Static Bubble Research Articles

Effect of Dynamic Bubble Nucleation on Bitumen Flotation

Bubble nucleation in water under dynamic conditions was investigated using an autoclave at an air saturation pressure of 7 atm with different operating conditions. Agitation during air saturation of water was found to be crucial in enhancing tiny bubble formation. Without agitation, virtually no bubbles nucleated on hydrophobic surfaces. More bubbles were found to nucleate on hydrophobic surfaces at a higher agitation rate due to the formation of more cavities by more intense hydrodynamic conditions. The effect of saturation temperature (20–90°C) on bubble nucleation under dynamic conditions was only marginal, which differed from static bubble nucleation where the nucleation event reduced with increasing temperature. Flotation recovery of bitumen from oil sands extraction demonstrated a significant role of tiny bubbles nucleated in water: more than a 50–170% increase in bitumen recovery from different oil sands was obtained by using air supersaturated water rather than regular water.RésuméOn a étudié la nucléation de bulle dans l'eau, sous des conditions dynamiques, en utilisant un autoclave à une pression de saturation de l'air de 7 atm, à différentes conditions d'opération. On a trouvé que l'agitation lors de la saturation en air de l'eau était cruciale pour améliorer la formation de bulles minuscules. Sans agitation, virtuellement aucune bulle n'était nucléée sur les surfaces hydrophobes. On a trouvé qu'un plus grand nombre de bulles étaient nucléées sur les surfaces hydrophobes à une vitesse d'agitation plus élevée à cause de la formation d'un plus grand nombre de cavités sous l'effet des conditions hydrodynamiques plus intenses. L'effet de la température de saturation (20–90°C) sur la nucléation de bulle sous des conditions dynamiques était marginal, ce qui différait de la nucléation statique de bulle où l'événement de nucléation était réduit avec l'augmentation de la température. La récupération par flottation du bitume par extraction des sables bitumineux a démontré un rôle significatif des bulles nucléées dans l'eau: on a obtenu une augmentation de plus de 50–170% de la récupération du bitume à partir de différents sables bitumineux en utilisant de l'eau sursaturée à l'air plutôt que de l'eau régulière.

2상 격자 볼츠만 방법을 이용한 상승하는 기포 유동 2차원 수치 모사

Free energy based lattice Boltzmann method (LBM) has been used to simulate the rising bubble flows with large density ratio. LBM with compact discretization is able to reduce the spurious current of the static bubble test and be satisfied with the Laplace law. The terminal rise velocity and shape of the bubbles are dependent on Eotvos number, Morton number and Reynolds number. For single bubble flows, simulations are executed for various Eotvos number, Morton number and Reynolds number, and the results are agreed well with the experiments. For multiple bubbles, the bubble flow characteristics are related by the vortex pattern of the leading bubble. The coalescence of the bubbles are simulated successfully and the subsequent results are presented. The present method is validated for static, dynamic bubble test cases and compared to the numerical, experimental results.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L 2 ( Ω ) -norm is of order h 1 2 ). We propose a modification of the P 1 -conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O h 3 2 . The new pressure space is implemented for the stable P 1 + / P 1 mini-element discretization, and for the stabilized equal-order P 1 / P 1 discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P 1 space. In addition, two Navier–Stokes simulations with moving interfaces (Rayleigh–Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations.

Vacuum bubbles in a de Sitter background and black hole pair creation

We study the possible types of nucleation of vacuum bubbles. We classify vacuum bubbles in a de Sitter background and present some numerical solutions. The thin-wall approximation is employed to obtain the nucleation rate and the radius of vacuum bubbles. With careful analysis we confirm that Parke's formula is also applicable to the large true vacuum bubbles. The nucleation of the false vacuum bubble in a de Sitter background is also evaluated. The tunneling process in the potential with degenerate vacua is analyzed as the limiting cases of the large true vacuum bubble and false vacuum bubble. Next, we consider the pair creation of black holes in the background of bubble solutions. We obtain the static bubble wall solutions of the junction equation with a black hole pair. The masses of created black holes are uniquely determined by the cosmological constant and the surface tension on the wall. Finally, we obtain the rate of pair creation of black holes.

On pressure separation algorithms (PSepA) for improving the accuracy of incompressible flow simulations

AbstractWe investigate a special technique called ‘pressure separation algorithm’ (PSepA) (see Applied Mathematics and Computation 2005; 165:275–290 for an introduction) that is able to significantly improve the accuracy of incompressible flow simulations for problems with large pressure gradients. In our numerical studies with the computational fluid dynamics package FEATFLOW (www.featflow.de), we mainly focus on low‐order Stokes elements with nonconforming finite element approximations for the velocity and piecewise constant pressure functions. However, preliminary numerical tests show that this advantageous behavior can also be obtained for higher‐order discretizations, for instance, with Q2/P1 finite elements. We analyze the application of this simple, but very efficient, algorithm to several stationary and nonstationary benchmark configurations in 2D and 3D (driven cavity and flow around obstacles), and we also demonstrate its effect to spurious velocities in multiphase flow simulations (‘static bubble’ configuration) if combined with edge‐oriented, resp., interior penalty finite element method stabilization techniques. Copyright © 2008 John Wiley & Sons, Ltd.

Static and dynamic behaviour of gas bubbles in T-shaped non-clogging micro-channels

Preventing micro-channels from clogging is a major issue in most micro and nanofluidic systems (Gravesen et al., J Micromech Microeng 3(4):168–182, 1993; Jensen et al., In: Proc. of MicroTAS 2002, Nara, Japan, pp 733–735, 2002; Wong et al., J Fluid Mech 292:71–94, 1995). The T-shaped channel first reported by Kohnle et al. (In: IEEE MEMS, the 15th international IEEE micro electro mechanical conference (ed), Las Vegas, pp 77–80, 2002) prevents micro-channels from clogging by the aid of the equilibrium bubble position in such a geometry. This work is concerned with the static and dynamic behaviour of bubbles in such T-shaped micro-channels. The aspect ratio of a rectangle enclosing the T-shaped channel and the contact angle of the walls are the main parameters influencing the static and dynamic bubble behaviour. It is investigated in this article how these parameters relate to the equilibrium bubble shape and how optimum bubble velocities can be achieved inside the channel. An analytical model depending on the contact angle and the channel geometry is presented that allows to determine the bubble configuration inside the channel by minimizing the bubble’s surface energy. A second model is derived to predict the velocity of gas bubbles driven by buoyancy in vertical T-shaped channels. The model is applied to design T-shaped channels with a maximum mobility of gas bubbles. Experiments with MEMS fabricated devices and CFD simulations are used to verify the models. Furthermore design rules for an optimum non-clogging channel geometry which provides the highest gas bubble mobility are given.

Three-dimensional lattice Boltzmann simulations of droplet formation in a cross-junction microchannel

An immiscible liquid–liquid multiphase flow in a cross-junction microchannel was numerically studied by the lattice Boltzmann method. An improved, immiscible lattice BGK model was proposed by introducing interfacial tension force based on the continuum surface force (CSF) method. The recoloring step was replaced by the anti-diffusion scheme in the mixed region to reduce the side-effect and control the thickness of the interface. The present method was tested by the simulations on a static bubble and the simulations of Taylor deformation. Laplace’s law, spurious velocities, the thickness of interface, the pressure distribution and the small deformation theory were examined. It proves that our model is more advantageous for the simulation of immiscible fluids over the original immiscible lattice BGK model. The simulations of droplet formation in a cross-junction microchannel were performed and compared with the experiments. The numerical results show good agreements with the experimental ones for the evolution of droplet and the droplet size at various inlet velocities. Besides, a dimensionless analysis was carried out. The resulting droplet sizes depend on the Capillary number to a great extent under current conditions.

Numerical simulations of droplet formation in a cross‐junction microchannel by the lattice Boltzmann method

AbstractAn immiscible liquid–liquid multiphase flow in a cross‐junction microchannel was numerically studied using the lattice Boltzmann method. An improved, immiscible lattice BGK model was proposed by introducing surface tension force based on the continuum surface force (CSF) method. Recoloring step was replaced by the anti‐diffusion scheme in the mixed region to reduce the side‐effect and control the thickness of the interface. The present method was tested by the simulation of a static bubble. Laplace's law and spurious velocities were examined. The results show that our model is more advantageous for simulations of immiscible fluids than the existing immiscible lattice BGK models. Computational results of multiphase flow in a cross‐junction microchannel were obtained and analyzed based on dimensionless numbers. It is found that the flow pattern is decided mostly by the capillary number at a small inlet flux. However, at the same capillary number, a large inlet flux will lead to much smaller droplet generation. For this case, the flow is determined by both the capillary number and the Weber number. Copyright © 2007 John Wiley & Sons, Ltd.

Hydrodynamic characterization of a needle sparger rectangular bubble column: Homogeneous flow, static bubble plume and oscillating bubble plume

In this work a detailed experimental hydrodynamic characterization of a needle sparger rectangular bubble column has been performed. The liquid velocity profiles and bubble plume oscillation frequency have been measured by means of laser Doppler anemometry (LDA), and the bubble velocity map by particle image velocimetry (PIV). In this way, the influence of the superficial gas velocity, liquid height and aeration pattern on the column flow structure was analysed. A highly uniform upward flow structure with down flow near the walls was obtained by means of a full-length aeration pattern. This flow structure was preserved even for high gas fractions values. The partial-length aeration patterns with the aerated zone (defined as the aerated width divided by the column width) larger than 0.7 provide a bubble plume and two pure liquid vortical structures in the column bottom, although they are static in nature. With aerated zones lower than 0.6, an oscillating bubble plume is obtained. A non-dimensional analysis of bubble plume oscillation frequency shows a dependence of bubble plume behaviour with the aerated zone. In this way, two different types of bubble plume oscillations, namely confined bubble plume oscillation and free bubble plume oscillation, are introduced and analysed.

Experimental investigation of dc electrical breakdown of long vapour bubbles in capillaries

The dc electrical breakdown of long vapour bubbles in capillaries generated by external heating of the capillary is studied. The fluid columns in the capillary on both sides of the vapour bubble serve as electrodes for the electrical discharges inside the bubble. When a dc voltage is applied across a static vapour bubble, a self-pulsing corona regime is observed, which is followed by a transient spark. The sparking or breakdown voltage of the vapour bubble decreases with increasing conductivity of the NaCl solution. After the transient spark a constricted glow-like discharge is observed in the bubble whilst the bubble expands due to the energy deposition of the discharge. Electrical and optical emission properties of the corona, spark and glow-like regime are discussed.

Effect of solid characteristics on hydrodynamic and mass transfer in a fixed bed reactor operating in co-current gas–liquid up flow

In order to understand better which parameters control the mass transfer efficiencies in biofilters, hydrodynamic and mass transfer parameters have been investigated for seven different packings in a three phase fixed bed reactor operating in co-current gas–liquid up flow. For this purpose, the packing characteristics (bed porosity, particle size and particle shape) and hydrodynamics parameters have been determined. Thus, the pressure drops, global gas hold-up, static gas fraction, slip velocities and bubble size have been investigated. For each type of solid, volumetric oxygen mass transfer coefficients have been measured under different operating conditions of gas (air) and liquid (tap water). The experiments were performed in a cylindrical PVC column with co-current up-flow of gas and liquid at laboratory temperature and atmospheric pressure. Air was injected at the bottom of the column using a porous disc diffuser. The superficial gas velocity ranged from 2.3E−3 m/s to 2.5E−2 m/s, the superficial liquid velocity varied from 1.2E−3 m/s to 3.3E−3 m/s. The column of 0.15 m in diameter and 4 m height was filled with packing. The following values were determined: • Pressure drop through the bed height was measured using differential manometers. • The average values of the global gas hold-up and static gas fraction were determined in the experimental set up by a new technique which is based on a monitoring of liquid flow. • The bubble sizes and slip velocities were determined by image acquisition and data treatment systems on a particular glass cell. • The volumetric oxygen mass transfer coefficient was determined by gas and liquid mass balance techniques. These different techniques applied on the fixed bed bubble column enabled for each type of solid a complete characterisation of hydrodynamic and mass transfer to be described. These experimental tools were used to compare and evaluate the influence of solid characteristics on the reactor performances and to initiate a mass transfer model.

Electrical breakdown of a bubble in a water-filled capillary

In this Communication, the electrical breakdown of a static bubble in a water-filled capillary generated in a dc electrical field is studied. We present experimental results which indicate that the liquid layer between capillary and bubble wall can have an important influence on the breakdown mechanism of the bubble. The breakdown electrical field (atmospheric pressure) without a liquid layer in a (vapor) bubble is 18kV∕cm. When a liquid layer is present, the electrical breakdown of an air bubble is observed at electrical fields typically two times smaller. Local plasma formation is observed in this case possibly due to bubble deformation.

No naked singularities in homogeneous, spherically symmetric bubble spacetimes?

We study the evolution of bubble spacetimes in vacuum and electrovac scenarios by numerical means. We find strong evidence against the formation of naked singularities in (i) scenarios with negative masses displaying initially collapsing conditions and (ii) scenarios with negative masses displaying initially expanding conditions, previously reported to give rise to such singularities. Additionally, we show that the presence of strong gauge fields implies that an initially collapsing bubble bounces back and expands. By fine-tuning the strength of the gauge field we find that the solution approaches a static bubble solution.

Bubble propagation in a helicoidal molecular chain.

We study the propagation of very large amplitude localized excitations in a model of DNA that takes explicitly into account the helicoidal structure. These excitations represent the "transcription bubble," where the hydrogen bonds between complementary bases are disrupted, allowing access to the genetic code. We propose these kinds of excitations in alternative to kinks and breathers. The model has been introduced by Barbi et al. [Phys. Lett. A 253, 358 (1999)], and up to now it has been used to study on the one hand low amplitude breather solutions, and on the other hand the DNA melting transition. We extend the model to include the case of heterogeneous chains, in order to get closer to a description of real DNA; in fact, the Morse potential representing the interaction between complementary bases has two possible depths, one for A-T and one for G-C base pairs. We first compute the equilibrium configurations of a chain with a degree of uncoiling, and we find that a static bubble is among them; then we show, by molecular dynamics simulations, that these bubbles, once generated, can move along the chain. We find that also in the most unfavorable case, that of a heterogeneous DNA in the presence of thermal noise, the excitation can travel for well more than 1000 base pairs.

Behavior of fine particles in the vicinity of a gas bubble in a stagnant and a moving fluid

In order to explain the mass transfer enhancement factor obtained in slurry reactors, a static experimental system and a dynamic one are used to observe the behavior of fine activated carbon particles in the vicinity of a gas bubble. We first investigate the possible adhesion of fine particles in a static system. A gas bubble formed at a needle point, is maintained in a beaker filled with the liquid phase, while injections of concentrated activated carbon particles solutions are made with a syringe over the gas bubble. Visual observation of the bubble show that there is adhesion of particles on the gas bubble, which can be totally covered by activated carbon. This adhesion depends on the ionic strength and on the pH of the liquid solution. Further, we investigated the case of a static gas bubble in a hydraulic tunnel. Use of a movie camera allows to visualize the particles trajectories around the gas bubble. It has been found that there is no adhesion of the fine particles used in this study on the gas bubble when the liquid–solid solution is flowing, the particles follow the streamlines of the fluid; for the highest values of the fluid velocity investigated, we observed a small helicoidal vortex of the carbon particles behind the gas bubble. No influence of the ionic strength, the pH nor of the particle diameter can be pointed out. The activated carbon particles behavior is obviously controlled by hydrodynamic forces in a dynamic liquid system. Observed phenomena are fundamentally different from the static case. Therefore, the enhancement factors obtained using these particles cannot be explained by particle adhesion at the interface.

Evaluation of Two Lattice Boltzmann Models for Multiphase Flows

Two lattice Boltzmann models for multiphase flows, the immiscible fluid model proposed by Rothman and Keller (R–K) and the multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S–C), are studied numerically to compare their abilities to simulate the physics of multiphase flows. The test problem is the simulation of a static bubble. Isotropy, strength of surface tension, thickness of the interface, spurious currents, Laplace's law, and steadiness of the bubble are examined. The results show that the S–C model is a major improvement over the R–K model.

Roles of different hydrophobic constituents in the adsorption of pulmonary surfactant

Surface tension-time adsorption isotherms were measured at 37 degrees C for calf lung surfactant extract (CLSE) and subfractions of its constituents: the complete mix of surfactant phospholipids (PPL), phospholipids depleted in anionic phospholipids (mPPL), hydrophobic surfactant proteins plus phospholipids (SP&PL, SP&mPL), and neutral lipids plus phospholipids (N&PL). Adsorption experiments were done using a static bubble surfactometer where diffusion resistance was present, and in a Teflon dish where diffusion was minimized by subphase stirring. The contribution of diffusion to bubble adsorption measurements decreased as phospholipid concentration increased, and was small at 0.25 mM phospholipid. At this phospholipid concentration, PPL, mPPL, and N&PL all adsorbed more rapidly and to lower final surface tensions than dipalmitoyl phosphatidylcholine (DPPC) on the bubble. However, none of these phospholipid mixtures adsorbed to surface tensions below 46 mN/m after 20 min, behavior that was significantly worse than CLSE, SP&PL, and SP&mPL which additionally contained hydrophobic SP. Both CLSE and SP&PL rapidly adsorbed to surface tensions below 25 mN/m at 0.25 mM phospholipid concentration on the bubble, as did SP&mPL at a somewhat reduced rate. Further experiments defining the influence of hydrophobic protein content showed that addition of even 0.13% SP (by wt) to PPL improved adsorption substantially, and that mixtures of PPL combined with 1% SP had adsorption very similar to CLSE. Mixtures of SP combined with mPPL had faster adsorption than corresponding mixtures of SP:DPPC, and neither fully matched the adsorption rates of CLSE and SP&PL even at high SP levels (4% in SP:mPPL and 5.2% in SP:DPPC). These results demonstrate that although the secondary zwitterionic and anionic phospholipids and neutral lipids in lung surfactant enhance adsorption relative to DPPC, the hydrophobic SP have a much more pronounced effect in promoting the rapid entry of pulmonary surfactant into the air-water interface.

Iodine Mass Transfer from Xenon-Iodine Mixed Gas Bubble to Liquid Sodium Pool, (II) Development of Analytical Model

Iodine mass transfer in a xenon-iodine mixed gas bubble rising through a liquid sodium pool is analyzed on the basis of a diffusion model applied to the first short stage just after the bubble generation and a convection model applied to the successive stage. In the diffusion model, production of sodium iodide aerosols and generation of the heat caused by the chemical reaction of iodine vapor and sodium vapor are taken into account in addition to the diffusion of vapor and aerosols and the heat conduction in a static spherical bubble. The diffusion of aerosols is composed of Brownian motion, thermophoresis and diffusiophoresis. In the convection model, the analysis is made for aerosol settling caused by inertial deposition, sedimentation and Brownian motion in an internal flow induced by a spherical cap bubble rising. Increase in the initial iodine concentration in the bubble is shown to enlarge the temperature difference across a region between the reaction front and the bubble surface and to enhance a c...

Iodine Mass Transfer from Xenon-Iodine Mixed Gas Bubble to Liquid Sodium Pool, (II). Development of Analytical Model.

Iodine mass transfer in a xenon-iodine mixed gas bubble rising through a liquid sodium pool is analyzed on the basis of a diffusion model applied to the first short stage just after the bubble generation and a convection model applied to the successive stage. In the diffusion model, production of sodium iodide aerosols and generation of the heat caused by the chemical reaction of iodine vapor and sodium vapor are taken into account in addition to the diffusion of vapor and aerosols and the heat conduction in a static spherical bubble. The diffusion of aerosols is composed of Brownian motion, thermophoresis and diffusiophoresis. In the convection model, the analysis is made for aerosol settling caused by inertial deposition, sedimentation and Brownian motion in an internal flow induced by a spherical cap bubble rising.Increase in the initial iodine concentration in the bubble is shown to enlarge the temperature difference across a region between the reaction front and the bubble surface and to enhance a contribution of thermophoresis to the aerosol diffusion through the region. The decontamination factor obtained from the calculation describes well a rapid increase at the first stage and a slow increase in the successive period, which are seen in measured decontamination factors, and suggests the breakup of the original bubble during rising through the pool.

Modelling the Dissolution of a Static And Rising CO2 Bubble Into Athabasca Bitumen

Abstract The dissolution of a single CO2 bubble into Athabasca bitumen was modelled for the cases of static and rising bubbles. The models for the dissolution of the static bubble included a quasistationary model and a simpler molecular diffusion model. For the rising bubble, the models were based on Brian Hales Levich's Nusselt number correlations and Higbie's penetration theory. The predictions for the static bubble case, over a temperature range of 300 –400 °K and a pressure range of 1 – 6 MPa, suggest that the diffusion is enhanced at lower temperatures and higher pressures due to the high CO2 solubility in bitumen. The dissolution of the rising bubble is predicted to be influenced by both molecular and convective diffusion, leading to a much faster bubble dissolution as compared to the static bubble. Due to a combination of effects, the models predict a minimum to exist in the dissolution time for the rising bubble with respect to temperature. Introduction Bitumen is a viscous, dense crude oil composed of a multitude of paraffinic, naphthenic and aromatic hydrocarbons. It is contained in extensive oil sand reserves in Alberta, principally in the Lloydminster, Peace River, Cold Lake and Athabasca regions. The diffusion of gases into bitumen is of practical interest, as it has applications in the modelling and implementation of both the in situ enhanced oil recovery techniques, such as fire-flooding and CO2 miscible flooding, and the surface viscosity reduction methods. including CO2 injection. Limited discussion of diffusion of gases into bitumen is available in the literature; therefore, there is a need for developing a predictive method for the diffusional process dealing with the dissolution of gases into the bitumen phase. It is pointed out that no experimental data exist with which the predictions can be compared. The dissolution of a gas into the bitumen could be affected by the presence of other phases in the reservoir. including the aqueous and the (inorganic) sand/clay phases. In addition, inclusion of the geometrical details of the gasliquid/ solid phases would add further complexities in the dissolution calculations. In view of the above, this study examines as a first step the dissolution of a single bubble of CO2 gas into a surrounding mass of bitumen. The models considered for the dissolution of a static bubble include a quasi-stationary approach and a semi-empirical approach in which the Nusselt number for mass transfer from the bubble was set as 2.0 (which is a theoretical value for purely molecular diffusion). For the rising bubble, essentially at the terminal velocity conditions under Stokes' law, mass transfer from the bubble is described by Higbie's penetration theory and by the Brian Hales Levich's correlations. In addition to assessing the effect of translatory motion on bubble dissolution, the parameters varied in order to consider their impact upon CO2 dissolution into bitumen include temperature, pressure initial bubble radius and mass and the initial gas concentration in bitumen. The properties of the CO2 bitumen system needed in the models Include surface tension, mass diffusivity, bitumen density, gas solubility and viscosity.