Prediction of cellular structure in free expansion polymer foam processing

A model is presented for free expansion polymer foam processing that includes simultaneous nucleation and bubble growth. The nucleation model includes dissolved gas, small critical cluster size, elastic, and non-ideal solution effects. An influence volume approach, which couples nucleation and bubble growth, is used to account for the limited supply of dissolved gas. The resulting set of equations are solved using a combination of numerical techniques. A parametric study is conducted to examine the effects of key process variables on bubble growth, nucleation, and final bubble size distribution.     

Slow bubble growth and dissolution in a viscoelastic fluid

A simple equation is derived for the time dependence of the bubble radius for the diffusion-induced slow growth or dissolution of a spherical gas bubble in a viscoelastic fluid of infinite extent. The constitutive equation for a first-order fluid and a surface–volume perturbation scheme are used to develop the solution, and the effect of viscosity level and elasticity on the bubble dynamics is considered. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:2093–2103, 1998     

Prediction of foam growth and its nucleation in free and limited expansion

The influence volume approach (IVA) is often utilized for modeling the mass transfer process dictating bubble growth dynamics in physical foaming. However, the assumed concentration profile in the IVA method is only valid when the changes in dissolved gas concentration are small (less than 5%). In addition, the validity of the IVA method is difficult to justify in chemical foaming applications because of the difficulties involved in defining the dissolved gas concentration profile.In the present work, we define two distinct stages of bubble growth for physical foaming. These two stages are termed as free and limited expansion and are controlled by the bubble nucleation rate. Bubble nucleation is assumed to occur only in the free expansion stage. In this stage, the bubble pressure drops substantially from an initially high pressure in the supersaturated state while the dissolved gas concentration changes very little. The second stage of our two-stage mass transfer model is termed the limited expansion stage and accounts for bubble growth in the late stages of foam evolution, when the pressure changes become small. However, in the limited stage of bubble growth the dissolved gas concentration drops significantly, as the available dissolved gas is depleted. To summarize our two-stage mass transfer model of foam expansion, the pressure difference between the bubble phase and the liquid phase is the primary mechanism for driving mass transfer in the early (free) stages of foam growth and the concentration difference is the driver for bubble growth in the late (limited) stages of growth. The first stage can be regarded as the nucleation stage and it is relatively short; while the second stage can be regarded as the bubble growth stage and is much longer. Most of the bubble volume expansion takes place in the second stage.The concentration gradient at the bubble edge, which is often ignored in other models, is analyzed in detail in this paper. The details of our novel mass transfer model are also presented.     

竖直窄流道内过冷流动沸腾的单汽泡生长模型

The process of bubble growth on heating wall in subcooled boiling includes the micro-layer evaporation on heating wall and the bubble top coagulation when the bubbles grow to a certain size and emerge into the subcooled mainstream fluid. Based on this consideration, a model for the single bubble growth of subcooled flow boiling in vertical narrow rectangular channel was proposed.Compared with experimental results, the error of the simulation results using the proposed model is less than ±25%. The simulation results indicated that as the wall superheat increases, the bubble growth gets faster, with the subcooled degree of mainstream increases, the bubble growth in later stage would be slowed, with the contact angle increases, the contact radius of the bubble bottom and the wall tension would be strengthened, resulting in faster bubble growth to make the bubble to be flat and more easily exposed to the mainstream. The velocity of mainstream has no significant effects on bubble growth rate.     

溶气式泡载分离器内减压成泡过程

通过对压力饱和溶气水减压成泡过程的热力学分析表明,溶气压力越高,形成气泡越细密,释气较完全。采用Kolmogoroff各向同性湍流理论得出湍流场中气泡稳定存在的条件和气泡大小随操作条件的变化规律。实验考察了操作条件对气泡分布的影响,采用Gamma分布能较好地描述实验。     

聚丙烯挤出发泡中的关键技术——发泡体系的性能和发泡机理研究

从聚丙烯挤出发泡体系的性能包括聚丙烯熔体的黏弹性、发泡剂的溶解度和扩散系数、聚丙烯的结晶行为和成核剂的性能以及聚丙烯挤出发泡的气泡成核机理和气泡增长机理系统介绍了聚丙烯挤出发泡中的一些关键技术。研究表明：具有显著应变硬化行为和高熔体强度的长链支化聚丙烯是获得优质PP发泡材料的前提；发泡剂的溶解度和扩散系数、聚丙烯的结晶行为和成核剂的种类和性能对发泡材料的泡孔密度、泡孔尺寸和泡孔尺寸分布有显著影响；气泡成核和气泡增长机理对于聚丙烯挤出发泡的配方设计、工艺确定和设备选型具有极其重要的意义。     

Water blown free rise polyurethane foams

A model is developed in this work for predicting the bubble size distribution in polyurethane foams generated by using water as a chemical blowing agent. The model combines equations of energy balance, kinetics of the reactions of isocyanate with water and polyol, and nucleation and growth of CO₂ bubbles. It is found that as the water content of the reaction mixture is increased, the mean bubble size decreases and the bubble size distribution become narrower. Exactly the opposite occurs in polyurethanes foamed with a physical blowing agent, e.g., DuPont Freons. This suggests that a combination of physical and chemical blowing agents can be employed to control bubble size distribution.     

HYDRODYNAMIC CHARACTERISTICS OF THE PROCESS OF DEPRESSURIZATION OF SATURATED WATER

Experiments were carried out to find the effects of dissolved gas pressure,liquid flow rateand nozzle geometry on the bubble generation when saturated water was depressurized through anozzle.A new method,high speed camera system was developed to measure the generated microbubblesdynamically.On the basis of the laws of ideal gas and solution,theoretical generated gas flow ratewas deduced,while the Smoluchowski′s equation was applied to describe the kinetics of bubblenucleation.It was found that the size distribution of nucleated bubbles was of skewed distribution.An explanation to this phenomenon was made and the Gamma function distribution was employedfor mathematical simulation.The results show good agreement between the experimental data and thepredictions by proposed model.     

二维鼓泡床内气液流动特性实验与数值模拟

采用高速摄像法测量了0.20 m×0.02 m×2.00 m拟二维床内气泡尺寸分布和流型等变化规律,结果表明,随着表观气速的增大,鼓泡床内依次呈现均匀鼓泡区、过渡区和湍动区3种形式,以气泡个数概率表示的气泡尺寸分布呈对数正态分布。以计算流体力学软件ANSYS CFX 10.0为平台,采用k-ε湍流模型和GRACE曳力模型对气液鼓泡床内流体动力学行为展开了数值模拟,其结果与实验值比较吻合。研究表明,从多相流理论出发的计算流体力学模拟方法可以用来预报鼓泡床内流型过渡等流体动力学特性。     

鼓泡塔气液两相流不同曳力模型的数值模拟

采用欧拉-欧拉双流体模型对圆柱形鼓泡塔内气液两相流动进行了三维数值模拟. 通过UDF自定义程序对气相出口边界进行了速度修正,解决了模拟中自由区域内有漩涡的问题;分别使用单一气泡尺寸模型和群体平衡模型(PBM)计算气泡尺寸,并比较其对气含率分布的预测结果,分别采用Schiller-Naumann, Grace和Tomiyama曳力系数模型进行模拟. 结果表明,在全塔径均匀进气的简化条件下,单一气泡尺寸模型不适用,在合适的Hamaker数下,PBM模型中原用于颗粒计算的Abrahamson模型可计算气泡聚并速率;Tomiyama曳力模型耦合PBM模型可更好地描述塔内流动情况,并与文献值吻合良好. Schiller-Naumann模型所得平均气含率与实验值相差约40%,而Grace模型所得湍动耗散比Tomiyama的结果高14.5%,气含率分布与文献值相差16.3%.     

Mechanism and analytical models for the gas distribution on the SiC foam monolithic tray

Silicon carbide (SiC) foam material has been applied as monolithic tray for distillation column in our previous study. A systematic understanding of the gas distribution process on the foam tray should help to the design of commercial application. In this article, local gas holdup distribution and bubble size distribution are used to measure the gas distribution. The local gas holdup is tested by the conductive probe and the number of test point is counted in different local gas holdup. The bubbles are captured by the high‐speed camera to measure the bubble size. Bubble size is calculated as ellipsoidal bubble and counted with different pore sizes. Furthermore, a three‐stage process model is put forward to explain the uneven distribution of gas phase, and verified by the experimental values. The results show that the structure and the thickness of SiC foam is the decisive factor for the gas distribution performance. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4509–4516, 2015     

Modeling the crystallization of proteins and small organic molecules in nanoliter drops

Drop‐based crystallization techniques are used to achieve a high degree of control over crystallization conditions in order to grow high‐quality protein crystals for X‐ray diffraction or to produce organic crystals with well‐controlled size distributions. Simultaneous crystal growth and stochastic nucleation makes it difficult to predict the number and size of crystals that will be produced in a drop‐based crystallization process. A mathematical model of crystallization in drops is developed using a Monte Carlo method. The model incorporates key phenomena in drop‐based crystallization, including stochastic primary nucleation and growth rate dispersion (GRD) and can predict distributions of the number of crystals per drop and full crystal size distributions (CSD). Key dimensionless parameters are identified to quickly screen for crystallization conditions that are expected to yield a high fraction of drops containing one crystal and a narrow CSD. Using literature correlations for the solubilities, growth, and nucleation rates of lactose and lysozyme, the model is able to predict the experimentally observed crystallization behavior over a wide range of conditions. Model‐based strategies for use in the design and optimization of a drop‐based crystallization process for producing crystals of well‐controlled CSD are identified. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

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     

双组分制冷工质R11-R113气泡动力学特性的可视化研究

A digital photographic study of pool boiling with binary mixture Rll（CC13）-Rll3（CCl3CF3） was performed on a horizontal transparent heater at pressure of 0.1MPa. A high speed digital camera was applied to record the bubble behaviors in boiling process. Strong effects of composition on bubble departure diameter, deparatre time, nucleation density were observed, which was attributed to the nature of the activation of the boiling surface and mass diffusion effects. The bubble departure diameter, departure period and nucleation density as functions of composition for binary mixtures R 11-R 113 were presented respectively. From the video images, it can be concluded that evaporation of microlayer is very important to the growth of bubble. It is also observed that there is not any liquid recruited into the microlayer below the bubble.     

Deep ocean bubble transport model coupled with multiple hydrate behavior characteristics

Submarine gas seepage is a widely observed process. In this study, a unified mechanistic model of bubble transport both inside and outside the gas hydrate stability zone (GHSZ) was developed. Multiple hydrate-related behaviors were considered, including hydrate nucleation, hydrate film lateral spread, hydrate shell dynamic growth, hydrate dissolution and decomposition, and collapse and fracture deformation of hydrate-coated bubbles. Using the proposed model, a series of simulation studies about bubble dissolution and rising fate were conducted. The results indicate that the formation of solid hydrates in the deep-sea environment can provide a fairly effective barrier for the dissolution and shrinkage of bubbles, and the deeper the initial release water depth, the smaller the critical size of the bubble required for arriving at the water surface. Furthermore, the majority of gases released from the seafloor would be absorbed by the shallow oceanic layer, but larger bubbles could still pass through the water column to the atmosphere.     

Single bubble formation in high pressure liquid—solid suspensions

Bubble formation from a single nozzle is investigated analytically and experimentally in nonaqueous liquid and liquid—solid suspensions at pressures up to 17.3 MPa. A mechanistic model is proposed to predict the initial bubble size in liquid—solid suspensions, by taking into account the various forces affecting the bubble growth including those induced by the presence of the particles, such as the suspension inertial force and the particle-bubble collision force. It is found that the initial bubble size in the suspensions is generally larger than that in the liquid mainly due to the inertia effect of the suspension. The initial bubble size increases with the solids holdup. The pressure has an insignificant effect on the initial bubble size in both the liquid and liquid—solid suspensions under the conditions of this study. The model can reasonably predict the initial bubble sizes obtained in this study and those reported in the literature.     

Local hydrodynamics modeling of a gas–liquid–solid three-phase bubble column

A three-dimensional (3D) transient model was developed to simulate the local hydrodynamics of a gas–liquid–solid three-phase bubble column using the computational fluid dynamic method, where the multiple size group model was adopted to determine the size distribution of the gas bubbles. Model simulation results, such as the local time-averaged gas holdups and axial liquid velocities, were validated by experimental measurements under varied operating conditions, e.g., superficial gas velocities and initial solid loadings at different locations in the three-phase bubble column. Furthermore, the local transient hydrodynamic characteristics, such as gas holdups, liquid velocities, and solid holdups, as well as gas bubble size distribution were predicted reasonably by the developed model for the dynamic behaviors of the three-phase bubble column. © 2007 American Institute of Chemical Engineers AIChE J, 2007     

The effect of bubble size on oil-water separation efficiency for a novel oil-water separation column

Bubble size is a key factor in froth flotation for oil-water separation. In this paper, the bubble size which impacts on oil removal efficiency for a novel oil-water separation column was researched systematically. The bubble size distribution was researched by using the photographic method and Matlab software. In addition, several operating parameters which impact on the bubble size were investigated, including circulating pressure, aeration rate, and the foaming agent. Based on the results of experimental data and image analysis, the frother consumption and aeration rate has important influence on the bubble size. The bubble size can be controlled by adjusting the operation conditions including the circulating pressure, aeration rate, and the frother consumption. The optimum operating conditions for the oil-water separation column were determined. Furthermore, the mathematical model of oil removal efficiency for the oil-water separation column was established.     

气液错流条件下孔口气泡直径的模型预测(英文)

The size of initial bubbles is an important factor to the developed bubble size distribution in a gas-liquid contactor. A liquid cross-flow over a sparger can produce smaller bubbles, and hereby enhance the performance of contactor. A one stage model by balancing the forces acting on a growing bubble was developed to describe the formation of the bubble from an orifice exposed to liquid cross-flow. The prediction with this model agrees with the experimental data available in the literatures, and show that orifice size strongly affects the bubble size. It is showed that the shear-lift force, inertia force, surface tension force and buoyancy force are major forces, and a simplified mathematical model was developed, and the detachment bubble diameter can be predicted with accuracy of ±21%.     

池沸腾孤立气泡生长过程中微液层蒸发影响的实验和模拟耦合分析

微液层蒸发是沸腾过程中重要的换热机理。本文旨在通过单个气泡池沸腾实验中测得的气泡动态参数探究孤立气泡生长过程中加热表面的换热机理。首先通过沸腾池和加热表面的严格设计实现了单个气泡沸腾。进一步通过对孤立气泡生长时序图像的处理,得到了气泡在一个生长周期内气泡直径、纵横比以及气泡根部基圆半径的变化。对比发现,气泡生长速率与气泡根部基圆半径随时间的变化呈现显著正相关,而与大液层区域的变化相关程度较低,这表明微液层蒸发直接影响气泡体积变化,在孤立气泡沸腾过程中起主导作用。在此基础上进一步建立了加热表面换热过程的数值模型,基于实验中测得的气泡动态参数对气泡底层的微液层厚度进行了预测;通过多次迭代计算并匹配气泡生长速率和加热棒的温度发现,当表面过热度为4.82 K时,气泡底层微液层厚度约为3.43 μm,与相关文献中的微液层厚度测量值基本一致,进一步证实了微液层蒸发在孤立气泡沸腾换热过程中的重要性。本研究揭示了孤立气泡池沸腾过程中近壁面处的换热机制,为进一步的孤立气泡沸腾传热过程数值模拟奠定了理论基础。