Gas-liquid Surface Tension Research Articles

Impact of bubble dynamics on aerosol transport based on CFD analysis

The fundamental process of submicron particle transport through a rising bubble is investigated based on the VOF-LPT method. Since the presence of particle interfacial behavior is generally disregarded in previous studies, an interfacial penetration model is applied in this work to include its effect on the scrubbing efficiency, whereby the process of how bubble dynamics affects aerosol transport is analyzed in detail via parametric studies including Eötvös and Galilei numbers. The results indicated that the dependence of the scrubbing efficiency on increasing Eötvös numbers is non-monotonic, which is linked to the weakened internal flow in the approaching process and the deteriorated surface tension force in the impacting process. By contrast, the decreasing Galilei numbers exert a trapping effect on submicron particles inside scrubbing bubbles, which is manifested as the dampened bubble shape oscillation in the approaching process and the escalated viscous drag in the impacting process. Aerosol removal contributions from different mechanisms are found to be highly dependent on gas-liquid surface tension but insensitive to liquid viscosity for submicron particles. In general, the present method is proven to be viable to simulate the submicron particle transport inside scrubbing bubbles under the circumstance of changeable bubble dynamics.

Modeling of submicron particle transport based on VOF-LPT method

The submicron particle transport inside a single bubble rising in water is investigated by the VOF-LPT method. As an improvement of the previous particle transport assumption in numerical studies, a new interfacial penetration model is developed according to the observed particle behavior in experimental works. The new criterion, namely particle Weber number is derived based on the dimensional analysis of the kinetic energy equation. The developed model is calibrated and evaluated based on the experimental data and parametric studies including particle size, density and gas–liquid surface tension are performed. The results indicated that the consideration of the interfacial penetration model is reasonable due to the presence of particle interfacial behavior dominant by surface tension force. The application of particle Weber number as the criterion is found to agree well with the experimental observations from both quantitative and qualitative aspects. In the presence of large particle inertia, the particle may deviate from the gas streamline and impact the bubble surface on one side, while the particle presents enhanced penetration capacity through the gas–liquid interface on the other side. With the decreasing gas–liquid surface tension, a competitive mechanism between the weakened internal flow and the enhanced penetration capacity is found, which complexes the effect of surface tension on particle transport in a non-monotonic way. In general, the interfacial penetration model developed in this study is proven to be feasible to describe submicron particle transport inside the rising bubble.

Study of pool boiling heat transfer of nanofluid in the PCD electrical fields

Nanofluids with excellent thermal properties can be used for a coolant and the heat exchange. Actually, the heat transfer between the nanoparticles and working medium benefits from the nanoparticles movement, which could be controlled actively by the electrical field with periodically changed direction (PCD electrical field). Therefore, the coupled effect of nanofluid and switching period and the prediction model were investigated. Concretely, the boiling heat transfer coefficient (BHTC) and the critical heat flux (CHF) with various switching periods of the electrical field were compared. Meanwhile, the mechanism of heat transfer enhancement was discussed. Besides, the predicted model was developed. The present study finds that the BHTC and the CHF will be further strengthened due to the coupled effect of the PCD electrical field and nanofluid. However, this enhancement has an optimal concentration. Moreover, the heat transfer performance enhancement is attributed to the continuous heat transfer by nanoparticle and the further decrease of surface tension. The prediction curves mostly coincide with experimental data, and the prediction models are proposed by considering the influence of the switching period, the nanoparticles movement, the gas-liquid interface surface tension and the dynamic thermal conductivity.

Анализ сопряженного тепломассопереноса при аэрозольной флотации золота из россыпей

Introduction. The probability of replenishing the SME of placer gold by registering the reserves of new deposits is low, and the involvement of man-made waste in the economic circulation will allow maintaining the achieved level of gold production from placers for 10-15 years. Purpose of research. The aim of the study is to develop a technology for extracting gold from old wastes of alluvial mining based on the identified patterns of conjugate heat and mass transfer during aerosol flotation of metallic gold. Methodology. For the development of technogenic wastes of alluvial gold mining, an enrichment module based on gravity and flotation methods has been developed. The module equipment has passed research tests in industrial conditions. During flotation, the increase in the gold content in the operation of the main flotation is carried out by mixing the crude concentrate isolated from ½ of the original feed with the other ½ of it. A mixture of air and hot steam was used as the gas phase during flotation. Research results and discussion. The temperature difference at the gas-liquid interface is the driving force of the vapor-liquid phase transition with the release of significant condensation heat. The time of particle sticking to the bubble is commensurate with the time of heating the interfacial surface due to the heat of vapor condensation. This allows us to consider temperature as one of the reasons for changing the result of flotation by a mixture of air and water vapor. Due to vapor condensation, the bubble size and the intensity of interfacial heat transfer decrease. When the minimum size is reached, overheating of the vapor in the bubble leads to an increase in the evaporation of the solvent and pressure in the gas phase: the heat transfer between the phases and the size of the bubble begin to increase. Transient processes in steam are non-polytropic and the limiting bubble sizes decrease with time: at the minimum size and maximum temperature, the heat transfer of steam is higher than the heat transfer of water with an increase in the size of the bubble and a drop in temperature in it. The limiting transitions of the bubble size are the cause of high-speed oscillations of the bubble walls, which decay with time. When the bubble surface is stretched in the three-phase contact zone, the gas-liquid surface tension increases due to a decrease in the density of the adsorption layer of surfactant molecules, which causes an increase in the force holding the hydrophobic extractable particle on the bubble surface. Radial tensile-compression deformations lead to shedding from the bubble surface of hydrophilic gangue minerals randomly retained by the bubble surface (for example, in the case of high occupation of the bubble surface by extracted particles). Conclusion. It is substantiated that the combined gravity-flotation technology is economically justified: the added value of marketable products provides an increase in the value of the net present value and the return on investment index, and a reduction in their payback period. It has been proven that the addition of gravity technology with flotation methods for extracting gold provides an increase in annual metal production by ~27% rel. due to the additional extraction of forms of gold that are “resistant” to gravitational methods.

Spray Characteristics of Standard and Alternative Aviation Fuels at Cold-start Conditions

The spray characteristics of standard and alternative aviation fuels created by a hybrid pressure-swirl airblast (HPSA) atomizer were investigated at conditions corresponding to engine cold start for an aviation gas turbine. Drop size and drop velocity of sprays from three different fuels, Jet-A (A-2), JP-5 (A-3), and a JP-5/farnesane blend (C-3) were investigated using a phase Doppler anemometry. The spatially resolved drop measurements were obtained at three axial locations downstream of the swirler exit plane and up to 30 mm in the radial direction from the spray centerline. Smaller , , and were observed when increasing the pressure drop across the atomizer swirler (). Increasing also increased the mean axial velocity. No definitive trend was observed with viscosity on drop size, while liquid–gas surface tension showed a weak correlation with drop size due to its small variation in value among fuels. The spray unsteadiness was examined using interparticle arrival time distribution functions. A semi-empirical model was also developed using a phenomenological three-step model for the atomization process of the HPSA atomizer and was used to predict drop-size values at engine cold-start conditions in this work and near lean blowout conditions presented in earlier work.

Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional.

This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid-gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5kBT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes.

Modeling of Partially Wetting Liquid Film Using an Enhanced Thin Film Model for Aero-Engine Bearing Chamber Applications

Abstract In the case of aero-engine, thin lubricating film servers dual purpose of lubrication and cooling. Prediction of dry patches or lubricant starved region in bearing or bearing chambers are required for safe operation of these components. In this work, thin liquid film flow is numerically investigated using the framework of the Eulerian thin film model (ETFM) for conditions, which exhibit partial wetting phenomenon. This model includes a parameter that requires adjustment to account for the dynamic contact angle. Two different experimental data sets have been used for comparisons against simulations, which cover a wide range of operating conditions including varying the flowrate, inclination angle, contact angle, and liquid–gas surface tension coefficient. A new expression for the model parameter has been proposed and calibrated based on the simulated cases. This is employed to predict film thickness on a bearing chamber which is subjected to a complex multiphase flow. From this study, it is observed that the proposed approach shows good quantitative comparisons of the film thickness of flow down an inclined plate and for the representative bearing chamber. A comparison of model predictions with and without wetting and drying capabilities is also presented on the bearing chamber for shaft speed in the range of 2500 RPM to 10,000 RPM and flowrate in the range of 0.5 liter per minute (LPM) to 2.5 LPM.

Numerical simulation of bubble and arc dynamics during underwater wet flux-cored arc welding

The dynamic behaviors of underwater bubbles and arcs are critical to welding processes and weld quality in underwater wet flux-cored arc welding. In this study, bubble evolution promoted by an arc plasma and flux decomposition was simulated using hydrodynamic equations. The influence of water on bubble and arc behavior was considered with regard to ionization of hydrogen in the arc, gas-liquid interfacial surface tension, and the absolute pressure. The interface between the water and bubble was determined via the volume of fluid and level-set methods. Physical parameters of mixed gas or plasma in the bubble were calculated by mass weighted average method based on the values of pure gas or plasma. The arc and bubble temperature distributions, fluid flows, and internal pressures were analyzed to reveal heat and mass transfer in the arc. The cycle of arc bubble evolution was about 0.056−0.063 s in calculation. The velocity of arc plasma could reach up to 500 m/s, which was one of the major factors to influence the arc bubble behaviors. Experiments were performed and the results showed that the simulated bubble shape, growth cycle, and evolution process agree well with the experimental data.

Force approach for the pseudopotential lattice Boltzmann method.

One attractive feature of the original pseudopotential method consists on its simplicity of adding a force dependent on a nearest-neighbor potential function. In order to improve the method, regarding thermodynamic consistency and control of surface tension, different approaches were developed in the literature, such as multirange interactions potential and modified forcing schemes. In this work, a strategy to combine these enhancements with an appropriate interaction force field using only nearest-neighbor interactions is devised, starting from the desired pressure tensor. The final step of our procedure is implementing this external force by using the classical Guo forcing scheme. Numerical tests regarding static and dynamic flow conditions were performed. Static tests showed that current procedure is suitable to control the surface tension and phase densities. Based on thermodynamic principles, it is devised a solution for phase densities in a droplet, which states explicitly dependence on the surface tension and interface curvature. A comparison with numerical results suggest a physical inconsistency in the pseudopotential method. This fact is not commonly discussed in the literature, since most of studies are limited to the Maxwell equal area rule. However, this inconsistency is shown to be dependent on the equation of state (EOS), and its effects can be mitigated by an appropriate choice of Carnahan-Starling EOS parameters. Also, a droplet oscillation test was performed, and the most divergent solution under certain flow conditions deviated 7.5% from the expected analytical result. At the end, a droplet impact test against a solid wall was performed to verify the method stability, and it was possible to reach stable simulation results with density ratio of almost 2400 and Reynolds number of Re=373. The observed results corroborate that the proposed method is able to replicate the desired macroscopic multiphase behavior.

Simple Parameter-Free Bridge Functionals for Molecular Density Functional Theory. Application to Hydrophobic Solvation.

Computer simulations have been fundamental in understanding the fine details of hydrophobic solvation and hydrophobic interactions. Alternative approaches based on liquid-state theories have been proposed, but are not yet at the same degree of completeness and accuracy. In this vein, a classical, molecular density functional theory approach to hydrophobic solvation is introduced. The lowest, second-order approximation of the theory, equivalent to the hypernetted chain approximation in integral equations, fails in describing correctly cavitation free-energies. It is corrected here by two simple, angular-independent, so-called bridge functionals; they are parameter-free in the sense that all variables can be fixed unambiguously from the water bulk properties, including pressure, isothermal compressibility, and liquid-gas surface tension. A hard-sphere bridge functional, based on the known functional of a reference hard fluid system, turns out to face strong limitations for water. A simpler weighted density approximation is shown to properly reproduce the solvation free energy of hydrophobes of various sizes, from microscopic ones to the nanoscale, and predicting the solvation free energy of a data set of more than 600 model hydrophobic molecules having a variety of shapes and sizes with an accuracy of a quarter of kBT compared to Monte Carlo simulations values. It constitutes an excellent starting point for a general functional describing accurately both hydrophobic and hydrophilic solvation, and making it possible to study nonidealized hydrophobic interactions.

Nano-to-Microporous Networks via Inkjet Printing of ZnO Nanoparticles/Graphene Hybrid for Ultraviolet Photodetectors

Inkjet-printed photodetectors have gained enormous attention over the past decade. However, device performance is limited without postprocessing, such as annealing and UV exposure. In addition, it is difficult to manipulate the surface morphology of the printed film using an inkjet printer because of the limited options of low viscosity ink solutions. Here, we employ a concept involving the control of the inkjet-printed film morphology via modulation of cosolvent vapor pressure and surface tension for the creation of a high-performance ZnO-based photodetector on a flexible substrate. The solvent boiling point across different cosolvent systems is found to affect the film morphology, which results in not only distinct photoresponse time but also photodetectivity. ZnO-based photodetectors were printed using different solvents, which display a fast photoresponse in low-boiling point solvents because of the low carbon residue and larger photodetectivity in high-boiling point solvent systems due to the porous structure. The porous structure is obtained using both gas–liquid surface tension differences and solid–liquid surface differences, and the size of porosity is modulated from nanosize to microsize depending on the ratio between two solvents or two nanomaterials. Moreover, the conductive nature of graphene enhances the transport behavior of the photocarrier, which enables a high-performance photodetector with high photoresponsivity (7.5 × 102AW–1) and fast photoresponse (0.18 s) to be achieved without the use of high-boiling point solvents.

Impacts of motileEscherichia colion air-water surface tension

Immiscible multiphase flow in porous media is largely affected by interfacial properties, manifested in contact angle and surface tension. The gas-liquid surface tension can be significantly altered by suspended particles at the interface. Particle-laden interfaces have unique properties, for example, a lower surface tension of interfaces laden with surfactants or nanoparticles. This study investigates the impacts of a motile bacteriumEscherichia coli(E. coli, strain ATCC 9637) on the air-water surface tension. Methods of the maximum bubble pressure, thedu Noüyring, and the pendant droplet are used to measure the surface tension of the motile-bacteria-laden interfaces. Measured surface tension remains independent to theE. coliconcentration when using the maximum bubble pressure method, decreases with increasedE. coliconcentration in thedu Noüyring method, and presents time-dependent changes by the pendant drop method. The analyses show that the discrepancies may come from the different convection-diffusion processes ofE. coliin the flow among various testing methods.

Effect of ambient pressure oscillation on the primary breakup of cylindrical liquid jet spray

The present simulation study investigates the effects of ambient pressure oscillation on cylindrical liquid jet sprays, using the volume of fluid method. The research is motivated by combustion instability in combustion engines, where strong harmonic pressure oscillation can damage internal structures. Oscillating pressure modulates not only the fuel mass flow rate but also the ambient gas density and liquid surface tension, and in liquid sprays, the ambient fluid density and surface tension can have substantial effects on spray breakup. In order to investigate the multiple property changes with ambient pressure oscillation, therefore, a new solver in OpenFOAM is developed. In the solver, liquid mass flow rate, ambient gas density, and liquid surface tension change simultaneously as a result of pressure oscillation. Simulations were conducted at a Reynolds number of 2000 and Weber number over 2000, conditions that are conducive to primary breakup in laminar flows. The simulations show that oscillations in ambient pressure significantly strengthen the surface instability of the liquid ligament, which depends on the surface tension–pressure coefficient, the mean pressure, and the amplitude of oscillation.

Simulation of evolution mechanism of dynamic interface of aqueous foam in narrow space base on level set method

The properties of foam fluid are substantially determined by its interfacial dynamics changes during foam transport. In this research, a foam flow simulation model based on the level set method and the N–S equation with surface tension term is established to simulate the dynamic interface evolution mechanism of group foam and individual foam from various aspects such as drainage process and foam migration in porous media, coalescence and Jamin effect. The results show that the foam life decreases linearly with the logarithm of the surface tension and enhances linearly with the liquid viscosity. For foam transport in porous media, both flowing foam and trapped foam exist, and the pressure fluctuates at a certain pressure value and the best foam structure is achieved at the optimum conditions with the optimum values of gas-liquid ratio, surface tension, and porosity being 1:1˜3:2, 0.1˜0.3, and 44.4%, respectively. Besides, the temporary blocking effect of foam has been verified. During the foam coalescence, foam gradually evolves towards minimum interfacial energy with oscillating and gradually decreasing foam volume. During the process of the foam passing through the throat, the maximum pressure occurs when the front end of the foam reaches the narrowest point, and the minimum pressure occurs when half of the foam passes through the narrowest point. The maximum pressure elevates linearly with the surface tension and the inverse of the throat radius.

Energy conversion during the crown evolution of the drop impact upon films

The energy conversion is proposed to analyze the effects of inertial force, surface tension, gravitational force and viscous force during the crown evolution of the drop impact phenomena. The incompressible laminar Navier–Stokes equations coupled with the volume of fluid model are solved numerically in the axisymmetric frame to simulate the impact process. The influences of both the ratio of the initial kinetic energy to the surface tension energy of the drop as well as the initial film thickness on the energy conversion during the impact process are studied in detail. The ratio of the initial kinetic energy to the surface tension energy of the drop can affect the energy conversion at a very early stage of the impact process, thus it can affect the occurrence of prompt splash significantly; while the initial film thickness can affect the energy conversion process during the whole impact process, and it is related to the occurrence of delayed splash. The energy conversion process corresponds to the type of impact phenomena, which is affected by the film depth significantly. according to the differences in energy curves and flow characteristics, the impact phenomenon is divided into three types: the drop impacts on shallow, medium and deep films. A typical impact process of the medium film is analyzed in detail. The impact process is divided into five stages, namely, crown formation, crown growth, crown stabilization, crown collapse and central jet formation. In the crown formation and growth stages, inertial force promotes the deformation of the liquid-gas interface and surface tension prevents the deformation; while in the crown collapse stage, inertial force prevents the deformation and surface tension does the opposite effect. During the whole process, the viscous force plays a prevention effect.

Thermal effects on the instability of coaxial liquid jets in the core of a gas stream

The breakup of coaxial liquid jets in a co-flowing gas stream under the radial thermal field is studied by the linear instability theory. A simplified physical model is established, and an analytical dimensionless dispersion relation for temporally axisymmetric perturbations is derived and solved numerically. The outer liquid-gas surface tension coefficient is assumed to be a linear function of temperature. Due to the radial temperature gradients, the time-dependent spatial variation of surface tension gives rise to a shear stress and induces Marangoni force upon the flow. The effects of different process parameters on the characteristics of unstable modes including the para-sinuous mode and the para-varicose mode are explored. It is found that the para-sinuous mode always dominates the jet instability in the parametric regions and the increasing temperature ratio of the surrounding gas stream and the inner liquid jet (T31) can reduce the maximum growth rates of unstable modes and corresponding dominant wavenumbers. The Reynolds number destabilizes the jet instability, and the Weber number suppresses it at relatively long wavelengths for both isothermal and non-isothermal situations. The Marangoni number and the Peclet number have a destabilizing effect for T31 < 1, but it is opposite for T31 > 1. These theoretical predictions would provide insight into underlying physical mechanisms of thermal jet breakup and compound droplet formation.

Length-scale cascade and spread rate of atomizing planar liquid jets

The primary breakup of a planar liquid jet is explored via direct numerical simulation (DNS) of the incompressible Navier–Stokes equation with level-set and volume-of-fluid interface capturing methods. PDFs of the local radius of curvature and the local cross-flow displacement of the liquid-gas interface are evaluated over wide ranges of the Reynolds number (Re), Weber number (We), density ratio and viscosity ratio. The temporal cascade of liquid-structure length scales and the spread rate of the liquid jet during primary atomization are analyzed. The formation rate of different surface structures, e.g. lobes, ligaments and droplets, are compared for different flow conditions and are explained in terms of the vortex dynamics in each atomization domain that we identified recently. With increasing We, the average radius of curvature of the surface decreases, the number of small droplets increases, and the cascade and the surface area growth occur at faster rates. The spray angle is mainly affected by Re and density ratio, and is larger at higher We, at higher density ratios, and also at lower Re. The change in the spray spread rate versus Re is attributed to the angle of ligaments stretching from the jet core, which increases as Re decreases. Gas viscosity has negligible effect on both the droplet-size distribution and the spray angle. Increasing the wavelength-to-sheet-thickness ratio, however, increases the spray angle and the structure cascade rate, while decreasing the droplet size. The smallest length scale is determined more by surface tension and liquid inertia than by the liquid viscosity, while gas inertia and liquid surface tension are the key parameters in determining the spray angle.

Measurements and correlations for gas liquid surface tension at high pressure and high temperature

Surface tension of water/nitrogen and water–phenol/nitrogen systems was successfully measured by the hanging drop method in a wide domain of temperature (from 100 to 300°C) and pressure (from 4 to 30MPa), conditions little explored in litterature. Results show that surface tension of water–phenol mixtures decreases as phenol mass fraction increases. This decrease is observed under saturated and unsaturated conditions and is more pronounced at low temperatures and does not seem to depend on pressure. The effect of saturation on surface tension in the water/nitrogen system has been correlated with water vapor pressure by using experimental points with a great accuracy. For the water–phenol/nitrogen system, experimental data obtained with different mass fraction of phenol were correlated using Macleod‐Sugden equation for mixtures. © 2018 American Institute of Chemical Engineers © 2018 American Institute of Chemical Engineers AIChE J, 64: 4110–4117, 2018

Generalization and Modelling of Rigid Polyisocyanurate Foam Reaction Kinetics, Structural Units Effect, and Cell Configuration Mechanism

PIR/PUR ratio was derived from differential manipulation of generalized polyisocyanurate kinetic model. The structural unit effects on polymerization of isocyanurate, urethane and urea linkages were evaluated based on Mayo-Lewise tercopolymerization scheme. The cell microstructural configuration model was further developed from profiled FOAMAT reactivity parameters with integrated analysis of cell interface physics. The interstitial border area was defined by interface free energy theory, the shear viscosity was evaluated by foam motion, gas fraction, and partial pressure, and the cell inflation was re-examined by gas-liquid surface tension variability. The cell anisotropic degree, assumed as an aspect ratio of infinitesimal volume elements in cell uniformity, was characterized by equilibrated work increase of surface energy approximated by 2D stretching deformation from sphere cell to spheroid cell. The relationship between pressure and surface tension of elongated cells was also derived from modelling at the same condition of cell deformation.

A novel numerical approach for investigation of the gas bubble characteristics in stagnant liquid using Young-Laplace equation

In the present study, the Young-Laplace equation was applied to simulate the adiabatic gas bubble growth from a submerged needle in stagnant liquid column. In order to solve the Young-Laplace equation the axisymmetric bubble height was used as input from experimental data. To increase the accuracy of Young-Laplace equations’ prediction during the bubble growth, the bubble was divided into four sections with the same height, and Young-Laplace equation was solved for each section individually. By dividing the bubble into four sections, the effects of viscosity and inertia forces within each section were reduced as compared to that of buoyancy and liquid-gas surface tension. Unlike the conventional Young-Laplace approach (one Young-Laplace equation for the entire bubble), the new approach was able to predict bubble characteristics reliably during the growth cycle. The bubble growth was investigated in a column of liquid with a triple contact line that fixed to the needle perimeter. To validate the numerical results, the bubble profiles that predicted by numerical simulation were compared with the experimental results. Experiments were performed by injection of air at constant gas flow rate of 600ml/h in the quiescent deionized water and SiO2 nanofluid. The nanoparticle concentrations were 0.05, 0.1 and 0.2wt%, and air flow injected from G14 and G17 standard needles. Eventually, evaluation of bubble characteristics, such as the bubble volume, the center of gravity, the instantaneous contact angle, and the bubble aspect ratio were investigated, and the effects of variation of liquid properties on the bubble characteristics were discussed. The results show that the present method can predict the bubble shape during 97.5% of growth time with mean absolute error of 6%. Furthermore, the results revealed that the bubble size decreased with increment of Bond number. Also, bubble instantaneous contact angle and bubble aspect ratio were almost irrelative to Bond number during the growth cycle.