Spatial distribution of nucleated bubbles in molten glasses undergoing coalescence and growth

Two‐dimensional spatial distributions and growths of nucleated bubbles during the re‐melting of “float” glass samples are experimentally investigated. To follow the bubble population undergoing coalescence, the temporal behavior of the Voronoï tessellation built by the bubble positions are monitored. During coalescence, the Voronoï cell areas are fitted by a single‐parameter Gamma distribution. Numerical time simulation of population of bubbles undergoing coalescence shows an exponential increase in the parameter associated to the Gamma distribution with the fraction of coalesced bubbles in agreement with experimental observation. An initial density of nuclei is then estimated; direct observation would require an extremely high space resolution. The bubble number density is two orders of magnitude larger on the side which was in contact with tin bath than on the other side in contact with atmosphere. Moreover, bubbles grow faster on tin side. From a thermodynamic and mass transfer models, we prove that tin reduces the glass former liquid which leads to an increase in dissolved sulfur explaining the more abundant bubble population and the enhanced growth rate on tin side.     

幂律流体中平行上升双气泡间相互作用研究

采用流体体积(VOF)法对非牛顿幂律流体中平行上升双气泡间相互作用进行了模拟研究.结果表明:剪切变稀效应及气泡周围流场结构对气泡间相互作用的贡献分别随着气泡间距增大而减小,气泡间相互作用主要受气泡间流体涡旋结构控制.当初始间距很小时,气泡平行聚并发生;随着初始间距增大,双气泡行为转变为相互影响的平行上升;当初始间距增大...     

Modeling of bubble coalescence in bubbly co-current flows restricted by confined geometry

Principles of kinetic theory are used to model the coalescence of bubbles in horizontal and vertical upflows where bubble movements are restricted by channel geometry. There are four critical variables that determine the rate at which a swarm of small bubbles will coalesce: the initial bubble population, the average initial bubble diameter, the average relative velocity of the bubbles, and the efficiency of bubble collisions. A model based on dimensional considerations is proposed to predict bubble size as a function of flow position. This model agrees well with experimental results for air/water and air/water/glycerin systems performed in a rectangular channel with an aspect ratio of 12.5 and a cross-sectional area of under both vertical and horizontal orientations.     

Mass transfer at gas evolving electrodes

To elucidate the mechanism of the mass transfer at a gas evolving electrode, the thickness of the diffusion layer δ has been determined as a function of the volume rate of the gas evolution ν, for both hydrogen and oxygen evolving electrodes in alkaline solution. The effect of electrode material, alkaline concentrations, roughness, position and disk diameter of the electrode, gas pressure and of temperature upon the δ/gn relation is given. A low absolute value of the slope of the log δ/log ν, of about 0.3 is found experimentally when no coalescence of gas bubbles occurs and a high one, that is about 0.9 when coalescence occurs frequently. It has been concluded from the experimental results that the mass transfer can be explained on the basis of the hydrodynamic model when no coalescence of gas bubbles occurs and on that of the penetration model when coalescence occurs frequently.     

Bubble coalescence efficiency near multi-orifice plate

Bubble coalescence reduces specific area and weakens the work performance of bubble column. The bubble coalescence near gas sparger which is caused mainly by bubble growing is different from the ones occurring in major liquid. Bubble coalescence efficiency near gas sparger is influenced by many factors including sparger configuration, gas flow rate, bubble deformation, solution composition, etc. This work has conducted a set of visual experiments to study the coalescence characteristics near multi-orifice plate. The experiment parameters cover a wide range of conditions including large scope of gas flow rate,different kinds of solution and orifice configurations. The experimental results suggest that coalescence time is applicable to reflect the influence of the pitch of orifices and gas flow rate on bubble coalescence efficiency. As the number of orifices increases, bubble coalescence efficiency is reduced by the disturbance from the bubbles at adjacent orifices. A hindering coefficient is used to consider the hindering effect of additives on bubble coalescence efficiency. Finally a new calculation expression is established to predict bubble coalescence efficiency near multi-orifice plate whose fundamental form is based on the logistic curve of binary response. The calculated values that refer to this calculation expression are well consistent with the experimental results.     

垂直惰性阳极铝电解槽内的析气行为

垂直惰性阳极铝电解槽内,析气行为会影响氧化铝浓度分布和电流效率。利用新设计的透明电解槽进行了电解试验,观察了大尺寸惰性阳极气泡的析出及逸出过程。试验结果表明：在阳极底掌下,气泡进行周期性的生长、长大、并聚和脱离,但大尺寸阳极上气泡的滑动和并聚过程与小尺寸阳极上的不同。阳极工作面上则形成了气泡群,新形成的气泡迅速脱离。紧贴着阳极的气泡运行速度慢,外层的气泡运动速度快。所有气泡最终都经液面逸出,大部分气泡到达液面时立即逸出,少部分未及时逸出的气泡随着电解质做一段水平运动后才逐步逸出。测量到的惰性阳极的气泡运动速度为0.006~0.445 m·s^-1,底部的气泡运动速度分布范围宽,然而,受电解质的限制,中上部的范围窄。     

Theoretical modelling of the effect of surface active species on the mass transfer rates in bubble column reactors

The complex composition of the liquid media in bubble column reactors makes their understanding and theoretical modelling challenging. In this work we have studied the effect of surface tension and contaminants, salts, on the mass transfer rates from a theoretical point of view, looking for a deeper understanding on the effect of surface active species which usually reduce surface tension and modify bubble surface behaviour. The specific contact area is obtained using a population balance where the effect of the presence of contaminants is addressed by the proper theoretical closures for bubble coalescence efficiency, for partially and fully immobile surfaces, and bubble break-up. Meanwhile, the contribution of contaminants to the liquid-film resistance is implemented as function of the coverage of the surface of the bubbles. It was found that the degree of bubble surface coverage not only affects bubble coalescence but also their break-up. The ion strength defines bubbles stability and the critical Weber number can be predicted as function of ion strength. Furthermore, the mass transfer rates are function of the surface coverage by the electrolytes. The model was able to predict k_La taking into account the fact that the concentration profiles surrounding individual bubbles are not completely developed due to the presence of other bubbles, in agreement with previous results from the literature.     

Monte Carlo Simulation of Coalescence Processes in Oil Sands Slurries

Conditioning of an oil sand slurry is a critical step in the extraction of bitumen from oil sand ore. To model the conditioning process, a constant‐number Monte Carlo algorithm is used to simulate the mean‐field kinetics of coalescing bitumen drops and air bubbles. The coalescence rate of drops and bubbles is described by the model of Coulaloglou and Tavlarides (1977). Simulations yield results that are consistent with aerated bitumen drop sizes and conditioning times reported in the literature. The effects of turbulent energy, bitumen concentration, and initial bitumen drop size on the evolution of drop size distributions are investigated.     

Velocity Evolution for the Coalescence of Two In-Line Bubbles Rising in Non-Newtonian Fluids

This study experimentally investigates velocity evolution for the coalescence of two in-line bubbles rising in non-Newtonian fluids by using a high speed camera. Due to the wake of the leading bubble and the shear-thinning effect of non-Newtonian fluids, the following bubble is accelerated to approach the leading bubble, leading to the coalescence of the two bubbles. Based on the Newton’s second law and Schlichting’s wake theory, a theoretical model was developed to estimate the instantaneous rising velocity of the following bubble in the coalescence process of the two bubbles. The predicted values by the present model showed a good agreement with the experimental data.     

基于FTM方法的双气泡融合特性模拟

采用界面追踪法(FTM)对气泡融合现象进行数值模拟,将模拟结果与文献结果进行对比,验证了计算模型的准确性。结果表明,同轴双气泡上升速度均高于单独气泡的上升速度,且融合后气泡与等直径单气泡上升速度相同。气泡间距较小时,跟随气泡的上升速度更高。引导气泡的厄特沃什数Eo=0.36~9,Eo较大时两气泡上升阶段时间较短,但接触阶段时间较长,接触阶段气泡间的液膜在压力作用下逐渐变薄,最终破裂,气泡融合。Eo?4.16时,气泡融合所需时间随Eo增加而增加;Eo?4.16时,气泡融合所需时间不再变化。莫顿数Mo=0.57,Eo=5.04~18.72时,存在特定的双气泡初始角度?c,当0?≤?≤?c时,双气泡相互排斥;当?c≤?≤90?时,双气泡融合,且?c随Eo增加而降低.     

On the role of the macroscopic deformation in liquid film drainage between bubbles

The collision of bubbles in multiphase reactors is critical to bubble size distribution. However, the theoretical models that can reasonably predict collision outcomes and the experimental data that can be used to directly verify the models are still very lacking. We studied the collision of two bubbles in clean water through experiments and theoretical modeling, revealing the mechanism that the collision result shifts from coalescence to rebound with increasing collision velocity. The macroscopic deformation (MacrD) of bubbles is associated with the film drainage via a segmented linear equation as a function of the film radius and initial Weber number. Thus, the current model can reflect the effect of MacrD in a self-consistent way. The coalescence times and critical coalescence velocities predicted by the model were in good agreement with the experiments. This work provides novel insights into bubble coalescence modeling and serves to improve the accuracy of reactor simulations.     

Flowrate effects on the lateral coalescence of two growing bubbles

The coalescence of two growing bubbles presents unique characteristics compared to static bubble coalescence. The gas injection flowrate significantly affects the different stages of bubble evolution, which is poorly understood. In this study, we investigate the flowrate effects on the lateral coalescence of two growing bubbles experimentally. The synchronous bubbling from adjacent needles is achieved using water to push air. During the bubble growth process, we find that the initial nonlinear evolution of bubble volume is because the bubble emerges as a small spherical cap with a large curvature radius and apparent contact angle. As the neck expands after bubble coalescence, the injection flowrate accelerates the neck evolution compared to the case without air injection. We find the neck expansion time decreases linearly with increasing flowrate, while the expansion speed increases with flowrate, but only in the early stage. Moreover, we propose a new theoretical expression that predicts the neck radius well at all the flowrates. At the post-coalescence oscillation stage, the average projection area of the coalesced bubble increases linearly with time, except for periodic oscillations. Besides, we find that the injected air primarily influences the coalesced bubble's height, which in turn affects the projection area.     

精馏塔板相界面积的粒数衡算模型

通过对气液湍流系统中气泡的动力学行为进行分析推导出气泡破碎速率与聚并速率的表达式,在此基础上建立了描述气泡分散特性的粒数衡算模型.求解粒数衡算方程可以计算精馏塔板上气泡的粒度分布以及气液相界面积,模拟计算的结果与实验测量的数据相当一致,证明可以利用粒数衡算模型较准确地预测气液湍流系统的分散性质.     

Initial particle velocity spatial distribution from 2-D erupting bubbles in fluidized beds

Some results on particle image velocimetry (PIV) in 2-D freely bubbling fluidized beds are presented. The PIV applications were used in order to determine the initial particle velocity of bubble eruptions. A two-dimensional non-reacting fluidized bed was constructed to measure the origin of the ejected particles and the initial particle velocity distribution, using coarse sand particles. The bubble ejection mechanism was observed taking into account the origin of particles ejected, the initial particle velocity distributions as well as the effect of other neighbor exploding bubbles. Our results show that the assumption of linear dependence of initial velocity with the angle predicts the velocity faithfully only for purely vertical-ascent bubbles. Measurements of ejection velocities show that initial velocities in the combined layer are higher than those of the particles in the nose of the leading bubble. Avoiding coalescence of bubbles at the bed surface can lead to less particle entrainment out of the bed and consequently to shorter fluidized beds.     

Coalescence of bubbles and stability of foams in aqueous solutions of Tween surfactants

Coalescence of air bubbles and stability of foams in aqueous solutions of Tween 20, 40, 60 and 80 are reported in this work. Adsorption of the surfactants at air–water interface was studied by measuring the surface tension of the surfactant solutions. The surface tension profiles were fitted using a surface equation of state derived from the Gibbs and Langmuir adsorption equations. The critical micelle concentration and surface tension at this concentration were determined. The effect of surfactant concentration on coalescence of air bubbles at flat air–water interface was studied. The role of steric force on coalescence time was investigated. The coalescence time distributions were fitted by the stochastic model. The mean values of the distributions were compared with the predictions of seven film-drainage models. Stability of foams was analyzed by the Ross–Miles test. The initial and residual foam heights were measured at different surfactant concentrations. The stability of foams was compared with the coalescence time of the bubbles.     

Theoretical prediction of flow regime transition in bubble columns by the population balance model

Theoretical prediction of flow regime transition in bubble columns was studied based on the bubble size distribution by the population balance model (PBM). Models for bubble coalescence and breakup due to different mechanisms, including coalescence due to turbulent eddies, coalescence due to different bubble rise velocities, coalescence due to bubble wake entrainment, breakup due to eddy collision and breakup due to large bubble instability, were proposed. Simulation results showed that at relatively low superficial gas velocities, bubble coalescence and breakup were relatively weak and the bubble size was small and had a narrow distribution; with an increase in the superficial gas velocity, large bubbles began to form due to bubble coalescence, resulting in a much wider bubble size distribution. The regime transition was predicted to occur when the volume fraction of small bubbles sharply decreased. The predicted transition superficial gas velocity was about 4 cm/s for the air-water system, in accordance with the values obtained from experimental approaches.     

泡沫相塔壁对泡沫分离牛血清蛋白分离性能的影响

In order to enhance foam drainage, the column with an inner sleeve in the foam phase was designed for studying effect of the column wall of foam phase on foam separation performances using bovine serum albumin(BSA) as the research system. The effects of the wall on the liquid holdup out of the top column, bubble size, enrichment and recovery percentage were investigated. The results indicated that the experimental column with the inner sleeve decreased the liquid holdup, accelerated the coarsening and coalescence of bubbles and increased enrichment of BSA compared the contrasted column without the inner sleeve. Under the conditions of the initial concentration 0.2 g?L-1 of BSA, air flow rate 400 ml?min-1, the experimental column achieved up to a 2.06 fold increase in enrichment compared to the contrasted column. The enrichment of BSA increased with the increase of inner sleeve length. Channel theoretical analysis showed that the ratio of exterior channels to interior channels increased with the increase of bubble diameter. So the experiment column obtained the better performances at the lower concentration and the lower air flow rate. The better performances obtained by experimental column showed that the drainage rate of plateau borders on wall was greater than that of plateau borders between bubbles. So the inner sleeve provided more plateau borders on wall and improved foam drainage.     

Coalescence Deformation of Bubble Pairs Generated from Twin Nozzles in CMC Solutions

A coupled level‐set/volume‐of‐fluid method, under the consideration of the rheological characteristics of a fluid, is employed to investigate numerical coalescence deformation of bubble pairs generated at two adjacent nozzles in carboxymethyl cellulose aqueous solutions. The satisfactory agreement between numerical results and experimental measurements proves the validity of this approach in predicting the surface evolution of bubbles. Simulated results show that the bubble coalescence process involves four stages of independent growth, rapid mergence, radial expansion, and vertical stretching. The various effects of surfactant concentration, gas flow rate, nozzle spacing, and nozzle diameter on the aspect ratio depend greatly on each coalescence period.     

基于相群平衡模型的浮选气泡聚并模拟

气泡尺寸分布直接影响气浮分离效率,而聚并是导致气浮池内气泡尺寸变化的主要因素。首先用实验方法测量气浮接触区气泡尺寸分布,然后用计算流体力学方法对气泡/水两相流动及气泡聚并进行模拟,最后通过对实验和数值模拟结果进行对比建立基于相群平衡模型的浮选气泡聚并行为的模拟方法,分别运用Luo、Free molecular和Turbulent聚并模型对气浮接触区气泡聚并行为进行模拟。结果表明:Turbulent聚并模型计算所得气泡尺寸分布与实验值最接近,适合模拟接触区气泡聚并;气泡平均直径随高度升高先变大后保持不变,气泡聚并主要发生在接触区中下部;气泡的加入增强了接触区流动混乱程度,上部产生对称涡流,中下部呈由边壁向中心的水平流动。