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Gas bubbles can be generated naturally or introduced artificially in porous media. Gas bubble migration through porous media governs the rate of gas emission to the atmosphere as well as the hydraulic and mechanical properties of sediments. The migration of air bubbles through water-wet porous media of uniform geometry was studied using a glass micromodel. Experiments were conducted to measure the velocity of bubbles of various lengths rising in a glass micromodel saturated with different test liquids and varying elevation angles. The results showed a linear dependency of the average bubble velocity on the bubble length and the sine of inclination angle of the micromodel. Comparisons were made using experimental data for air bubbles rising in kerosene, Soltrol 170 and dyed white oil. The effective permeability of the micromodel for the gas bubble, Kg, was calculated for different systems at different inclination angles, assuming that the effective length for viscous dissipation is equal to the initial static bubble length. It was found that the calculated permeability of the medium for gas bubbles had an increasing trend with increasing the bubble length. To visualize the periodic nature of the flow of rising bubbles in a porous medium, the motion of the air bubbles in white oil was video recorded by a digital camera, reviewed and analyzed using PowerDVDTM11 software. The bubble shape, exact positions of the bubble front and bubble tail during motion and, hence, the dynamic bubble length were determined through image analysis. Numerical simulation was performed by modifying an existing simulation code for the rise velocity of a gas bubble and the induced pressure field while it migrates through the pore network. The results showed that the rise velocity of a gas bubble is affected by the grid size of the pore network in the direction perpendicular to the bubble migration. The findings of this study can have important implications for studies on the migration of injected gas bubbles in geoenvironmental applications, as well as fundamental studies on bubble transport and behavior in porous media.

In a non-uniform temperature gradient fluid medium, the surface tension varies according to the local temperature conditions. The surface tension in the cold fluid region is greater than that in the hot region. Therefore, in a zero-gravity stagnant fluid of a non-uniform temperature field, this difference in surface tension creates a net force acting on the fluid particles, which leads to a general fluid motion from the hot region to the cold region. In present paper the influence of the vibrations on the thermocapillary flow is considered for isolated bubble migration toward the hotter side for different frequencies (f) from 0.01 to 0.2 Hz, which show small frequencies vibrations aboard space platforms can have significant effects on bubble movement and its direction. Thermocapillary bubble migration flow pattern under the effect of both Marangoni and vibration forces are also presented.

The spontaneous migration of droplet/bubble has widely application in manipulating droplet/bubble in microgravity. In this study the droplet/bubble migration due to thermal capillary force under uniform incoming thermal radiation is numerically investigated. The numerical model is based on the transient two-dimensional axisymmetric model with a level set method. After validation with the analytical solution under low Reynolds numbers and Marangoni numbers, the study is extended to the droplet/bubble migration under high Reynolds numbers and Marangoni numbers. The ratios are defined as the values in the outer continuous phase over those in the inner discrete phase. The ratios of dynamic viscosity, thermal conductivity, density and specific heat on the migration velocities of droplet/bubble are investigated under all Reynolds numbers. It is found that the droplet/bubble can migrate spontaneously under thermal radiation due to thermal capillary effect, the driving force is from the induced pressure drop in the middle region of droplet/bubble. Under low Reynolds numbers the migration velocities depend only on the ratios of dynamic viscosity and thermal conductivity, while under high Reynolds numbers they also depend on the ratios of density and specific heat. Under all Reynolds numbers the migration velocities are the lowest when the dynamic viscosity or thermal conductivity in the continuous phase is equal to that in the discrete droplet/bubble phase. With the increasing difference between the continuous phase and discrete phase, the migration velocities are increased. This study might be helpful for manipulating droplet/bubble through thermal capillary force with incoming thermal radiation.

In a non-uniform temperature gradient fluid medium, the surface tension varies according to the local temperature conditions. The surface tension in the cold fluid region is greater than that in the hot region. Therefore, in a zero-gravity stagnant fluid of a non-uniform temperature field, this difference in surface tension creates a net force acting on the fluid particles, which leads to a general fluid motion from the hot region to the cold region.

This paper investigated the bubble migration and evolution during gas-liquid flow in oil-pipelines. Multi-scale bubbles migrated in the pipe while interacting with each other, causing coalescence and disintegration. The bubbles collided and coalesced, forming a new air pocket in the downward inclined pipe that blocked the transportation of both the gas and liquid phases. Consequently, the buoyance weakened the migration ability of the bubbles, which is known as re-coalescence. To investigate, a new transient model applied with the population balance model (PBM), and Eulerian-Lagrangian coupling scheme is proposed. The complex flow field was modeled using the Eulerian scheme, while the migration of the bubbles was designed in the Lagrangian mesh. Furthermore, the PBM was employed to describe the multi-scale bubble interaction and migration. Smooth particle hydrodynamics were applied to connect the bubble-dimension and pipe-dimension descriptions. Therefore, the bubble fraction could be described to predict the re-coalescence of air pockets. The required unknown model parameters were extracted from the published experimental data, while the simulation results corresponded well with the measured results. During the simulation, the effect of the liquid Froude number and pipe inclination on the size distribution of the multi-scale bubbles were investigated. The results indicated that an increase in the pipe inclination and liquid Froude number improved the bubble migration capacity, leading to a broader distribution of bubbles of all sizes.

This work was supported by the research fund of Hanyang University (HY-201700000002411). The data presented in this study are available at http://jwjang1977.wixsite.com/mysite/data.

The spontaneous bubble migration and the active manipulation have widely applications in outer space. In this paper, the bubble migration driven by the thermal capillary effect is numerically investigated under variable buoyancy. The numerical model is built up through the transient two-dimensional axisymmetric model with a level set method. It is found that the magnitude and direction of bubble migration velocity is determined by the competition of upward buoyant effect and downward thermal capillary effect. These two effects can be controlled by changing the ratios of density, viscosity, thermal conductivity of bubble over surrounding liquid, as well as Reynolds number, Froude number, Peclet number and Marangoni number. With increasing Froude number or decreasing density ratio, the thermal capillary effect becomes dominant over the buoyant effect, the bubble will migrate from upward to downward. The Marangoni number has negligible effect on the bubble migration at low Reynolds numbers, while at high Reynolds numbers, increasing Marangoni number can reduce the upward migration velocity due to stronger thermal capillary effect. At low Reynolds numbers, with the increasing ratios of viscosity and thermal conductivity, the downward driving force is increased, while at high Reynolds numbers, the ratios have negligible effect on the bubble migration. These findings may provide the guidance for actively manipulating the bubbles under variable buoyancy.

Thermocapillary motion of initially spherical bubbles due to the constant temperature gradient in a liquid bounded medium is simulated numerically for low, intermediate, high Reynolds and Marangoni numbers using a three dimensional model. The volume of fluid (VOF) method was used to track the liquid/gas interface utilizing a geometric reconstruction scheme based on the piece-wise linear interface calculation (PLIC) method of Ansys-Fluent (2011) to capture the bubble interface. The simulation results are in good agreement with the earlier experimental observations, and the migration velocity of the bubble is greatly influenced by the temperature gradient which thrusts the bubble from cold to hot regime. The results indicate that the scaled velocity of bubbles decreases with an increase of the Marangoni number, which agrees with the results of previous space experiments. Thermal Marangoni number (MaT) of single bubble migrating in the zero gravity condition ranged from 106 to 904620, exceeding that in the previous reported experiments and numerical data that was limited to 10,000. In addition, an expression for predicting the scaled velocity of the bubble has been developed based on the obtained data in the present numerical study.

We report experiments on the migration of a large bubble in an otherwise monodisperse two-dimensional (2D) foam sheared in a wide-gap Couette device. The bubble migrates away from the walls toward an equilibrium position between the center of the gap and the inner cylinder. This differs from the situation in a narrow-gap Couette device, where the equilibrium position is at the center of the gap [Mohammadigoushki and Feng, Phys. Rev. Lett. 109, 084502 (2012)]. The shift in equilibrium position is attributed to the non-Newtonian rheology of the foam, which is brought out by the nonhomogeneous shearing in a wide-gap geometry. Two aspects of the rheology, shear-thinning and the first normal stress difference, are examined separately by comparing with bubble migration in a xanthan gum solution and a Boger fluid. Shear-thinning shifts the equilibrium position inward while the normal stress does the opposite. Bubble migration in the 2D foam is the outcome of the competition between the two effects.

Compared to the drawbacks of traditional experimental and numerical methods for predicting bubble migration, such as high experimental costs and complex simulation operations, the data-driven approach of using deep neural network algorithms can provide an alternative method. The objective of this paper is to construct a two-branch deep neural network (TBDNN) model in order to improve the high-fidelity bubble migration results and further reduce dependence on the quantity of experimental data. A TBDNN model is obtained by embedding the features of the Kelvin impulse into a basic deep neural network (BDNN) system. The results show that compared to the original BDNN model, TBDNN performs much better in accurately predicting bubble migration based on the same amount of training data. Using the TBDNN model, the critical condition of bubble oscillation at a fixed location can be detected under the influence of boundary properties (normalized stiffness and mass) and bubble standoff. Furthermore, the initial position of the bubble and normalized stiffness of boundaries have a positive correlation with bubble migration, whereas normalized mass has a negative impact. It was found that the normalized mass of boundaries plays the most important role in affecting bubble migration compared to the standoff and stiffness when using the method of variable sensitivity analysis.

Recent theoretical models have suggested that bubbles are unlikely to undergo significant migration in a compaction crystal mush by capillary invasion while the system remains partly molten. To test this, experiments of bubble migration during compaction in a crystal-liquid mush were modeled using deformable foam crystals in corn syrup in a volumetric burette, compacted with rods of varying weights. A bubble source was provided by sodium bicarbonate (Alka-Seltzer®). Large bubbles (>several crystal sizes) are pinched by the compacting matrix and become overpressured and deformed as the bubbles experience a load change from hydrostatic to lithostatic. Once they begin to move, they move much faster than the compaction-driven liquid. Bubbles that are about the same size as the crystals but larger than the narrower pore throats move by deformation or breaking into smaller bubbles as they are forced through pore restrictions. Bubbles that are less than the typical pore diameter generally move with the liquid: The liquid + bubble mixture behaves as a single phase with a lower density than the bubble-free liquid, and as a consequence it rises faster than bubble-free liquid and allows for faster compaction. The overpressure required to force a bubble through the matrix (max grain size = 5 mm) is modest, about 5 %, and it is estimated that for a grain size of 1 mm, the required overpressure would be about 25 %. Using apatite distribution in a Stillwater olivine gabbro as an analog for bubble nucleation and growth, it is suggested that relatively large bubbles initially nucleate and grow in liquid-rich channels that develop late in the compaction history. Overpressure from compaction allows bubbles to rise higher into hotter parts of the crystal pile, where they redissolve and increase the volatile content of the liquid over what it would have without the bubble migration, leading to progressively earlier vapor saturation during crystallization of the interstitial liquid. Bubbles can also move rapidly by ‘surfing’ on porosity waves that can develop in a compacting mush.

Bubble migrations in liquid titanium melt under hypergravity field is modeled using commercial computational fluid dynamics software FLUENT 6.3 (Fluent inc., USA). The two-phase fluid model, incorporated with the Multiple Reference Frames (MRF) method is used to predict the movement of the bubble in the melt. Simulated results are compared with experimental data from the water model measurement and reasonable agreements are obtained. Furthermore, the computed results show that the bubble migration under hypergravity field includes the movement forward to the casting rotating shaft and the movement opposite to the direction of the rotating mould. In addition, the initial bubble size and the surface tension between the melt and the gas bubble have an important effect on the distortion of the bubble.

It is known that, in upward pipe or channel flow, bubbles migrate toward the wall and the distribution of the local void fraction has saddle shape. In our experiment, 1mm mono-dispersed bubbles were generated in the vertical channel by the addition of surfactant. In the case with a small amount of 3-Pentanol in the liquid-phase, the bubbles accumulated near the wall and formed bubble clusters. On the other hand, in the case with Triton X-100 which has much higher molecular weight, the bubbles did not migrate toward the wall. The surfactants cause Marangoni effect and change the boundary condition of the bubble surface. One of the factors of the bubble migration is thought to be the shear-induced lift force. It is indicated that the shear-induce lift force is strongly influenced by the change of the boundary condition due to the presence of surfactants.

Marangoni convection, whether thermal or solutal, is known to have a profound impact on many technological processes involving gas inclusions in a liquid phase. Evidently, similar phenomena may arise both in thermocapillary and solutocapillary situations, due to similarity of the motion driving mechanisms. However, the fact that the characteristic times of heat and surfactant diffusion generally differ by several orders of magnitude lends singularity to the behavior of Marangoni convection in inhomogeneous mixtures. Moreover, in the solutocapillary case one can meet the action of some additional effects associated with dissolution of the surfactant in a liquid, its adsorption at the interface and evaporation into a gas phase. This paper presents a comparative analysis of the results of ground experiments studying the behavior of air bubbles in a liquid under the action of thermocapillary and solutocapillary forces. The use of original experimental techniques makes it possible to eliminate the influence of gravity effects. A new Marangoni phenomenon—solutocapillary bubble migration—was detected and investigated. The results of studying thermal and concentration convective flows and bubble motion, in relation to bubble size, time, liquid layer thickness and fluids properties, are presented and discussed.

To provide insight into the mechanism of bubble migration in in situ air sparging in a coarse porous medium, the rise of air bubbles through a granular porous medium is studied through video photography enhanced with image analysis. The porous medium is simulated by a fully saturated cylindrical glass column filled with 4-mm glass beads in random packing order. The experimental procedure for introducing and visualizing a single air bubble is discussed, and the average rise velocity as a function of the emerging bubble radius is directly measured. Compressed air is injected into the base of the column through the use of an electronically controlled solenoid valve. The resulting bubble motion is recorded by camcorder, and still frames are captured and enhanced from the videotape with an image analyzer. The vertical rise of a bubble through the porous medium displays a linear dependence on time. This is the first study to quantify the terminal velocity of an air bubble rising in a stationary porous medium. Comparison is made to experimental data on air bubbles in water and Soltrol obtained using the same video photography and image analysis techniques. Although a porous medium is sometimes represented as a bundle of capillary tubes, an air bubble rising in a granular porous medium is shown to exhibit significantly different behavior from a bubble rising in either a capillary tube or a tube with a diameter comparable to the equivalent diameter of the bubble. The effect of a bubble chain, a series of single bubbles separated vertically from each other by a few centimeters, on air bubble migration in a granular porous medium is also discussed.

While the Bjerknes force is not the only force experienced by a bubble subjected to an acoustic field; studies of bubble translation in non-flowing fluid have identified Bjerknes force as being the most influential. Therefore, Bjerknes force can be used to trap bubbles in predefined locations of maximum and minimum absolute pressure. Specifically challenging is to determine these locations in complex geometries because direct measurement of the acoustic pressure for the whole system is generally not possible. The objective of this research is to numerically predict Bjerknes force effect on bubble migration and accumulation in a complex 3D geometry that includes piezoelectric materials, elastic materials and a fluid media. A numerical solution of the acoustic pressure field was obtained for this geometry, valid in the range of small pressure oscillations. Additionally, using the linearized Rayleigh-Plesset equation, which gives the volumetric oscillations of a bubble subjected to an acoustic field, the Bjerknes force was numerically computed. By knowing the Bjerknes force, a bubble migration pattern upon entering the system was predicted. A CMOS high speed camera was used to experimentally monitor bubble multimode excitation and bubble response to a stationary pressure field validating our numerical results. Results are presented for experiments conducted for a 1mm bubble diameter with acoustic fields ranging from 7 to 10 kHz which correspond to values of the structure and/or the bubble’s resonant frequency.

Significant unplanned discoveries are becoming more commonplace in low-g fluids experiments aboard the ISS. Such 'science of opportunity' often takes place on the periphery of other experiments prompting further, though perhaps tangential, investigations. For example, during the routine liquid fill of a test cell for a separate experiment, rapidly compressed air bubbles are observed to drift along paths with vector components common to the residual acceleration. This is expected. However, the bubble velocities measured are up to three orders of magnitude higher than those attributable to buoyancy in the appropriate Stokes flow limit. We present quantitative data of the repeated phenomena that cannot be reconciled from a conventional theoretical perspective. We offer a candidate mechanism for the flow, while citing prior theoretical work that may have anticipated such phenomena. Such compressed bubble migration may lead to elegant methods of phase separation for certain fluid systems aboard spacecraft.

The migration of an isolated gas bubble in an immiscible liquid possessing a temperature gradient is analyzed in the absence of gravity. The driving force for the bubble motion is the shear stress at the interface which is a consequence of the temperature dependence of the surface tension. The analysis is performed under conditions for which the Marangoni number is large, i.e. energy is transferred predominantly by convection. Velocity fields in the limit of both small and large Reynolds numbers are used. The thermal problem is treated by standard boundary layer theory. The outer temperature field is obtained in the vicinity of the bubble. A similarity solution is obtained for the inner temperature field. For both small and large Reynolds numbers, the asymptotic values of the scaled migration velocity of the bubble in the limit of large Marangoni numbers are calculated. The results show that the migration velocity has the same scaling for both low and large Reynolds numbers, but with a different coefficient. Higher order thermal boundary layers are analyzed for the large Reynolds number flow field and the higher order corrections to the migration velocity are obtained. Results are also presented for the momentum boundary layer and the thermal wake behind the bubble, for large Reynolds number conditions.

The aim of this paper is to advance the numerical investigation of unsteady thermocapillary migration of gas bubbles in a fully confined non-isothermal liquid. The relevance of the study is twofold: to support space experiments such as the Italian experiment on board of the Spacelab IML-2 Mission and to fill a lack in thermocapillary migration studies mainly devoted to slow motion in infinite medium (so that no comparison is possible with experimental results). The motion due to surface tension gradients of one and two spherical bubbles inside a liquid filling a cylindrical box, with differentially heated ends disks, is herein analysed, both for linear and quadratic temperature dependence of the surface tension at the bubble-liquid interface. A Galerkin finite elements method is employed to solve the unsteady axisymmetric governing equations casted under a velocity, vorticity, temperature formulation. The flow field into the liquid medium, the net force exerted on the bubbles, the bubbles speed and location are determined as a function of the time; pressure and temperature fields around the bubble are reported.

The wall void peaking distribution observed in an upward turbulent bubbly boundary layer along a flat plate is generated by bubbles that move towards the plate, come into contact with the wall and then slide along it. This transverse ‘migration’ has been studied using flow visualization, high speed video and particle tracking techniques to measure the trajectories of mono-disperse air bubbles at very low void fractions. Investigations have been performed at four Reynolds numbers in the range 280 3), the interface deformation is such that bubbles do not remain at the wall, even when they are released at the surface. Also, bubble migration is shown to be non-systematic, to have a non-deterministic character in the sense that trajectories differ significantly, to increase with Reynolds number and to take place on a short time scale. A series of experiments with isolated bubbles demonstrates that these results are not influenced by bubble–bubble interactions and confirm that two-way coupling in the flow is limited. Flow visualizations show that the migration originates with the capture of bubbles inside the large turbulent structures of the boundary layer (‘bulges’). The bubbles begin to move towards the wall as they cross these structures, and the point at which they reach the wall is strongly correlated with the position of the deep ‘valleys’ which separate the turbulent ‘bulges’. The analysis of the mean Lagrangian trajectories of migrating bubbles confirms these observations. Firstly, the average time of migration calculated from these trajectories coincides with the mean transit time of the bubbles across the structures. Secondly, once the trajectories have been scaled by this transit time and the boundary layer thickness δ, they all have the same form in the region y/δ

Introduction: Air bubble location following embryo transfer (ET) is the presumable placement spot of embryos. The purpose of this study was to document endometrial air bubble position and migration following embryo transfer. Design: Multicenter prospective case study. Materials and Methods: Eighty-eight embryo transfers were performed under abdominal ultrasound guidance in two countries by two authors.(EC, FR) A single or double air bubble was loaded with the embryos using a soft, coaxial, end opened catheters. The embryos were slowly injected 10–20 mm from the fundus. Air bubble position was recorded immediately, 30 minutes later and when the patient stood up. Results: Bubble marker location analysis revealed a random distribution without visible gravity effect when the patients stood up. The bubble markers demonstrated splitting, moving in all directions and dispersion. Conclusion: Air bubbles move and split frequently post ET with the patient in the horizontal position, suggestive of active uterine contractions. Bubble migration analysis supports a rather random movement of the bubbles and possibly the embryos. Standing up changed somewhat bubble configuration and distribution in the uterine cavity. Gravity related bubble motion was uncommon, suggesting that horizontal rest post ET may not be necessary. This report challenges the common belief that a very accurate ultrasound guided embryo placement is mandatory. The very random bubble movement observed in this two-center study suggests that a large “window” of embryo placement maybe present.

When a bubble moves subject to the combined action of buoyancy and a vertical temperature gradient, the flow in the surrounding fluid reveals complex topology whether in the laboratory frame of reference or a reference frame traveling with the bubble. Two cases are considered, the first corresponding to neglecting convective transport altogether, and the second when convective transport of energy is permitted in the model. Results are illustrated via streamlines in meridian section. The results demonstrate that fresh intuition must be developed regarding this class of problems.

DNS of turbulent bubble-laden channel flow has been used with one-way coupling to investigate consequences of a postulated dependence of acceleration on drag. This dependence is known to hold for converging and diverging steady streamlines, and is here postulated to also exist for the instantaneous acceleration of micro-bubbles that arises from turbulent velocity fluctuations. Bubble segregation is found to be considerably increased through this dependency of drag on acceleration, particularly for smaller bubbles.

Under microgravity environments, the thermocapillary migration of a deformable gas bubble placed in a liquid with a constant temperature gradient is investigated numerically. A finite difference method with boundary-fitted coordinates is employed to solve the axisymmetric governing equations. An iterative procedure is introduced for the computation of the deformable shape and the thermal velocity of the gas bubble. The influence of the Marangoni and capillary numbers is considered

Thermocapillary flow is driven by temperature-induced surface tension variations along a liquid free surface. The experiments and the calculations for the flows in open cylindrical containers were carried out both in space and on ground. The detail phenomena have been made clear from these investigations. In 1995, however, numbers of air bubbles were merged incidentally in the cylindrical container and moved along the flows while the Oscillatory Thermocapillary Flow Experiment 2 (OTFE-2) was carried out on the Second United States Microgravity Laboratory (USML-2). These bubbles gradually moved to the flow centers and finally all the distances between two bubbles became almost the same.

Most Hanford waste tanks do not have buoyant displacements, even those with deep submerged sediment layers and moderate gas generation rates. Most tanks apparently achieve a steady state where gas generation is balanced by a steady background release so they never attain the neutral buoyancy gas fraction. In a few tanks, however, gas generation exceeds the background release, which allows gas to accumulate to the point of buoyancy. The mechanism for this background release is unknown, but we postulate that the background release is a slow migration of bubbles through the sediment. This document, an addendum to PNNL-13337, ''Preventing Buoyant Displacement Gas Release Events in Hanford Double-Shell Waste Tanks,'' presents the derivation of the equation in the Bubble Migration Model that explains buoyancy.

This paper presents the results from a one-way coupled, Euler–Lagrangian, direct numerical simulation of bubbles injected into a turbulent boundary layer. The Reynolds number of the turbulent boundary layer varies from 420

The migration of a gas bubble under the combined action of buoyancy and a downward temperature gradient is analyzed. Inertial effects are considered negligible, but allowance is made for convective transport of energy in the model. Results from a numerical solution of the governing equations are presented and discussed.

This article proposes that the experimental data associated with Treuner et al. (Treuner, M., Galindo, V., Gerbeth, G., Langbein, D., and Rath, H. J., J. Colloid Interface Sci. 179, 114 (1996)) indicates that a secondary oscillation may exist for bubble motion due to thermocapillary effects in a low gravity environment. This oscillation in the velocity appears to have a frequency of about 4 Hz for a 2.0-mm bubble in octane with a temperature gradient of about 0.56°C/mm.

The migration rate of bubbles in UO2 has been studied. Migration was induced by a temperature gradient caused by a laser beam focused on one surface of the UO2 sample. Temperatures within the specimen were computed from knowledge of the boundary conditions for heat flow and the temperature-dependent physical properties of the material. (The hot surface temperature was calculated from the rate of evaporation of the material, and the cold surface temperature was measured by a thermocouple.) The migration velocities were determined from the length of columnar grains lying behind lenticular bubbles. We found that bubble migration velocities were much slower than forecast by a diffusion-controlled migration mechanism. In the case of one bubble, we estimated that of a total driving force of 8.6 deg C, about 5.8 deg C was used to develop new ledges on the condensing surface, and only about 0.2 deg C was used to promote diffusion of UO2 molecules across the bubble. From this study we conclude that bubble migration in nuclear fuels is likely to be variable, and especially sensitive to impurities which might affect the processes involved in migration (particularly surface active materials, which grossly affect layer nucleation). Consequently, the response of the fuel to bubble migration under irradiation (swelling and gas release) is in principle subject to control.

The initial size distribution of gas bubbles in lava flows is modified by bubble rise and coalescence during post eruptive cooling and crystallization. A simple model which computes the effects of rise and coalescence accounts for observed features and may provide a means whereby the initial bubble size distribution can be inferred. A model lava flow of assumed thickness, viscosity, and volume percentage of gas bubbles is given an initial bubble size distribution. Bubbles coalesce due to differences in their relative rise velocities. Using a gravitational collection kernel, the process may be modeled by numerical integration of the stochastic collection equation, which yields the change in the number density spectrum of the population from the number densities of all pairs of bubbles and their probabilities of collision. Bubbles rise and coalesce within a fluid interior sandwiched between fronts of crystallization that advance inward from top and bottom. Bubbles that are overtaken by the crystallization f...

In this paper the influence of irradiation-induced helium on the rupture temperature of first wall materials under the combined influence of thermal gradients and transient heating conditions is investigated. The results indicate that for the case of high temperature embrittlement a decrease of the rupture temperature will only be expected below a critical heating rate TC. For the general case of a combined embrittlement and hardening of the matrix a more complex picture has to be expected. The additional influence of helium distributed in the matrix has been taken into account by assuming that He migrates as bubbles under the influence of the thermal gradient to the grain boundaries. Eventually helium bubble growth by coalescence phenomena can occur.

Bubble coalescence in solids is assumed to result when collisions occur between bubbles as they migrate by surface diffusion through the solid. The migration of an isolated pore is examined in detail and the results are applied in a finite‐difference approach, programmed for a digital computer, to predict the variation of the number of bubbles per unit volume as a function both of bubble size and of post‐irradiation annealing time. Two idealized models of bubble coalescence have been treated. The first model considers coalescence resulting from random migration of the bubbles, and the second considers coalescence resulting from unidirectional, biased migration, such as would result in the presence of a thermal gradient. Both models are based on surface diffusion migration of randomly distributed bubbles in a perfect, infinite solid. The results give the predicted variation with time of the entire distribution of bubble sizes, so that various parameters, including the mean bubble radius and volume change, can be predicted. Comparison of the predicted values to parameters measured in appropriate experiments could provide a means of measuring fundamental properties of materials. The results can also be applied to the problem of swelling of reactor fuel materials because of trapped fission gases. Although the present analysis is limited by a number of simplifying assumptions, it is clear that the presence of a thermal gradient can greatly enhance the swelling rate.

Commercial production of glasses for advanced applications often requires processing techniques substantially different from those in common use. In particular, containerless processing is desirable where melt temperatures are sufficiently high that the container wall reacts chemically with the melt and/or promotes crystallization. An ideal environment for containerless processing is provided by the NASA Space Shuttle program because in orbit, near free fall conditions prevail and little levitation is necessary. In such an environment, however, there are serious problems associated with convective mixing and buoyant fining (bubble removal) of glass melts. Alternate techniques for the promotion of mixing and for managing bubbles in space have been proposed by Subramanian and Cole and include thermocapillarity, rotation, oscillation, etc. This paper will describe these experiments and discuss two of a number of ongoing ground-based projects in support of the flight experiments.

Results and analysis of ground-based experiments performed to aid in designing experiments on the behavior of bubbles in a rotating liquid body on board the Shuttle in free fall are presented. Spherical shells filled with silicone oil containing a small gas bubble were spun and filmed by high speed motion picture photography. The rotation of the shell and the trajectory of the bubble motion were recorded and the film was exposed to a motion analyzer connected to a keypunch. The analyzer measured Cartesian coordinates as well as angle, frame number, and rotation rate. Optical correction equations were employed to determine the apparent bubble trajectory relative to an inertial frame of reference. An analytical model for the bubble motion was defined, yielding predictions of velocity and position at different times. Rotation of the fluid container is concluded to aid in centering the bubbles.

Based on the phase-field interface-capturing scheme, a novel and common simulation strategy is put forward with the finite volume method to study the thermocapillary flows, which avoids the fourth-order derivative efficaciously and adopts the mean parameter method to preserve the convergence in the large density ratio flows. Through simulating the thermocapillary migration of bubble, the results show that the new strategy can successfully describe the performance of bubble with different density ratios, i.e. 0.1 and 0.01, and dimensionless parameters Re=1.5×10-2 and 1.5×102. When Re is 1.5×102, the bubble has an apparent deformation, and a larger migration velocity of the bubble is observed with a larger temperature gradient along the surface.

The response of a submerged structure to an underwater explosion (UNDEX) depends on highly nonlinear interactions between the structure, nearby boundaries, the shock wave and the bubble of gaseous explosion products. These complex interactions may significantly influence the loads imparted to a submerged structure by an underwater explosion. This research presents the experimental validation of a coupled Eulerian–Lagrangian numerical modelling approach for simulating the interaction between an underwater explosion, a submerged cylinder, and a free surface or rigid bottom. The three-dimensional simulations in account concurrently for shock wave propagation, cavitation, and gas bubble migration and jetting. The validated simulation methodology is employed to demonstrate how the presence of a submerged cylinder influences bubble migration and its period of oscillation in the vicinity of a boundary.

The bubble evolution in the liquid titanium melt under vertical centrifugal field has been studied by the hydraulic experiment simulation. The bubble migration process in the simple and complex cavities, the bubble morphology, bubble dimensional size diversification under different mould rotational speed has been investigated. The results show that the mould wall has a blocking effect on the bubble migration. The bubble migration in the simple cavity deviates from the line between the bubble initial position and the rotation shaft of the casting mould. Also, the bubbles in the complex cavity gather, re-nucleate and form new big ones for the blocking effect of the complex geometry shape on the radial movement of the bubble. The shape of bubbles in both the simple and complex cavity during the migration process is not a perfect sphere, but an elliptical shape. The critical size of bubble released from the bubble generation chamber decreases with the increment of the mould rotational speed. The diameter of the gas bubbles in the simple cavity during the migration process become bigger and bigger for the pressure difference at different positions of the cavity in the vertical centrifugal field.

Mass transfer from nonaqueous phase liquid (NAPL) to entrapped air induced by a fluctuating water table commonly occurs in residual NAPL zones in aquifers. Gas bubble expansion and vertical migration due to interphase mass transfer could facilitate the upward transport of volatile organic compounds (VOCs) in the aquifer and result in higher mass fluxes into a building relative to those of diffusion-limited (D-L) VOC transport. However, the current vapor intrusion models have not considered bubble migration. In this study, an analytical solution of bubble-facilitated (B–F) VOC transport in the unsaturated-saturated zone was developed. The analytical solution was tested by a numerical solution using the finite-difference method. Sensitivity analyses of model parameters were implemented to understand the VOC transport behaviors. The effects of bubble migration on vapor intrusion pathway completion time ( t c ) and the attenuation factor (AF) were investigated by comparison with the D-L VOC transport model. The results indicate that the D-L model significantly overestimates the t c and underestimates the AF because the model neglects the impacts of bubble migration. Therefore, one may make an inappropriate decision and set up an inappropriate response action schedule if using the D-L model to assess the risk of bubble-facilitated vapor intrusion. The analytical solution was applied to a laboratory experiment. The analytical model managed to interpret the laboratory experiment data, showing that the mass flux of B–F VOC transport is two orders of magnitude higher than that of D-L VOC transport.

Phase field models are developed to study the gas bubble migration in uranium dioxide nuclear fuel in which a large temperature gradient exists during the operation. In this work, thermal diffusion mechanism for nanosized gas bubbles and vapor transport process for micron-sized gas bubbles are considered, respectively. In both cases, gas bubbles migrate to the high-temperature area. Due to the velocity difference between leading and trailing edges of the gas bubbles, nanosized gas bubbles are elongated along the temperature gradient direction when thermal diffusion is dominated. Micron-sized gas bubbles are either compressed along temperature gradient direction to form lenticular shape bubbles or elongated along temperature gradient direction, depending on the location of the gas bubbles within the fuel pellet. Initial gas bubble radius has no significant effect on the gas bubble migration velocity for both thermal diffusion and vapor transport mechanisms. We notice that the shape change of the gas bubble due to vapor transport mechanism has no significant effect on the migration velocity. Furthermore, the center cavity formation is also captured by our model which is due to the migration and accumulation of lenticular gas bubbles at the center of the fuel pellet. The modeling results compare well with experimental observations and theoretical analysis in the literature.

The oscillation and migration of bubbles within an intensive ultrasonic field are important issues concerning acoustic cavitation in liquids. We establish a selection map of bubble oscillation mode related to initial bubble radius and driving sound pressure under 20 kHz ultrasound and analyze the individual-bubble migration induced by the combined effects of pressure gradient and acoustic streaming. Our results indicate that the pressure threshold of stable and transient cavitation decreases with the increasing initial bubble radius. At the pressure antinode, the Bjerknes force dominates the bubble migration, resulting in the large bubbles gathering toward antinode center, whereas small bubbles escape from antinode. By contrast, at the pressure node, the bubble migration is primarily controlled by acoustic streaming, which effectively weakens the bubble adhesion on the container walls, thereby enhancing the cavitation effect in the whole liquid.

In this paper, the governing continuum conservation equations for two-phase flow are solved using the commercial software package (Ansys-Fluent 1) to investigate the thermocapillary movement of a single bubble in stagnant liquid under zero-gravity condition. The current results show that different temperature gradients lead to different bubble migration velocities, and bubble migration velocity varies linearly with the temperature gradient for the given conditions. Furthermore the inside column diameter was found to have a significant influence on the thermocapillary migration of the bubble. Calculation were made in columns with inside diameters Dr 15, 20, 30, 40, 60, 80, 100 and 120 mm. Reduction on bubble migration velocity only occurred when the ratio of the bubble diameter to the column diameter, db/Dr, is greater than 0.267 due to column wall effect. On the other hand, the influence of the column diameter on the rise velocity is negligible when db/Dr is equal to or smaller than 0.267. No bubble shape deformation were observed and the bubble were spherical in shape for all column width. Present investigation of the shape and trajectory of bubble motion driven by surface tension-gradient in different column width is a new area of study and aims to support research into space applications which can help to determine the new migration time and speed.

Three-dimensional interface tracking simulations were carried out to investigate the role of surface tension force in the process of vapor bubble lift-off from a hydrophilic heated surface in nucleate boiling. Since bubbles are frequently flattened along the heated surface in photographic experiments reported in literature, a bubble was assumed to be spheroidal in shape in the initial condition. The effect of phase change at the bubble interface was not taken into consideration for the sake of simplicity. In the present numerical simulations, the initially spheroidal bubble approached the spherical shape due to the surface tension force and was eventually lifted off the surface. The change in bubble shape induced local liquid flow directing toward the bubble base, that was the direct cause of the occurrence of the bubble lift-off. The dependence of the bubble migration velocity on several important parameters including the bubble size, surface tension coefficient and the density of surrounding liquid was also investigated. The change in bubble shape from flattened to more rounded causes the reduction of the surface energy, while the formation of local liquid flow leads to an increase in the kinetic energy. It was demonstrated that the bubble migration velocity after the lift-off can successfully be interpreted from the standpoint of energy conservation during the lift-off process.

This work experimentally studies the behaviour of underwater explosion bubbles near different boundaries. The results are compared with theoretical and experimental data on cavitation bubbles. Although explosion and cavitation bubbles behave similarly on a macroscopic level, there are still some differences, most of which are from the explosive nature of the explosion bubble. The relationship between bubble migration and the Kelvin impulse, surface inertia m* and surface stiffness k* is investigated. We found that none of them comprehensively predicts the migration of both cavitation and explosion bubbles when boundary elasticity is considered. This elasticity should be considered as a relative value with respect to bubble size. On the other hand, the phase between local vibration of boundaries and the pulsation of bubbles could be a useful predictive index of bubble migration. When using research results developed for cavitation bubbles in relation to explosion bubbles, the material presented here may be useful for pointing out their similarities and differences.

A population balance model (the Inhomogeneous MUSIG model) has recently been developed in close cooperation between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf and implemented into the CFD-Code CFX [Krepper, E., Lucas, D., Prasser, H.-M, 2005. On the modelling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611; Frank, T., Zwart, P.J., Shi, J.-M., Krepper, E., Rohde, U., 2005. Inhomogeneous MUSIG Model—a population balance approach for polydispersed bubbly flows, International Conference “Nuclear Energy for New Europe 2005”, Bled, Slovenia, September 5–8, 2005; Krepper, E., Beyer, M., Frank, Th., Lucas, D., Prasser, H.-M., 2007. Application of a population balance approach for polydispersed bubbly flows, 6th Int. Conf. on Multiphase Flow Leipzig 2007, (paper 378)]. The current paper presents a brief description of the model principles. The capabilities of this model are discussed via the example of a bubbly flow around a half-moon shaped obstacle arranged in a 200 mm pipe. In applying the Inhomogeneous MUSIG approach, a deeper understanding of the flow structures is possible and the model allows effects of polydispersion to be investigated. For the complex flow around the obstacle, the general structure of the flow was well reproduced in the simulations. This test case demonstrates the complicated interplay between size dependent bubble migration and the effects of bubble coalescence and breakup on real flows. The closure models that characterize the bubble forces responsible for the simulation of bubble migration show agreement with the experimental observations. However, clear deviations occur for bubble coalescence and fragmentation. The models applied here, which describe bubble fragmentation and coalescence could be proved as a weakness in the validity of numerous CFD analyses of vertical upward two-phase pipe flow. Further work on this topic is under way.

A detailed experimental database, obtained for a 195-mm inner diameter, 9-m-long pipe was used for the validation of models applied in computational fluid dynamics codes for the simulation ofbubbly flow. Since the bubbles were injected via holes at the pipe wall, very useful information on the bubble migration from the pipe wall toward the pipe's center was obtained by measurements at different distances between gas injection and measuring plane. The bubble migration is determined by the forces acting on the bubbles. The multibubble-size group test solver, introduced earlier but with some new extensions, was used to analyze the data. A comparison of results from a simulation and the experimental findings indicate that the turbulent dispersion force according to the Favre averaged drag model is too strong compared with the drag in the radial direction. No appropriate models for bubble coalescence and breakup, which can be applied for a wide range of gas and liquid volume flow rates, are available as yet. Nevertheless, for selected combinations of volume flow rates, the calculated bubble size distributions and radial gas volume fraction profiles show an acceptable agreement with the experimental data.