Theoretical Analysis on Flow of Polymer Melts in Screw Die

Abstract

Flow of polymer melt in screw dies is theoretically analyzed by the broken section method with the uniformity of the extrudates. An isothermal, laminar and steady state power law fluid is assumed. The analysis is discussed in two parts, i.e., screw flow and die slit flow. A way of computer calculation by means of a method of iteration is presented by considering volume balance between screw flow and slit flow.

An ideal screw die is one in which pressure distribution is constant along the screw axis, i.e., the shape of the die slit is constant along the axis and the screw is such that the depth of screw channel decreases almost linearly.     

Investigation of Unsteady Elongational Flow of Polymer Melts

Abstract

A method for estimation of the viscoelastic characteristics of polymer melts in the prestationary elongational flow is given. The experimental data show that at specific strain rates the polymer starts to respond to dynamic deformation as a highly elastic material. The viscoelastic characteristics of the polymer in the prestationary extensional flow can be described by a modified Maxwell equation.     

复合共挤出技术的现状和发展

共挤出技术是当代广泛应用的先进的高聚物复俣共挤出的理论和实验发展以及复合共挤出的技术和设备的发展进行了回顾,从中可以得到共挤出的发展轨迹,从而我们今后的研究方向及研究方法提供依据。     

Planar Entry Converging Flow During Extrusion of Polymer Melts

In this article, a planar entry converging flow during die extrusion of polymeric melts was analyzed and a differential equation of entry converging boundary streamline equation with rheological parameters and channel geometry is established. By applying limit theory, the entry converging boundary streamline equation in the case with different non-Newtonian index (n) was discussed, and the corresponding expressions of entry natural convergent half angle and convergent region length were derived. The entrant flow pattern might be described with the half angle of entry natural convergence (α₀) and the convergent region length (L _e ) of the melts, and α₀ and L _e were mainly a function of the entry elastic storage deformation energy (e) and n. The values of α₀ and L _e were calculated by means of these simplified expressions. It was found that the estimations of α₀ decrease nonlinearly white L _e increases linearly with an addition of e. Finally, a preliminary verification of the natural converging half angle equation was made. The results showed that the estimations of 2α₀ based on the experiments of a low-density-polyethylene (LDPE) and a high-density-polyethylene (HDPE) were close to the data reported in reference.     

高聚物熔体挤出不稳定流动的研究进展

对近年来国内外关于熔体挤出不稳定流动现象的研究进展进行了介绍。阐述了关于形成鲨鱼皮和压力振荡及其他挤出不稳定流动的相关机理，并总结了抑制挤出不稳定现象所采取的措施。     

聚合物熔体在圆锥口型的挤出胀大方程

在聚合物熔体入口收敛流变中引入纯拉伸流变概念，应用张量理论进行了定量分析，导出了一个描述圆锥口型的挤出胀大方程。研究表明，入口收敛拉伸流变，是取合物熔体产生了强烈的弹性形变，导致了较大的挤出物胀大比。     

Mathematical Description of Deformation of a Dispersed Phase Polymer in Flow of Melts of Polymer Blends

A mathematical model of deformation of a dispersed phase polymer drop in flow of a polymer blend melt from a wide tank into a narrow tank was created using a structurally continuous approach. The model allows calculating deformation of a drop in flow, determining its location, and taking into account the effect of the elasticity of the dispersed phase polymer, ratio of the viscosities of the components, and the hydrodynamic interaction of the drops on their deformability. The system of differential equations obtained satisfactorily describe processes of flow of polymer blend melts in the input zone of the spinning opening: drop size q is a function of the ratio of the viscosities of the initial components, their absolute values, and the volume concentration of dispersed phase; the elasticity of the drop worsens its deformability.     

Nonisothermal Flow of Polymer Solutions and Melts in Channels of Constant Cross Section

Under the assumption that the temperature of a polymer solution or melt is constant over a channel cross section, the nonisothermal flow in various channels of constant longitudinal geometry was investigated in the cases where the polymeric liquid viscosity varies with temperature exponentially or hyperbolically. It was demonstrated that solving the problem of the flow of polymeric liquids under nonisothermal conditions is reduced to solving identical equations for different channels, and the pressure difference in channels and the power consumption are determined from the corresponding isothermal solutions with allowance made for a certain factor, which is constant for different channels.     

在挤出机口模中聚合物不稳定流动的模拟

对挤出机口模流道中高聚物的流动情况进行了分析。引用高聚物黏弹性流体本构方程,建立了高聚物在挤出机机头口模中流动的数学模型。用MathCAD软件对该模型进行了数值模拟,结果表明:机头压力、材料的松弛时间以及口模流道的几何尺寸对高聚物在机头中应力张量的变化影响较大,适当调整口模流道尺寸会有利于高聚物的稳定挤出。     

聚合物熔体的介电性能研究

研究了聚碳酸酯（PC）、低密度聚乙烯（LDPE）两种聚合物熔体的介电性能。结果表明, PC熔体在220~320 ℃范围内,PE-LD熔体在120~300 ℃温度范围内,两种聚合物熔体的介电常数在低频时随频率的增加而显著减小;频率为10 Hz时,PC熔体的介电常数在220~320 ℃范围内随温度的升高而增大,介电常数变化较大,而频率为100~1 000 Hz时,PC熔体的介电常数在此温度范围内随温度的升高变化较小;频率为10 Hz时,PE-LD熔体的介电常数在120~300 ℃范围内随温度的升高表现出先增大后减小,再增大的复杂关系,频率为1 000 Hz时,PE-LD熔体的介电常数受温度的影响较小。     

复合材料夹层结构翼型件的有限元分析

利用有限元方法对一种复合材料夹层结构翼型件在一定压力下的力学性能进行了数值分析。计算结果显示最大变形区域为翼型件右上半部分,最大位移为6．2mm。应力分析表明面板部分受力较小,应力主要集中在右边铝合金下半部分。将计算所得应力值代入TsAi—Wu破坏准则进行校核,结果表明,翼型件在所加载荷下安全,为翼型件的强度设计提供了理论依据。通过真空辅助模压成型工艺试制了若干件翼型件并进行了静力学测试,结果表明,理论计算与试验结果具有较好的一致性。试验完成后对翼型件的内部质量进行了无损检测,结果表明,与拉力试验前相比翼型件内部没有损伤产生。     

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.     

Equal Low-Order Finite Element Simulation of the Planar Contraction Flow for Branched Polymer Melts

The rheological characteristics of branched polymer melts is described by the modified XPP model, which is discretized by inconsistent streamline-upwind method. A finite increment calculus procedure is introduced to reformulate the mass equation and to overcome oscillations of the pressure field. Moreover, the governing equations are discretized and solved by the iterative fractional step algorithm. Thus the equal low-order finite elements for velocity-pressure-stress variables are adopted to calculate the planar contraction viscoelastic flows. The influences of the Weissenberg number and the amount of branched-arms on the rheological behavior of the Pom-Pom molecule are discussed. Results demonstrate good agreement with those given in the literatures.     

振动场对聚合物熔体在异型材挤出口模内的流动影响

利用ANSYS软件对受口模入口处周期性振动的压力驱动的非牛顿幂率聚合物熔体在“Y”型异型材挤出口模内的流动过程进行了三维等温数值模拟。研究了入口压力的振动参数对流场压力和速度的影响情况。结果表明：流场中压力和速度的振动频率与入口压力的振动频率相等，而流场压力和速度的振幅随入口压力振幅的增大或者频率的降低丽增大，亦即低频高幅的振动容易得到较大的振动幅值。研究还表明流场速度的振动滞后于压力，且速度振动的衰减也比压力的衰减慢。     

聚合物熔体延伸粘度的研究方法

聚合物熔体的延伸粘度是影响聚合物熔体流动特性和成型制品性能的重要因素。本文较为系统地介绍了聚合物熔体延伸粘度的理论和实验研究方法,着重介绍了Cogswell、Gibson、Binding和Berstered等人的理论研究工作,为进一步研究熔体的延伸粘度提供思路。     

聚合物熔体在振动场中的流变行为研究

利用自行研制的振动试验装置研究了振动场中聚合物ＨＤＰＥ、ＰＳ熔体在不同压力、温度、频率、振幅条件下的流变行为。试验结果表明,熔体表观粘度随振动频率的增加而降低,但降低的幅度随压力、温度和振幅的不同而不同。     

The Rheology of Wetting By Polymer Melts

Theoretically, the rate of capillary penetration of a polymer melt into a slit, a model for a surface irregularity, has been shown to depend on γcosθ/η) where γ refers to the surface tension of the liquid, η its viscosity and θ a time-dependent contact angle. Analytical expressions relating the depth of penetration with time have been experimentally verified by observations of the penetration of molten polyethylene and poly-(ethylene-vinyl acetate) into aluminum channels. Values of η, calculated from the observed data, agree closely with independent determinations of this material parameter. A theoretical treatment has also been developed which describes the velocity of spreading of a liquid drop over a flat surface. Flow equations for the flow of free films were adapted for this purpose. The spreading velocity is predicted to depend on the product of three factors (1) a scaling factor, (γ/η1R_o), where R_o is the initial radius of curvature, (2) cosθ_∞. (l-cosθ/cosθ_∞) where θ_∞ refers to the equilibrium value of θ, and (3) geometric terms. After demonstrating that a drop of molten polymer may be treated as a spherical cap, the predicted dependence of spreading rate on drop size, cosθ_∞ (nature of the substrate) and the scaling factor was experimentally verified. Some discrepancies noted at long times and high temperatures are discussed.     

一个新的聚合物熔体粘性模型

本文分析了了聚合物熔体于稳态剪切流动中的粘性特性，进而提出一新的四参数粘性模型η＝ηｆ／｛Ｋ「１＋（ｒ／ｒｆ）＾１－ｎ｝。应用毛细管流变仪，考察了几种热塑性树脂的流动性，并对模型进行了初步的验证。     

无定型聚合物熔体的PVT特性

采用带有PVT口模的流变仪测定无定型聚合物熔体在压力0～50 MPa,温度453～563 K时的PVT(压力-体积-温度)特性曲线,分别用基团贡献修正胞腔模型(GCMCM)和胞腔模型对实测的PVT数据进行预测.结果表明:在实验中用基团贡献修正胞腔模型的比容平均预测误差较胞腔模型要大得多,其预测精度要略差于胞腔模型,这说明基团贡献修正胞腔模型的应用具有一定的局限性.同时还计算出了2种模型所对应的特征值,并分析了其特征值存在的共同点和差异的原因.