Semi‐empirical,squeeze flow and intermolecular diffusion model. I. Determination of model parameters

This article reviews the development of molecular healing models that couple squeeze flow and intermolecular diffusion. Historically there are a few studies that combine these processes for fusion bonding of thermoplastic composites. The motivation of this work was to develop similar models for welding of polymer films and films to substrates. These models are theoretically developed and experimentally verified. It was found that the time dependence for squeeze flow is of the same order of magnitude as that for intermolecular diffusion, making models for these processes indistinguishable experimentally, and therefore, they were assumed to occur simultaneously. Furthermore, it was found that healing of the weld can be better defined as a function of time and temperature instead of temperature alone, as historically done for welding applications. Comparison of the weld strength predictions with experimental data for impulse welds showed that the developed models were able to predict weld strength over a wide range of parameters. In Part 2, moving heat source heat transfer models together with the coupled squeeze flow and intermolecular diffusion model are used to predict healing during laser microwelding. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

An axisymmetric model of flow in the annulus of a spouted bed of coarse particles. Model,experimental verification and residence time distribution

An axisymmetric model of flow in the annulus of a spouted bed of coarse particles which takes into account non-Darcy flow and utilizes a new and general axial pressure boundary condition at the spout-annulus interface is presented. The pressure boundary condition and the annulus pressure distribution are experimentally verified and the model used to calculate the residence time distribution and the flowrate at the top of the annulus. In addition, the average axial velocity profile in the annulus is calculated and compared with predictions of several one-dimensional flow models.     

Laminar radial flow electrochemical reactors. II. Convective diffusion of inert tracer

Mixing is investigated in three laminar radial flow cells (capillary gap cell (stationary discs), pump cell (one disc spinning) and the rotating electrolyser (co-rotating discs)) using numerical and semianalytical methods for inert tracer transport. Results are compared to existing data. Mixing in the three cells is modelled using finite element techniques applied to convection-dominated inert tracer transport. For the capillary gap cell modes of tracer tagging and detection are commented on with respect to which type provides the correct representation of the residence time distribution. The extent of cross-gap communication, from anode to cathode, is quantified and compared to that observed in the other radial cell designs. Two semi-analytical solutions (convection only, Taylor diffusion) are derived for inert tracer transport in this configuration and are compared to the detailed numerical results. Convection only is relevant fort _d/t _c ratios of greater than 100 and the Taylor diffusion model applies fort _d/t _c ratios of about 0.10 and only beyond a critical radius defined herein. Pump cell (PC) mixing is modelled using finite element techniques for the tracer, the velocity field being provided by a semi-analytical solution. Mixing is quantified in this cell and cross-gap communication evaluated. The large axial velocities provide for significant cross-gap mixing. The rotating electrolyser is modelled and the efficiency of separation of catholyte/anolyte streams is observed to be determined by Taylor number (Taylor number () — ratio of half-gap width divided by theoretical boundary layer thickness). The superiority of separation in this cell is quantified by definition of the zeroth wall moment and comparison with the other two radial cells. For the example modelled, cross-gap communication was less than half that of the other cells.     

Experiment and simulation using diffusion flux model for gas-particle two-phase flow in a suspension bed

A mathematical model of multi-phase turbulent flow based on the diffusion flux model and the numerical simulation method to analyze the gas-particle flow structures have been developed. The diffusion flux model in which the accelerations due to various forces are taken into account for the calculation of the diffusion velocity of the particles enables its application to the analysis of multi-dimensional gas-particle two-phase flow. In order to verify the accuracy and efficiency of the numerical simulations, an experimental study of gas-particle flow in a suspension bed has been conducted. The numerical analysis results by using the diffusion flux model agree reasonably well with the experimental investigation. It is confirmed that the diffusion flux model has the capacity of correctly simulating the multi-dimensional gas-particle two-phase flow.     

基于段塞流的通用气液两相流模型的建立与验证

气液两相混输流动中,由于段塞流与其他流型均有联系,从段塞流出发建立模型可以使不同流型下的计算模型得到统一。基于段塞流建立气液两相流动量方程和连续性方程,完善模型对气泡和液滴夹带的处理。建立模型的闭合关系式,对关键参数(壁面及气液相间水力摩阻系数、液塞平移速度、平均液塞长度)的计算闭合关系式进行优选,得到适用于模型的闭合关系式,同时,对液滴和气泡的夹带给出夹带条件及相关参数计算式,最终建立基于段塞流的通用气液两相流模型。使用3组不同来源的实验数据验证了模型计算压降和持液率的准确性,实验数据分别来自中国石油大学(华东)、大庆油田实验基地的气液两相流实验以及国外研究人员的实验研究,包含各个气液流型。模型具有较高的计算精度,优于未经关系式完善和优化的原始模型,大部分压降及持液率参数的计算误差在±15%以内。     

Effect of backwashing on activated carbon adsorption using plug flow pore surface diffusion model

A fixed bed is gradually exhausted from top to bottom without backwashing; however, backwashing can rearrange the concentration gradient in the bed. After backwashing, saturated particles which are located at the top of the bed are homogeneously distributed in the bed. The used model to predict adsorption and backwashing effect of organic component is the plug flow pore surface diffusion model (PFPSDM). A sensitivity analysis was performed to determine which parameters have the greatest impact on the model results for components which can represent various organics. In addition, the effects of backwashing were examined by rearranging concentration gradient. For single component sensitivity analysis, the molecular weight was an important parameter. The breakthrough of the smaller molecular weight component was impacted more by backwashing. The SPDFR showed a significant impact on the breakthrough pattern. When surface diffusion was the dominant mechanism, high SPDFR, the breakthrough profile was sharper than when pore diffusion was dominant, low SPDFR. The adsorbability was an important parameter in determining the breakthrough pattern. As expected, the strongly adsorbable component showed the later breakthrough. Backwashing yielded earlier breakthrough for all single components and multi-components examined.     

Water diffusion in polymer coatings containing water-trapping particles. Part 2. Experimental verification of the mathematical model

The influence of the water microtraps (cross-linked poly(methacrylic acid) sodium salt spherical particles) with high sorption capacity and low diffusion coefficient on the water penetration through the epoxy coating has been investigated. Water diffusion coefficients for the pure epoxy coating as well as composite coatings with 5% and 3.7% content of water traps have been estimated by attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) and microbalance measurement methods. Experimental results were compared with the mathematical model of diffusion in composite media. The presence of the particles capable of binding water reversibly (water traps) significantly slows down the diffusion rate. Composites with water traps dispersed in the whole volume of the coating and sandwich-structured coatings composed of 3 layers with particles located only inside the middle layer have been examined. The diffusion rate has been found to depend not only on the concentration of the water traps but also on the location of the particles inside the coating. Both kinds of composites exhibit lower diffusion coefficient in comparison with the pure coating, however in the case of the sandwich-structured composites this effect is significantly stronger and much closer to that predicted by the model. Water diffusion coefficient for the sandwich-structured composite with 5% addition of water traps is ca. three times lower than for the pure epoxy coating.     

平行流换热器两相流分配模型的建立与验证

制冷剂的分配不均对平行流换热器的换热性能会产生重大影响。基于T型管的T-junction模型,联立质量方程和压力方程,设计合适的算法建立平行流换热器两相流流量分配的模型,该模型的优势在于无需已知分歧管流量可模拟分歧管的分配特性。在此基础上,将模型的计算结果与实验数据对比验证,验证了模型有效性,为平行流换热器的设计提供合理的依据。计算并分析了干度与质量流量对平行流换热器分配的影响,结果表明干度对平行流换热器分配的影响不大。在干度不变时,提高流体的质量流量可以对平行流换热器流量分配进行改善。     

Model discrimination for the propionic acid diffusion into hydrogel beads using lifetime confocal laser scanning microscopy

Hydrogels are increasingly used for the entrapment of biocatalysts, especially for the use of enzymes in organic solvent systems. Hence, it is necessary to understand the influence of the hydrogel matrix on the transport kinetics (diffusion and phase transfer) and on the reaction kinetics (activity and stability of the enzymes). Here, the diffusion of propionic acid into Ca-alginate hydrogel beads is studied using a structured methodology, model-based experimental analysis (MEXA).The basis for all further investigations is a rigorous model of all processes occurring during the diffusion of the propionic acid into the Ca-alginate hydrogel bead. As competing model assumptions the Fickian and Nernst-Planck diffusion laws are integrated. Then, an optimal experimental design is performed to determine those experiments that allow an efficient discrimination of the rival model candidates. The change in pH-value over time resulting from the diffusion of propionic acid into the hydrogel bead is observed in the centre of the hydrogel bead. The fluorescent pH-indicator resorufin shows pH-dependent lifetimes that are measured by time-correlated single photon counting using a confocal laser scanning microscope at high temporal resolution (every 1 s). To our knowledge lifetime confocal laser scanning microscopy is used for the first time in this study for the quantification of dynamic pH-changes in macroscopically large particles. The model parameters for each candidate model are estimated based on 16 independent experimental data sets. Finally, the likelihood function is used to evaluate and discriminate the competing diffusion laws.For the diffusion of propionic acid into spherical Ca-alginate hydrogel beads, it could be shown that Fickian diffusion is not able to describe the process accurately in contrast to Nernst-Planck diffusion. The influence of the Ca-alginate hydrogel density was found to be insignificant for the estimated diffusion coefficient.     

Thermodynamics of plasticized triblock copolymers. Part II: Model verification by light transmittance and rheology

An earlier paper proposed a theoretical model for the thermodynamics of microphase separation in a plasticized triblock copolymer. Data on laser light transmission through plasticized films and on dynamic viscosity: of these films are presented in support of model predictions. Two styrenebutadiene-styrene copolymers were tested: Kraton 1101 with block weights (12.5-75-12.5) × 10³ and TR-41-1467 with weights (9.6-47.5-9.4) × 10³ using the solvent dipentene (p-mentha 1, 8 diene), which is favorable for both blocks. The role of such solvents is to depress the temperature of microphase separation, T_s. Optical and rheological measurements of T^s agreed with each other arid, in most cases, with the theory; discrepancies with theory were noted only when T_s was less than T_s for polystyrene. These data along with electron microscopy also support the prediction that the favored morphology for these systems is a mixture of planar and inverted (middle-block) cylinders and spheres.     

基于段塞流捕捉的高黏油气两相流模型的建立与验证

随着传统油田的快速消耗,高黏稠油的开发逐渐引起了重视。有关高黏油的气液两相流研究主要集中在国外,国内的相关研究目前还较少。本文针对高黏油气混输管路,建立了一种捕捉段塞流的形成和发展过程,并进行两相流水力计算和液塞长度统计的组合模型。通过气液相间滑移速度和液相连续性方程的求解得到管路中不同时刻和位置的持液率,以持液率的变化反映段塞的形成和发展。建立气液动量守恒方程关联持液率和压力,得到管路中各位置的压力变化。闭合关系式中,通过液塞平移速度、壁面及气液相界面的剪切力关系式加入黏度的影响,最终建立适用于高黏油气两相流的段塞捕捉模型。使用不同来源的数据验证模型计算压降和液塞长度的准确性,数据分别来源于国外研究者的实验数据和大庆油田的现场数据。结果表明,模型具有较高的计算精度,大部分压降误差在±15%以内,大部分液塞长度误差在±20%以内。     

Automatic verification of operating schedules for batch processes using symbolic model checking: Latch model vs. real-time

This study proposes two models for reading Gantt charts and finding embedded errors in the operating schedules of batch processes. Two automatic techniques for finding errors, a real-time model and a latch model, are developed using the symbolic model verifier (SMV) and are compared to verify that the schedules are error free and to represent the scheduling information and policies. These models are designed to automatically detect embedded errors relating to unavailability, superimpositions, and violation of intermediate storage policies in batch processes with various intermediate storage policies.     

Determination of eugenol diffusion through LLDPE using FTIR-ATR flow cell and HPLC techniques

A time-resolved Fourier Transform Infrared-Attenuated Total Reflectance Spectroscopy (FTIR-ATR) technique was set up and used to study the diffusion of eugenol through Linear Low Density Polyethylene (LLDPE) at 16, 23 and 40 °C. The 1514 cm⁻¹ peak for eugenol (aromatic -CC- stretching) was monitored over time and used to determine the diffusion coefficient (D). The Fickian model was found to fit well to the experimental data and the D value of eugenol through LLDPE was found to be between 1.05 ± 0.01 and 13.23 ± 0.18 × 10⁻¹⁰ cm²/s. The FTIR-ATR results were compared with one and two side diffusion process using a permeation cell and quantified by High Performance Liquid Chromatography (HPLC) technique. Eugenol sorbed in LLDPE samples at different times, was extracted in methanol and the concentration determined by HPLC. The diffusion coefficient by both two-sided and one-sided HPLC technique was found to be approximately three times higher than the FTIR-ATR values although they were in the same order of magnitude of 10⁻¹⁰ cm²/s. The difference between the FTIR-ATR and HPLC results was mainly attributed to difference between the two measuring techniques.     

A generalized two-environment model for micromixing in a continuous flow reactor—II. Identification of the model

The dynamic behavior of an actual continuous stirred tank reactor in which a second-order reaction takes place was measured and the model which describes the micromixing phenomena within the reactor was identified. The generalized two-environment model was adopted and its environment function and the collision frequency of each fluid element were determined. Although the conventional two-environment model and the conventional coalescence-redispersion model were also identified, the applicability of these models was poor relative to that of the generalized two-environment model.     

基于行波法的段塞流瞬态捕捉模型建立与验证

气液两相流中,准确预测段塞流的特征参数具有重要的现实意义。Renault模型是基于非黏性Kelvin-Helmholtz（IKH）稳定性准则与黏性Kelvin-Helmholtz（VKH）稳定性准则建立的能够捕捉段塞前后界面运动的双流体模型,但该模型在液相单元格之间采用Riemann精确解,求解速度较慢。为简化计算,本文将行波法引入到Renault模型的液相方程求解过程,并对可能出现的干区用薄液膜代替,使行波法适用于所有计算单元,在保证模型精度的条件下,极大地提高了计算速度,运算时间相比Renault模型平均减少28%。对比本模型计算结果与室内小型环道实验数据,持液率与实测结果相一致,压降、段塞长度计算相对误差分别在25%、30%以内,且主要分布在20%以内。说明本文改进的瞬态段塞流模型具备运算快速、计算精度较高的特点,具有一定的工程应用价值。     

七氟丙烷灭火剂施放、流动及扩散过程的数值模拟

基于流体力学基本理论,分析七氟丙烷灭火剂灭火过程中灭火剂施放、流动和扩散行为特点,并基于流体力学基本理论,结合k-ε双方程湍流模型,建立了描述七氟丙烷灭火剂施放、流动和扩散过程的数学模型,并给出了相应的数值求解方法。利用建立的数学模型对试验舱体内七氟丙烷灭火剂的施放、流动和扩散过程进行了模拟分析,得到了详细的流场和浓度分布情况。模拟结果表明,在喷嘴附近七氟丙烷灭火剂流动速度较快,且七氟丙烷浓度较高;随着施放时间的延长,七氟丙烷灭火剂在舱内的流动和扩散速度和浓度逐渐降低。当七氟丙烷用量为0.85kg时,舱体内七氟丙烷浓度约为4%,达不到灭火浓度要求(5.8%);当七氟丙烷用量增加到1.75kg时,舱体内七氟丙烷浓度约为7%,可达到灭火浓度要求。