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[Display omitted] • The formation mechanism and characteristics of Taylor bubbles in small-scale microchannels was determined. • The Taylor bubbles formation process was analyzed based on details variation of different stages. • The variation of Taylor bubbles length under the influence of pressure was summarized. Taylor flow in microchannels has been applied in various fields, including chemistry, biology, and pharmaceutical engineering. However, the exact process of Taylor flow formation and movement in small-scale microchannels was not systematic enough. We investigated how Taylor bubbles form in small-scale microchannels examining the differences in the transformation of bubble formation mechanisms and stability. The study broke down the Taylor bubble formation process under the squeezing formation mechanism into three detailed stages. By analyzing factors such as bubble formation frequency and surface velocity, the law of Taylor bubble formation in small-scale microchannels were explored. The study also fitted the typical shape (bubble length, liquid film thickness) and its variations during bubble formation, shedding light on the evolution of bubble shape in small-scale microchannels. This research offered insights for the advancement and application of microchannel reactors. [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]

• 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]

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]

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]

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]

Axisymmetric liquid-fluid interface (ALFI) and axisymmetric drop shape analysis (ADSA) are the methods used in surface phenomena investigations. A photographed contour of a drop or a bubble is detected and fitted to numerically integrated Young-Laplace equation. However, ALFI fails in the stationery points, while ADSA gives the wrong surface tension value at the apex. An analytical expression for an interface shape overcome the weaknesses of the numerical models. It shows that pressure inside a drop is higher than outside, while a bubble encloses gas with negative gauge pressure. Since, the close-formed solutions origin from a force balance which preserves constant volume as well as temperature, entropy, and masses of ingredients are invariable the new formulas can be considered in the surface tension measurements. Hence, surface tension can be determined in the new ways. Each new method needs the measurements of two dimensions only and a solution of quite simple set of the equations. Moreover, the spare equations verify the solution. Then achieved surface tension is an input to obtain bubble shapes which are compared with experiment successfully. [ABSTRACT FROM AUTHOR]

We present an analytical and experimental study of the formation of bubbles from a submerged vertical needle under mixed injection conditions, where neither the gas flow rate nor the feeding pressure remain constant during the process. In particular, we focus on the temporal evolution of the pressure inside the gas injection chamber during the bubble formation process, p ( t ), modeling it and analyzing the bubble size and shape as functions of the volume of the chamber, V c , and the mean gas flow rate, Q i , for a given needle radius, a . Under this configuration, it has been shown that the water column penetrating inside the injection needle plays an important role on the bubble formation process. Consequently, an analytical model that includes the description of the time evolution of the liquid column penetrating inside the needle after the separation of a bubble, and the subsequent pressurization of the gas chamber, has been proposed. The results given by the model agree well with the experimental measurements. [ABSTRACT FROM AUTHOR]

Lift coefficients, C L , of single bubbles in linear shear flows are measured to investigate effects of the bubble shape, the liquid velocity gradient and the fluid property on C L . The range of the Morton number, M , tested is from log M = − 6.6 to − 3.2. The shapes of bubbles are spherical and ellipsoidal. A correlation of bubble aspect ratio for single bubbles in infinite stagnant liquids proposed in our previous study can give good evaluations for bubbles in the linear shear flows. The C L of spherical bubbles at low bubble Reynolds numbers, Re , depend on the dimensionless shear rate Sr and Re and decrease with increasing Re . These characteristics agree with the Legendre-Magnaudet correlation. The use of a single dimensionless group such as Re , the Eötvös number, the Weber number and the Capillary number cannot correlate C L of non-spherical bubbles. The trend of the critical Re for the reversal of the sign of C L is the same as that for the onset of oscillation of bubble motion, which supports the mechanism proposed by Adoua et al., at least within the range of −6.6 ≤ log M ≤ −3.2. An experimental database of C L is provided for validation of available C L models and CFD. [ABSTRACT FROM AUTHOR]

The bubble shape is fundamental for every aspect of modeling bubbly flows. The interface is usually highly deformable so that the bubble shape is in general dependent on the surrounding turbulent flow field. Since recent work on this topic addressed almost entirely single-bubbles rising in quiescent flow, the extent of such flow field dependencies as well as swarm effects is rather unknown. This study examines the effect on the bubble shape in bubbly flows with a liquid background flow that is generated by natural convection in the bubbly flow regime when flow properties, i.e. the gas flow rate, sparger setup, and column geometry, are changed by evaluating six different bubble column experiments. The results of this integral approach reveal that the bubble shape of small bubbles is distinctly influenced whereas the shape of large bubbles is unchanged. Averaged over all flow rates, we find that the size-dependent bubble shapes are quite similar for all six experiments. Further studies focusing on single local effects like the shear rate or wake effects are highly desirable to obtain a deeper understanding of the underlying processes; for this purpose, the given results can help to assess the most important effect and in which extend it should be studied. [ABSTRACT FROM AUTHOR]

A mechanistic model to study the growth of a bubble from nucleation to departure in pool boiling is proposed in this work taking into account the change in shape of a bubble as it grows. The model consists of three sub-models: (a) a heat transfer sub-model to compute the bubble growth rate based on the evaporation of the microlayer, the macrolayer, the thermal boundary layer and the bulk liquid surrounding the bubble; (b) a force sub-model to calculate the forces acting on a bubble; and (c) a contact angle and bottleneck sub-model to account for the change in shape of the bubble. Analysis of past experiments on bubble growth in nucleate pool boiling has shown that the shape of a bubble transitions from a truncated sphere to a balloon-like shape before departure. In the present work, a novel method to model this balloon-like shape of the bubble as a truncated sphere atop a conical bottleneck is presented. The model is validated against high-fidelity CFD simulations and pool boiling experiments of water and methanol from literature. In particular, the bubble departure time, wall temperature, bubble shape and microlayer profile obtained from the model are in good agreement with experimental and CFD results. • A mechanistic model is developed to study the growth of a bubble from nucleation to departure in pool boiling. • A balloon-like shape of the bubble prior to departure is modelled as a truncated sphere atop a conical bottleneck. • Bubble growth rate is modelled based on the heat transferred from different mechanisms. • Good agreement between the modelled contact radius with experimental data is demonstrated. • Transition in bubble shape is qualitatively well-predicted by the model. [ABSTRACT FROM AUTHOR]

‘Microlayers’, the thin (less than 10 μm) films of liquid left behind beneath rapidly-growing steam bubbles at a heated wall, can be a large, and even the dominant, source of the vapour in such bubbles by the time they depart the wall. Given their slenderness (compared to the 1–10 mm diameter of the bubble), and their high aspect ratio, (with radial extents of perhaps order >100 times their thickness), such microlayers are incorporated relatively simplistically in microscopic CFD analyses of bubble growth. However, their role is particularly important because the evaporation of the microlayer generates vapour rapidly, which itself expands the bubble and generates even more microlayer to evaporate. Plainly, a good understanding of the microlayer formation process is desirable. In this paper we present first-principles calculations of the hydrodynamics of the formation of such microlayers. These seem to show overwhelmingly that the determinant of the existence and radial extent of a microlayer is the bubble growth rate, with higher growth rates leading to more flattened and less spherical bubbles, allowing larger microlayers being trapped beneath them. When they are formed, microlayer thickness is then to a degree dependent on the fluid surface tension and liquid viscosity. The need for an extension of these hydrodynamic studies to include a mechanistic self-consistent model of the evaporative depletion of the microlayer is noted. [ABSTRACT FROM AUTHOR]

We experimentally investigate the effect of ethanol (0.05% in mass) on the hydrodynamics of a large-diameter and large-scale bubble column. The bubble column is 5.3 m in height, has an inner diameter of 0.24 m, and we consider gas superficial velocities in the range of 0.004–0.20 m/s. The experimental investigation consists of gas holdup measurements and image analysis. The gas holdup measurements are used to investigate the flow regime transition and the global bubble column hydrodynamics. The image analysis is used to investigate the bubble shapes and size distributions near the sparger and in the developed region of the column. The presence of ethanol increases the gas holdup, stabilizes the homogeneous regime and modifies the bubble shapes and size distributions. In particular, the addition of ethanol increases the mean bubble aspect ratio and decreases the bubble diameters. The results suggest that the addition of ethanol changes the bubble properties, which modifies the bubble size distribution and shapes, thus, stabilizing the homogeneous flow regime and, finally, increasing the gas holdup. [ABSTRACT FROM AUTHOR]

An understanding of the bubble properties, size distributions and shapes is of fundamental importance for comprehending flow dynamics and mass transfer phenomena in bubble column reactors. A large number of studies have focused on open tube bubble columns, and the knowledge concerning bubble columns with internals is still limited. This paper contributes to the existing discussion experimentally investigating a counter-current annular bubble column with 0.24 m inner diameter and two internal pipes. The experimental investigation consists in holdup measurements and image analysis. The former is used for identifying the flow regime transition and studying the bubble column hydrodynamics, whereas the latter is used for investigating the bubble shapes and size distributions. The definition of the transition point is important because the size distribution and bubble shapes depend on the operating conditions and a change of the bubble properties is expected near the transition. The image analysis is applied at different superficial gas and liquid velocities, corresponding to a gas holdup between 2.9% and 9.6%. It is difficult to measure bubble size distribution accurately in large-diameter bubble columns owing to the overlapping of bubbles, even at low void fractions, and—in an annular gap bubble column—the fact that cap bubbles have also been reported in the homogeneous flow regime. The use of a bubble image analysis method to study the bubbly flows in a large-diameter annular gap bubble column is described. In the proposed method, each bubble is approximated and reconstructed using an ellipse. The proposed approach is used to quantify the bubble size distribution, as well as to study the bubble shape and orientation as function of the superficial gas and liquid velocities. The experimental data obtained are used to develop a correlation between non-dimensional parameters and aspect ratios. Also, the experimental data are compared with non-dimensional diagrams from the literature, revealing good agreement. Finally, the image analysis is used for supporting the flow regime transition prediction in the stability analysis method: the virtual mass formulation is obtained by using the aspect ratio correlation provided by the image analysis. The stability analysis—supported by the image analysis—was able to predict the transition point in very good agreement with experimental data and performed better than literature correlations. [ABSTRACT FROM AUTHOR]

An experimental and theoretical study on the bubble shape of intermittent flow in the horizontal and inclined pipes has been carried out. The experiment results show that the bubble shape depends on the Froude number, bubble length and pipe inclination. The bubble with staircase pattern tail is observed at low Froude numbers, which is corresponding to plug flow. A model for the prediction of the bubble shape in horizontal and inclined pipes is proposed. The model is able to predict the bubble shape, flow pattern transition between plug and slug flow regimes as well as nose-tail inversion phenomenon observed in the downwardly inclined pipe. Validation shows the model can well predict the bubble shapes in horizontal and inclined pipes. The model discloses that the transition between plug and slug flow regimes occurs within a region. The Froude number range for plug flow regime in the downwardly inclined pipe is much wider than that in the horizontal or upwardly inclined pipe. The assumption of fully developed liquid film under the long bubbles tends to under-estimate the liquid fraction in this part of the slug structure, especially, for the intermittent flow in the upwardly inclined pipe with high Froude numbers. [ABSTRACT FROM AUTHOR]

The dynamics of a bubble, initially stationary and spherical, rising in a viscous Newtonian liquid have been studied numerically using 3-D Volume-of-Fluid (VOF) method implemented in the Gerris flow solver. The study encompasses 8.7≤ Eo (= Δ ρ g D 2 / σ )≤641 and Re ≤151. Additionally, results published in the literature encompassing bubbles with lower values of E o numbers were also considered, such that the overall dependencies of bubble shape, wake characteristics, and drag coefficient over a large range of Eo and Re values can be identified. While it was found that the deformation of the bubbles as predicted through the numerical study can generally replicate experimental observations presented, several limitations were identified, such as in the representation of skirt formation behind a skirted bubble and the formation of satellite bubbles behind a bubble rising at high Reynolds numbers. The dependency of the bubble aspect ratio on the Weber and Morton numbers was confirmed for cases of spherical and ellipsoidal bubbles; whilst for spherical cap and skirted bubbles the aspect ratio was found to depend largely on the Reynolds and Capillary numbers, respectively. Finally, the expansion and formation of closed/open laminar wakes behind the rising bubble were analysed and was found to correlate well with the bubble Re and Eo numbers. [ABSTRACT FROM AUTHOR]

A numerical study on rising bubbles in still liquids employing the Volume of Fluid (VOF) technique to track the interface is presented here. First, a combination of the correlation provided by Rastello et al. (2011) for the rectilinear motion of a bubble with that given by Clift et al. (1978) in the zig-zag ascension regime, conveniently made dimensionless, is proposed to determine the bubble terminal velocity for a wide range of bubble sizes and fluid properties. Furthermore, the crosspoint of both correlations gives the critical Weber number, We c = ρ l U T 2 D / σ c , at which the transition from a rectilinear to a zig-zag bubble motion takes place in a liquid of a given Morton number, Mo = g μ l 4 / σ 3 ρ l . Concerning the numerical simulations, two different open source solvers have been evaluated, i.e. InterFoam and Gerris Flow Solver, to describe the motion of a stable bubble rising with a rectilinear path by performing two-dimensional axisymmetric simulations. The simulations show the presence of parasitic currents and variable results depending on the mesh resolution in the case of InterFoam, whereas no spurious results are observed in Gerris, which is therefore more suitable for these kinds of flows. Finally, the numerical results indicate that the gas properties hardly affect the bubble terminal velocity and shape, although they show that the flow field inside the bubble is highly affected by the gas density and viscosity. This result can be of relevance in heat and mass transfer processes where the mass diffusion or heat exchange can be enhanced by the convective motion induced inside the bubble. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study of the shape of isolated bubbles in horizontal and near horizontal intermittent flows. It is found that the shapes of the nose and body of bubble depend on the Froude number defined by gas/liquid mixture velocity in a pipe, whereas the shape of the back of bubble region depends on both the Froude number and bubble length. The photographic studies show that the transition from plug to slug flow occurs when the back of the bubble changes from staircase pattern to hydraulic jump with the increase of the Froude number and bubble length. The effect of pipe inclination on characteristics of bubble is significant: The bubble is inversely located in a downwardly inclined pipe when the Froude number is low, and the transition from plug flow to slug flow in an upward inclined pipe is more ready to occur compared with that in a downwardly inclined pipe. [ABSTRACT FROM AUTHOR]

This paper is concerned with single bubble dynamics over a wide experimental data set in stagnant water and glycerol aqueous solution. The bubble trajectory in three-dimensional space was deduced by analyzing the bubble characteristics in two-dimensional plane captured by a single high-speed camera and the bubble trajectory in the water was ascertained by this method. Bubble shape, trajectory and terminal velocity in water, which closely related and strongly influenced by each other, are not only determined by bubble diameter, but also dramatically influenced by nozzle diameters, i.e. the bubble dynamics is sensitive to the disturbance of detachment process. The bubbles remain spherical and rise up rectilinearly when their diameters are small enough. Otherwise, the bubbles begin to deform to ellipsoidal, oblate ellipsoidal, or cap shape, with surface wobbling strongly, and proceed in a zigzagging, helical, nearly zigzagging or helical motion. In this case, periodic oscillations occur at the velocity and aspect ratio of the bubbles. Moreover, there exists an inverse function relationship between them, a large deformation, i.e. a small aspect ratio will lead to a high velocity and vice versa. However, in glycerol aqueous solution, bubble shape, trajectory and velocity is stable under a certain bubble diameter. In the water, bubble shape is mainly dominated by the inertial force and surface tension, and the influence caused by the viscous force could be neglected. The influence of gravity should be taken into consideration if the bubble diameter is large enough. However, the bubble shape is mainly dominated by the viscous force, surface tension and inertial force in the glycerol aqueous solution. Available correlations in the literature do not give fully satisfactory results in predicting aspect ratio, and new correlations combined Weber number with Eötvös number and Weber number with Reynolds number were proposed to correlate bubble shape in water and glycerol aqueous solution, respectively, showing that a good relevance between them in the range of the present experimental data set. [ABSTRACT FROM AUTHOR]

[Display omitted] • Study of velocity and shape of ellipsoidal bubble rising in water – propanol mixtures. • Structure of alcohol-water solutions on molecular level influences bubble behaviour. • Three regions of hydrodynamic behaviour found for ellipsoidal bubbles. • Formation of microstructures accelerates propanol desorption from l – g interface. • Bubble surface changes from immobile to mobile at high alcohol concentrations. Various anomalies are typical for aqueous solutions of simple alcohols, with viscosity maxima and changing bubble surface mobility being significant for multiphase systems. Three regions of the hydrodynamic behaviour of spherical and ellipsoidal bubbles are described, depending on the propanol concentration. At low concentration (x P ≤ 0.005), alcohol behaves as a surfactant and the increase in concentration increases the drag coefficient and decreases bubble deformation. At intermediate concentration, the increase of concentration leads to more deformed bubbles with increasing rise velocity, because of the advantage of formation of bulk clusters. At high concentration (x P ≥ 0.07), bubbles behave as fully mobile with a low drag coefficient. Because of the fast desorption of molecules from the bubble surface, neither a concentration gradient nor a surface tension gradient arises, and thus the conditions for bubble surface mobility are fulfilled. The transition in the hydrodynamic behaviour is evident for all bubble sizes. [ABSTRACT FROM AUTHOR]

This study investigates the effects of hydrophilic-to-superhydrophobic discontinuous wall contact angles on gas-liquid slug flow in a T-junction microchannel. The two-phase volume-of-fluid model with dynamic contact angle are used by solving wall-adhesion equations, which determine the shape of the fluid's interface at and close to the wall. The governing equations of the flow field are solved numerically using a finite volume method. The obtained results are first validated against previously reported experimental data. Subsequently, the effects of changes in the wall contact angles on the slug flow behavior are examined resulting in the new insights into the size, shape, and velocity of slug flow as a function of the wall contact angle. Using a hydrophilic-superhydrophobic hybrid surface leads to the formation of an asymmetric bubble and separation of the bubble from the hydrophobic part. It also causes adhesion to the hydrophilic part, a change in slug length, a reduction in pressure drop, and a variation in the heat transfer characteristics and continuous phase structure. It is shown that using a particular pattern significantly increases the thickness of the liquid wall film. [Display omitted] [ABSTRACT FROM AUTHOR]

The rise of single air bubbles in inclined rectangular channels was experimentally investigated. Two-segment electrodiffusion probes were used to measure wall shear rate profiles along the passing bubbles. They provided information on reverse flow in a liquid film separating the bubble from the wall, capillary waves appearing at the bubble tail, and near-wall flow fluctuations in the bubble wake. The corresponding bubble shapes and rise velocities were obtained from simultaneous visual observations done by a high-speed camera. The experiments were carried out for three channel depths (1.5, 4, and 8 mm), various channel inclinations (from 5° to 90°), bubble volumes (from 1 to 80 ml), and liquid up-flow velocities (from 0 to 0.2 m/s). In vertical channels, the wall shear rate trace of a bubble rise is primarily influenced by the channel depth. As the frontal shape of large bubbles does not change with the bubble size, also the wall shear rate measured under these bubbles evolves in the same manner. In inclined channels, the liquid film is unequally distributed above and under the bubble with the maximum reverse flow observed under the bubble at middle inclinations. Laminar liquid co-flow makes the liquid film around the bubble thicker and in inclined channels slightly pushes the bubble toward the center-line position. The bubble velocity scaling based on the channel perimeter is confirmed to be suitable for vertical channels with stagnant liquid. The linear relationship between the bubble rise and liquid mean velocity is identified under co-flowing conditions at all channel inclinations. [ABSTRACT FROM AUTHOR]

Highlights: [•] A VOF simulation of bubble in low viscosity fluid was conducted. [•] Lift force in different viscosity fluid had different lateral migration characteristics. [•] Bubble with different size migrated to different direction. [•] Shear stress triggered the bubble deformation process and the bubble deformation came along with the oscillation behaviors. [Copyright &y& Elsevier]

Abstract: Accurate tracking of multiphase interfaces (such as an air bubble in a fluid) is difficult yet significant to many engineering processes. Computationally, various tracking methods have been developed, including the volume of fluid (VOF), and coupled level set and volume of fluid (CLSVOF) methods. In order to accurately assess the small-scale differences between different interface capturing methods, a comprehensive experimental dataset is required for validation, including detailed information describing the interface deformation, and transient development of the stage by stage shape data. These interfacial details are better investigated from a two-dimensional (2D) rather than three-dimensional (3D) comparison, because the computational resources for determining an accurate shape can be maximized, and the interfacial complex deformation is difficult to analyze in 3D. In this paper, the fully developed shape and subsequent deformation of 2D rising bubbles have been captured experimentally and analyzed in detail using image processing. These results are then compared with the corresponding VOF and CLSVOF results, demonstrating the usefulness of the experimental dataset as a validation tool. [Copyright &y& Elsevier]

The evaluation of the multi-sensor probe methodology is required to accurately measure local bubbles or droplet parameters in the two-phase flow conditions. This study evaluated two- and four-sensor probes through Monte Carlo simulation and air-water benchmark experiments. In the simulation, it was found that the lateral distance of sensing elements should be minimized, and their axial distance should be longer than 10% of bubble diameter for the optimal design of the probe. From the benchmark experiments, the V b,axial uncertainties of two- and four-sensor probes were 6.5% and 4.5% in the velocity range of 0.4–3.7 m/s, respectively. The D 32 uncertainty was significantly affected by the bubble shape and data reduction methods for each probe. For the two-sensor probe, the maximum error was 9% when the bubble shape was close to the sphere of which diameter was less than 2 mm, and it increased to 28% when the bubble diameter exceeded 2 mm due to the bubble shape distortion in the experiment. While, the four-sensor probe showed excellent performance with a 14% error regardless of the bubble shape under the distorted bubbly flow. • The multi-sensor probe methodology was numerically and experimentally evaluated. • The V b uncertainties of the two- and four-sensors were 6.5% and 4.5%, respectively. • The optimal probe type for D 32 was suggested considering the bubble shape. • The best multi-sensor probe methods were suggested for the bubble parameters. [ABSTRACT FROM AUTHOR]

Highlights: [•] ADSA-P modification for bubbles adhering to an inclined solid surface. [•] Contact angles on lower and upper bubble parts are described separately. [•] Very good agreement of calculated and experimental data was obtained. [•] The method could improve description of TPC line expansion. [ABSTRACT FROM AUTHOR]

Abstract: A hydrodynamic model describing gas–solid two phase flow has been used to numerically study the effect of wall on the bubble shape, size, detachment time and the bubble trajectory in a two-dimensional fluidized bed. Using the numerical model, the influence of the wall is analysed by moving the jet from the centre of the bed towards the wall. The bubble characteristics are compared for different nozzle locations, thus presenting the effect wall has on asymmetrical injection as compared to symmetrical injection. A 30% increase in the bubble detachment time for an asymmetric injection (jet velocity of 10m/s) is found when the nozzle is displaced from the centre of the bed towards the wall (80mm offset from wall). In addition, the bubble evolution reveals an asymmetric wake formation during detachment indicating an early onset of mixing process. The wall forces acts tangentially on the bubble and has a significant impact on the bubble shape, neck formation during detachment, holdup time near the wall and its trajectory through the bed. [Copyright &y& Elsevier]

Abstract: We analyze numerically the transition from straight to zigzag motion during the rising of a single bubble in a still liquid. Results are reported for the regime in which the inner fluid motion is negligible, i.e., in the limit of μ g /μ l ≪1 and ρ g /ρ l ≪1, where μ denotes dynamic viscosity, ρ is density and subscripts g and l correspond to the gas and liquid phase, respectively. In such a regime the flow dynamics is governed by a set of two nondimensional parameters, which are chosen as the Bond, Bo= ρ l g D 2/σ, and the Galilei, , numbers, being σ the surface tension coefficient, g the acceleration due to gravity and D the bubble equivalent diameter. We report the neutral curve for the onset of zigzag motion corresponding with the realistic fore-and-aft axisymmetric bubble shape and discuss its relation with the critical curve for the existence of standing eddy. By mapping the results into the {χ,Re}-plane, where χ denotes the transverse-to-streamwise aspect ratio and Re= ρ l U T D/μ l is the Reynolds number based on the terminal velocity of the bubble U T , we demonstrate the existence of substantial differences with respect to previous theoretical works performed assuming a spheroidal (or revolution ellipsoidal) bubble for all χ and Re, and obtain a good agreement with available experimental data. The fore-and-aft asymmetry of the axisymmetric bubble is shown to be a relevant parameter affecting the strength of the azimuthal vorticity along the neutral curve, a phenomenon that has not been reported before. [Copyright &y& Elsevier]

Abstract: Gas-lift pump in liquid metal cooling fast reactor (LMFR) is an innovative conceptual design to enhance the natural circulation ability of reactor core. The two phase flow characteristics of gas–liquid metal make significant improvement of the natural circulation capacity and reactor safety. It is important to study bubble flow in liquid metal. In present study, the rising behaviors of a single nitrogen bubble in 5 kinds of common stagnant liquid metals (lead bismuth alloy (LBE), liquid kalium (K), sodium (Na), potassium sodium alloy (Na–K) and lithium lead alloy (Li–Pb)) and in flowing lead bismuth alloy have been numerically simulated using two-dimensional moving particle semi-implicit (MPS) method. The whole bubble rising process in liquid was captured. The bubble shape, rising velocity and aspect ratio during rising process of single nitrogen bubble were studied. The computational results show that, in the stagnant liquid metals, the bubble rising shape can be described by the Grace''s diagram, the terminal velocity is not beyond 0.3 m/s, the terminal aspect ratio is between 0.5 and 0.6. In the flowing lead bismuth alloy, as the liquid velocity increases, both the bubble aspect ratio and terminal velocity increase as well. This work is the fundamental research of two phase flow and will be important to the study of the natural circulation capability of Accelerator Driven System (ADS) by using gas-lift pump. [Copyright &y& Elsevier]

Abstract: In this research we focus on the differences caused by the experimental conditions in bubble rise tests at the initial phases of motion in Dowfroth 200, Nasfroth 240 and Dowfroth 250 solutions. Two bubble release techniques were used and the first 50ms of the rise were recorded with high-speed camera. The results suggest that the method of bubble release strongly influences the behaviour of bubbles. The extent of surface deformation caused by different bubble release techniques effect on form drag and therefore the bubble rise velocity due to the different surface stabilization capabilities of frothers. [Copyright &y& Elsevier]

Abstract: This work deals with the study of bubble-liquid mass transfer coupled with chemical reactions. The absorption of carbon dioxide in aqueous solution of sodium carbonate and bicarbonate is used as a reference case. The influences of the interface contamination state and of the ellipsoidal shape of the bubble on the mass transfer rate are studied using a two-dimensional (2D) axisymmetric model. On the one hand, the case of a spherical bubble with a partially contaminated interface is investigated. It is assumed that a fixed stagnant cap lies on a part of the bubble surface in the rear. On the other hand, the case of an ellipsoidal bubble with a clean interface is investigated. In a first stage, correlations to estimate the transfer rate without reaction are presented and compared to the 2D model results. In a second stage, the mass transfer rate is computed with chemical reactions for several reaction rates. The influences of the coupling reactions – contamination state and the coupling reactions – ellipsoidal shape are then presented and discussed. These 2D model results are also compared to mass transfer rate estimations based on classical one-dimensional (1D) models. It is shown that 1D approaches are useful to provide a rough estimation of the mass transfer rate but 2D models have to be used when an accurate estimation of the mass transfer rate is required. [Copyright &y& Elsevier]

Abstract: An analysis of liquid film models for horizontal and near horizontal gas–liquid slug flows is developed. The models’ formulations employ the one dimensional separated phase momentum equations. The formulations differ among themselves, by neglecting some terms on the momentum balance and also on the closure relations. A comparative analysis discloses the differences amongst the formulations. The sensitivity of the liquid film models to the changes on the bubble velocity, liquid slug holdup and liquid viscosity is accessed through a series of parametric runs. Finally, the model is tested against experimental data taken for continuous horizontal slug flow. The tests were designed to check if the models are able to capture the stochastic film properties provided the properly closure relations. [Copyright &y& Elsevier]

Abstract: The effect of frother and NaCl salt on the shape and velocity of a ca. 2.4mm diameter bubble close to the generation point at an orifice was studied using high-speed imaging. Bubbles accelerate to reach a maximum velocity at a given time depending on frother type and concentration, followed by deceleration and then oscillation about a mean velocity. A relationship between bubble shape and velocity is observed: the more spherical the bubble, the slower the rise, which is in agreement with recent literature. The findings support the argument that surfactants may affect bubble rise velocity through control of bubble shape. [Copyright &y& Elsevier]

Abstract: Particle image velocimetry (PIV) is a promising technique to measure dispersed phase size, dispersed phase hold-up and velocity of both the phases. The current work reports measurement of the shape, size, velocity and acceleration of bubbles using shadowgraphy, and liquid velocity measurement obtained using PIV/LIF with fluorescent tracer particles. Measurements were performed in a narrow rectangular column at moderate gas hold-up (∼5%) with wide variation of bubble sizes (0.1–15mm). The liquid velocity field was subjected to 2D discrete wavelet transform (DWT) to visualize the flow structures in the bubbly flow. Further, the slip velocity of individual bubbles was obtained from the DWT filtered liquid velocity field. The results are compared with the slip velocity correlations reported in literature for single bubbles rising in quiescent water. The comparison shows the difference in slip velocity of single bubbles and bubbles rising in swarm. The scale wise decomposition obtained from DWT was also used to quantify the liquid velocity field in terms of wavenumber spectrum. The velocity and acceleration measurements are demonstrated on a single spherical cap bubble rising in quiescent water. The measurements show the potential of the 2D acceleration measurement to facilitate the estimation of unsteady drag on bubbles. [Copyright &y& Elsevier]

Abstract: Dynamic behavior of a two-phase bubble, i.e. a steam bubble containing a droplet evaporating in the bubble, in the molten alloy was clearly visualized using high-frame-rate neutron radiography. In relation to some direct contact heat exchanger design with molten lead–bismuth (Pb–Bi), experiments have been done at JRR-3M of JAEA (Japan Atomic Energy Agency) with water droplets evaporating in a stable thermally stratified Newton''s alloy pool. The instantaneous shape and size of the bubble has been iteratively estimated from the void fraction distributions and total void volume by assuming a symmetrical bubble shape. [Copyright &y& Elsevier]

Abstract: Numerical simulations have been carried out for the transient formation of Taylor bubbles in a nozzle/tube co-flow arrangement by solving the unsteady, incompressible Navier–Stokes equations. A level set method was used to track the two-phase interface. The calculated bubble size, shape, liquid film thickness, bubble length, drift velocity, pressure drop and flow fields of Taylor flow agree well with the literature data. For a given nozzle/tube configuration, the formation of Taylor bubbles is found to be mainly dependent on the relative magnitude of gas and liquid superficial velocity. However, even under the same liquid and gas superficial velocities, the change of nozzle geometry alone can drastically change the size of Taylor bubbles and the pressure drop behavior inside a given capillary. This indicates that the widely used flow pattern map presented in terms of liquid and gas superficial velocities is not unique. [Copyright &y& Elsevier]

Abstract: The influence of the liquid properties on the dynamical bubble shape and on the bubble motion has been investigated for bubbles moving under a downward facing inclined surface. The Morton number Mo varied from 2.59×10−11 to 2.52×10+01. The Bond number Bo covered the range from 10 to 150 and the surface inclination angle θ was varied from 2° to 6°. To cover the wide range of Mo, several liquids such as glycerine, propanediol, water and isopropanol were used. The results have shown that the relation Fr = Fr(Bo, Mo, θ) is not adequate to describe the bubble motion, where Fr is the terminal Froude number. The choice of the terminal Reynolds number Re as the dependent parameter, allowed the clarification of the role of the Morton number on the bubble motion. At a given Bond number, the bubble Reynolds number decreases monotonously with the Morton number. Furthermore, an empirical correlation Re = Re(Bo, Mo, θ) is given that can be readily used in the mathematical modelling of bubble laden flows under solids. [Copyright &y& Elsevier]

Abstract: The movement of single air bubbles under a downward facing inclined solid surface has been investigated in motionless distilled water body. The effects of surface inclination θ and bubble volume V on the terminal Froude number are studied in details. The bubble volume was varied in the 0.3–9cm3 range and the inclination angles up to 10° in a gravity driven system. For a typical correlation curve of the terminal velocity u T versus the volume at a given inclination it was found that the increase of u T with V is not monotonous and that four distinct sub-regimes, each characterized by a specific bubble shape, exist. The effect of inclination on u T is more sensitive at both low V and low θ. The different sub-regimes are explained qualitatively. In addition, the drag coefficients for moving bubble underneath a solid surface are presented. [Copyright &y& Elsevier]

Abstract: The bubble shape on heating surfaces is simulated by numerically solving the Young–Laplace equation including a dynamic pressure term. This dynamic pressure is calculated by a correlation involving several empirical coefficients. By adjusting these coefficients, a given bubble shape can be well represented. Thus the pressure around the bubble and various forces acting on the bubble can be accurately calculated. Some calculation examples are given. The results show an important effect of dynamic forces on the bubble shape. Therefore, the assumption of spherical bubbles could lead to big errors in force evaluations. [Copyright &y& Elsevier]

Abstract: In this paper a three-dimensional (3D) volume of fluid (VOF) method is presented featuring (i) an interface reconstruction technique based on piecewise linear interface representation, (ii) a 3D version of the CSF model of Brackbill et al. [1992, Journal of Computational Physics 100, 335]. Our model can handle a large density and viscosity ratio and a large value of the surface tension coefficient. First the results of a number of test cases are presented to assess the correctness of the advection and interface reconstruction algorithms and the implementation of the 3D version of the CSF model. Subsequently the computed terminal Reynolds numbers and shapes of isolated gas bubbles rising in quiescent liquids are compared with data taken from the bubble diagram of Grace (1973). Finally results of two calculations are reported involving the co-axial and oblique coalescence of two gas bubbles. The computed bubble shapes compared very well with the experimentally observed bubble shapes of Brereton and Korotney [1991, In: Dynamics of Bubbles and Vortices Near a Free Surface, AMD-vol. 119. ASME, New York]. [Copyright &y& Elsevier]

This paper presents experimental results of the surface phenomena effect on bubble formation from a single orifice (1 mm diameter) submerged in water with air blowing at an extremely small flow rate (2 cm3 min−1). Bubble formation was studied for a wide range of contact angles (68°≤θ0≤110°) at liquid–orifice plate–gas interface using key geometrical parameters of a bubble: volume (V), surface area (S), radius at the tip (R0) and the dimension of bubble periphery at the base (D). The meaningful stages, termed (1) nucleation period, (2) under critical growth, (3) critical growth and (4) necking, were identified during bubble formation. It was determined that bubble volume essentially depends on wettability. It increases by more than half as wetting conditions worsen, e.g. equilibrium contact angle, θ0, increases from 68° to 110°. Bubble formation is found to be substantially controlled by hysteresis of contact angle. [Copyright &y& Elsevier]

With regard to improving the blending performance of biodiesel with hydrogen, it is important to generate smaller hydrogen bubbles in biodiesel at low energy consumption. In this context, a strong non-uniform direct current (DC) electric field has been created between a needle-ring electrode configuration, which is used to study the effect of EHD on hydrogen bubble behaviors in biodiesel considering the various gas flow rates and applied voltages. The special geometry of gas cones similar to the Taylor cone in liquid droplets under an electric field is demonstrated. The hydrogen bubble features—which are characterized by the bubble heights, frequencies, velocities, bubble sizes, and shapes—show that the bubble geometry and dynamic characteristics in the electric field are performed in manners different from those reported in the literature. It is found that the hydrodynamic behavior of the bubbles is also modified by the EHD effect. The distributions of bubble size in different cases follow the Gaussian distribution. Small bubbles are more likely to be associated with high separation velocities. Further, the diversity of bubble shapes at the separation is demonstrated, and two regimes of impact mechanism based on the surface tension and electric forces are revealed. [Display omitted] [ABSTRACT FROM AUTHOR]

• For a spherical bubble, the direct numerical integration of Young-Laplace equation works very well in computing the bubble shape. • The approximate analytical solution computes a non-spherical shape of a bubble at a high superheat much better than the direct numerical integration of Young-Laplace equation non-spherical bubbles. • The shape of a bubble has been found to be influenced by superheat and Bond number Bo. • The Young-Laplace equation seems to include the growth force to produce the hemispherical shape of non-spherical bubbles. • A very low Bo results in a train of small bubbles that coalesce to a big bubble with increase in Bo. In this work, we have developed an improved numerical model to simulate the dynamics of bubble shape and departure in nucleate pool boiling at a heated surface at low and high superheats. The numerical model computes the bubble shape solving Young-Laplace equation directly and considering the effect of radial variation of film pressure in our numerical model of microlayer evaporation. The numerical results of bubble shape and departure have also been compared with the CFD-results in literature and with the results of our experiments. For a spherical bubble, the direct numerical integration of Young-Laplace works very well in computing the bubble shape. For a non-spherical bubble, an approximate analytical solution for bubble shape proposed in literature works better than the numerical solution of Young-Laplace equation. The shape of a bubble has been found to be influenced by superheat and Bond number Bo. We have also analyzed the forces acting on the bubble surface while departing the heated surface. The Young-Laplace equation seems to include the growth force to produce the hemispherical shape of non-spherical bubbles. A very low Bo results in a train of small bubbles that coalesce to a big bubble with increase in Bo. [ABSTRACT FROM AUTHOR]