The effect of coalescence on drop size distribution in an agitated liquid-liquid dispersion

A procedure involving high speed cine photography and novel optical probes has been used to study droplet interaction phenomena in liquid-liquid dispersions. Coalescence and breakup events were observed and the rate of coalescence was measured at various positions in a stirred tank for dispersions of methylisobutylketone in water. For the conditions studied, drop breakup occurred near the impeller and droplet coalescence predominated at other locations, as expected. However, the extent of this behavior was unexpected. Beyond distances from the impeller region of order of only $\text{1}\text{6}$ the impeller diameter, breakup was virtually nonexistent. Outside the impeller region, extensive coalescence measurements showed (1) collisions between droplets are extremely inefficient for this chemically equilibrated system—at most 10% of collisions result in a coalescence, (2) only binary coalescence occurs even at the highest dispersed phase concentration investigated, (3) coalescence rate shows little preference on drop size, and (4) the coalescence rate is directly proportional to turbulence level; that is, the highest coalescence rates occur closest to the impeller. On the basis of these measurements, drop balance methods and a circulation path model were used to relate the drop size distribution at various locations in the region where coalescence predominates. In this case good agreement was obtained between measured and predicted drop size distributions.     

Predicting the diameters of droplets produced in turbulent liquid–liquid dispersion

The droplet size distribution in liquid–liquid dispersions is a complex convolution of impeller speed, impeller type, fluid properties, and flow conditions. In this work, we present three a priori modeling approaches for predicting the droplet diameter distributions as a function of system operating conditions. In the first approach, called the two-fluid approach, we use high-resolution solutions to the Navier–Stokes equations to directly model the flow of each phase and the corresponding droplet breakup/coalescence events. In the second approach, based on an Eulerian–Lagrangian model, we describe the dispersed fluid as individual spheres undergoing ongoing breakup and coalescence events per user-defined interaction kernels. In the third approach, called the Eulerian–Parcel model, we model a sub-set of the droplets in the Eulerian–Lagrangian model to estimate the overall behavior of the entire droplet population. We discuss output from each model within the context of predictions from first principles turbulence theory and measured data.     

LIQUID-LIQUID MIXING IN STIRRED VESSELS: A REVIEW

Liquid-liquid mixing is a key process in industries that is commonly accomplished in mechanical agitation systems. Liquid-liquid mixing performance in a stirred tank can be evaluated by various parameters, namely minimum agitation speed, mixing time, circulation time, power consumption, drop size distribution, breakup and coalescence, interfacial area, and phase inversion. The importance of these liquid-liquid mixing parameters, the measurement method, and the results are discussed briefly. Input parameters such as impeller type, power number, flow pattern, number of impellers, and dispersed phase volume fraction, in addition to physical properties of phases such as viscosity and density, are reviewed. Scale-up aspects are also included.     

Experimental investigation of phase inversion in a stirred vessel using LIF

A non-intrusive dye tracing technique, laser-induced fluorescence (LIF), has been applied to investigate phase inversion in concentrated immiscible organic-aqueous liquid dispersions. The phase inversion process from oil-in-water (o/w) dispersion to water-in-oil (w/o) dispersion has been recorded by a high-speed video camera. Apart from phase inversion, secondary dispersion, drop coalescence and breakup mechanisms, have also been observed in great detail. The experimental results demonstrate that phase inversion is a gradual phenomenon: the process occurs only over 1-2 s, may not occur globally and depends on the local phase distribution. During phase inversion, two opposing pairs of processes, namely drop coalescence and break-up, and the inclusion and escape of small drops in larger drops, play a key role in phase inversion. The structure of the dispersion is extremely complex and a great number of secondary dispersions and multi-dispersions appear during phase inversion, which include water-oil-water secondary dispersions.     

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.     

Multicompartment hydrodynamic model for slurry bubble columns

A core-annulus multicompartment two-dimensional two-bubble class model accounting for slurry recirculation and coupled with catalyst transport was developed as a part and parcel of the analysis of the behavior of slurry bubble column reactors at high gas throughputs corresponding to the churn turbulent flow regime. The model analyzed the contributions of bubble-induced turbulence closures, bubble coalescence and breakup phenomena, and catalyst axial distribution as the resultant of sedimentation, advection via liquid-solid slip, per-compartment axial dispersion and core-annulus lateral exchange of catalyst by bubble-induced turbulence. The model was also used to analyze the effects of catalyst loading, gas density and superficial velocity, and column diameter and vessel aspect ratio on the hydrodynamics of slurry bubble column reactors, namely, the per-compartment phase holdups and interstitial velocities, pressure gradient, bubble coalescence and break-up rates, and loci of velocity inversion for the gas and slurry profiles.     

基于介尺度PBM模型的生物反应器放大模拟及实验研究

对于通气搅拌式工业生物反应器的放大设计而言,精确预测气泡尺寸和体积传质系数非常重要,因此需要建立合适的气泡聚并和破碎模型,以保证反应器的高效操作。以5 L通气搅拌式生物反应器为对象,以气泡尺寸和体积传质系数的实验数据为基准,模拟并考察了两种聚并模型和四种破碎模型对生物反应器内流体流动行为以及传质能力的影响。结果表明,基于介尺度理论的修正聚并模型与考虑黏流剪切的破碎模型组合,所得模拟结果与实验数据吻合最好,这为大型生物反应器的桨型优化提供了模型基础。因为工业化生物发酵通常是在大型生物反应器中进行,搅拌桨型对生物反应器效能至关重要,故本研究在选定最优气泡聚并破碎模型的基础上,通过叶轮末端剪切力相等的放大原则将5 L通气搅拌式工业生物反应器放大到400 m³,同时考察了六斜叶圆盘搅拌桨、非对称式抛物线搅拌桨、布鲁马金式搅拌桨以及六直叶圆盘搅拌桨等桨型组合对气泡破碎能力和气体分散效果的影响,并通过综合对比气含率、体积传质系数等参数,得到400 m³通气搅拌式生物反应器的最优桨型组合。     

Parameter estimation in a multidimensional granulation model

A new multidimensional model for wet granulation is presented, which includes particle coalescence, compaction, reaction, penetration, and breakage. In the model, particles are assumed to be spherical and consist of two kinds of solid, two kinds of liquid, and pore volume. The model is tested against experimental results (Simmons, Turton and Mort. Proceedings of Fifth World Congress on Particle Technology, paper 9d, 2006) from the granulation of sugar particles with different PEG based binders in a bench scale mixer, being carried out for different impeller speeds, binder compositions and process durations. The unknown rate constants for coalescence, compaction, reaction, and breakage were fitted to the experiments and the sensitivities of the mass of agglomerates were calculated with respect to these parameters. This is done by employing experimental design and a response surface technique. The simulations with the established set of parameters show that the model predicts the trends, not only in time, but also for crucial process conditions such as impeller speed and the binder composition. As such it is found that more viscous binder promotes the formation of porous particle ensembles. Furthermore, the statistics of the different events such as collisions, coalescence and breakage reveal for instance that successful coalescence events outnumber the breakage events by a factor of up to three for low impeller speeds.     

Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures

Two-dimensional axisymmetric Eulerian/Eulerian simulations of two-phase (gas/liquid) transient flow were performed using a multiphase flow algorithm based on the finite-volume method. These numerical simulations cover laboratory scale bubble columns of different diameters, operated over a range of superficial gas velocities ranging from the bubbly to the churn turbulent regime. The bubble population balance equation (BPBE) is implemented in the two-fluid model that accounts for the drag force and employs the modified k-ε turbulence model in the liquid phase. Several available bubble breakup and coalescence closures are tested. Quantitative agreements between the experimental data and simulations are obtained for the time-averaged axial liquid velocity profiles, as well as for the kinetic energy profiles, only when model predicted breakup rate is increased by a factor of ten to match the coalescence rate. The calculated time-averaged gas holdup profiles deviate in shape from the measured ones and suggest that full three-dimensional simulation is needed. Implementation of BPBE leads to better agreement with data, especially in the churn-turbulent flow regime, compared to the simulation based on an estimated constant mean bubble diameter. Differences in the predicted interfacial area density, with and without BPBE implementation, are significant. The choice of bubble breakup and coalescence closure does not have a significant impact on the simulated results as long as the magnitude of breakup is increased tenfold.     

Bivariate moment methods for simultaneous coagulation,coalescence and breakup

Aerosol reactors pass through regimes where subsets of the population balance terms are dominant. Initially, mixing, reaction, nucleation and accretional growth dominate. This is generally followed by a regime in which coagulation and coalescence control evolution of the particle population into sintered aggregates. Conventionally, the boundary between regimes where coalescence is or is not important is assumed to be sharp, and the collision–coalescence regime is followed by a regime dominated by coagulation and breakup which controls the growth of loosely bonded agglomerates that grow large enough to be captured in conventional gas–solids separation equipment. When this boundary is not sharp, there can be a regime in which coagulation, coalescence and breakup all occur simultaneously. This paper describes the daughter distributions required to model breakup in a bivariate population, the moment models describing simultaneous collision, coalescence and breakage, and exhibits reconstructed steady-state distributions formed when the rate kernels are size independent. A criterion is developed to guide the choice of when a bivariate formulation is necessary and when it is not.     

Liquid phase mixing model for stirred gas-liquid contactor

Impulse response experiments were carried out on the liquid phase of a continuous flow air/water system contained in a 22 cm diameter vessel stirred with a 7.62 cm diameter six-bladed disc turbine impeller. Experimental results were obtained for three impeller speeds, ten air rates and four inlet and outlet combinations of top and bottom.The application of a numerical procedure for Laplace transform inversion and an optimisation routine for curve fitting, allowed a consideration of models of considerable complexity. A digital computer was used to determine the appropriate values of the parameters of the most suitable model which satisfied the experimental responses.The effects of the impeller speed and air flow rate on the values of the various parameters of the model were examined. Good agreement was found between the values of the parameters and similar published data for the unaerated system. Also it was shown that the presence of the gas does not greatly affect the liquid phase mixing characteristics.     

Microencapsulation of hydrophilic solid powder as fire retardant agent with epoxy resin by droplet coalescence method

To give water resistance to Bistetrazol–diammonium (BHT–2NH₃) as a fire retardant agent, microencapsulation with epoxy resin was tried by the droplet coalescence method. In this method, two kinds of epoxy resin droplets were prepared; one is the larger epoxy resin droplet containing BHT–2NH₃ as a core material and the other the smaller droplets containing Imidazole as a gelation agent. The larger epoxy resin droplets were made to coalesce with the many smaller droplets during the microencapsulation process to prepare microcapsules. In the experiment, the agitation velocities for preparation of the droplets and for coalescence were mainly changed. With increase in the impeller speed, the content of core material increased, became maximum because of increase in the coalescence frequency, and then decreased because of breakup of droplets. With increase in the impeller speed, the leakage ratio of core material decreased, became minimum, and then increased. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008.     

Steady state multiplicity depending on coalescence in liquid—liquid continuous stirred reactors with reaction in the dispersed phase

The influence of drop coalescence and breakup on the existence of multiple steady states is studied for a two-phase stirred isothermal reactor where the chemical reaction in the d?ispersed phase obeys the rate expression ? r = kC/(1 + KC)². The random coalescence model developed by Curl was simulated using a modified Spielman and Levenspiel Monte Carlo technique.For certain range of the coalescence rate, Damköhler number, and dimensionless feed concentration, multiple steady states have been investigated.A special case has also been considered wherein the existence of multiple steady states for finite values of the coalescence rate is contrasted to the unique steady state solution for an infinite coalescence rate.     

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.     

About bubble breakup models to predict bubble size distributions in homogeneous flows

We present results of a study of the equilibrium between coalescence and breakup of bubbles in homogeneous media with isotropic turbulence. The Boltzmann equation for the particle distribution function (pdf) was evaluated in steady state, using a multigroup approach. Binary bubble breakup was assumed. We used uniform function, delta function, and the model proposed by Luo and Svendsen (1996) for the bubble size distributions resulting from a breakup. The bubble breakup rate was calculated with Luo and Svendsen (1996) and Prince and Blanch (1990) models. Significant differences in bubble breakup rate, and therefore in bubble size distribution, are predicted by both models. The models were compared to the bubble size distributions measured by Boyd and Varley (1998) in air-water flow. The transient response of the bubble size distribution and interfacial area density was also analyzed. This work is of significance in the prediction of reaction rates when they are dependent on bubble size distribution.     

Dynamics of liquid-liquid mixing: A 2-zone model

The development of multiphase liquid-liquid morphologies during mixing at small Reynolds numbers has been modeled. The mixing process is divided into (i) stretching of dispersed drops. (ii) breakup of the liquid threads formed, and (iii) coalescence of the final droplets upon collision. Rules and criteria of the distinct processes are presented and combined to a general 2-zone mixing model simplifying the flow field into a sequence of alternating “strong and weak zones.” In a “strong zone,” dispersed drops and threads are stretched unless their radius is too small; meanwhile, the stretching threads might break up into droplets. In the subsequent “weak zone,” the remaining threads may disintegrate while any drops present may coalesce. After passing a number of zones, stretching, breakup, and coalescence lead to a dynamic equilibrium that could be considered as the “final” morphology. Using the 2-zone mixing model, the influence of material parameters and processing conditions on the morphology has been studied. Interestingly, increasing either viscosity (dispersed or continuous phase) yields a finer morphology due to the delay of thread breakup, allowing for further stretching and suppression of coalescence.     

ABOUT BUBBLE BREAKUP MODELS TO PREDICT BUBBLE SIZE DISTRIBUTIONS IN HOMOGENEOUS FLOWS

We present results of a study of the equilibrium between coalescence and breakup of bubbles in homogeneous media with isotropic turbulence. The Boltzmann equation for the particle distribution function (pdf) was evaluated in steady state, using a multigroup approach. Binary bubble breakup was assumed. We used uniform function, delta function, and the model proposed by Luo and Svendsen (1996) for the bubble size distributions resulting from a breakup. The bubble breakup rate was calculated with Luo and Svendsen (1996) and Prince and Blanch (1990) models. Significant differences in bubble breakup rate, and therefore in bubble size distribution, are predicted by both models. The models were compared to the bubble size distributions measured by Boyd and Varley (1998) in air-water flow. The transient response of the bubble size distribution and interfacial area density was also analyzed. This work is of significance in the prediction of reaction rates when they are dependent on bubble size distribution.     

Effect of the dispersed phase fraction on particle size in blends with high viscosity ratio

It has been reported that for polymer blends with high viscosity ratio (>1), the size of the dispersed particles decreases with increasing volume fraction of the dispersed phase. In order to explain this effect, an equation was derived for the affine deformation of an imaginary plane of the dispersed phase in stratified two‐phase steady, simple, shear flow. The model predicts that for viscosity ratio >1, the deformation rate increases with volume fraction of the dispersed phase, and the shear stress also increases, leading to an increase of the breakup time. Therefore, the total deformation of the dispersed phase, before breakup, increases with increase of volume fraction, resulting in a decrease of the size of the dispersed phase particles. Accordingly, one can expect that in industrial mixers, the particle size of the blends should decrease as the volume fraction increases, if coalescence is suppressed. Experiments were carried out in a Haake batch mixer, using polyethylene/polyamide‐6 blends compatibilized by adding maleic anhydride grafted polyethylene. Particle size decreased up to 20 wt% polyamide‐6, at 100, 150, and 200 RPM, and increased between 20 and 30 wt%. The decrease of the particle size is mainly due to increased deformation of the dispersed phase. The increase of the particle size above 20 wt% is due to coalescence at high fractions.     

流场下不相容聚合物共混物分散相形态的研究进展

介绍了流场下不相容聚合物共混物分散相形态及演变研究进展,并指出这是获得性能优异共混材料的关键。在流场下,不相容共混物分散相尺寸由破碎和凝聚等动力学过程决定。鉴于模型的理想化,早期研究主要针对牛顿流体,且分散相的变形、破碎和凝聚等理论均发源于此。对于聚合物共混物,其在本质上与牛顿流体有很多相似之处,然而,独特黏弹性质却是影响其相形态的重要因素。最后,对一些预测分散相尺寸的理论模型进行了总结,并重点讨论了分散相浓度、聚合物弹性、增容和填料等因素对流场下分散相形态的影响。     

A comparative study of dispersing a polyamide 6 into a polypropylene melt in a Buss Kneader,continuous mixer,and modular intermeshing corotating and counter‐rotating twin screw extruders

We have made a study of the development of phase morphology of an immiscible blend(75/25)(polypropylene–polyamide‐6) for different types of continuous mixers including (i) Buss Kneader, (ii and iii) modular intermeshing corotating and counter‐rotating twin screw extruders, and (iv) NEX‐T Kobelco Continuous Mixer. Comparisons are made using different screw configurations for each machine. Generally, in comparison of the different machines, the intermeshing counter‐rotating twin screw extruder produced the finest dispersed morphology. Using a droplet breakup kinetic model, we interpreted the blend dispersed phase droplet breakdown rate and coalescence rate. In comparison with our earlier study of the continuous mixing of agglomerates of CaCO₃ particles the polymer droplet breakup rate was smaller than that of the particle agglomerates and the coalescence rates of droplets were many times greater than the particle reagglomerates rates. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers