dioxide bubbles into common liquids (water, ethanol, and methanol) using microfluidic devices. Elongated bubbles are individually produced using a hydrodynamic focusing section into a compact microchannel. The initial bubble size is determined based on the fluid volumetric flow rates of injection and the channel geometry. By contrast, the bubble dissolution rate is found to depend on the inlet gas pressure and the fluid pair composition. For short periods of time after the fluids initial contact, the bubble length decreases linearly with time. We show that the initial rate of bubble shrinkage is proportional to the ratio of the diffusion coefficient and the Henry's law constant associated with each fluid pair. Our study shows the possibility to rapidly impregnate liquids with CO(2) over short distances using microfluidic technology.

A model for the temperature effect on onset velocity of turbulent fluidization of Geldart type A particles

This study proposes a model to predict the temperature effect on the onset velocity of turbulent fluidization (uc) of Geldart type A particles. It was found that void splitting could occur in the whole bed when the initial bubble size at the distributor (dbo) was greater than the maximum stable bubble size (dbmax) or the equilibrium bubble size (dbeq). The proposed model was successful to fit the trend of temperature effect on the uc. When the bubble growth was limited by the dbmax, the uc increased with an increase of temperature. However, when the dbeq was smaller than dbmax, the uc de- creased with an increase of temperature because the minimum fluidizing velocity and thus the dbeq decreased. The uc increased initially and decreased later when the dbeq/dbmax starting with the ratio >1 decreased to the ratio <1 as tem- perature increased. The present model predicted the trend properly that any other existing correlations could not be able to reflect.

Dynamics of gas bubbles in time-variant temperature fields

The effect of time-variant temperature on the dynamics of a single gas bubble in a liquid is investigated. With changes in temperature, several physical parameters controlling bubble behaviour change including surface tension, diffusivity, vapour pressure and gas solubility. A single-bubble model is formulated and a numerical simulation implemented to model the radius–time profile of a bubble, across a range of initial bubble sizes and rates of heating, taking into account the aforementioned parameter temperature dependences. The model is validated experimentally in a xanthan gum gel phantom, tracking the evolution of the bubbles using digital photography and an image analysis sizing algorithm. It is shown that the natural tendency for a bubble to dissolve can be reversed by an increase in temperature, but only above a certain radius-dependent threshold rate of heating.

Dependence of optimal seed bubble size on pressure amplitude at therapeutic pressure levels

Medical ultrasound has shown great potential as a minimally invasive therapy technique. It can be used in areas such as histotripsy, thermal ablation, and administering medication. The success of these therapies is improved by the cavitation of small microbubbles, and often it is useful to know which bubbles might provide the most effective therapy. When using therapies based on stable cavitation, the optimal bubble size is approximately given by R 0 ≅ 3 MHz μ m / f 0 lin . However, a similar expression is not available for therapies involving inertial cavitation. Therefore, the goal of our study was to develop an approximate expression relating the initial size of the bubble that resulted in the maximum response to the ultrasound operating frequency and pressure of the ultrasound wave when inertial cavitation is expected. The study was conducted by simulating the response of air bubbles in water to linearly propagating sine waves using the Gilmore–Akulichev formulation to solve for the bubble response. The frequency of the sine wave varied from 0.5 to 5 MHz while the amplitude of the sine wave varied from 0.0001 to 5 MPa. The optimal initial size for a particular frequency of excitation and amplitude, which is normally only established for stable cavitation, was defined in the study as the initial bubble size that resulted in the maximum bubble expansion prior to bubble radius dropping below its initial radius. A fit over pressure and frequency then yielded that the optimal size was approximately given by R optimal = ( 0.0327 f 2 + 0.0679 f + 16.5 P 2 ) - 0.5 where R optimal is in μm, f is the frequency of the ultrasound wave in MHz, and P the pressure amplitude of the ultrasound wave in MPa.

On the Numerical Study of Bubbly Wakes Generated by Ventilated Cavity Using Population Balance Approach

In this study, an Eulerian–Eulerian two-fluid model integrated with the population balance approach based on Multiple-Size-Group (MUSIG) model was proposed to simulate on the gas leakage bubbly wake of a ventilated cavitation problem. Three selected flow conditions with Froude number ranging from 20 to 29 have been selected for investigation. Predicted void fraction and bubble velocity profiles were validated against the experimental measurements in the high-speed water tunnel of Schauer (2003) and Wosnik (2005). Sensitivity studies on the mesh resolution and three different turbulence closures were first carried out. In comparison with experimental data, the shear stress transport (SST) turbulence model was found to be the best candidate in modelling the re-circulation motions within the cavity wake region. To consider the neighbouring effect of closely packed bubbles, an empirical equation was proposed to correlate the turbulent dispersion coefficient to the local gas void fraction. Based on the proposed empirical equation, the turbulent dispersion coefficient reduces to 0.1 when local gas void fraction is higher than 60%. In general, numerical predictions were in satisfactory agreement with the experimental data. Some discrepancies have nonetheless been found between the numerical and experimental results. The lack of exact gas leakage mechanism remains an outstanding challenge in determining the actual gas leakage rate and initial bubble size from the continuous cavity. Further effort should be also focused on combing free-surface tracking model with the present population balance approach to investigate the complex vortex structure and interaction between ventilated cavity and discrete leakage bubbles.

Strong Turbulence in the Wave Crest Region

Abstract High-resolution vertical velocity profiles in the surface layer of a lake reveal the turbulence structure beneath strongly forced waves. Dissipation rates of turbulence kinetic energy are estimated based on centered second-order structure functions at 4-Hz sampling. Dissipation rates within nonbreaking wave crests are on average 3 times larger than values found at the same distance to the free surface but within the wave trough region. This ratio increases to 18 times for periods with frequent wave breaking. The depth-integrated mean dissipation rate is a function of the wave field and correlates well with the mean wave saturation in the wave band ωp ≤ ω ≤ 4ωp. It shows a clear threshold behavior in accordance with the onset of wave breaking. The initial bubble size distribution is estimated from the observed distribution of energy dissipation rates, assuming the Hinze scale being the limiting size. This model yields the slope of the size distribution, , consistent with laboratory results reported in the literature, and implies that bubble fragmentation associated with intermittent high dissipation rates is a valid mechanism for the setup of bubble size spectra.

EXPERIMENTAL INVESTIGATIONS ON THE CONDENSATION OF STEAM BUBBLES INJECTED INTO SUBCOOLED WATER AT 1 MPA

Bubble condensation plays an important role, e.g., in subcooled boiling or steam injection into pools. Since the condensation rate is proportional to the interfacial area density, bubble size distributions have to be considered in an adequate modeling of the condensation process. To develop and validate closure models for computational fluid dynamics codes, new experimental data are required. The effect of bubble sizes is clearly shown in experimental investigations done at the TOPFLOW facility of Forschungszentrum Dresden Rossendorf. Steam bubbles are injected into a subcooled upward pipe flow via orifices in the pipe wall located at different distances from the measuring plane. Injection orifices measuring 1 and 4 mm are used to vary the initial bubble size distribution. Variation of the distance between the location of the gas injection and the measuring plane allows investigation of the evolution of the flow along the pipe. Measurements are done using wire-mesh sensors and thermocouples. Condensation is clearly faster in the case of the injection via the smaller orifices, i.e., in case of smaller bubble sizes. Data on averaged void fraction, radial gas volume fraction profiles, profiles of the gas velocity, and bubble size distributions in dependency of the L/D ratio are presented in the paper.