Linear and nonlinear melt rheology and extrudate swell of acrylonitrile‐butadiene‐styrene and organoclay‐filled acrylonitrile‐butadiene‐styrene nanocomposite

Melt viscoelastic behavior and the die swell of Acrylonitrile‐Butadiene‐Styrene (ABS) and ABS/clay nanocomposites varying in organoclay loading were studied. A pronounced low‐frequency nonterminal behavior exhibited in linear viscoelastic experiments along with an apparent yield stress in transient startup flow tests suggested the existence of a network type, because of interconnection of rubber particles in ABS matrix. From the results of linear and nonlinear viscoelastic measurements, it was found that the incorporation of organoclay can lead to the formation of an additional network formed between organoclay tactoids that caused reduced temperature dependency of linear viscoelastic properties of the nanocomposite samples compared with ABS matrix. The swelling behavior of samples was interpreted using the results of stress relaxation experiments after cessation of steady shear flow. The great reduction in the die swell of nanocomposite samples could be explained in terms of great surface area and anisometric nature of organoclay tactoids and/or platelets, which promote energy consumption and less energy to be stored in chains. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

Experimental studies on radial extrudate swell and velocity profiles of flowing PS melt in an electro‐magnetized die of an extrusion rheometer

This article investigates the radial extrudate swell and velocity profiles of polystyrene melt in a capillary die of a constant shear‐rate extrusion rheometer, using a parallel coextrusion technique. An electro‐magnetized capillary die was used to monitor the changes in the radial extrudate swell profiles of the melt, which is relatively novel in polymer processing. The magnetic flux density applied to the capillary die was varied in a parallel direction to the melt flow, and all tests were performed under the critical condition at which sharkskin and melt fracture did not occur in the normal die. The experimental results suggest that the overall extrudate swell for all shear rates increased with increasing magnetic flux density to a maximum value and then decreased at higher densities. The maximum swelling peak of the melt appeared to shift to higher magnetic flux density, and the value of the maximum swell decreased with increasing wall shear rate and die temperature. The effect of magnetic torque on the extrudate swell ratio of PS melt was more pronounced when extruding the melt at low shear rates and low die temperatures. For radial extrudate swell and velocity profiles, the radial swell ratio for a given shear rate decreased with increasing r/R position. There were two regions where the changes in the extrudate swell ratio across the die diameter were obvious with changing magnetic torque and shear rate, one around the duct center and the other around r/R of 0.65–0.85. The changes in the extrudate swell profiles across the die diameter were associated with, and can be explained using, the melt velocity profiles generated during the flow. In summary, the changes in the overall extrudate swell ratio of PS melt in a capillary die were influenced more by the swelling of the melt around the center of the die. Polym. Eng. Sci. 44:2298–2307, 2004. © 2004 Society of Plastics Engineers.     

Effect of molecular structure on extrudate swell behavior for different thermoplastic melts in an electro‐magnetized die

The extrudate swell ratio of five different thermoplastic melts flowing in a constant shear rate rheometer having a capillary die with and without application of magnetic field was studied. The effects of the magnetic flux direction and density, die temperature, and wall shear rate on the extrudate swell and flow properties were investigated. The experimental results suggested that an increasing wall shear rate increased the swelling ratio for the polystyrene (PS), LLDPE, and PVC melts, but the opposite effect was observed for the ABS and PC melts. The extrudate swell ratio for the PS, ABS, PC, and LLDPE melts decreased with increasing die temperature, the effect being reversed for the PVC melt. Thermoplastic melts having high benzene content in the side‐chain and exhibiting anisotropic character were apparently affected by the magnetic field, the extrudate swell ratio increasing with magnetic flux density. The effect of the magnetic field on the extrudate swell ratio decreased in the order of PS → ABS → PC. The extrudate swell ratio for the co‐parallel magnetic field system was slightly higher than that for the counter‐parallel magnetic field system at a high magnetic flux density. POLYM. ENG. SCI., 47:270–280, 2007. © 2007 Society of Plastics Engineers.     

马鞍型异型材挤出成型过程三维等温粘弹性的数值模拟

基于PTT粘弹性本构模型,通过马鞍型异型材挤出成型过程的全三维稳态等温有限元数值模拟,系统研究了聚合物粘弹性流变性能参数和成型工艺参数对异型材口模挤出成型过程的影响规律,并揭示了其影响机理.研究结果表明,聚合物异型材口模挤出离模膨胀是由口模出口处的二次流动引起,离模膨胀比随着口模出口处的二次流动强度增加而增大.聚合物异型材口模挤出离模膨胀随着进口流量和聚合物熔体松弛时间的增加而增加,而随着聚合物熔体材料常数和粘度比的增大而减小.     

L形异型材共挤胀大及变形的三维非等温数值模拟

采用PTT本构方程,应用Arrhenius方程来描述温度对黏度的影响,建立了L形双层共挤模型,通过有限元方法分析了聚丙烯（PP）和聚苯乙烯（PS）熔体的三维非等温黏弹流动过程,对比分析了2种材料在不同组合情况下口模出口面的速度场、剪切速率场以及共挤出胀大和变形情况。结果表明,L形分层共挤的胀大和变形不仅与2种熔体黏度差异有关,还与口模截面形状有关;黏度较低的PP会向黏度较高的PS一侧偏转,且PP有包覆PS的趋势;黏度较低的PP位于L形内侧时共挤出胀大和变形程度大于其位于外侧时,且两熔体黏度差异越大,两方案的共挤出胀大和变形程度的差异越大。     

聚合物熔体矩形流道挤出胀大的数值模拟

运用Picard迭代格式的有限元方法,采用Wagner积分型本构方程对黏弹流体挤出胀大进行三维模拟分析。每次迭代根据新的自由面边界位置重新划分网格,由前一次迭代得到的速度场,算出单元高斯点流线,沿流线积分计算应力,把应力作为拟体力,建立非线性方程组迭代格式。对不同宽度和长度的矩形流道的挤出胀大进行模拟计算,分析了流道宽度和长度对胀大率的影响,结果表明,随着宽厚比的增加,厚度胀大率随之增加,随着流道长度的增加,胀大率逐渐下降。并把结果与二维狭缝流道的数值模拟和实验结果相比较, 结果表明,用该方法对黏弹流体挤出胀大流动进行三维模拟是可行的和准确的。     

Numerical investigation of spinneret geometric effect on spinning dynamics of dry‐jet wet‐spinning of cellulose/[BMIM]Cl solution

In this study, the effect of spinneret geometry, including the entrance angle α of the entrance channel, the length L_s, and the diameter D₀ of the exit channel, on the spinning dynamics of dry‐jet wet‐spinning of cellulose/1‐butyl‐3‐methylimidazolium chloride ([BMIM]Cl) solution was simulated by using finite element method. Based on the mathematical model of dry‐jet wet‐spinning established in our previous work (Xia et al., Cellulose 2015, 22, 1963) the radial and axial profiles of velocity, pressure, and shear rate in the spinneret and the profiles of diameter, temperature, and tensile stress in the air‐gap region were obtained. From the simulated profiles, the effect of spinneret geometric parameters on the flow behavior and the pressure drop of polymer solution in the spinneret and the die‐swell ratio near the spinneret was discussed. The entrance angle α of the entrance channel mainly influences the flow behavior of polymer solution in the spinneret and the die‐swell effect near the spinneret. As the decrease of the entrance angle α of the entrance channel, the vortices in the spinneret could be removed and the die‐swell ratio decreases. The increase of the length L_s of the exit channel results in the increase of pressure drop in the spinneret and the decrease of the die‐swell ratio. It is also found that the increase of the diameter D₀ of the exit channel reduces the flow velocity of polymer solution and decreases the pressure drop in the spinneret at a constant mass flow rate. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43962.     

熔体挤出速度对共挤吹塑型坯离模膨胀影响的数值模拟

基于三维非等温黏弹性熔体多相分层流动有限元数值模拟技术,模拟研究了熔体挤出速度对多层共挤吹塑成型环坯离模膨胀和初始温度场的影响规律,揭示了型坯离模膨胀的产生机理。结果表明,多层共挤吹塑成型环坯离模膨胀是由熔体的二次流动诱发而产生,与熔体流出机头进入自由膨胀段的二次流动强度成正比,而其二次流动强度随着熔体挤出速度的增大而增强,因而导致环坯离模膨胀随着熔体挤出速度的增加而增大;多层共挤吹塑成型熔体的二次流动强度与其第二法向应力差成正比关联关系,这与Debbaut的试验研究结论完全吻合,表明二次流动是由第二法向应力差驱动而产生。     

Numerical simulation of entry and exit flows in slit dies

A general-purpose finite element program has been used to simulate the flow of Newtonian, power-law, and viscoelastic fluids in the entry and exit regions of a slit die. It was found that shear-thinning increases the entrance correction while it decreases the exit correction. Shear-thinning reduces the size of the small corner vortex that forms in the entry flow of a Newtonian fluid. The swelling ratio had a value of 1.196 for Newtonian fluids and decreased as the value of the power-law index decreased. Viscoelastic calculations were performed using the Criminale-Ericksen-Filbey (CEF) constitutive equation. Convergence of the iterative scheme was unattainable for Deborah numbers above 1.0. The results showed a decrease of the entrance correction and an increase of the exit correction with elasticity. Extrudate swell first decreased slightly and further increased with the Deborah number.     

聚合物多层共挤成型离模膨胀过程的三维黏弹性数值模拟

共挤成型中,聚合物黏弹特性与过程参数波动的耦合作用会产生波动的离模膨胀,使得根据共挤制品的形状设计相应的共挤定型口模在工程上仍是一项技术挑战。基于这一技术问题,通过建立的稳态有限元数值算法,系统研究了过程参数和黏弹性流变性能参数对共挤成型离模膨胀的影响规律和机理。研究结果表明,多层共挤口模芯壳层熔体离模膨胀是由熔体的二次流动引起,主要取决于芯壳层熔体二次流动的方向与强度。熔体二次流动的方向与第二法向应力差的正负号有关,而熔体二次流动的强度则与第二法向应力差大小呈正比。芯层熔体的离模膨胀与口模出口和混合区进口处芯层熔体向外的二次流动强度呈正比,而壳层熔体的离模膨胀取决于壳层熔体内外界面向外的二次流动的相对强度。研究还表明芯、壳层熔体及口模整体的离模膨胀随着壳层熔体黏度的增大而增加,而随着壳层熔体进口流量的增大而减小。     

Rheological behavior of highly filled ethylene propylene diene rubber compounds

The rheological behavior of highly filled ethylene propylene diene rubber (EPDM) compounds was studied with respect to the effect of curative system, grafted rubber, shear rate, temperature and die swell using a Monsanto Processability Tester (MPT) to gain an understanding of the molecular parameters that control the surface finish. All systems show pseudoplastic behavior. At a particular shear rate, shear viscosity increases with blend ratio. The dependence of flow behavior on extrusion velocity indicates a surface effect. The extrudate die swell and maximum recoverable deformation are related by a linear relationship, which is independent of sulfur/accelerator ratio, extrusion temperature and shear rates and blend ratio. The principal normal stress difference increases nonlinearly with shear stress. Activation energy decreases with shear rate in most cases. The faster relaxing system produces extrudate of better surface quality.     

Numerical simulation of blow molding—Viscoelastic flow analysis of parison formation

The simulation of the parison formation process in blow molding has been studied. The flow field was divided into two regions, namely, the extrudate swell region near the die lip and the parison formation region after the exit swell. In the swell region, we predicted the swelling ratio and residual stress distribution for high Weissenberg numbers for steady planar well using the 1-mode Giesekus model. In the parison formation region, the flow is assumed to be an unsteady unaxial elongational flow including drawdown and recoverable swell and is modeled using the 10-mode Giesekus model. We calculated the time course of parison length and thickness distribution, and compare the calculation results of parison length with experimental data. It was found that the predicted values agreed rather well with the experimental values. The calculation results could especially predict the shrink-back, which is the phenomenon where the parison length becomes shorter after the cessation of extrusion, and it was found tat this was caused by the recoverable swell of the parison, which depends on the tensile stress generation in the die. Various flow rates and die geometries were studied and confirmed the reliability and usefulness of the method.     

Modeling contraction flows and swell of polymer melts extruded from dies of various lengths

This article describes isothermal contraction flows and extrudate swell, using our recent model for fast (high Deborah number) contraction flows of polymers melts. The model analyzes the polymer flow in several regions as one continuous process. This approach makes possible to evaluate the extrudate swell as a result of complex contraction polymer flow in dies of various length. Using the asymptotic matching conditions for the change in flow type at the die exit allowed us to calculate the swelling profile for extrudate in the flow direction. The present calculations performed using a multi-mode viscoelastic constitutive equation of differential type, are compared with the experimental/direct numerical data including basic rheological tests. The presented complex model for contraction flow and swelling consists of no fitting parameter and is applicable for calculations using any viscoelastic constitutive equation. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Viscoelastic breakup in a high velocity airstream

Viscoelastic fluids were injected into a high velocity airstream (200 m/s) to investigate how the addition of small polymer quantities to fluids significantly increase the resultant disseminated drop size. For each liquid tested several hundred resultant drops were sampled and measured using an automated image analyzer. The resultant mass median diameter (MMD) for a viscoelastic fluid was an order of magnitude larger than a comparable viscous Newtonian fluid. A relaxation time measured from a die swell experiment correlates the dissemination results suggesting, an elongational rather than shear breakup mechanism.     

发射药药料离模膨胀和流动均匀性模拟及在模具设计中的应用

为了分析挤出成型过程中模具结构参数对七孔硝基胍发射药离模膨胀率及流动均匀性的影响规律,采用计算流体力学方法,对挤出成型过程进行模拟计算,讨论了模具各结构参数重要性的主次关系;对七孔发射药制备模具进行了结构优化,并进行了实验验证。结果表明,模具收缩角对膨胀率和药料出口速度均匀性的影响最大,压缩段高度次之,成型段长度的影响最小。模具优化后流道出口端速度分布均匀性提高36.53%,表明该模拟计算的可靠性与实用性。     

A method for approximate prediction of extrudate swell

The extrudate swell problem is modeled as the stratified flow of two Newtonian isothermal fluids with differing viscosities. If the viscosity of the thin outer layer is the greater of the two, then enhanced swelling relative to the case of equal viscosity is observed. By suitable selection of the the viscosity ratio, this model can be used to represent thermal, shear-thinning, and elastic effects in extrusion. The stratified flow problem is solved using an efficient boundary element method. The model then provides a means of studying and predicting complex geometrical effects in profile extrusion without the burden of a full viscoelastic solution, which may yield a practical aid to the die design process.     

Quantitative Characterization of Viscoelastic Properties and their Relationship During Extrusion Flow of Polymer Melts

The viscoelastic behavior, such as end pressure losses, die swell, and normal stress difference, is a very important rheological phenomenon of viscoelastic fluids in channel flow. Therefore, understanding the elastic behavior and the mechanisms is quite necessary and meaningful for polymer rheology. Extrusion is a usual processing way in polymer industry. The viscoelastic behavior and the factors affecting it during die extrusion flow of polymeric melts are discussed, and the relationships among these viscoelastic properties, such as entry pressure drop (ΔP _en), exit pressure drop (ΔP _ex), die-swell ratio (B), and the first normal stress difference (N ₁), are analyzed in this article. The results showed that there are some simple and available expressions for describing the relationships among these viscoelastic property parameters and the values of these parameters can be evaluated. Furthermore, the recent progresses in the quantitative expressions for prediction of these viscoelastic property parameters and their correlations are briefly reviewed.     

Experimental studies on extrudate swell behavior of PS and LLDPE melts in single and dual capillary dies

Extrudate swell behavior of polystyrene (PS) and linear low‐density polyethylene (LLDPE) melts was investigated using a constant shear rate capillary rheometer. Two capillary dies with different design configurations were used, one being a single flow channel and the other being a dual flow channel. A number of extrudate swell related parameters were examined, and used to explain the discrepancies in the extrudate swell results obtained from the single and dual flow channel dies, the parameters including output rate and output rate ratio, power law index, wall shear rate, wall shear stress, melt residence time, pressure drop induced temperature rise, flow channel position relative to the barrel centerline, and the flow patterns. It was found in this work that the power law index (n value) was the main parameter to determine the output rate ratio and the extrudate swell between the large and small holes for the dual flow channel die: the greater the n value the lower the output rate ratio and thus decreased extrudate swell ratio. The differences in the extrudate swell ratio and flow properties for PS and LLDPE melts resulted from the output rate ratio and the molecular chain structure, respectively. The extrudate swell was observed to increase with wall shear rate. The discrepancies in the extrudate swell results from single and dual dies for a given shear rate were caused by differences in the flow patterns in the barrel and die, and the change in the melt velocities flowing from the barrel and in the die to the die exit. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1713–1722, 2003     

A parallel coextrusion technique for simultaneous measurements of radial die swell and velocity profiles of a polymer melt in a capillary rheometer

This article proposes a new experimental technique to simultaneously measure radial die swell and velocity profiles of polystyrene melt flowing in the capillary die of a constant shear rate rheometer. The proposed technique was based on parallel coextrusion of colored melt‐layers into uncolored melt‐stream from the barrel into and out of the capillary die. The size (thickness) ratio of the generated melt layers flowing in and out of the die was monitored to produce the extrudate swell ratio for any given radial position across the die diameter. The radial velocity profiles of the melt were measured by introducing relatively light and small particles into the melt layers, and the times taken for the particles to travel for a given distance were measured. The proposed experimental technique was found to be both very simple and useful for the simultaneous and accurate measurement of radial die swell and velocity profiles of highly viscous fluids in an extrusion process. The variations in radial die swell profiles were explained in terms of changes in melt velocity, shear rate, and residence time at radial positions across the die. The radial die swell and velocity profiles for PS melt determined experimentally in this work were accurate to 92.2% and 90.8%, respectively. The overall die swell ratio of the melt ranged from 1.25 to 1.38. The overall die swell ratio was found to increase with increasing piston speed (shear rate). The radial extrudate swell profiles could not be reasoned by the shear rate change, but were closely linked with the development of the velocity profiles of the melt in the die. The die swell ratio was high at the center (～1.9) and low (～0.9) near the die wall. The die swell ratio at the center of the die reduced slightly as the piston speed was increased. Polym. Eng. Sci. 44:1960–1969, 2004. © 2004 Society of Plastics Engineers.     

An experimental study of the relationship between rheological properties and spinnability in the dry spinning of cellulose acetate–acetone solutions

The elastic and viscous properties of five cellulose acetate–acetone solutions, varying from 19.9% to 28.6% solids concentration, are independently determined at 60°C by capillary rheometry techniques. The viscous flow behavior of the solutions is determined over four decades of shear rate. The Bagley analysis is used to determine the entrance pressure drop and the true shear stress at various shear rates. A plot of the entrance pressure drop at the maximum experimental shear rate versus solution concentration undergoes a rapid increase in slope at 24.0% solids concentration, the significance of which is discussed with respect to the development of an elastically deformable chain entanglement network. The die swell behavior of the solutions at 60°C is determined on a commercial-type dry-spinning apparatus. When the die swell ratio is plotted versus volumetric flow rate, all five solutions are found to possess a characteristic curve with a distinct maximum. Photographs illustrating the variation of die swell with volumetric flow rate are shown. Die swell measurements are also shown to correlate well with entrance pressure drop measurements. The degree of spinnability of each cellulose acetate–acetone solution at 60°C is found by determining first godet speed at which one or more threads break abruptly. Spinnability is found to go through a maximum at 24.0% solids concentration. The rheological measurements and spinnability results are discussed through the aid of a single rheological parameter incorporating both elastic and viscous solution responses.