Development of polymer blend morphology during compounding in a twin-screw extruder. Part II: Theoretical derivations

In Part II of the work, the intermeshing twin-screw extruder is briefly described and the theoretical procedures used to model its operation are summarized. Based on the microrheological considerations discussed in Part I, a predictive procedure of the morphology evolution during compounding of two immiscible polymers is proposed. In this first generation model, only the shear flow effects are considered. Furthermore, to avoid complications due to coalescence a low concentration of the dispersed phase was assumed. In the procedure, two drop breakup mechanisms are discussed. The first assumes that the drops do not break under flow while the second postulates that breakup occurs under flow. Two dispersion mechanisms are considered, the first postulating continuously increasing polydispersity of drop size and the second postulating that drop polydispersity is inversely proportional to deformation strain. The influence of the screw configuration and operating conditions on blend morphology evolution is studied. It is expected that the computed drop size distribution provides limiting values for the experimental data. Dependency of predicted morphology on operating conditions is also investigated. Increasing screw rotating speed (resulting in increasing energy consumption) and decreasing throughput (resulting in decreasing productivity) lead to prediction of finer drop size. In practice, therefore, a compromise would be required. The proposed procedure is limited to melt flow (excluding the die region) within the region of large capillary parameter values, k > 4k_crit.     

The modeling of continuous mixers. Part I: The corotating twin-screw extruder

In many operations in polymer processing, such as polymer blending, devolatilization, or incorporation of fillers in a polymeric matrix, continuous mixers are used; e.g., corotating twin-screw extruders (ZSK), Buss Cokneaders and Farrel Continuous Mixers. Theoretical analysis of these machines tends to emphasize the flow in complex geometries rather than generate results that can be directly used (1–5). In this paper, a simple model is developed for the hot melt closely intermeshing corotating twin-screw extruder, analogous to the analysis of the single-screw extruder carried out in 1922 and 1928 (6, 7). With this model, and more specifically with its extension to the complete nonisothermal, non-Newtonian situation, it is possible to understand the extrusion process and to calculate the energy, specific energy, and temperature rise during the process with respect not only to the viscosity of the melt, but also to the screw geometry (location and number of transport elements, kneading sections and blisters, pitch, positive or negative, screw clearance, and flight width) and screw speed. To support the theoretical analysis, model experiments with a Plexiglas-walled twin-screw extruder were performed, in addition to practical experiments with melts on small- and large-scale extruders, with very reasonable results, In Part 2, the Buss Cokneader will be analyzed analogously.     

Three-dimensional flow modeling of a self-wiping corotating twin-screw extruder. Part I: The transporting section

A three-dimensional modeling of the transporting elements in a self-wiping corotating twin-screw extruder has been carried out by using the finite element package Sepran (1). This simulation uses the 3D geometry of the channel rolled over the twin-screw, which consists of the intermeshing and normal areas. The flow profile, the backflow volume, the pressure buildup, the shear and elongation rates, and the adiabatic axial temperature gradient have been calculated by solving the Navier-Stokes equations and the continuity equation for a Newtonian fluid. These results are given for different extruder parameters such as the throughput of the extruder, the rotation speed of the screws and the helix angle of the screws to better understand the influence of different extruder configurations. This study belongs to a program of research on the self-wiping corotating twin-screw extruder that also includes the modeling of the kneading elements (Part II) and, in the future, the study of scale-up and heat transfer.     

Three-dimensional flow modeling of a self-wiping corotating twin-screw extruder. Part II: The kneading section

Three-dimensional flow simulations of kneading elements in an intermeshing corotating twin-screw extruder are performed by solving the Navier Stokes equations with a finite element package, Sepran. Instead of using the whole geometry of the 8-shaped barrel a simplified geometry is used, representing a large part of the geometry during the rotating action of the kneading paddle. The goal of these calculations is to study the dependence of several factors that influence mixing, such as shear rate, elongation rate, pressure, and the flow profile in the extruder on various extruder parameters, such as fluid viscosity, rotation speed, and throughput. The shear and elongation rate and the pressure drop are calculated for varying viscosities. The various stagger angles possible for disc configurations in the corotating twin-screw extruder are modeled. The axial backflow volume is calculated for varying values of rotation speed and throughput.     

啮合异向双螺杆挤出过程轴向循环流道三维流场分析——轴向循环流场分析(Ⅲ)

介绍了作者在啮合异向双螺杆某一轴向位置设置一非啮合段 (且该段其中一根螺杆是反向输送元件 ) ,从而将轴向循环流动的概念引入到啮合异向双螺杆挤出过程中 ,并利用ANSYS有限元分析软件对啮合异向双螺杆挤出过程轴向循环流道中的非牛顿流体等温流动进行的三维模拟分析 ;在得出速度场和压力场的基础上 ,对剪切速率、剪切应力及剪切粘度进行了模拟 ,并将各模拟结果与未引入轴向循环段的啮合异向双螺杆挤出过程常规螺纹元件流道的模拟结果进行了比较。     

LDPE熔体在双螺杆挤出机中流动的有限元分析

利用大型有限元分析软件包ANSYS分析了低密度聚乙烯(LDPE)在双螺杆挤出机三头常规螺纹元件中的流动情况,讨论了整个流道的速度分布、压力分布、粘度分布及螺杆挤出特性曲线。计算结果表明：LDPE熔体在双螺杆挤出机中得到了充分的混合。     

Finite element modeling of a counter-rotating,non-intermeshing twin screw extruder

This paper is concerned with Newtonian flow in a counter-rotating non-intermeshing twin-screw extruder. Both the matched and the mismatched screw flight configurations are considered. A three-dimensional analysis of the pressure flow through the complete extruder cross-section is included. The model predictions agree well with the experimental data. Computed examples are given to illustrate the utility of this work.     

Transport in a twin-screw extruder for the processing of polymers

The fluid flow and heat transfer in polymer extrusion in a twin-screw extruder was studied numerically by using the finite volume method. In the mathematical model, the coordinate system is fixed to the screw so that it is held stationary and the barrel is moved to simplify the complicated geometry. The screw channel of a twin-screw extruder is approximated as two regions: translation and intermeshing. The flow in the translation region is similar to that in a shallow single screw extruder and is treated by the numerical methods given in the literature. In the nip or intermeshing region, strong mixing effects are expected, along with the diffusion of energy and momentum. The full governing equations are solved in this region to determine the velocity components in all the three coordinate directions. The energy equation is coupled with the equations of motion through viscosity, since the viscosity of the polymeric, non-Newtonian, fluids considered here is dependent upon the shear rate and temperature. There is no clear physical demarcation between the nip region and the translation region. Therefore, a domain matching was employed at an arbitrary location that was varied numerically to ensure that the results were independent of this location. The variation of pressure and bulk temperature along the helical channel of the twin-screw extruder is obtained, along with the shear rate. An experimental investigation of the velocity profiles in the translation region of a self-wiping twin-screw extruder, which is often used in practical applications, was carried out using a Laser Doppler Anemometer. The numerically predicted velocity profiles are compared with those from the experiments, yielding fairly close agreement.     

Inhibited transesterification and enhanced fibrillation of TLCP by nano-SiO2 in polycarbonate matrix

Hybrid composites composed of a thermotropic liquid crystalline polymer (TLCP), nano-SiO₂ and polycarbonate (PC) were prepared by melt blending in a twin-screw extruder. Infrared spectroscopy analysis indicated that the transesterification between PC and TLCP molecules during melt blending was significantly reduced in TLCP/PC blends filled with nano-SiO₂, compared to the unfilled TLCP/PC one. Scanning electron microscopy (SEM) observation showed that better compatibility and finer TLCP dispersion were reached in the unfilled blend, which made the fibrillation of TLCP difficult in capillary flow even at high shear rate. In contrast to this, well-developed TLCP fibrils were formed by capillary flow in nano-SiO₂ filled TLCP/PC blends. By increasing the nano-SiO₂ concentration and shear rate, the fibrillation of TLCP was significantly enhanced. Thermodynamically the interfacial tension between these components and dynamically the viscosity ratio of TLCP to PC were used to investigate the mechanism of nano-SiO₂ in inhibiting the transesterification and enhancing the fibrillation of TLCP droplets in these hybrid composites.     

双螺杆挤出过程数值模拟研究进展

在聚合物的双螺杆挤出过程的研究中,采用数值模拟的方法可以克服传统实验方法的局限,可为挤出机的设计加工提供参考。回顾了近年来国内外对双螺杆挤出过程数值模拟的研究成果,介绍了一维数学模型和三维数学模型对挤出过程进行数学描述的优缺点,从双螺杆挤出机内部的流场特性、瞬态混合性能、停留时间分布以及反应挤出等方面综述了相关研究进展,并对双螺杆挤出过程数值模拟的今后发展方向进行了展望。     

Extension-dominated improved dispersive mixing in single-screw extrusion. Part 2: Comparative analysis with twin-screw extruder

In Part 1 of this work, the possibility of improving single-screw extruders (SSE) better dispersive mixer was explored by harnessing extensional flows provided by the hyperbolic contracting–diverging channels of extensional mixing elements (EME). Addition of the EME to the pin screw generated enhanced breakup for polymer blends and nanocomposite systems without significant penalty in flow rate. In Part 2, experiments are performed on immiscible polymer blends (low-viscosity ratio and high-viscosity ratio) and nanocomposites on both SSE and twin-screw extruder (TSE) with the same rotation speed and throughput. Morphological results show tremendous improvement in dispersive mixing capability of SSE when equipped with EME that are mainly comparable to conventional TSE that is, with kneading blocks as mixing sections, although not as good as TSEs equipped with EMEs. Mechanical results also show enhanced modulus when EME is used in SSE operations.     

Study on Extrusion Characteristics of the Tri-Screw Extruder

A novel kind of extruding machinery is proposed—a tri-screw extruder (TRISE), in which three intermeshed screws are arranged in the three corners of a triangle; three meshing regions and a center zone also comprise the special construction. The flow rate and the pressure-generating ability of the melt in the thread-zone flow field of the tri-screw extruder, especially the pumping formed by the action of taking in and sending out melt in the unique center zone, are also described. The results of simulation and experiments clearly show that the tri-screw extruder has stronger conveying capacity. The shear frequency of material in the tri-screw extruder is higher than that in the twin-screw extruder, which means that filler could be loaded to a much higher point in the TRISE than in the twin-screw. Results from the TRISE also show that energy consumption of the TRISE is lower than that of the twin-screw extruder.     

啮合同向双螺杆挤出机中组合螺杆性能的数值研究（Ⅰ）瞬态流场分析

采用聚合物流动分析软件POLYFLOW,数值模拟了聚合物熔体在组合式啮合同向双螺杆挤出机ZSK60的组合螺杆中的三维等温流动。在计算所得速度场和压力场的基础上,全面分析并讨论了由不同厚度和不同错列角的捏合块元件组成的组合螺杆的流场分布规律;研究了组合螺杆的输送性能和挤出稳定性;并分别采用平均剪切速率、平均特征剪切应力以及平均拉伸流动指数等瞬态混合指数表征了组合螺杆的瞬态混合特性。此外还考察了两种不同流变性质的聚合物熔体在组合螺杆中的瞬态流场分布规律。所得结论可为双螺杆挤出的数值模拟研究提供一定的方法指导,并为其工程实践提供一定的理论指导。     

Theoretical and experimental study of the flow of a molten polymer in a micro-compounder

Micro-compounders are more and more used to characterize and optimize the formulations and the flow conditions of complex materials, with very low quantities, around a few grams. These machines are composed of a small-size conical twin-screw extruder, coupled with a recirculating channel, in which the material can be processed during a fixed time and a certain number of cycles, before being purged. However, the precise flow conditions inside these machines are not well known, what makes an optimal interpretation of the results difficult. Therefore, in this paper, a theoretical model based on continuum mechanics is proposed to calculate the flow in the recirculating mode. An experimental study on a well-chosen polymer is carried out to define the influences of the main processing parameters (screw speed, mass of material, barrel temperature) and to validate the model. Despite the simplicity of the theoretical approach, the calculated results are in satisfactory agreement with the experiments.     

Development of polymer blend morphology during compounding in a twin-screw extruder. Part III: Experimental procedure and preliminary results

Currently, selection of screw configurations as well as the operating conditions for compounding polymer blends with desired morphology in a co-rotating twinscrew extruder is an art based on experience. In this paper a quenching section of a twin-screw extruder is described. The section may replace any segment of the extruder barrel. It allows, on the one hand, a regular operation of the machine, and on the other, a rapid quenching and removal of blend specimens for morphology analysis from any place along the extruder barrel and at any time of the blending. The experimental observation of development during compounding of polymer blends enables verification and improvement of the theoretical model, aimed at predicting and controlling the size and polydispersity of the minor phase. Development of the predictive model for blend morphology will provide a valuable guide to the polymer processing industry. The preliminary data were collected using polystyrene/high density polyethylene (PS/HDPE) blends at low concentration of the dispersed phase, 5 wt% of either PS or HDPE. It was observed that the viscosity ratio, blend composition, screw configuration, temperature, throughput, and screw speed significantly influence the blend morphology.     

高分散混合元件设计及混合性能的研究

根据啮合同向双螺杆挤出机的啮合原理,设计了一种高分散混合双螺杆元件。运用Polyflow有限元分析软件对该双螺杆元件的3种螺杆构型的流场进行了模拟分析,并且对这3种螺杆构型进行了实验研究。研究表明,错列角为150°的元件的分散混合性能最好,其次是错列角为30°的元件,错列角为90°的元件的分散混合性能最差。     

三螺杆挤出机端面二维流场混沌混合拉格朗日拟序结构分析

三螺杆挤出机是一种新型的聚合物流体加工设备,其独有的中心区呈现出几何结构和受力状态的周期性变化,混合机理非常复杂。区别于传统的线性混合分析,从拉格朗日体系的新视角对三螺杆挤出机混沌混合进行拉格朗日拟序结构分析,利用有限时间Lyapunov指数（FTLE）、拉格朗日拟序结构（LCS）,结合Poincaré截面和粒子可视化技术研究三螺杆挤出机二维流场的流体输运和混沌混合机理,讨论了中心区动态结构特性对FTLE和LCS分布的影响,并与单螺杆挤出机和双螺杆挤出机进行了对比分析。结果表明,LCS将三螺杆挤出机流域划分为近螺杆区、远螺杆区和中心区3个具有不同运动特性的区域,扭结是连接近螺杆区、远螺杆区和中心区物质交换的桥梁。随着混合时间的增加,扭结的弯曲和折叠程度逐渐增大,增强了3个区域的物质交换,强化了三螺杆流场的混沌混合。三螺杆挤出机啮合区附近存在3个双曲固定点,混合能力较好。Poincaré截面中椭圆周期点的出现说明在流域中心有非混沌区存在,因此三螺杆挤出机的中心区混合能力相对较弱。     

基于ANSYS软件的双螺杆挤出机的计算机模拟与分析

介绍了应用ANSYS软件对常用的啮合型同向旋转双螺杆挤出机挤压加工过程进行计算机模拟分析的方法、过程和主要结论;同时介绍了其他常用流体软件对双螺杆挤出机模拟分析的应用情况。分析表明:用ANSYS软件可以对双螺杆挤出机的螺纹流道、捏合块进行压力场、速度场、流量及回流、剪切速率、剪应力和混合效果等计算机模拟分析分,析结果与实验结果基本一致。     

Solid transportation in the feeding zone of intermeshing co-rotating twin-screw extruders

A mathematical model was proposed for the characteristics of solid transportation in the feeding zone of an intermeshing co-rotating twin screw extruder. The model was based on the observations made from a “transparent” extruder. The analysis considered optimal solid conveyed with maximum throughput rate, i.e., when the upper and lower intermeshing zones, and the two sides of the screws were all partially filled with solid resin to an extent that a slight increase in the solid filling would immediately cause blocking of the solid transportation. Because of these starve-fed characteristics, the conventional approach for analysing solid feeding used in single-screw extruders was inadequate for twin-screw extruders. This paper also suggests a solution for the mathematical expressions describing the stress and velocity fields in the solid feeding zone of a twin-screw extruder. Finally, the predicted values are compared with our experimental findings.     

双螺杆挤出机与机头间过渡体中的流场分析

构建了多个双螺杆挤出机与机头之间过渡体的模型,以Carreau模型作为本构方程,利用POLYFLOW软件,对不同过渡体模型的三维等温流场进行了数值模拟,并运用后处理软件Fieldview,对不同过渡体模型流道的压力场、速度场和黏度场等进行了分析比较。研究结果为过渡体结构的优化提供了理论参考依据。