Modelling of phase redistribution of horizontal annular flow divided in T-junctions

A phase redistribution model for annular flow divided in T-junctions is developed. The model consists of two sub-models accounting for phase distribution in the inlet to the junction and phase redistribution in the junction, respectively. In modelling phase redistribution in the junction, the dividing streamlines for each phase were determined separately assuming that the phenomena is mainly governed by the fluid inertia and pressure distribution in the junction. The overall model is capable of predicting phase redistribution in T-junctions having horizontal inlet and any branch orientation. The predictions of this model and those of other available models are compared with experimental data. The predictions of the present model were found to be in better agreement with the experimental data than other available models and correlations.     

Gas-liquid-liquid slug flow and mass transfer in hydrophilic and hydrophobic microreactors

Gas-liquid-liquid three-phase slug flow was generated in both hydrophilic and hydrophobic microreactors with double T-junctions. The bubble-droplet relative movement and the local mass transfer within the continuous slug and the dispersed droplet were investigated. It was found that bubbles moved faster than droplets under low capillary number (Ca), while droplets moved faster upon the increase of Ca due to the increased inertia. For the first time, we observed that the increased viscosity of droplets fastened the droplet movement. The mass transfer in the continuous slug was dominated by convection, leading to nearly constant global mass transfer coefficient (k_La); while that in the dispersed droplet was dominated by diffusion, resulting in k_L decreasing along the channel. Such features are analogical to the corresponding gas-liquid or liquid-liquid two-phase slug flow, but the formation of bubble-droplet clusters caused by relative movement lowered the absolute mass transfer coefficient. These results provide insights for the precise manipulation of gas-liquid-liquid slug flow in microreactors towards process optimization.     

Signal modelling and algorithms for parameter estimation in pneumatic conveying

Capacitive measurement principles offer a non-invasive approach to determine particle velocity as well as particle concentration in pneumatic conveying. In order to assess the quality of a reconstruction method, it is mandatory to know the prevailing velocity and concentration profiles. For particulate bulk solids transportation, accurate reference systems are either not available or very expensive. Based on measurement data, a signal model of the particle flow is developed for dilute phase and dense phase conveying. These models are used to demonstrate the applicability of proposed algorithms for parameter determination — a cross-correlation technique for dilute phase and a two-step approach using the Fourier transform for dense phase.     

Dynamic formation and scaling law of hollow droplet with gas/oil/water system in dual‐coaxial microfluidic devices

Based on the one‐step microfluidic method of producing hollow droplet with thin film, this article studies the effect of water and oil flow rate, gas pressure, and viscosity of aqueous phase on the dynamic formation and size of hollow droplet by analyzing large amounts of data acquired automatically. The results show that the filling stage of hollow droplet is similar to that of microbubble formation, while the necking stage is similar to that of droplet formation process. Furthermore, based on the data and mathematical model describing droplet formation mechanism, a filling stage model including Capillary number of continuous phase is developed. Considering the dynamic interface breakup and displacement of droplet in necking stage, a necking stage model is developed. The results show that the model results considering filling and necking stage fit well with the experimental data, and the relative error is less than 5%. Finally, the same model with parameters is used to predict the size of hollow droplet with other systems and devices, and the model is proved to be relative precise in our experimental conditions. The results presented in this work provide a more in‐depth understanding of the dynamic formation and scaling law of hollow droplet with G/L/L systems in microfluidic devices. © 2017 American Institute of Chemical Engineers AIChE J, 64: 730–739, 2018     

Mathematical modeling of heat and mass transfer in hot gas spray systems

A mathematical model is developed to study simultaneous heat and mass transfer in hot gas spray systems. The model is obtained by writing mass, energy, and momentum balances for both continuous and discontinuous phases. Governing equations along with suitable correlations for heat and mass transfer coefficients have been solved numerically. In order to develop a realistic model for such complicated systems, a droplet size distribution was implemented in the model instead of using an average size. A steady state spray-cooling problem is analyzed to illustrate the applicability of the model. To validate the mathematical model for this case, necessary data was collected and measured in commercial cement plants. A good agreement between plant data and the model was noticed in general, and results obtained from the model indicate that size distribution of water droplets and physical dimensions of the spray-cooling system are important parameters. This model is very useful in determining the so-called "critical operation condition" at which sludge formation at the bottom of spray-cooling systems will happen. The predicted parameters in spray-cooling systems both for droplet phase and gas phase aptly illustrate the ability of the model to treat the complex phenomena associated with two-phase flows.     

MATHEMATICAL MODELING OF HEAT AND MASS TRANSFER IN HOT GAS SPRAY SYSTEMS

A mathematical model is developed to study simultaneous heat and mass transfer in hot gas spray systems. The model is obtained by writing mass, energy, and momentum balances for both continuous and discontinuous phases. Governing equations along with suitable correlations for heat and mass transfer coefficients have been solved numerically. In order to develop a realistic model for such complicated systems, a droplet size distribution was implemented in the model instead of using an average size. A steady state spray-cooling problem is analyzed to illustrate the applicability of the model. To validate the mathematical model for this case, necessary data was collected and measured in commercial cement plants. A good agreement between plant data and the model was noticed in general, and results obtained from the model indicate that size distribution of water droplets and physical dimensions of the spray-cooling system are important parameters. This model is very useful in determining the so-called "critical operation condition" at which sludge formation at the bottom of spray-cooling systems will happen. The predicted parameters in spray-cooling systems both for droplet phase and gas phase aptly illustrate the ability of the model to treat the complex phenomena associated with two-phase flows.     

Structure formation during polymer blend flows

The structure formation processes that occur during the flow of dilute blends of high density polyethylene (HDPE) or polypropylene (PP) In a linear low density polyethylene (LLDPE) carrier phase have been studied. Due to low surface tensions, high deformations of the dispersed minor phase can be induced under slow flow conditions leading to the formation of slender filaments. Measurements on a slit die, having a large, converging flow entrance region, demonstrate that the mechanism for filament formation is droplet bursting, yielding growing tails during shear flow, or, unsteady drop elongation during extensional flow. Tail growth can be modeled as the flow of a slightly tapering cylinder in a fluid of different viscosity, For dispersed to carrier phase viscosity ratios greater than unity, extensional flow occurs in the tail phase, which can induce oriented crystallization. For ratios less than unity, the flow is compressive, which. Inhibits crystallization. Drop deformation and crystallization in the converging flow entrance region is greatly enhanced by the extensional flow, and droplet growth can be described by a model assuming a time-dependent, planar, extensional flow field. Data for birefringence and melting points of as-crystallized fibers are also presented and discussed.     

Nanoparticle evolution in flame spray pyrolysis—Process design via experimental and computational analysis

In flame spray pyrolysis (FSP), the evolution of metal oxide nanoparticles relies on quite a number of droplet (liquid) and vapor phase related physical mechanism as for instance precursor evaporation, oxidation, nucleation via gas-to-particle conversion mechanism, and subsequent particle (solid) growth mechanisms based on coagulation, sintering/coalescence, and agglomeration. The liquid precursor and dispersion oxygen feed rates are relevant control parameters of the FSP process for tailoring the nanoparticle size (diameter) and structure as well as the atomizer nozzle configuration. Sophisticated nonintrusive, laser-based in situ and ex situ diagnostics with multiscale spatial resolution (micrometer to meter range) are applied for analyzing droplet formation and size, gas velocity, temperature, species concentration, as well as primary and agglomerate diameters along the flow direction. Computational fluid dynamics (CFD) are coupled with population balance modeling (PBM) to elucidate the nanoparticle dynamics within the reactive spray. It is found that the CFD-PBM approach allows estimations of primary and agglomerate nanoparticle diameters within 80 and 75% accuracy compared to experimental data, suggesting that the methods presented could pave the way for designing next-generations of flame reactors.     

The liquid–liquid flow dynamics and droplet formation in a modified step T-junction microchannel

The droplet generation mechanism in the asymmetrically enhanced step T-junction remains unknown, especially for the transition stage from dripping to jetting regimes. In this work, the droplet generation mechanism was systematically investigated in a modified step T-junction by modulating a large flowrate range and altering different interfacial tensions. We found that under different fluid regimes, both the capillary number and flow rate ratio of continuous and dispersed phase showcase completely different impacts over droplet generation. In dripping regime, the interfacial tension, which was controlled by changing the surfactant concentration, dominated the formation mechanism when the surfactant concentration was found below micelle concentration. In jetting regime, our experimental results showed that the influence of the surfactant concentration on the size of generated droplets was rather negligible while the flow rate ratio of continuous and dispersed phase indeed determined such a parameter. In the dripping-jetting transition stage, an increase of droplet size was observed despite the increase of continuous phase flow. After reaching a peak, the droplet dimension started to decrease with the increase of continuous phase flow as expected. To the best for our knowledge, it is the first study to report generation mechanism in modified step T-junction from dripping to jetting regimes.     

The influence of surfactant properties on critical supersaturations of cloud condensation nuclei

Due to the complex nature of atmospheric surfactants, their effect on cloud droplet formation is still quite unknown. Most of the earlier studies of surface tension effects on cloud formation have been done either with model compounds or by neglecting the correct thermodynamic approach thereby giving no general idea of how the partitioning of surfactant between the droplet interior and the surface layer affects droplet growth. The neglect of partitioning leads to overestimated decrease in surface tension as well as to enhanced solute effect. Here, we study the extent to which surfactant partitioning affects critical supersaturation with different types of surfactants. The idea is to systematically vary the surface tension parameters that ultimately control how the surfactant is distributed between the bulk and the surface of the droplet, and to compare the critical supersaturations calculated with and without account of the partitioning. This study shows the importance of correct thermodynamical approach to partitioning with an example of three different classes of compounds found in atmospheric aerosols.     

湿工况下泡沫金属内换热和压降的数值模拟和实验验证

泡沫金属应用到换热器空气侧有望提高析湿工况下的换热性能。为了了解湿空气在泡沫金属内的热质传递和压降特性,建立了泡沫金属内液滴形成、生长和运动特性的数值模型。基于液滴成核数目和成核临界半径得出液滴形成过程的传质率模型;通过建立液滴与湿空气相界面附近湿空气中水蒸气的组分守恒方程,得出液滴生长过程的传质率模型;通过对不同孔棱柱表面液滴的受力分析,建立在重力和风力的共同作用下的液滴接触角模型。将液滴形成及生长的传质率模型和接触角模型分别作为质量源项和表面张力源项,加入连续性方程、动量方程和能量方程组中,实现对泡沫金属内液滴生长、形成和运动过程模拟。模型的实验验证结果表明,换热量预测值与实验结果的最大偏差为11.9%,压降预测值与实验结果的最大偏差为17.7%。     

三维微管液滴形成及破碎的数值模拟

基于多相流模型的VOF方法求解三维坐标下微管末端液滴形成过程,参考丙三醇溶液,分别探讨不同表面张力、密度、射流速度下液滴形成过程,和液滴断裂长度、形成时间、主液滴直径受其影响情况,并分析断裂阶段轴线上压力和轴向速度分布。     

Effect of drainage channel dimensions on the performance of wave-plate mist eliminators

We investigated the effects of drainage channel dimensions on droplet removal efficiency and pressure drop of the gas droplet flow in a wave-plate mist eliminator. Droplet dispersion in turbulent gas flows is numerically simulated using eddy interaction model (EIM) and Eulerian-Lagrangian method. Reynolds stress transport model (RSTM) with enhanced wall treatment and shear stress transport (SST) k-ω model are used for simulating the turbulent airflow. Comparison between the numerical simulations and available experimental data shows that eddy lifetime constant (C _L ) can affect the results significantly, and by selecting suitable values of the eddy lifetime constant, both turbulence models give reasonable predictions of droplet removal efficiency. Simulations of gas droplet flow in the eliminators with various drainage channel dimensions show that the drainage channel length (L _DC ) has a greater effect on droplet removal efficiency than the drainage channel width (W _DC ).     

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.     

Bubble Formation at Variously Inclined Nozzles

Bubble formation at variously inclined submerged nozzles, fed with a continuous gas flow rate, is investigated. The average liquid velocity induced by bubble motion is determined, leading to a simple correlation for estimation of the liquid velocities induced by the repeated passage of bubbles. An effective model for the prediction of bubble sizes at their detachment from vertical nozzle orifices is presented which encompasses a bound expansion stage, followed by an accelerated expansion phase, and ends by an original bubble detachment criterion. The existence of a liquid‐phase effective entrainment velocity, generated by the continuous passage of the bubble stream, is quantified and included in the model. Model predictions are found to correlate well with experimental and literature data.     

Effects of fluid–fluid interfacial elasticity on droplet formation in microfluidic devices

Biomolecules adsorb at fluid–fluid interfaces and can form a cohesive interfacial network imparting distinctive local interfacial mechanics. This modification of interfacial behavior is empirically known to significantly affect the stability and flow behavior of foams and emulsions. Droplet formation in the presence of interfacial networks is investigated in a flow‐focusing microfluidic device using designed peptide surfactants, which allow decoupled control of interfacial rheology and interfacial tension. The influence of interfacial elasticity on droplet breakup, satellite droplet formation and droplet size are reported. The presence of high interfacial elasticity strongly affects the mechanism of droplet breakup by delaying neck thinning and altering interfacial shape at the point of droplet detachment, resulting in the suppression of satellite droplet formation and a decrease in droplet size. We report a correlation between dimensionless droplet size and a new dimensionless grouping which combines flow‐rate ratio with the ratio of interfacial tension and interfacial elasticity. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Stochastic simulation of agglomerate formation in fluidized bed spray drying: A micro-scale approach

A stochastic model that describes agglomerate growth during fluidized bed spray agglomeration is presented and numerically solved by constant volume Monte Carlo method. The methodology overcomes the difficulties of solving multivariate population balance equations and includes continuous binder addition and drying. Agglomerate formation is treated as a complex combination of consecutive and parallel micro-mechanisms. Due to the discrete nature of the approach, the individual role of the micro-mechanisms on the agglomeration behavior can be analyzed.The results suggest that the droplet capture mechanism governs the agglomeration speed while the maximum agglomerate diameter is ruled by the equilibrium reached between coalescence, rebound and breakage. The mechanism of deposited binder drying is found to play a negligible role on agglomerate formation because of an extremely rapid droplet consumption. The main process variables affecting each micro-mechanism have been identified showing that the liquid spraying rate affects directly the droplet capture mechanism whereas binder properties influence mainly the agglomeration and rebound interactions.The model presented in this study is able to predict qualitatively the experimentally observed response of the system as well as the general shape of the agglomerate size distribution under the variation of several process parameters, demonstrating the potential of the discrete micro-level approach.     

Low-Field High-Resolution PFG-NMR to Predict the Size Distribution of Inner Droplets in Double Emulsions

In double emulsions, the inner and outer droplet size distribution (DSD) determines the quality of the double emulsion and is therefore essential to be measured. Low-field high-resolution pulsed-field gradient nuclear magnetic resonance is used to measure the inner DSD in water-in-oil-in-water double emulsions. The Gaussian phase distribution approach is employed with a mixture of two normal distributions to predict bimodal inner droplets. This approach allows the prediction of the swelling of inner droplet during storage of double emulsions, and thus to validate a phenomenological population balance model estimating inner droplet swelling. Only a fraction of the inner droplets are found to swell during storage, due to differences in the Laplace pressure, thus leading to the formation of a bimodal size distribution of the inner droplets. Practical Applications: This methodology is useful to predict the evolution of double emulsions during storage, in a wide range of applications, such as food and pharmaceutical products.     

The experimental observation and modelling of microdroplet formation within a plastic microcapillary array

This paper reports an experimental study of the formation of a two-phase liquid mixture in a circular capillary tube of 0.74 mm diameter. Organic liquid, the continuous phase, flowed through the capillary. Aqueous liquid, the dispersed phase, was injected through a hypodermic entering the side of the capillary and a stream of aqueous droplets was formed in the flowing organic liquid. The observed droplet diameters depended strongly on the ratio of the flow-rates between the dispersed and continuous phases: droplet diameters ranged between 480 and 64 μm. A simple model gave good predictions, matching the data and showing how the droplet diameter is dependant on the flow rates of the two phases. The flow geometry was similar to the T-junction configuration used for emulsion formation in microfluidic devices and was fabricated from an extruded plastic capillary array termed a microcapillary film (MCF).     

Y聚焦型微通道内磁流体液滴的生成与调控

利用高速摄像仪研究了截面为400 μm×400 μm Y聚焦型微通道内磁流体液滴在矿物油中的生成过程。以水基磁流体EMG 807为分散相,含4%表面活性剂Span-20的矿物油为连续相。实验观察到了3种流型：弹状流、滴状流和喷射流。分别考察了两相流量、连续相毛细数及磁感应强度对液滴尺寸及生成过程的影响。结果表明：可通过改变两相流量及磁场调控液滴尺寸。当分散相流量不变时,液滴尺寸随着两相流量比的增加而减小。液滴尺寸随着连续相毛细数及磁感应强度的增加而减小,随着分散相流量的增加而增加。以两相流量比、连续相毛细数和磁Bond数为参数提出了一个液滴尺寸的关联式,预测值与实验值吻合良好。