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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.

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

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

The migration of a drop or bubble in a fluid, onto which a temperature gradient is being applied, is treated analytically. The original calculation by Young, Goldstein and Block /1/ neglects the convective terms in the momentum equation and in the energy equation. Accounting for these terms by perturbation theory fails due to convergence problems. Numerical methods have been applied instead. In this paper convergence is achieved by splitting the convective contributions into terms proportional to the velocity u 0 of migration and terms proportional to the local flow velocity u 1 ( r ). Inclusion of the overall convective heat transport u 0 · V T( r ) into the homogeneous differential operator of the energy equation entails representing the temperature field by modified spherical Bessel functions and convergence at large Marangoni numbers. Likewise, inclusion of the overall convective momentum transport u 0 · V u ( r ) into the homogeneous differential operator of the momentum equation causes a representation of the flow field by modified spherical Bessel functions and convergence at large Reynolds numbers. — For the case of equal physical parameters of the migrating particle and the outer fluid, an exact analytical representation of the velocity of migration in terms of an exponential integral valid for arbitrary Marangoni numbers is derived. The velocity u 0 of migration decreases inversely proportional to the Marangoni number at large Marangoni numbers. - The local contributions u 1 · V T( r ) and u 1 · V u ( r ) to the convective heat transport and momentum transport are treated by a Green's function formalism. The resulting set of equations for the flow field and the temperature field is solved self-consistently.

The thermocapillary migration of a bubble in a liquid possessing a temperature gradient is analyzed in the limit of large Reynolds and Marangoni numbers. Crespo and Manuel (1983) performed an analysis in this limit wherein energy conduction is completely neglected and obtained the bubble migration velocity using energy dissipation arguments. In the present analysis, performed in a coordinate system moving with the bubble, the velocity field in the convection term in the energy equation is approximated in an Oseen-like manner by replacing it by the velocity field far away from the bubble (i.e., the migration velocity of the bubble). Conduction is retained to satisfy the zero conductive heat flux boundary condition on the bubble surface. An approximate solution has been obtained for the Oseen-like energy equation. The bubble velocity obtained using energy dissipation considerations is in agreement with the result of Crespo and Manuel. The solution shows the thermal boundary layer and wake structure in the vicinity of the bubble. The Oseen-like analysis, however, has inherent limitations, as the flow penetrates the bubble surface. These issues are discussed and the result are compared to those in the literature.

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.

The migration of a drop or bubble in a fluid, onto which a temperature gradient is being applied, is treated analytically. The original calculation by Young, Goldstein and Block /1/ neglects the convective terms in the momentum equation and in the energy equation. Accounting for these terms by perturbation theory fails due to convergence problems. Numerical methods have been applied instead. In this paper an Oseen-type method is applied. Convergence is achieved by splitting the convective contributions into terms proportional to the velocity \(\overrightarrow {{\text{u}}_0 }\) of migration and terms proportional to the local flow velocity \(\overrightarrow {{\text{u}}_1 } \:(\overrightarrow {{\text{r}})}\). Inclusion of the overall convective heat transport \(\overrightarrow {\text{u}} _0 \cdot\:\vec \nabla {\text{T}}(\overrightarrow {\text{r}} )\) into the homogeneous differential operator of the energy equation entails representing the temperature field by modified Bessel functions and convergence for Marangoni numbers up to forty. Likewise, inclusion of the overall convective momentum transport \(\overrightarrow {\text{u}} _0 \cdot\vec \nabla \overrightarrow {\text{u}} (\overrightarrow {\text{r}} )\) into the homogeneous differential operator of the momentum equation causes a representation of the flow field by modified Bessel functions and convergence for Reynolds numbers up to forty. — For the case of equal physical parameters of the migrating particle and the outer fluid, an exact analytical representation of the velocity of migration in terms of an exponential integral is derived. Although this situation may hardly be achieved, it enables a fair extrapolation of the numerical results to large Marangoni numbers. The velocity \(\overrightarrow {{\text{u}}_0 }\) of migration decreases inversely proportional to the Marangoni number. — The local contributions \(\overrightarrow {\text{u}} _1 \cdot\vec \nabla {\text{T}}(\overrightarrow {\text{r}} )\) and \(\overrightarrow {\text{u}} _1 \cdot\vec \nabla \overrightarrow {\text{u}} (\overrightarrow {\text{r}} )\) to the convective heat transport and momentum transport are treated by a Green’s function formalism. The resulting set of equations for the flow field and the temperature field is solved self-consistently.

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.

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 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.

Since the last decades, extensive work have been done on the numerical modeling of mono-frequency sonoreactors, we here consider the modeling of dual-frequency sonoreactors. We first present the basic features of the CAMUS code (CAvitating Medium under UltraSound), for mono-frequency excitation. Computation at low, medium and high frequency are presented. Extension of the numerical tool CAMUS is also presented: Caflisch equations are modified to take into account the dual-frequency excitation of the sound. We consider 28–56, 28–100 and 28–200 kHz sonoreactors. Fields of cavitation bubble emergence are quite different from the ones under mono-frequency. Study of spatio-temporal dynamics of cavitation bubbles in a 28–56 kHz sonoreactor is also considered. Taking into account the pressure field induced by the dual-frequency wave propagation, we compute the Bjerknes force applied on the cavitation bubble that is responsible for the bubble migration. A two phase flow approach allows to compute the bubble migration.

Two-dimensional and unsteady problems of drop and bubble Marangoni migration are calculated for cases of larger Reynolds numbers in the microgravity environment. A global treatment method is introduced to solve numerically the complete problem by using the finite differential method, and the thermocapillary force acting on the interface is considered as a body force acting in the computational mesh elements which are passed by the interface. The program of numerical simulation is checked with the symmetric model of bubble migration in Ref. [1]. The asymmetric model of bubble migration is calculated, and the results are different fi om that of the symmetric model. The asymmetric model of drop migration is also calculated. The trajectory of drop in larger Reynolds number fluid is oscillated periodically due to the vortex separation in the wake. (C) 1998 Elsevier Science Ltd. All rights reserved.

The dynamics of a gas bubble situated in a sound-irradiated liquid and near a rigid boundary was studied theoretically to get a better understanding of the role of cavitation microjets in the therapeutic applications of ultrasound (US). The boundary integral method was adopted to simulate the temporal development of the bubble shape, jet formation during bubble collapse and bubble migration. It was found that the dynamic behaviour of the jet and the migratory characteristics of the bubble depend not only on the distance between bubble and boundary but, also, on the properties of the acoustic field. For frequencies of sound fields smaller than or equal to the resonance frequency of the bubble, jet formation and bubble migration toward the boundary are the main features of the interaction. No jet formation was observed for frequencies of sound fields larger than the resonance frequency of the bubble, and the bubble kept its initial position from the boundary throughout its motion. The pressure generated by the impact of the jet developed during bubble collapse close to the boundary may result in the fragmentation of brittle objects, such as renal calculi, dental tartar or intraocular lens.

Two-fluid model simulations of a bubbly vertical boundary layer with point injection are presented. A new bubble turbulence dispersion model, designed to be used with RANS type turbulence models, was formulated and compared with recent data of [1] and [2]. These data showed that bubble migration toward the wall is controlled by the coherent large scale liquid structures within the boundary layer. The model is based on the application of a kinetic transport equation, similar to Boltzmann’s equation, and the idea that by selectively removing bubbles from the liquid eddies within the boundary layer, bubble capture at the wall introduces a preferential direction of migration and/or nonhomogeneous, anisotropic dispersion. This is the first model capable of predicting all the types of void fraction profiles observed experimentally for point injection. It is shown that without this new model, two-fluid model simulations fail to predict the experimental data. In addition, a new physical interpretation of the data of [1] and [2] is presented, which strongly suggests that the quantity controlling bubble migration toward the wall and bubble dispersion, is the boundary layer drift parameter (i.e., the ratio of the bubble’s terminal velocity to the free-stream liquid velocity).

The dynamics of a gas bubble in a square channel with a linearly increasing temperature at the walls in the vertical direction is investigated via three-dimensional numerical simulations. The channel contains a so-called ‘self-rewetting’ fluid whose surface tension exhibits a parabolic dependence on temperature with a well-defined minimum. The main objectives of the present study are to investigate the effect of Marangoni stresses on bubble rise in a self-rewetting fluid using a consistent model fully accounting for the tangential surface tension forces, and to highlight the effects of three-dimensionality on the bubble rise dynamics. In the case of isothermal and non-isothermal systems filled with a ‘linear’ fluid, the bubble moves in the upward direction in an almost vertical path. In contrast, strikingly different behaviours are observed when the channel is filled with a self-rewetting fluid. In this case, as the bubble crosses the location of minimum surface tension, the buoyancy-induced upward motion of the bubble is retarded by a thermocapillary-driven flow acting in the opposite direction, which in some situations, when thermocapillarity outweighs buoyancy, results in the migration of the bubble in the downward direction. In the later stages of this downward motion, as the bubble reaches the position of arrest, its vertical motion decelerates and the bubble encounters regions of horizontal temperature gradients, which ultimately lead to the bubble migration towards one of the channel walls. These phenomena are observed at sufficiently small Bond numbers (high surface tension). For stronger self-rewetting behaviour, the bubble undergoes spiralling motion. The mechanisms underlying these three-dimensional effects are elucidated by considering how the surface tension dependence on temperature affects the thermocapillary stresses in the flow. The effects of other dimensionless numbers, such as Reynolds and Froude numbers, are also investigated.

The bubble dynamics in a viscous liquid have significant applications, but the influence of viscosity on bubble dynamics near a solid wall are still not fully understood, especially for the toroidal bubble. In this paper, a numerical method is presented to study toroidal bubble dynamics near a solid wall in the viscous liquid. The liquid phase is assumed to be incompressible and separated from the gas by a free surface. Based on the finite volume method, the incompressible and viscous Navier–Stokes equations are discretized on the staggered grids, which are solved using the explicit projection method. A Lagrange multiplier method is used to deal with the additional constrain that the tangential stress equals zero, and the bubble surface is advected using a front tracking method. The numerical method is compared with the Rayleigh–Plesset solution for a single bubble with multi-oscillations, and the results between them are favorable with regard to bubble radius history. Finally, the toroidal bubble dynamics near a solid wall with different stand-off parameter (γ= 1.5, 0.95 and 0.6, respectively, where γ= d/Rmax, d is the distance between the solid wall and the bubble center at the moment of formation and Rmax is the maximum bubble radius) at different Reynolds number are studied, including water jet, peak pressure induced by water jet, water layer, bubble rupture, bubble migration, etc, where some important conclusions are obtained.

Liquid-gas multiphase flows occur in many engineering and environmental applications, with the former ranging from the flow of oil and gas in pipelines, of steam and water in nuclear reactors and steam generators, and the evaporation and condensation of refrigerants in refrigeration and air conditioning equipment. In this paper, the dispersion and interaction between microbubbles and turbulence in a horizontal channel flow is investigated using a two-way coupled Eulerian–Lagrangian approach based on large eddy simulation. The microbubbles are considered to be spherical and non-deformable, and are represented by a Lagrangian bubble tracking technique, with the bubbles subject to drag, gravity, buoyancy, shear lift, added mass and pressure gradient forces. Dynamic calibration of a Smagorinsky-type sub-grid scale (SGS) closure is employed to account for the unresolved stresses, whilst a stochastic Markov method is used to describe the effect of the SGS velocity fluctuations on bubble dispersion. Channel flows of water at two shear Reynolds numbers, R e τ = 150 and 590, and three different bubble diameters, d b = 100 , 220 and 330µm, are simulated. The results show acceptable agreement with DNS predictions of single- and two-phase flows, with the low density microbubbles migrating towards the upper channel wall with time under the influence of buoyancy, and segregating in the upper half of the channel, with this effect increasing with bubble diameter. The accumulated bubbles near the upper wall modify the liquid velocity field, with the mean velocity profile becoming asymmetric as a consequence and with slight modification of the turbulent stresses. At higher mean velocity and turbulence levels, the buoyancy effect is reduced due to more effective turbulent dispersion of the microbubbles, leading to reduced bubble migration towards the upper channel wall.

Two dimensional axisymmetric and three-dimensional VOF simulations of gas/liquid transient flow were performed using a multiphase flow algorithm based on the finite-volume method. The results for motion of a multiple bubbles of a heterogeneous sizes aligned horizontally and perpendicular to a hot surface incorporating thermocapillary forces in a rotating liquid in a zero-gravity environment have been presented for the first time. No bubbles broke in any of the cases observed. The results also show that collision and agglomeration of bubbles of unequal sizes diameter are different from those of similar size diameters presented from earlier research work of Alhendal et al. Acta Astronaut. 117, 484–496 (2015). Different flow patterns such as thermocapillary bubble migration, collision, and stream function were observed and presented for the 2-D and 3-D models.

This paper is concerned with the dynamics of large bubbles subject to various strengths of buoyancy effects, which are associated with applications for underwater explosion. The bubble is produced by electric discharge in a low-pressure tank to enhance the buoyancy effects. Experiments are carried out for a bubble in an infinite field, below a free surface and above a rigid boundary. The effects of buoyancy are reflected by the dimensionless parameter ${\it\delta}=\sqrt{{\it\rho}gR_{m}/(p_{amb}-p_{v})}$, where $R_{m}$, $p_{amb}$, $p_{v}$, ${\it\rho}$ and $g$ are the maximum bubble radius, ambient pressure, saturated vapour pressure, density of water and the acceleration of gravity respectively. A systematic study of buoyancy effects is carried out for a wide range of ${\it\delta}$ from 0.034 to 0.95. A series of new phenomena and new features is observed. The bubbles recorded are transparent, and thus we are able to display and study the jet formation, development and impact on the opposite bubble surface as well as the subsequent collapsing and rebounding of the ring bubble. Qualitative analyses are carried out for the bubble migration, jet velocity and jet initiation time, etc. for different values of ${\it\delta}$. When a bubble oscillates below a free surface or above a rigid boundary, the Bjerknes force due to the free surface (or rigid boundary) and the buoyancy are in opposite directions. Three situations are studied for each of the two configurations: (i) the Bjerknes force being dominant, (ii) the buoyancy force being dominant and (iii) the two forces being approximately balanced. For case (iii), we further consider two subcases, where both the balanced Bjerknes and buoyancy forces are weak or strong. When the Bjerknes and buoyancy forces are approximately balanced over the pulsation, some representative bubble behaviours are observed: the bubble near free surface is found to split into two parts jetting away from each other for small ${\it\delta}$, or involutes from both top and bottom for large ${\it\delta}$. A bubble above a rigid wall is found to be subject to contraction from the lateral part leading to bubble splitting. New criteria are established based on experimental results for neutral collapses where there is no dominant jetting along one direction, which correlate well with the criteria of Blake et al. (J. Fluid Mech., vol. 170, 1986, pp. 479–497; J. Fluid Mech., vol. 181, 1987, pp. 197–212) but agree better with the experimental and computational results.

The lack of significant buoyancy effects in zero-gravity conditions poses an issue with fluid transfer in a stagnant liquid. In this paper, bubble movement in a stagnant liquid is analysed and presented numerically using a computational fluid dynamics approach. The governing continuum and conservation equations for two-phase flow are solved using the commercial software package Ansys-Fluent v.13. The volume of fluid method is used to track the liquid/gas interface in 2D and 3D domains, which has been found to be a valuable tool for studying the phenomenon of gas–liquid interaction, and the validation results are in reasonable agreement with earlier experimental observations. The flow is driven via Marangoni influence induced by the temperature difference, which in turn drives the bubble from the cold to the hot region. The results indicate that the inherent velocity of bubbles decreases with an increase in Marangoni number; this is in agreement with the results of previous experiments conducted in Kang et al. (Microgravity Sci Technol 20:67–71, 2008). Some three-dimensional simulations will also be performed to compare and examine the results with two-dimensional simulations. The thermocapillary bubble flow in a 2D swirl axisymmetry driven by the rotation of the walls was also carried out for different angular velocities in zero gravity. The bubble migration speed was found to decrease with increasing angular velocity. This occurrence is due to an increase in the pressure gradient between the cylinder’s outer wall and the axis of rotation, which forces the lowest pressure region to shift from the sides of the bubble to the axis of rotation. A deformation of the bubble and the formation of the two vortices inside the bubble are also observed. These new and original findings aim to help support research into space applications.

The dynamic underwater explosion bubble process is a complex phenomenon with many facets to consider. After detonation, the shockwave quickly strikes nearby structures. The bubble oscillation may then substantially damage the structures, even if the bubble pulse is not large. This is because other effects, such as whipping or water jet impact, often accompany the bubble pulse. This study applied the Eulerian Technique using ABAQUS software to simulate the process of underwater bubble explosion, pulsation and collapse. This approach allows many materials to be used in an Eulerian element and manages with large deformation of materials such as flows and gases. The simulated bubble is equivalent to a bubble generated by 55 g of TNT. Although boundary conditions simplify the model, the method is feasible for simulating bubble dynamics and provides acceptably accurate results on bubble migration in water, pressure pulse, water jet formation, and flow field velocity surrounding the bubble. Future research can use this method to study bubbles, including their interaction with free surfaces and the submerged structures or floating structures.

Directional motion of droplets or bubbles can often be observed in nature and our daily life, and this phenomenon holds great potential in many engineering areas. The study shows that droplets or bubbles can be driven to migrate perpetually on some special substrates, such as the Archimedean spiral, the logarithmic spiral and a cantilever sheet in large deflection. It is found that a bubble approaches or deviates from the position with highest curvature of the substrate, when it is on the concave or convex side. This fact is helpful to explain the repelling water capability of Nepenthes alata. Based on the force and energy analysis, the mechanism of the bubble migration is well addressed. These findings pave a new way to accurately manipulate droplet or bubble movement, which bring inspirations to the design of microfluidic and water harvesting devices, as well as oil displacement and ore filtration.

Large eddy simulation coupled with a Lagrangian bubble tracker is used to investigate the dynamics of a liquid containing microbubbles in a turbulent, horizontal channel flow. Such flows are relevant in a number of engineering and environmental applications, including bubble columns, gas-liquid reactors, fluidised beds and fluid transfer in pipelines. Sub-grid scale stresses are parameterised using a dynamic model, with the microbubbles assumed to be spherical and non-deformable, and subject to drag, lift, gravity, buoyancy, added mass and pressure gradient forces. The bubbles are also momentum-coupled with the carrier fluid. A channel flow of water at a shear Reynolds number, Reτ = 150, and bubble diameter, d = 80 μm, is considered. Results are consistent with those from previous direct numerical simulations, and demonstrate bubble migration towards the upper channel wall with time due to buoyancy effects, and the associated impact on the flow velocity and bubble concentration distribution.

A self-induced flip-flop flow phenomenon in diamond-shaped cylinder bundles has been disclosed in previous studies by the authors. The flip-flop flow oscillation promotes fluid mixing and thus contributes to an enhancement in convective heat and mass transfer when the cylinder bundles are used as heat and mass exchanger equipment. An experimental study was performed to disclose the occurrence of flip-flop flows in diamond-shaped cylinder bundles. Velocity and pressure fluctuations in divergent-flow region inside diamond-shaped cylinder bundles were measured by LDV and piezo-meter, respectively. The difference in the oscillations of flip-flop flows and von Karman vortex streets is disclosed quantitatively. The mechanisms that cause the reciprocating bubble migration in network ducts of diamond-shaped cylinders are explained.

Dynamical process of helium bubbles in face‐centred cubic (fcc) metals has been studied by in situ irradiation and electron microscopy with a video recording system. Brownian type motion of helium bubbles was demonstrated quantitatively by establishing a proportional relation between the mean square of the bubble migration distance and time. This relation yielded the diffusion coefficient of the bubble. Examples of Brownian motion in the matrix and along general grain boundaries in pure aluminium are shown comparatively. Similar Brownian motion was also observed in an Fe‐16Cr‐17Ni austenitic alloy. It was revealed from scanning transmission electron microscopy–electron energy‐loss spectroscopy that Cr was depleted around the bubble surface, but Ni was enriched. Response of the bubble motion to irradiation with high‐energy self‐ions was examined in pure aluminium and both effects of enhancement and retardation of the bubble mobility were found.

Thermocapillary migration of long gas bubbles in cylinders of regular-polygonal or rectangular cross sections is studied. An imposed axial temperature gradient produces a gradient of surface tension leading to a steady migration of the bubble towards the hotter region. A leading order approximation for the bubble migration speed is found by computing the volume flux of liquid through the corner regions of the cylinder, which provide a parallel channel for the flow of fluid driven by the Marangoni stress. A global mass balance is used to relate the dimensionless bubble speed to the modified capillary number Δσ*=γTβa/σ, where β is the temperature gradient, a the tube length scale, σ the mean surface tension, and γT the temperature coefficient of surface tension. The dimensionless bubble speed is found to be linear in this parameter at leading order. The approximation is improved by accounting for the deposition of a thin film on the cylinder walls at small capillary number. A modified Landau–Levich equation...

The effects of pulsed vortex generator jets on a naturally separating low-pressure turbine boundary layer have been investigated experimentally. Blade Reynolds numbers in the linear turbine cascade match those for high-altitude aircraft engines and industrial turbine engines with elevated turbine inlet temperatures. The vortex generator jets (30 deg pitch and 90 deg skew angle) are pulsed over a wide range of frequency at constant amplitude and selected duty cycles. The resulting wake loss coefficient versus pulsing frequency data add to previously presented work by the authors documenting the loss dependency on amplitude and duty cycle. As in the previous studies, vortex generator jets are shown to be highly effective in controlling laminar boundary layer separation. This is found to be true at dimensionless forcing frequencies F+ well below unity and with low (10 percent) duty cycles. This unexpected low-frequency effectiveness is due to the relatively long relaxation time of the boundary layer as it resumes its separated state. Extensive phase-locked velocity measurements taken in the blade wake at an F+ of 0.01 with 50 percent duty cycle (a condition at which the flow is essentially quasi-steady) document the ejection of bound vorticity associated with a low-momentum fluid packet at the beginning of each jet pulse. Once this initial fluid event has swept down the suction surface of the blade, a reduced wake signature indicates the presence of an attached boundary layer until just after the jet termination. The boundary layer subsequently relaxes back to its naturally separated state. This relaxation occurs on a timescale which is five to six times longer than the original attachment due to the starting vortex. Phase-locked boundary layer measurements taken at various stations along the blade chord illustrate this slow relaxation phenomenon. This behavior suggests that some economy of jet flow may be possible by optimizing the pulse duty cycle and frequency for a particular application. At higher pulsing frequencies, for which the flow is fully dynamic, the boundary layer is dominated by periodic shedding and separation bubble migration, never recovering its fully separated (uncontrolled) state.

The turbulence structure in a rising bubbly flow driven by bubble buoyancy has been analyzed using the Eulerian-Lagrangian model. A new method of calculating the two-way interaction between the dispersed bubbles and the liquid phase was proposed to accurately simulate the local fluctuations of liquid flow induced by bubble migration. The present two-dimensional simulation revealed that, (1) in the case of the larger bubble, the turbulence structure has the longer wavelength in the vertical direction, and, (2) the wave spectrum of kinetic energy of the liquid phase is sensitive to the average void fraction and the lift force of the bubbles.

Cavitation generated by lithotripter shock waves (SWs) in non-degassed water was studied using a 60 frames-per-second camcorder—recording the migration of microbubbles over successive SWs. Lithotripter SWs were produced using a Dornier DoLi-50 electromagnetic lithotripter at 0.5 and 2 Hz pulse repetition frequency (PRF). Cavitation was affected by PRF and by the power level (PL) of the lithotripter. At slow PRF, such as shots fired many seconds apart, cavitation was relatively sparse and bubble clouds flowed in the direction of SW propagation. When PRF was increased, the bubble clouds generated by one SW were amplified by subsequent SWs. Cloud amplification was accompanied by an apparent change in the pattern of bubble migration. Whereas bubbles continued to enter the field of view from the prefocal side, the main bubble cloud remained near the focal point. This was due to a streaming of bubbles opposite to the direction of SW propagation. Increasing the PL grew the cavitation field and enhanced the flow of bubbles opposite to the direction of SW propagation. Stepping up the PL acted to push the broad cloud progressively pre-focally (toward the SW source), shifting the position of the plane at which the opposing directional bubble flows collided. [NIH DK43881.]

The behavior of a gas bubble near a rigid boundary in an oscillatory pressure field is numerically investigated by means of two kinds of methods. The boundary integral method is utilized to simulate the bubble profiles at various times, and the image theory is also applied for solving the differential equations describing the nonlinear oscillations and migrations of a spherical gas bubble. Both calculations are performed, assuming that the liquid around a bubble is inviscid, incompressible, and irrotational and that the gas inside the bubble follows a polytropic gas law. The influence of the boundary proximity on the bubble motion is characterized by the bubble migration and the deformation of the bubble shape, especially by the liquid microjet formation. It is found that the period and the amplitude of the bubble oscillation are related not only to the nature of the time‐dependent pressure in the liquid but also to the bubble location from a rigid wall. Furthermore, the influence of the boundary proximity on the frequency response curve associated with the bubble oscillation is examined on the supposition that the surrounding pressure oscillates with small amplitude and a rigid boundary is relatively far from a bubble.

Gas dispersion in an airlift reactor focusing on the closure law on turbulent contribution of added mass is presented. A data bank for bubbly flow in an airlift reactor is presented. The liquid velocity is measured by hot film anemometry and gas fraction and velocity are measured with an optical probe. The sensitivity of numerical simulations of gas dispersion to the modeling of turbulent contribution of added mass is shown. Without the turbulent contribution, the bubbles move toward the region where the turbulence is high and the pressure is low. When the turbulent contribution is introduced, the bubble migration towards the low pressure region is counter-balanced and the void fraction profile is significantly modified. The modeling of the turbulent contribution of added mass is expressed in terms of the turbulent correlations in the gas phase, uGi′uGj′, that can be related to the Reynolds stress in the liquid phase, ui′uj′. © 2011 American Institute of Chemical Engineers AIChE J, 2011

Theoretical and experimental studies of the behavior of a bubble near a plane rigid wall were made. A bubble was generated by focusing a ruby laser into water and the subsequent behavior was observed by means of high-speed photography. The experimental results were compared with the numerical predictions obtained from the boundary integral method as well as from the image theory and we found excellent agreement. A systematic investigation has been carried out on bubble migration and microjet formation, which are considered to be very important phenomena in relation to the impulsive pressure generation during bubble collapse.

On 2007/338, a series of attitude control thruster leaks began on the B-string of the GOES-12 spacecraft. Initial anomaly response to these leaks were hampered by a latch valve cross connect. These leaks continued off and on until 2009/136, and also migrated back and forth between the positive yaw thruster and the negative pitch thruster. A comprehensive leak mass analysis occurred to verify that no oxidizer was leaking beyond the mechanical latch valves. Furthermore, several interesting effects were detected, such as leak precursor bubble migration and oxidizer line temperature transients due to changes in the spacecraft thermal environment. The long term operations of the spacecraft needed to be significantly modified to deal with the isolation of the B-side thrusters.

Results on bubble coalescences from the space experiment of thermocapillary bubble migration conducted on board the Chinese 22nd recoverable satellite are presented in this paper. Some coalescences of large spherical bubbles under microgravity are observed through bubbles staying at the upper side of the test cell. The data of bubble coalescence time are recorded and compared with theoretical predictions, which is based on a theory to describe the tendency of coalescence connected to chemical potential difference. It is implied that the theory is applicable for the experimental data of bubble coalescence. Moreover, the angle between the line of two bubble centers and temperature gradient falled mostly in the range 20 degrees-40 degrees. (C) 2007 Elsevier Inc. All rights reserved.