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Bubble behavior has a significant impact on the characteristics of two-phase flow and heat transfer. To investigate the dynamics of bubbles in a petal-shaped rod bundle channel, the behavior of bubbles in static water in the rod bundle channel was simulated using the volume of fluid method (VOF) and compared with the behavior of moving bubbles in a circular rod bundle channel. The trajectory, shape, and rise velocity of bubbles with different initial sizes were obtained and analyzed to understand the mechanism of bubble behavior through the flow and pressure fields around the bubbles. The results show that bubbles exhibit lateral movement during the ascent process. The smaller the bubble size, the more pronounced the lateral movement, making it more likely for the bubble to touch the wall surface. After touching the wall surface, the bubble slides along the wall surface. Bubbles that do not touch the wall move towards the center of the flow channel and finally rise steadily along the center. The calculated size range produces spherical and ellipsoidal bubble shapes. Before the bubble touches the wall, the bubble deformation increases and the aspect ratio decreases as the bubble gradually rises, reaching stability after a period of time. While after the bubble touches the wall, the bubble adheres to the wall and its shape changes to semi-circular and its aspect ratio decreases rapidly. The stabilization rate of bubble increases as the size of the bubble increases. In the first stage, the bubble velocity rises rapidly from zero and the wake begins to form. In the second stage, the bubble velocity rises slowly and the wake changes asymmetrically at both ends of the bubble. In the third stage, the bubble velocity decreases rapidly if it touches the wall, and the shape of the wake changes near the wall. If the bubble does not touch the wall, the bubble velocity will fluctuate around the stable velocity and the flow field will stabilize, and the wake will be generated and shed in a continuous cycle. The direction of bubble movement can be determined by the pressure distribution around the bubble. Compared to the circular rod channel, the bubbles in the petal-shaped fuel rod channel have a greater lateral displacement and are more likely to touch the wall, while the bubble shape is less variable. The study of bubble upward motion can clarify the bubble behaviour in the petal-shaped rod bundle channel and provide a basis for revealing the two-phase flow and heat transfer mechanism.

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The influences of bubble defects on the bond strengths of externally bonded fiber-reinforced polymer (EB-FRP) concrete joints were investigated using numerical method in this research. Studies of the influences of increasing bubble defect areas on interfacial bonding performance were first conducted. It was observed that the influence of a bubble deficiency located in the middle of the bond region is not significant when the size of the bubble area is less than 2.5% of the effective bond area. Then, further investigation was conducted on the influences of the distances between the bubble and the loaded end, as well as the distance between the bubble and the side of the FRP, the ratio of the bubble's width to the width of the FRP, the number of bubbles with a fixed total area and the distribution of multiple bubbles. It was found that the distances of the bubble to the loaded end and different numbers of bubbles distributed within a fixed area do not significantly affect the bond strength. When the bubble is positioned closer to the side of the FRP, a decrease in load capacity tends to occur earlier, and the amount of decrease also slightly increases. The bond capacity can be influenced by the shapes of the bubbles, and as the bubble width in the lateral direction increases while keeping the bubble areas constant, the load capacity decreases. [ABSTRACT FROM AUTHOR]

Copyright of Petroleum Refinery Engineering is the property of Petroleum Refinery Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study is dedicated to comparison of the results of two-dimensional (2D) and three-dimensional (3D) numerical modeling of dynamics of a single bubble rising in stagnant viscous liquid. The volume of fluid method is used to track the moving interface. This method makes it possible to take into account all the forces acting on the interface in a natural way without using empirical data. The solution of the continuity equation, Navier–Stokes equation, and equation for determining the position of interface is based on the finite volume method. When carrying out numerical experiments, the bubble diameter at the initial time is fixed. It is shown that the shape of the bubbles in the vertical section of the computational domain is different in the case of 2D and 3D simulations. It has been established that the rising velocity of bubble in 3D simulation is greater than in 2D simulation. [ABSTRACT FROM AUTHOR]

This work experimentally analyzed bubbles' coalescence with an air-water interface in the ellipsoidal-wobbling regime for different bubble approach velocities, encompassing the ranges of Eötvös, Weber, and Reynolds numbers of 2-3, 1-4, and 500-1100, respectively. We employed high-speed imaging to measure the bubbles' size, shape, velocity, coalescence time, and number of bounces at the interface. We investigated two criteria to determine the beginning of bubble-interface interaction ("collision"): the physical criterion, based on the distance between the bubble top surface and the interface, and the hydrodynamic criterion, based on the bubble velocity. Gamma distributions represented the coalescence times of bubbles at their terminal velocities well. We found a linear relationship between the coalescence time and the number of bounces. The hydrodynamic criterion was more consistent in representing our data on coalescence time.   • We performed experiments on the coalescence of wobbling bubbles with an interface. • We used physical and hydrodynamic collision criteria to determine coalescence times. • For bubbles at terminal velocity, gamma distributions represent coalescence times. • Coalescence time varied linearly with the number of bubble bounces at the interface. • The hydrodynamic criterion proved to be more consistent than the physical one. [ABSTRACT FROM AUTHOR]

In this study, the dissolution of a single oxygen bubble on a solid surface, here Titanium alloy Ti64, in ultrapure water with different oxygen undersaturation levels is investigated. For that purpose, a combination of shadowgraph technique and planar laser-induced fluorescence is used to measure simultaneously the changes in bubble geometry and in the dissolved oxygen concentration around the bubble. Two different wettabilities of the Ti64 surface are adjusted by using plasma-enhanced chemical vapor deposition. The dissolution process on the solid surface involves two distinct phases, namely bouncing of the oxygen bubble at the Ti64 surface and the subsequent dissolution of the bubble, primarily by diffusion. By investigating the features of oxygen bubbles bouncing, it was found that the boundary layer of dissolved oxygen surrounding the bubble surface is redistributed by the vortices emerging during bouncing. This establishes the initial conditions for the subsequent second dissolution phase of the oxygen bubbles on the Ti64 surfaces. In this phase, the mass transfer of O 2 proceeds non-homogeneously across the bubble surface, leading to an oxygen accumulation close to the Ti64 surface. We further show that the main factor influencing the differences in the dynamics of O 2 bubble dissolution is the variation in the surface area of the bubbles available for mass transfer, which is determined by the substrate wettability. As a result, dissolution proceeds faster at the hydrophilic Ti64 surface due to the smaller contact angle, which provokes a larger surface area. [Display omitted] • Mass transfer around an oxygen bubble interacting with solid surfaces was quantified. • Dissolved oxygen and bubble shape were measured by combined PLIF and shadowgraphy. • A bouncing and a dissolution phase were identified during bubble-surface interaction. • Stronger redistributed bubble boundary layer after bouncing in more hydrophobic case. [ABSTRACT FROM AUTHOR]

The influences of bubble defects on the bond strengths of externally bonded fiber-reinforced polymer (EB-FRP) concrete joints were investigated using numerical method in this research. Studies of the influences of increasing bubble defect areas on interfacial bonding performance were first conducted. It was observed that the influence of a bubble deficiency located in the middle of the bond region is not significant when the size of the bubble area is less than 2.5% of the effective bond area. Then, further investigation was conducted on the influences of the distances between the bubble and the loaded end, as well as the distance between the bubble and the side of the FRP, the ratio of the bubble’s width to the width of the FRP, the number of bubbles with a fixed total area and the distribution of multiple bubbles. It was found that the distances of the bubble to the loaded end and different numbers of bubbles distributed within a fixed area do not significantly affect the bond strength. When the bubble is positioned closer to the side of the FRP, a decrease in load capacity tends to occur earlier, and the amount of decrease also slightly increases. The bond capacity can be influenced by the shapes of the bubbles, and as the bubble width in the lateral direction increases while keeping the bubble areas constant, the load capacity decreases.

Due to the presence of liquid bridge forces, wet particles reveal totally different fluidization behaviours than dry fluidized beds. This paper studies the bubble dynamics of wet Geldart‐D particles in a wet 2D fluidized bed. A digital image analysis method is adopted to identify bubbles and extract bubble properties based on MATLAB software. During fluidization, the bubble feature analysis of optimized binary images captures the bubble size variation, bubble fraction, and bubble shape. The results show that the increasing liquid saturation promotes the gas holding capacity of the emulsion phase, leading to the decreasing bubble fraction. When the particle size grows, the stability of the emulsion phase is promoted and hence the average bubble diameter increases. As the liquid saturation increases, the enhancing liquid bridge forces limit the bubble growth and promote the bubble breakage, which contributes to the small bubbles. With respect to the wet particles, of which the diameter is 1 mm and the liquid saturation is over 15%, slugging is likely to be observed, resulting in the increasing equivalent bubble diameter. The growing liquid saturation increases the wide aspect ratio, decreases the shape factor, and disperses the dependence between the two parameters. This indicates that small and irregular bubbles are likely to be seen in wet fluidized beds. [ABSTRACT FROM AUTHOR]

• Reliable drag model identification: shear-thinning, -thickening, Newtonian fluids. • Investigation of temporal phenomena (periodic shape fluctuations). • Higher indexes (K, n) mean more sphericity and slow movement in more linear path. • Model extension for predicting small bubble rise in low-viscosity liquids. A study of the effects of fluid type (shear-thinning, Newtonian, and shear-thickening) and periodic shape fluctuations of bubbles on the drag coefficient is presented for three bubble sizes (2 mm, 4 mm and 6 mm), three flow consistency indexes (μ w a t e r , 10 μ w a t e r , 100 μ w a t e r) and three flow behavior indexes (0.8, 1, 1.2). Computational Fluid Dynamics (CFD) simulations were performed in addition to previous measurements to obtain local data of the flow hydrodynamics. The results were used to evaluate 12 different drag coefficient estimation models, which are essential for the design of bubble columns. The Dijkhuizen et al. and Rodrigue correlations are suitable for the prediction of terminal velocity in both Newtonian and non-Newtonian liquids with high or intermediate viscosity. Finally, a modification of the correlations enables the prediction of small bubble terminal velocity also in low-viscosity liquids. [ABSTRACT FROM AUTHOR]

In the motion of two spherical bubbles rising side by side, the bubbles are known to attract each other at a high Reynolds number (Re = ρUd/μ). Furthermore, spherical bubbles kiss and bounce under certain conditions; however, deformable bubbles repel each other without kissing. This paper experimentally and numerically presents the flow structures and shape of the nonkissing repulsion of deformable bubbles. For the experimental analysis, we organized bubble behaviors by Galilei number (Ga = ρg1/2d3/2/μ) and Bond number (Bo = ρgd²/σ). The bubbles repelled each other without kissing near the unstable critical curve of a single bubble. The curvature inside the gap, which is similar to the shape of a zigzag behavior bubble, was large. For the numerical analysis, the velocity of the equatorial plane inside the gap was larger due to the potential interaction, although the velocity behind was the opposite due to the strengthened vorticity generated at the surface. Furthermore, the double-threaded wake emerged behind the interacting bubbles, and it showed that the rotation direction was repulsion regardless of whether the bubbles attracted or repelled each other. The streamline behind the bubbles in the 2D plane was from the outside to the inside. [ABSTRACT FROM AUTHOR]

Effect of bubble shape on the terminal velocity of bubbles of three sizes (aspect ratio increased by frother addition and higher liquid medium viscosity). [Display omitted] • Bubble terminal velocity and aspect ratio are linked; corresponding maxima/minima reached at the same time. • Bubbles smaller than 5 mm rise in pure liquids with mobile surfaces and spherical and oblate spheroidal shapes. • Bubbles smaller than 5 mm rise in highly contaminated solutions with rigid surfaces and spherical shapes. • Models to predict bubble terminal velocities as a function of size do not produce reliable results. • Models to predict bubble terminal velocity must consider bubble shape parameters to work. Minerals flotation is a process that involves the formation of a population of bubbles to produce a concentrate by selective capture and separation of particles of valuable hydrophobic minerals on the surface of bubbles. The bubble rising velocity is a crucial piece of information for developing operating and control strategies, and for estimating metallurgical performance of flotation circuits. Bubble rising velocities depend on their size and on the physicochemical characteristics of the surrounding liquid medium. Velocities in pure liquids are the largest possible because gas-liquid interfaces remain clean and fully mobile allowing circulation of the gas phase, but when surfactants and ions from soluble mineral species are present (contaminated liquid), which is the case in minerals flotation, a molecular arrangement of adsorbed molecules develops on the surface of the bubbles. This structure reduces bubble surface mobility as internal gas circulation is restricted, velocity is reduced, and shape evolves from oblate spheroidal to spherical. Models proposed to predict the terminal velocity of bubbles have been devised, in general, for working at two extreme sets of conditions: bubbles rising either with fully mobile surfaces in pure liquids, or with rigid surfaces in highly contaminated liquids. The purpose of this work was the assessment of bubble velocity predictions of models that have been used in flotation applications; a data set of simultaneous measurement of velocity and shape of rising single bubbles under a broad set of conditions relevant for minerals flotation was used. The results demonstrated that bubble velocity and aspect ratio were intrinsically linked, and for bubbles of the same size, consistent trends between terminal velocity and aspect ratio that included measurements in frother and polymer solutions. Measurements in solutions of four frothers showed, as expected, significantly different terminal-velocity reduction trends as the frother concentrations were increased. This was considered as a demonstration that the frother molecular structure and the extent of equilibrium coverage were frother dependent. Model assessment demonstrated that prediction of terminal velocities was not possible for contaminated solutions with frother concentrations below the levels that get bubble surfaces fully covered. The measurements collected in this work were used to develop an empirical model for predicting bubble velocities as a function of aspect ratio; the comparison of measured and predicted velocities had a correlation coefficient of 0.9987. [ABSTRACT FROM AUTHOR]

Surface tension is a critical parameter in bubbles and foams, yet it is difficult to assess when microparticles are attached at the interface. By considering the interaction force between an air–liquid interface and microparticles, modified equations for sessile bubble tensiometry can be derived to determine the surface tension and shape of static microparticle-laden bubbles. A modified sessile bubble method, in which the forces between microparticles and the air–liquid interface are considered, was developed and used to analyse the surface tension of bubbles fully coated by a monolayer of silica microparticles of different sizes. The results are compared to those obtained using classical sessile bubble tensiometry. The new method is also used to investigate the contours of particle-laden bubbles of varying particle radius and contact angle. While the classical sessile bubble method overestimates the surface tension, results obtained using the modified sessile bubble method show that the surface tension of static microparticle-laden bubbles remains the same as that of uncoated bubbles, with no dependency on the particle size. The discrepancy is due to the fact that microparticles attached to the air–liquid interface deform a bubble in a similar way that changes in surface tension do for uncoated bubbles. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering for Thermal Energy & Power / Reneng Dongli Gongcheng is the property of Journal of Engineering for Thermal Energy & Power and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to improve the mass transfer efficiency of the high‐temperature molten pool area in the oxygen coal combustion melting and separating furnace, water model experiment and VOF model were used to study the mechanism of bubble formation in the area, investigate the changing rules of oxygen lance parameters on the shape and frequency of bubbles. The results show that the basic law of bubble generation is the transition from lateral injection to longitudinal growth, and the bubble generation frequency is 7.5 Hz under standard conditions. Increasing the oxygen lance mass flow will reduce the generation frequency, but the local bubble distribution is more compact. Increasing the oxygen lance inclination angle increase the generation frequency, but it will cause local gas phase accumulation, if too close to the bottom of the furnace. Small oxygen lances diameter is beneficial to increase the generation frequency and enhance mass transfer efficiency. Increasing the oxygen lance immersion depth is conducive to increasing the generation frequency, the gas‐liquid interface and improving molten and separation efficiency. On the other hand, it will weaken the effect of "adherence to the wall" and reduce the erosion of furnace lining by inhibiting the flow of bubbles and slag. [ABSTRACT FROM AUTHOR]

This work proposed a method to reconstruct the 3D bubble shape in a transparent medium utilizing the three orthographic digital images. The bubble was divided into several ellipse slices. The azimuth angle and projection parameters were extracted from the top view image, while the formulas for dimensionless semi-axes were derived according to the geometric projection relationship. The elliptical axes of each layer were calculated by substituting the projection width into the formulas. All layers of slices were stacked to form the 3D bubble shape. Reconstruction accuracy was evaluated with spheres, ellipsoids, and inverted teardrops. The results show that the position contributes greatly to the reconstruction accuracy of the bubbles with serious horizontal deformation. The method in Bian et al. (2013) is sensitive to both horizontal and vertical deformations. The vertical deformation has little influence on the method in Fujiwara et al. (2004), whereas the horizontal deformation greatly impacts its accuracy. The method in this paper is negligibly affected by vertical deformation, but it does better in reconstructing single bubbles with large horizontal deformation. The azimuth angle affects the accuracy of the methods in Bian et al. (2013) and Fujiwara et al. (2004) more than the method in this paper. [ABSTRACT FROM AUTHOR]

The orifice size has a significant influence on hydrodynamic characteristics and bubble size distribution (BSD) in gas‐liquid flow. However, the mechanism of the influence of orifice size on BSD and hydrodynamic characteristics in an external loop airlift reactor (EL‐ALR) has not been fully revealed. In this work, the effects of the orifice size on hydrodynamic characteristics and BSD in a laboratory scale EL‐ALR were investigated using the particle image velocimetry (PIV) technique and digital image analysis (DIA). The results show that the transition superficial gas velocity becomes greater when the orifice size is reduced. The time‐averaged bubble velocity profiles along the riser radius are parabolic, and the shape of the time‐averaged bubble velocity curve is strongly dependent on the orifice diameter. The larger the orifice diameter, the steeper the parabolas. For sparger with lager orifice diameters, the BSD curve is bimodal even at low superficial gas velocity, and its peaks shift to a larger equivalent bubble diameter. The bubble aspect ratio appears to be related only to the equivalent diameter of the bubbles, regardless of the diameter of the orifice. It has a defined relationship between the bubble aspect ratio and the bubble equivalent diameter, and a new correlation is obtained based on the experimental data. This study will help to gain an understanding of the influence of sparger orifice size on the hydrodynamic characteristics and BSD and provide a basis for numerical simulation. [ABSTRACT FROM AUTHOR]

Copyright of Nonferrous Metals (Mineral Processing Section) is the property of Beijing Research Institute of Mining & Metallurgy Technology Group and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The determination of the shape and rising velocity of gas bubbles in a liquid pool is of great importance in analyzing the radioactive aerosol emissions from nuclear power plant accidents in terms of the fission product release rate and the pool scrubbing efficiency of radioactive aerosols. This article suggests a simple parameterization for the gas bubble rising velocity as a function of the volume-equivalent bubble diameter; this parameterization does not require prior knowledge of bubble shape. This is more convenient than previously suggested parameterizations because it is given as a single explicit formula. It is also shown that a bubble shape diagram, which is very similar to the Grace's diagram, can be easily generated using the parameterization suggested in this article. Furthermore, the boundaries among the three bubble shape regimes in the Eo–Re plane and the condition for the bypass of the spheroidal regime can be delineated directly from the parameterization formula. Therefore, the parameterization suggested in this article appears to be useful not only in easily determining the bubble rising velocity (e.g., in postulated severe accident analysis codes) but also in understanding the trend of bubble shape change due to bubble growth.

In order to study the effect of anistropic properties of composite material on bubble shape, the shapes of bubbles near the carbon fiber composite material boundaries and the deformation of the carbon fiber composite material boundaries were recorded and observed by using high-speed camera. The shapes of bubbles near the composite material boundaries with different ply angles are studied. The changing processes of bubble shape and the deformation modes of the composite material boundaries at the same initial distance of bubble from the boundary are compared for the carbon fiber composite plates with the ply angles of 0°,90° and 0°+90°. The results show that the high-speed jet and shock wave generated by the collapse of bubble near the boundaries are the important factors for the damage of boundaries, and the different ply angles of carbon fiber composite material lead to different deformation modes, which has an important impact on the shapes of bubbles. [ABSTRACT FROM AUTHOR]

Based on experiments with single air bubbles rising in stagnant non‐Newtonian fluids, an innovative model containing the aspect ratio (E) and two parameters (α, β) was proposed and proved to be capable of characterizing the bubble shape from spherical/ellipsoidal to prolate/oblate‐tear with good accuracy. Several impacts on bubble deformation were investigated, involving the rheological properties of the fluids and different forces exerted on the bubble, which were quantified by multiple dimensionless numbers (e.g., Reynolds, Eötvös, and Deborah number). Within a wide range, the empirical correlations were obtained for parameter β, and between α and β. Together with the shape model, a complete system was set up for bubble shape characterization and prediction that will provide new ideas for future studies on bubble hydrodynamics. [ABSTRACT FROM AUTHOR]

Featured Application: The outcome of this study may beneficial to the researchers, engineers, designers while dealing with the motion of single bubbles in still water. Under the action of gravity, buoyancy, and surface tension, bubbles generated by wave breaking will rupture and polymerize, causing the occurrence of high-speed jets and strong turbulence in nearby water bodies, which in turn affects sea–air exchange, sediment transport, and pollutant movement. These interactions are closely related to the shape and velocity changes in single bubbles. Therefore, understanding the motion characteristics of single bubbles is essential. In this research, a large number of experiments were carried out to serve this purpose. The experimental data were used to develop three machine learning models for the bubble final velocity, bubble drag coefficient, and bubble shape, respectively. The performance of the feed forward back propagation neural network (FBNN) models for the final velocity and drag coefficient were evaluated. The coefficient of determination (R2) and root mean squared error (RMSE) value of final velocity prediction model was recorded at 0.83 and 0.0518, respectively. Meanwhile, for the drag coefficient prediction model, the values are 0.92 for R2 and 0.1534 for RMSE. The models can provide a more accurate output if compared to that from the empirical formulas. K-nearest neighbours (KNN), logistic regression, and random forest were applied as the algorithm while developing the bubble shape classification model. The best performance is achieved by the logistic regression. [ABSTRACT FROM AUTHOR]

Bubble manipulation in aqueous environment has attracted much attention due to its large-scale applications. Meanwhile, the bubble shapes on solid surface had played an important role in bubble manipulation. In this work, four types of bubble shape have been summarized of bubble on the slippery surface affected by the bubble volume, stripe width and substrate wettability. Understanding bubble shapes on narrow slippery stripes and how they change during manipulated processes is significant for both industrial and daily life applications. Moreover, bubble shapes are mainly affected by bubble volume, stripe width and substrate wettability. Revealing the relationship between those factors for bubble shapes is crucial for further study. While there are many studies of bubble manipulation underwater on slippery surfaces, the detailed evolution of bubble shapes on those substrates is still worthy of further study. In this research, the details of bubbles shapes in different conditions were studied and analyzed. Air bubbles were continuously released on substrates with different chemistries and different geometric parameters to study their effect on bubble shape evolution. Bubble shape can be categorized into four states according to the relationship between bubbles and the stripe widths. Bubble shapes have considerable differences in their top-view and side-view under each state. Furthermore, during the directional transportation of bubbles on a wedge-shaped slippery surface, bubble shapes change from the tip to the end by the width gradients. The outcomes of this work broaden the horizon for the understanding of bubble shapes on slippery surfaces and their changes during transportation. [ABSTRACT FROM AUTHOR]

Highlights • Experiments on the bubble motion and its ascension in viscous fluids were carried out. • A correlation of Velocity number vs. Flow number, at the detachment, is proposed. • Different regimes of bubble motion are separated by the Velocity number. • The results are valid and usable for both Newtonian and non-Newtonian fluids. Abstract In the present research, the rising behavior of air bubble in a viscous liquid is investigated experimentally. Aqueous solutions of glycerol and CMC were used as the Newtonian and shear-thinning non-Newtonian viscous liquids, respectively. The bubble is formed via injection of air by a syringe pump and rises in the quiescent viscous liquid. The process was captured using a high-speed camera (1000 fps) and was post processed to obtain the bubble characteristics such as the center of mass and aspect ratio. The experimental results were verified using the existing literatures and the non-dimensional numbers were reduced to two (Velocity number and Flow number) by lumping the parameters. In addition, an empirical correlation was presented for the Velocity number at the moment of detachment based on the Flow number. In our experiments, three regimes were observed during the bubble rise after its detachment. In regime 1, the bubble shape oscillates between disk and hemisphere. In regime 2, the bubble gradually deforms into an ellipsoidal shape and in regime 3, the bubble shape remains nearly unchanged. Furthermore, the results indicated that the velocity behavior is influenced by the shape of the bubble: in regime 1, the velocity fluctuates. In regime 2, the velocity decreases temporarily and then increases toward the terminal velocity and finally in regime 3, the velocity increases or decreases monotonically toward the terminal velocity. Also, a criterion was found for the Velocity number in order to simultaneously predict the regime of bubble rise in a viscous liquid for Newtonian and non-Newtonian fluids. [ABSTRACT FROM AUTHOR]

• Bubble terminal velocity increases with the gravity level, although bubbles are smaller at higher values of gravity. • The bouncing process has been modelled by a damped oscillator, in which the free surface acts as an elastic membrane. • The frequency of bouncing increases with gravity, in accordance with the theoretical model. • Viscosity is not the main responsible for damping in the bouncing process. Bubble detachment, rise, and bouncing upon impact with a free surface is studied experimentally in variable gravity conditions. Previous investigations focused on the effects of fluid properties such as viscosity or surface tension on the rise and bouncing dynamics. Gravity force is a crucial factor in the detachment, rise and bouncing processes. However, the effect of different gravity levels has never been studied experimentally. In this paper we analyze the role of gravity in the detachment, rise velocity and bouncing motion of millimetric bubbles colliding with a free surface. Single air bubbles in ethanol are detached from a nozzle by the buoyancy force. After reaching a terminal velocity, the rising bubble interacts with the free surface in a bouncing process prior to coalescence. The equivalent bubble diameter at detachment decreases as the gravity level increases, in agreement with the theoretical prediction. An expression for the terminal velocity as a function of gravity is proposed. The terminal velocity is found to increase with the gravity level, although bubbles are smaller at higher values of gravity. The bouncing process has been modelled by a damped oscillator, in which the free surface acts as an elastic membrane. An expression for the frequency of bouncing as a function of gravity has been obtained, showing a good agreement with the experimental results. The motion of the bubble during the bouncing process can be approximated by an underdamped oscillator even if viscosity is negligible. Therefore, viscosity is not the main responsible for damping, which is probably due to energy transfer from the bubble to the fluid in the form of vortex and surface waves generation. [ABSTRACT FROM AUTHOR]

Highlights • Bubble shape was experimentally studied at high temperature and pressure. • New correlations for bubble aspect ratio E were proposed by dividing into three parts. • The influence of high temperature and pressure on bubble rising velocity were studied. Abstract Industrial bubble column reactors use to operate at high pressure and temperature. However, few experimental investigations have been performed under such severe conditions. In this work the effects of high pressure (0.1–6 MPa) and high temperature (293–473 K) on the bubble shape and rising velocity in silicone oil and paraffin are experimentally investigated. The experiments are carried out in a stainless steel bubble column of 50 mm I.D with three pairs of high strength quartz windows. The bubble flow is visualized and recorded through high speed camera. New correlations for bubble aspect ratio E are proposed by use of the experimental data. The correlations are divided into three parts in terms of Weber number and Morton number. For We > 12, bubble aspect ratio is independent of Weber number, and is only related to Morton number. For We < 12 and Morton number larger than 3, bubble aspect ratio is only related to Reynolds number. For Morton number lower than 3, the aspect ratio could be expressed in terms of the Eötvös number and Reynolds number. Bubble rise velocity decreases with increasing pressure and decreasing temperature, which could be attributed to the variations of liquid viscosity, gas density, and bubble surface property. A modified correlation of Fan and Tsuchiya is recommended for bubble rise velocity valid at high temperature, high pressure and viscous liquids. [ABSTRACT FROM AUTHOR]

This work proposed a method to reconstruct the 3D bubble shape in a transparent medium utilizing the three orthographic digital images. The bubble was divided into several ellipse slices. The azimuth angle and projection parameters were extracted from the top view image, while the formulas for dimensionless semi-axes were derived according to the geometric projection relationship. The elliptical axes of each layer were calculated by substituting the projection width into the formulas. All layers of slices were stacked to form the 3D bubble shape. Reconstruction accuracy was evaluated with spheres, ellipsoids, and inverted teardrops. The results show that the position contributes greatly to the reconstruction accuracy of the bubbles with serious horizontal deformation. The method in Bian et al. (2013) is sensitive to both horizontal and vertical deformations. The vertical deformation has little influence on the method in Fujiwara et al. (2004), whereas the horizontal deformation greatly impacts its accuracy. The method in this paper is negligibly affected by vertical deformation, but it does better in reconstructing single bubbles with large horizontal deformation. The azimuth angle affects the accuracy of the methods in Bian et al. (2013) and Fujiwara et al. (2004) more than the method in this paper.

Abstract Bubbles properties play an important role in determining the characteristics of gas-solid fluidized beds and thus influence the bed performance significantly. In this work, the bubble properties such as bubble size and bubble shape are studied by the combined approach of CFD and DEM for bubbling gas-solid fluidized beds operated with a continuous central jet. The process of the continuous injection of a central air jet to the bed is successfully reproduced featured with the formation of series of bubbles which rise through the bed and burst at the bed top. The results show that the average initial bubble diameter increases with the increase of jet velocity, and can be well predicted by the leakage based empirical models. The bubble size distribution in the overall bed shows a decrease in frequency as the size of the bubble increases for all the jet velocities. At a higher jet velocity, the distribution is more scattered signifying the presence of small and large bubbles. The distributions of bubble aspect ratio and bubble shape factor are also examined in detail, showing a normal distribution. Specifically, the distribution of bubble aspect ratio exhibits a positively skewed distribution for all jet velocities while that of bubble shape factor shows a negatively skewed distribution. The study provides a useful basis for further work on the understanding of bubble dynamics. Graphical abstract Unlabelled Image Highlights • CFD-DEM is used to study bubble dynamics in central air jet gas fluidized beds. • The growth of bubbles comes to a saturation diameter at a certain bed height. • Bubble aspect ratio exhibits positively skewed distribution. • Bubble shape factor exhibits negatively skewed distribution. [ABSTRACT FROM AUTHOR]

Highlights • Measuring the lift coefficient in systems with low Morton numbers. • New measuring concept without moving parts and small fluid volumes. • Quantification of the lift coefficient with a method based on averaged values. • Applicable to turbulent conditions and wobbling bubbles. Abstract The lift force, which strongly influences the spatial bubble distribution, is one of the most important non-drag forces. However, measurements in systems with a low Morton number are limited. In the present work, a time-averaging measurement method with which this gap can be closed is discussed. The experimental setup is kept as simple as possible, avoiding any moving parts. The single bubble movement through a linear shear field was observed in three-dimensions over 75 min. In total, 85 measurement points cover 13 bubble sizes at 7 different shear rates. The results reveal that former empirical correlations obtained from experiments and simulations in predominantly high Morton number systems are applicable. In this context, the characteristic length scale that is used to describe the lift force needs to be carefully defined. From the present results, the major axis seems to be the most reasonable choice for wobbling bubbles. However, the major axis might be dependent on the flow properties, which leads to a flow dependent lift force formulation. [ABSTRACT FROM AUTHOR]

• Numerical simulation of bubble behavior in the channel of petal-shaped fuel rod bundle was conducted. • The bubble behavior such as bubble trajectory, shape and velocity are investigated. • The effects of bubble size and channel inlet flow rate on bubble behavior are discussed. • The comparison of bubble behavior parameters, vortex distribution inside and around the bubble, and bubble force reveal the bubble behavior mechanism. The petal-shaped fuel element is a novel type of fuel element suitable for small-scale reactors. The motion of bubbles in the rod bundle channel has a significant impact on the surrounding flow and temperature fields, thereby influencing the two-phase flow and heat transfer characteristics. To investigate the dynamics of bubbles in the rod channel of the petal-shaped fuel rod, we simulated the rising motion of bubbles with different inlet flow rates using the volume of fluid method (VOF). We obtained the trajectory, rising speed, and shape changes of the bubbles with varying initial sizes, and analyzed the flow field around the bubbles. Our results indicate that the transverse displacement of bubbles in the radius range of 0.5 mm–1.25 mm increases gradually with their initial size, and the degree of deformation and maximum rising velocity of the bubbles also increase. However, bubbles with a radius of 1.5 mm experience less transverse displacement due to their larger size and contact with multiple fuel rods during the ascent process. Furthermore, the transverse displacement distance of the bubble increases and then decreases with the increase of fluid flow rate in the channel, while the aspect ratio of the bubble remains unaffected by the inlet flow rate. The study of bubble behavior sheds light on the mechanism of bubble motion in the channel of petal-shaped rod bundles, and provides a foundation for the study of two-phase flow and heat transfer in the channel. [ABSTRACT FROM AUTHOR]

• The shape of the bubble is mainly affected by elasticity and appears as "inverted carrot" shape at the beginning of gas injection test, and then becomes "inverted teardrop" shape under the influence of viscoelasticity. • Based on the four newly defined bubble shape parameters, the method of identification for bubble shape is proposed. • A convenient model is proposed to predict the bubble shape at detachment based on the influence parameters. Reliable identification and prediction of a bubble shape are important to the research of bubble dynamics. The transparent MLPS colloidal suspensions, representing the viscoelastic behavior, were employed in this paper and the bubble morphology was investigated by the gas injection method. Several influencing factors, such as the concentration, the sample height, the pinhole diameter, and the gas flow rate, were analyzed. The observed data show that the bubble was initially controlled by elasticity and then by viscoelasticity. The corresponding bubble shapes revealed 'inverted carrot' and 'inverted teardrop' respectively. The bubble shape parameters including the aspect ratio, the tail proportion, the equivalent diameter ratio, and the top curvature ratio were considered in the proposed identification method. Furthermore, a prediction equation was proposed to identify a detached bubble shape based on several influence parameters including the concentration, the sample height, the pinhole diameter, and the gas flow rate. The calculated results were in good agreement with the test results. Therefore, combined with the bubble shape criterion, a bubble shape at the detachment could be accurately identified with the provision of some pre-known parameters such as the material properties and the test conditions, without the information in the bubble growth process such as the growth rate, the observation time, etc. [ABSTRACT FROM AUTHOR]

Under the action of gravity, buoyancy, and surface tension, bubbles generated by wave breaking will rupture and polymerize, causing the occurrence of high-speed jets and strong turbulence in nearby water bodies, which in turn affects sea–air exchange, sediment transport, and pollutant movement. These interactions are closely related to the shape and velocity changes in single bubbles. Therefore, understanding the motion characteristics of single bubbles is essential. In this research, a large number of experiments were carried out to serve this purpose. The experimental data were used to develop three machine learning models for the bubble final velocity, bubble drag coefficient, and bubble shape, respectively. The performance of the feed forward back propagation neural network (FBNN) models for the final velocity and drag coefficient were evaluated. The coefficient of determination (R2) and root mean squared error (RMSE) value of final velocity prediction model was recorded at 0.83 and 0.0518, respectively. Meanwhile, for the drag coefficient prediction model, the values are 0.92 for R2 and 0.1534 for RMSE. The models can provide a more accurate output if compared to that from the empirical formulas. K-nearest neighbours (KNN), logistic regression, and random forest were applied as the algorithm while developing the bubble shape classification model. The best performance is achieved by the logistic regression.