Styrene grafting onto a polyolefin in an internal mixer and a twin‐screw extruder: Experiment and kinetic model

There has been relatively little effort to quantitatively understand graft copolymerizaution in either batch mixers or twin‐screw extruders. Most efforts have concentrated on grafting maleic anhydride, which does not homopolymerize. In this paper we consider grafting with styrene, which may homopolymerize as well as graft. The influence of residence time on degree of grafting in an internal mixer and a twin‐screw extruder were studied by measuring reaction yields with respect to reaction time in a mixer and along the screw axis in a twin‐screw extruder. The degree of grafting increased with initial monomer and peroxide concentration. Grafting reactions with three different peroxides were also investigated. The degree of styrene grafting in an internal mixer is slightly higher than that in a twin‐screw extruder. The rate of reaction along the screw axis in terms of residence time seems higher than for the batch mixer. The melt viscosity dropped dramatically with addition of peroxide. A kinetic scheme is proposed and the experimental results are critically compared with it.     

Maleic anhydride modification of polyolefin in an internal mixer and a twin‐screw extruder: Experiment and kinetic model

There has been little effort. to quantitatively understand graft copolymerization in batch and continuous mixers. Little information exists on the evolution of grafting reactions with respect to residence time in an internal mixer or along the screw axis in a twin‐screw extruder. In this study, maleic anhydride was grafted onto polypropylene in both an internal mixer and a twin screw extruder. The influence of residence time on degree of grafting in an internal mixer and a twin screw extruder was studied through measuring reaction yields with respect to reaction time in the internal mixer as well as along the screw axis in the extruder. The dependence of the degree of grafting with monomer and peroxide concentration was determined. A free radical kinetic model of the process was developed and compared to experiment. Kinetic parameters were determined.     

Methyl methacrylate modification of polyolefin in a batch mixer and a twin‐screw extruder experiment and kinetic model

Free radical grafting with methyl methacrylate onto molten polypropylene was investigated in both an internal mixer and a modular co‐rotating twin‐screw extruder. There has been little open literature on melt free radical grafting copolymerization of methyl methacrylate. There is also little information on the evolution of grafting reaction with respect to reaction time in an internal mixer and along the screw axes with methyl methacrylate. The influence of residence time on the degree of grafting in an internal mixer and a twin‐screw extruder was studied through measuring reaction yields with respect to reaction time in a mixer and evolution of reaction yield along the screw axis. The degree of grafting increased with initial monomer and peroxide concentration. The grafting reactions with three different peroxides were also investigated. The grafting levels were similar to maleic anhydride and suggested that only an individual methyl methacrylate unit be grafted. The melt viscosity was dramatically reduced with addition of peroxide. A kinetic scheme of our reaction system for methyl methacrylate was proposed and compared with the experimental results.     

Continuous polymerization of ε‐caprolactone initiated by titanium phenoxide in a twin‐screw extruder

The continuous polymerization of ε‐caprolactone initiated by titanium phenoxide was carried out in both an internal mixer and a twin‐screw extruder. The polymerization was performed under different processing conditions, including various temperatures and screw speeds. To perform a kinetic study, samples were collected along the time axis (internal mixer) and along the screw axis (extruder). Size exclusion chromatography and proton nuclear magnetic resonance were used to study the evolution of the conversion degree with mixing time and with the extruder. The rheological behavior was also characterized. Temperature had a strong effect on conversion in the internal mixer, whereas in the twin‐screw extruder, both temperature and screw speed played major roles. The specificity of the titanium phenoxide to lead to high‐molar‐mass poly(ε‐caprolactone) under these processing conditions was also confirmed. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Correlation between processing conditions and fiber breakage during compounding of glass fiber‐reinforced polyamide

The inter‐relationship between processing conditions and fiber breakage has been studied for glass fiber‐reinforcedpolyamide 12, prepared using (i) an internal batch mixer, (ii) a laboratory scale corotating twin screw extruder, and (iii) an industrial scale twin screw extruder. The average fiber lengths and fiber length distributions were measured for various compounding conditions (screw or rotor speed, mixing time, feed rate). Experimental results have shown that fiber breakage depends on both screw speed and mixing time, the later being controlled, in an extruder, by the feed rate. For a given compounding system (batch mixer or twin screw extruder), the energy input (specific mechanical energy, SME) during the compounding process is found to be a reliable parameter, which governs fiber length (average, minimal, and maximal) evolution. Experimental data are correctly described with a model defining change in fiber length as a function of SME. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers     

新型静态混合器湍流特性数值模拟

结合新型静态混合器的结构特点,利用CFD软件采用标准的k-ε湍流模型对新型静态混合器内的湍流状态下的三维不可压缩流场进行数值模拟。通过研究新型静态混合器脉动速度分布的对称性及其间歇性发现:新型静态混合器内3个方向速度分量的偏斜因子和平坦因子分布具有周期性;x和z2个方向的速度概率密度分布存在较小不对称性且其平坦因子数值在2.3—5.7变化,径向偏斜因子的数量级均较轴向小1个数量级。采用新的数据处理方法计算和分析得到了不同长径比下新型静态混合器湍流流动阻力统一特性曲线及其关联式。     

Moisture Diffusion Inside Paper Materials in the Hygroscopic Range and Characteristics of Diffusivity Parameters

Some current models for moisture diffusion in paper in the hygroscopic range are analyzed. In general, two types of diffusion models can be recognized. Models of the first type treat paper as a homogeneous medium with moisture flux that is proportional to the gradient in moisture content. Although useful in some instances this approach fails frequently because it homogenizes the internal dynamics and relaxation processes occurring within the paper material. Recent studies have shown that a subtler approach which treats paper as a composite of fibers and void spaces is more successful at describing moisture transport dynamics. A review of these studies along with a generalization of this approach to three dimensions is considered here. The parameters appearing in such models can be identified with the physical processes of diffusion through the void space and through the fiber matrix. Diffusivities in these individual phases are supplemented by a local kinetic coefficient representing moisture flux interchange between the void and fiber phases. When the local moisture exchange coefficient takes on large values, the fibers and the void spaces are at local equilibrium with no net exchange of moisture. Under such conditions, the model reduces to the simpler Fickian diffusion model with nonlinear moisture diffusivity equivalent to earlier models.     

Continuous polymerization of ω‐lauryl lactam in an intermeshing corotating twin‐screw extruder

This article describes the synthesis of poly(ω‐lauryl lactam) by a reactive extrusion process. Anionic ring‐opening polymerization was performed in an intermeshing corotating twin‐screw extruder. We investigated the evolution of conversion of ω‐lauryl lactam as a function of reaction time, screw speeds, different feed rates, and different screw configurations along the screw axis in a twin‐screw extruder. For comparison with continuous polymerization in a twin‐screw extruder, we studied polymerization in an internal mixer, which was considered a batch reactor. We found the final conversion of ω‐lauryl lactam made in a twin‐screw extruder was higher than in an internal mixer. Higher molecular weights are found at lower screw speeds and feed rates. Melt viscosities and mechanical properties of the polymers were measured. Residence time, molecular weights, and shear mixing have the main effect on the mechanical properties of products. The twin‐screw extruder performance was interpreted in terms of commercial software. It was found that twin‐screw extruder reaction rate was higher than those in the batch reactor and increased locally with screw speed and feed rate. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1605–1620, 2005     

SD型静态混合器压力降的特性分析

借助计算流体力学软件FLUENT5/6,对含有3个流道的螺旋式静态混合器在不同的长宽比和雷诺数下的流动特性进行了数值模拟。模拟结果表明,当螺旋片长宽比为4∶1时该混合器压力降与雷诺数的1.715次方成正比;当雷诺数一定时,压力降与混合元件单元数在双对数坐标下成线性分布规律;压力降随着螺旋叶片长宽比的减小而增大;该混合器的压力降与对应结构的SK型静态混合器基本相同,大约是相同直径和管长的光滑空管压力降的10倍。     

Moisture Diffusion Inside Paper Materials in the Hygroscopic Range and Characteristics of Diffusivity Parameters

Abstract

Some current models for moisture diffusion in paper in the hygroscopic range are analyzed. In general, two types of diffusion models can be recognized. Models of the first type treat paper as a homogeneous medium with moisture flux that is proportional to the gradient in moisture content. Although useful in some instances this approach fails frequently because it homogenizes the internal dynamics and relaxation processes occurring within the paper material. Recent studies have shown that a subtler approach which treats paper as a composite of fibers and void spaces is more successful at describing moisture transport dynamics. A review of these studies along with a generalization of this approach to three dimensions is considered here. The parameters appearing in such models can be identified with the physical processes of diffusion through the void space and through the fiber matrix. Diffusivities in these individual phases are supplemented by a local kinetic coefficient representing moisture flux interchange between the void and fiber phases. When the local moisture exchange coefficient takes on large values, the fibers and the void spaces are at local equilibrium with no net exchange of moisture. Under such conditions, the model reduces to the simpler Fickian diffusion model with nonlinear moisture diffusivity equivalent to earlier models.     

Screw Machines with Longitudinal Circulation of Fluid. Communication 3. Intensification of Mixing Processes

Flow of melts and solutions of polymers with Newton's law of flow was investigated in a double screw mixer with screw channels of different depth and width in the presence of a radial gap on one screw ridge. With the radial gap, the pressure gradients along both channels are the same, the pressure along the entire length of the shallow and deep channels differ by a constant value and the higher pressure is always established in the second channel along the path of movement of the upper plate. By intensive exchange between channels, flow which gives zero flow of fluid in each section in the direction across the channels is organized in the deep and shallow channels of the mixer. The overall pressure differential and output of the mixer do not decrease in the presence of a radial gap on one of the ridges of the screw.     

Kinetics of gas hydrate formation from mixtures of methane and ethane

Experimental data on the kinetics of formation of gas hydrates from three mixtures of gaseous methane and ethane are reported. the experiments were conducted in a semi-batch stirred tank reactor at temperatures from 273 to 284 K and of pressures from 0.68 to 5.60 MPa. An intrinsic kinetic model for the growth of the gas hydrate is proposed. It is extension of the model for pure component hydrate formation. The model is based on the crystallization theory coupled with the two-film theory for the gas absorption into the liquid phase. the model does not contain any adjustable parameters. The kinetic rate constants which appear in the model are those obtained previously from pure component formation data. The results indicate that the formation rate is proportional to a lienar combination of the differences in the fugacities of the dissolved gases and their three-phase equilibrium fugacities at the experimental temperature. The effect of the mixture composition is taken into account indirectly through the computation of the three-phase equilibrium conditions and of the fugacities. the total gas consumption rate is proportional to the second moment of the particle size distribution.     

The recirculating screw mixer: A new small-volume mixer for the polymer laboratory

The recirculating screw mixer (RSM), a new small-volume intensive mixer for the polymer laboratory, is designed, built, modeled, and tested. This type of batch mixer is intended for the mixing of 1 to 30 cm³ of viscous material at high shear rates. A material element in the mixer experiences alternating screw pump and tubular flows with reorientation between these flows. A mixer with a 10 cm³ sample capacity is built for testing and evaluation. Flow visualization experiments are used to investigate the quality of the distributive mixing achieved. The flows in the mixer are modeled for the cases of a Newtonian fluid and a power law fluid. The Newtonian model accurately predicts the recirculation time for particles suspended in Newtonian silicone oils. The power law model accurately predicts the screw torque obtained with a polystyrene and polyethylene. A method for the measurement of fluid rheology from the operating conditions of the RSM is proposed and tested. The mixing achieved by the RSM is compared to that obtained by a batch mixer with roller blades. Both mixers are used to prepare blends of ethylene-propylene rubber in polystyrene. The morphologies of the resultant blends are compared and differences in the mixing action are discussed. The mixers are also used to prepare composites of fumed silica in polyethylene. The quality of mixing obtained in the RSM compares quite favorably with that obtained in the batch mixer with roller blades for polystyrene/ethylene-propylene rubber reactive blends and polyethylene/silica composites.     

Kinetics of formation of methane and ethane gas hydrates

An intrinsic kinetic model with only one adjustable parameter is proposed for the formation of methane and ethane gas hydrates. Experimental formation data were obtained in a semi-batch stirred tank reactor. The experiments were conducted at four temperatures from 274 to 282 K and at pressures ranging from 0.636 to 8.903 MPa. The kinetic model is based on the crystallization theory, while the two-film theory model is adopted for the interfacial mass transfer. Experiments were performed at various stirring rates to define the kinetic regime. The study reveals that the formation rate is proportional to the difference in the fugacity of the dissolved gas and the three-phase equilibrium fugacity at the experimental temperature. This difference defines the driving force which incorporates the pressure effects. The gas consumption rate is also proportional to the second moment of the particle size distribution. The rate constants indicate a very weak temperature dependence.     

EVALUATION OF DISTRIBUTIVE MIXING EFFICIENCY IN MIXING EQUIPMENT

A framework was developed to evaluate the distributive mixing efficiency during processing in a mixer. The dynamics of distributive mixing was studied numerically by means of tracking the evolution of particles originally gathered as clusters. The goodness of mixing was characterized in terms of length stretch, pairwise correlation function and volume fraction of islands. The length stretch reflects the capability of the mixer to spread particles away from their neighbors initially present in the same cluster. The pairwise correlation function characterizes the global distribution of particles in the mixing region. The volume fraction of islands quantifies the regions void of minor component and provides a better local analysis of the mixing. This framework was applied to study distributive mixing in the C-shaped chamber of an intermeshing counter-rotating twin screw extruder.     

不同结构静态螺旋混合器强化湿法脱硫数值模拟

变螺距静态螺旋混合器可作为一种新型高性能气液传质脱硫装置,为优化其结构参数,利用欧拉-拉格朗日方法,在Barracuda^TM软件中建立了气液两相流动模型,并根据上述模型及二氧化硫吸收速率方程,分别模拟了静态螺旋混合器在不同变螺距系数m、长径比l/d、流道截面回转角φ下SO₂出口浓度和脱硫率的变化规律。结果表明：在反应物充足的情况下,脱硫率随m的增大而降低,并于m≥0.5时趋于稳定;脱硫率随l/d的增大而提高,并于l/d=11~13时趋于稳定,l/d=14时又出现上升;脱硫率随φ的增大而提高,并于φ≥720°趋于稳定。根据上述规律,结合压降等指标,给出了各结构参数的建议值：m=0.45,l/d=11,φ=630°,并在建议结构参数下进行了脱硫试验,SO₂出口浓度为19.56 mg.m^-3,脱硫率达99.35%,达到超净排放标准。为今后工业规模静态螺旋混合脱硫装置的设计与制造提供了依据。     

变燃速发射药芯料体积流率波动值的数值模拟

利用POLYFLOW软件,对不同操作条件下变燃速发射药芯料在机筒内的流动情况进行三维数值模拟,对其体积流率波动因素进行研究。结果表明,芯料的体积流率与螺杆转速成正比,不同转速下芯料体积流率高频波动值在0.02%~0.03%之间,芯料的体积流率波动值与螺杆转速波动值成正比关系;芯料的体积流率与入口压力成正比,不同入口压力下体积流率高频波动值为0.024%~0.026%;入口压力波动较大时,芯料的体积流率波动随着入口压力的增大而较快增加。     

Characterization of transverse mixing in a screw mixer by image analysis

Transverse mixing of particles in a screw mixer is investigated by a digitized image analysis method coupled with a solidification technique. The effects of screw rotation speed, filling level, and particle size on the transverse mixing index and mixing rate constant are investigated experimentally. The results show that a decrease in screw rotation speed and filling level results in an increase in the mixing rate. Faster mixing is observed with large particles, and the mixing rate constant of coarse particles is 1.5–2 times higher than that of fine particles. The particle size difference of materials puts the particles at a risk of segregation.     

不同结构单螺杆屏障混炼元件混合特性研究

运用有限元分析软件Polyflow对不同结构和不同螺杆转速下的修正Maddock混炼元件流场进行三维非等温数值模拟,得到了流场的压力、速度、温度和剪切速率的分布;利用粒子示踪法(PTA)对不同结构和不同螺杆转速的修正Maddock混炼元件流场内聚合物熔体所经历的混合过程进行模拟,并对结果进行了统计学分析;通过比较平均解聚功等参数对不同结构和不同螺杆转速下修正Maddock混炼元件的分散混合效果进行分析研究,并借助实验进行验证。结果表明,等腰反向型修正Maddock混炼元件对聚合物熔体的剪切作用和分散混合性能最好;适当提高螺杆转速可以有效地促进物料的分散混合。     

Glass fiber breakup in corotating twin screw extruder: Simulation and experiment

The damage of glass fibers at various conditions was investigated in a corotating twin screw extruder by varying viscosity, screw speed, and screw configuration. Increasing the screw speed and melt matrix viscosity were found to increase the extent of fiber breakage. Based on the experimental data and Euler buckling theory, a composite modular kinetic model to describe glass fiber breakage was developed. Regions of the major and minor fiber breakage in a corotating twin screw extruder were found. The simulation program based on the experimental data and kinetic constants was developed for fiber breakage along the screw length. Comparisons were made between simulated results and experimental data indicating a reasonable quantitative agreement between them. Predictions of the model are also in general qualitative agreement with many published data on fiber breakage in twin screw extruders. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers