A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow

Several models for the daughter bubble/droplet size distribution are reviewed and a detailed discussion is given to get a better understanding of the daughter size distribution. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow, based on an eddy-bubble/droplet collision method, is developed. It takes into account the energy distribution of turbulent eddies, effect of capillary pressure and surface energy increase during bubble/droplet breakup. An increase in the mother bubble/droplet size and energy dissipation rate increases the probability of unequal breakup. The model prediction is in good agreement with experimental results and the underlying physical situation.     

A unified theoretical model for breakup of bubbles and droplets in turbulent flows

Pressure has a significant effect on bubble breakup, and bubbles and droplets have very different breakup behaviors. This work aimed to propose a unified breakup model for both bubbles and droplets including the effect of pressure. A mechanism analysis was made on the internal flow through the bubble/droplet neck in the breakup process, and a mathematical model was obtained based on the Young–Laplace and Bernoulli equations. The internal flow behavior strongly depended on the pressure or gas density, and based on this mechanism, a unified breakup model was proposed for both bubbles and droplets. For the first time, this unified breakup model gave good predictions of both the effect of pressure or gas density on the bubble breakup rate and the different daughter size distributions of bubbles and droplets. The effect of the mother bubble/droplet diameter, turbulent energy dissipation rate and surface tension on the breakup rate, and daughter bubble/droplet size distribution was discussed. This bubble breakup model can be further used in a population balance model (PBM) to study the effect of pressure on the bubble size distribution and in a computational fluid dynamics‐population balance model (CFD‐PBM) coupled model to study the hydrodynamic behaviors of a bubble column at elevated pressures. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1391–1403, 2015     

Direct measurement of droplet breakage in a pulsed disc and doughnut column

The lack of experimental data for the droplet breakup has been one of the limitations for the application of population balance model (PBM). In this work, a high‐speed camera was used to directly measure the droplet breakup frequency and daughter size distribution in a pulsed disc and doughnut column. It was found from the captured video that multiple breakup events were more frequently observed than binary breakup. The multiple breakup was treated as an original breakup and several intermediate breakups to characterize the process quantitatively. The effects of pulsation intensity, dispersed phase flow rates, and the spatial locations were investigated in detail. Empirical correlations were finally established for both the breakup frequency function and the daughter droplet size distribution function and fitted well with the experimental data. The correlation equations were then used in a simplified PBM to calculate the droplet number density, which further proved the feasibility of the correlations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4188–4200, 2017     

Droplet breakup in the square microchannel with a short square constriction to generate slug flow

Droplet breakup in microconstrictions is an important phenomenon in industrial applications. This work aimed to investigate the droplet breakup in the square microchannel with a short square constriction to generate the slug flow, which drew little attention before. Mechanism analysis indicated that this breakup process included the shear-force-dominated, squeezing-force-dominated, and pinch-off stages. Nonuniform daughter droplets were generated in the constriction with their interface restricted in the horizontal and perpendicular directions by the microchannel walls. The average relative deviation of the daughter droplet size was <30%, much lower than that for the breakup with the daughter droplet restricted only in one direction. An empirical equation with a deviation of <20% was provided to show the dependence of the daughter droplet size on the operation conditions. The comparison results suggested that the different restriction effects of microchannel wall on daughter droplets led to the different breakup mechanisms in different constrictions.     

气流式雾化过程的有限随机分裂模型

滴径分布是描述喷嘴雾化性能的一个重要指标.从液滴分裂的自相似性出发,提出了描述气流式雾化过程的液滴有限随机分裂模型.实验和模拟计算结果表明,该模型能较好地模拟三通道喷嘴气流式雾化过程的平均滴径和滴径分布的非线性关系.     

Experimental measurement of bubble breakup in a jet bubbling reactor

The bubble breakups in a jet bubbling reactor are captured using a high-speed camera and the velocity field is measured by particle image velocimetry. Two typical breakup patterns, jet breakup and jet-vortex breakup are observed. The breakup time interval of the jet-vortex breakup is two orders of magnitude higher than the jet breakup. The probability of the jet-vortex breakup and the jet breakup accounting in the total breakup events increases and decreases with the jet velocity and the mother bubble size, respectively. The bubble breakup region increases with the jet velocity. The bubble breakup frequency increases with the turbulent dissipation rate and the mother bubble size. The average number of daughter bubbles increases with the Weber number. An L-shaped daughter bubble size distribution is observed. Empirical correlations are established for the bubble breakup frequency, the average number of daughter bubbles and daughter bubble size distribution, and fitted well with the experimental results.     

Prediction of droplet size distribution in sprays of prefilming air-blast atomizers

Droplet size distribution is a crucial parameter of atomization process besides droplet mean diameter. In this paper, the finite stochastic breakup model (FSBM) of prefilming air-blast atomization process has been proposed according to the self-similarity of droplet breakup. There are four parameters in FSBM, which are the initial droplet diameter D₀, the maximum stable droplet size D_c, the minimum mass ratio of a sub-droplet to the mother droplet a, and the droplet breakup probability P(D). The simulation results of droplet size distribution with this model agreed well with the experimental results of prefilming air-blast atomizers. With this model, the nonlinear relationship between the mean droplet diameters and droplet size distribution of the air-blast atomization process can be predicted exactly.     

三维孔喉结构微通道内液滴的破裂行为研究

利用高速摄像仪研究了三维孔喉结构微通道内液滴的破裂行为。采用不同黏度的甘油-水溶液作为分散相,含4%（质量）表面活性剂（Span 20）的矿物油作为连续相。液滴通过孔喉结构后,观察到了三种流型：球形破裂、非球形破裂和不破裂。除极低连续相毛细数的情形外,分散相黏度和两相流量的增加不利于液滴破裂,液滴的破裂位置均接近于喉道出口。研究了液滴的球形破裂,结果表明,球形破裂中子液滴平均尺寸随分散相黏度和连续相流量的增加而降低,且与两相总毛细数呈幂律关系,模型预测值与实验结果吻合良好。     

A model for turbulent binary breakup of dispersed fluid particles

Accurate predictions of particle size distributions, and therefore of the underlying processes of fluid particle breakup and coalescence are of vital importance in process design, but reliable procedures are still lacking. The present paper aims at developing a modular formulation for the turbulent particle breakup process. The model is to be included in a population balance model which is formulated such as to facilitate the direct future implementation into a full multifluid CFD model.The breakup process is described without introducing adjustable parameters. The current model is a further development of an existing model by Luo and Svendsen (AIChE J. 42 (5) (1996) 1225), which has been expanded and refined, and where an inherent weakness regarding the breakup rate for small particles and small daughter particle fragments are removed. A new criterion regarding the kinetic energy density of the colliding turbulent eddy causing breakup has been introduced. This new criterion is a novel concept describing the breakup process. The details are thoroughly discussed together with possible further modifications. The results from the new model are encouraging because the breakup rate is greatly reduced when the dispersed fluid particles are reduced in size. Further, the response to changes in system variables is reasonable and the distribution of daughter sizes vary in a reasonable way for the different collision possibilities.     

对置液柱撞击液膜破裂特征

采用高速摄像仪对两液柱撞击产生液膜的破裂过程进行了实验研究。分析了撞击液膜的破裂过程及表面波产生和传播过程,考察了射流直径、喷嘴间距和射流Weber数（We）对撞击液膜破裂的影响;定量分析了液膜表面波频率的变化及液膜破裂后的粒径分布情况。研究结果表明,液膜表面波传播频率随We的增大而增大,并沿液膜径向方向逐渐减小;随着射流We的增加,液膜边缘的液滴脱落频率增加;当We>1000时,液膜表面产生大量液滴团,且液滴团对液膜破裂具有促进作用;液柱撞击液膜发生破裂后90%以上的量纲1液滴粒径分布在0～1之间。     

Drag-induced breakup mechanism for droplet generation in dripping within flow focusing microfluidics

Based on viscous drag-induced breakup mechanism, a simple model was proposed to predict the dripping drop-let size as a function of controllable parameters in flow focusing micro devices. The size of t...     

Kinetics of oil dispersion in the absence and presence of block copolymers

A phenomenological model proposed describes droplet breakup in the turbulently agitated lean oil-in-water dispersions and provides a correlation between the median droplet size in an agitated vessel of standard geometry and the time of dispersion. It was assumed that the droplet breakup takes place in the dispersion-only region and coalescence is negligible. The model described the data from this study and the literature quite satisfactorily under these conditions. The effect of adding triblock PEO/PPO/PEO copolymeric surfactants on the dispersion kinetics of oil was also investigated. Addition of surfactant reduced the median oil droplet size significantly, and the extent of this reduction was a strong function of surfactant concentration. Application of the model on these data demonstrated that the change in the median droplet size could be divided into two distinct regions. The breakage rate was high initially, most probably due to continuous adsorption of surfactant molecules at the oil/water interface. A lower breakage rate was attained at longer times, as the surfactant molecules were depleted from the solution. The time of transition between the two was affected strongly by the concentration of the surfactant added. Furthermore, the time of addition of the surfactant did not affect the final droplet-size distribution in the system.     

Modeling fluid behavior and droplet interactions during liquid-liquid separation in hydrocyclones

A mechanical separation process in a hydrocyclone is described in which disperse water droplets are separated from a continuous diesel fuel phase. This separation process is influenced by droplet-droplet interaction effects like droplet breakup and coalescence resulting in a change of droplet size distribution. A simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics with population balances. The droplet size distribution is discretized and each discrete droplet size fraction is assumed to be an individual phase within a multiphase-mixture model. The droplet breakup and coalescence rates are defined as mass transfer rates between the discrete phases by the aid of user-defined functions. All model equations are solved with the CFD software package FLUENT™. The investigations show the impact of the cyclone geometry on the coupled population and separation dynamics. Cyclone separators with an optimized geometry show less steep velocity gradients increasing the coalescence rates and improving the separation efficiency. The calculated droplet size distributions at the cyclone overflow and at the underflow show good accordance with experimental data. The basic modeling approach can be extended and adapted to other disperse multiphase flow systems.     

Spray characteristics of a swirl atomiser in trigger sprayers using water–ethanol mixtures

Pressure swirl atomisers are widely used in both industry and daily life. It is critical to understand the spray transient behaviour for better design of these systems. This paper presents an experimental study of conical liquid sheets breakup from a swirl atomiser nozzle in trigger sprayers. Spray and atomisation characteristics were measured and analysed. Water–ethanol mixtures were used to simulate different fluids on the breakup and atomisation quality of the spray development process with a wide range of surface tension while maintaining relatively small changes in fluid viscosity and density. The spray images were taken by a high speed digital camera and post‐processed to analyse the global spray structure, spray cone angle, and breakup length. The droplet size and its distribution were measured using a laser diffraction technique. It was observed that the surface waves grow rapidly on the cone‐shaped liquid sheets and breakup into liquid ligaments and droplets during the initial stage of fluid dispensing. Then the spray transitions into the developed stage. Near the end of the dispensing process, the liquid cone collapses with poor atomisation (large droplets) due to momentum loss. The comparison between different fluids showed that the spray cone angle and liquid breakup length decreased with the increase of ethanol percentage ratio. The percentiles parameters, Sauter mean diameter (SMD) and particle size distribution were measured and compared for different locations. High surface tension fluids produce larger droplets than lower surface tension fluids, which have the same trend as the percentiles parameters and SMD. Results also show that droplet size and its distribution depend on the location of the measurement. Generally speaking, smaller droplet size is found for a location away from the nozzle axis in the vertical direction. In the horizontal direction, larger droplet sizes are found for a location closer to the nozzle exit. © 2013 Canadian Society for Chemical Engineering     

Y型气流式喷嘴的雾化滴径和滴径分布

索特平均滴径(SMD)和滴径分布是描述喷嘴雾化性能的主要指标.根据Y型喷嘴雾化过程的特征,提出了Y型喷嘴的液滴随机分裂模型,得到了SMD的表达式.考察了Y型喷嘴对氯化聚氯乙烯(CPVC)氯化液的雾化过程,利用Mastersizer2000型测粒仪测定了雾化滴径分布.关联了SMD的经验方程,得到了初次雾化平均滴径.采用液滴随机分裂模型模拟计算了雾化滴径分布,计算结果与实验结果吻合,说明模型和平均滴径方程可以用来预测Y型喷嘴的雾化性能.     

Theory of competition between breakup and coalescence of droplets in flowing polymer blends

The Smoluchowski equation for the breakup and coalescence of dispersed droplets has been solved for flowing polymer blends. A scaling form for the distribution of droplet sized derived and published for a system of clusters with fragmentation and coagualation was used in our dervation. Equations are developed here for the average droplet size and for the characteristic time of transition to steady state flow of blends with a high content of the dispersed phase. Expressions reasonably describing the average size of droplets for all concentrations were obtained by a theory modification. Measured dependences of droplet size on the blend composition can be matched only if simultaneous collisions of three and more droplets are considered. The results of the theory indicate that the mechanism of droplet breakup (formation of pieces with the same or different volumes) has only a small effect on their average size in concentrated systems. The dependence of droplet size on the shear rate in flow is determined by properties of the blend components, and is generally nonmonotonic.     

喷淋塔液滴粒径分布及比表面积的实验研究

以水和空气为实验介质,通过拍照法获得喷淋塔内液滴粒径分布,考察了不同喷淋量及空塔气速对塔内不同高度处液滴Sauter平均直径(SMD)的影响,并对液滴粒径分布进行了理论分析.结果表明,喷淋塔顶部液滴分布密集,底部稀疏,液滴群在下落过程中,平均粒径减小且趋于均匀化;塔顶处液滴SMD随喷淋量的增加而增大,处在塔中下部的液滴SMD则随喷淋量增大而减小,提高空塔气速,可减小平均粒径;理论分析认为,液滴粒径减小主要是由于发生了碰撞破碎的缘故,而塔内液滴大小不一是碰撞的主要原因;通过量纲1化拟合得到喷淋塔内液滴SMD经验关联式,其计算结果与实验值吻合较好;考虑液滴破碎的喷淋塔比表面积比不考虑破碎的比表面积大70%左右.     

Computational fluid dynamics model of viscous droplet breakup

A computational fluid dynamics (CFD) model is being developed to help guide the design of equipment to enhance viscous droplet breakup. The first generation model was able to show qualitative agreement with experimental results. This 2D model follows a single droplet (with a specified initial diameter) flowing past a series of cylinders using a volume of fluid (VOF) method to track the interface. The model is able to predict droplet breakup and provide insights into the physics of the breakup process. Three different breakup mechanisms are hypothesized that help explain experimental observations, including a minimum in breakup efficacy (ability to create smaller droplets) versus velocity data. Important parameters include the system rheology, velocity, cylinder size versus droplet size, and cylinder layout.     

具有冲击平板的雾化喷雾流中汽液流动的模拟

A comprehensive three-dimensional model of droplet-gas flow was presented to study the evolution of spray in the effervescent atomization spray with an impinging plate.For gas phase,the N-S equation with the k-ε turbulence model was solved,considering two-way coupling interaction between droplets and gas phase.Dispersed droplet phase is modeled as Lagrangian entities,accounting for the physics of droplet generation from primary and secondary breakup,droplet collision and coalescence,droplet momentum and heat transfer.The mean size and statistical distribution of atomized droplets at various nozzle-to-plate distances were calculated.Some simulation results were compared well with experimental data.The results show that the existence of the impinging plate has a pronounced influence on the droplet mean size,size distribution and the droplet spatial distribution.The air-to-liquid ratio has obvious effects on the droplet size and distribution.