Effect of die temperature on the flow of polymer melts. Part I: Flow inside the die

The effect of die wall temperature on the flow of polymer melts in circular capillary dies was studied. At constant flow rates, it was found that die wall temperature had a greater effect on the pressure drop than melt temperature. A capillary die with two circular channels with different diameters was designed to simulate the profile extrusion. Changes of wall temperature varied the flow rate ratio between the two channels. An implicit finite difference method was used to simulate the velocity and temperature profiles inside the die. Values predicted by this model matched well with experimental data for both dies.     

Extrudate swell of high density polyethylene. Part III: Extrusion blow molding die geometry effects

Two high density polyethylene resins—801 and 802— are examined with regard to their isothermal, time-dependent, and nonisothermal swelling properties when emerging from two annular and three diverging dies. The short time swelling characteristics of samples 801 and 802 are very important for these dies, resulting in a lower diameter swell for the latter, independent of the die geometry or flow rate. Output variations have much less impact on the swelling behavior than small changes in the geometry of the die mandrel. Accordingly, shear stress and shear rate parameters alone cannot be used to explain the swelling properties of a HDPE resin in the different die geometries. Straight annular dies induce higher diameter swelling than diverging dies.     

Extrudate swell and extrusion pressure loss of polymer melts flowing through rectangular and trapezoidal dies

A theoretical and experimental study of pressure losses and extrudate swell of flow through dies with complex crosssections is presented. The range of utility of models based on one-dimensional shearing on pressure loss-extrusion rate behavior is indicated. A procedure to predict extrudate profiles emerging from complex dies is developed. This is based on consideration of the idea of unconstrained elastic recovery from long dies. The theoretical predictions are contrasted with experiments on polystyrene and polypropylene.     

A method for the measurement of the true die swell of polymer melts

A new device has been designed for the measurement of the die swell of extruded polymer melts. According to the proposed procedure, samples can be collected, annealed, and photographed. The device may be used in conjunction with any capillarytype rheometer. It can accommodate simultaneously as many samples as it is needed. The samples are suspended in a thermostated liquid, carefully selected for each polymer. The liquids must be thermally stable and of proper density and thermodynamic and interfacial properties. The device was used in conjunction with the Instron capillary rheometer, ICR. Three types of polymer were tested: polystyrene (PS), polyethylene (PE), and a semirigid poly(vinyl chloride) formulation (PVC). The swelling of the extrudates was followed for ca. 40 min; the equilibrium dimensions were usually reached within the first 2 min. Parallel with these measurements, the samples were tested in the Weissenberg rheogoniometer (WR) recording both shear and normal stresses. For PS and PE, the flow curves determined in these two rheometers overlapped, while they differed for PVC. The swell ratio, B_exp = D/D₀ (where D and D₀ are the equilibrium diameter of the extrudate and diameter of the capillary, respectively), was converted to recoverable shear strain, s, as follows. First, B_exp and s were determined in ICR and WR, respectively, for a PS sample over wide and overlapping ranges of rate of shear. This experimental dependence was found to follow Tanner's theoretical relation. Consequently, this relation was used to compute s from B_exp for all the other samples. Excellent agreement was observed between the s values calculated from B_exp and s values determined in WR.     

Extrudate swell of high density polyethylene. Part II: Time dependency and effects of cooling and sagging

For two high density polyethylene resins, the isothermal time dependency of extrudate swell has been measured. Very minor differences in the large molecular weight part of the molecular weight distribution, hardly detectable with gel permeation chromatography and low angle laser light scattering techniques, dramatically influence the time dependency of extrudate swell as well as the maximum swell attainable. The presence of larger molecules in sample 802 than in 801 is reflected in a lower short time (after seconds) and a larger long time (after minutes) or maximum extrudate swell value. Extruding the polymers through a capillary die L:D = 30:2 mm into air at ambient temperature allows only the short time swelling behavior to be observed, because cooling and sagging of the strand.     

ABS/中空微珠复合材料挤出流动中的弹性行为

应用熔体流动速率测定仪考察了丙烯腈-丁二烯-苯乙烯三元共聚物（ABS）／中空微珠复合材料的弹性行为。结果表明,在200℃,当剪切应力（τw）小于120kPa时,挤出胀大比（B）随着τw的增大而增大,但增幅减小;当τw大于120kPa时,B增幅增大。在200℃时,B随着剪切速率的增大而增大;随着温度的上升,B增大,两者较好地符合线性关系;在200℃时,B随着填料含量的增加而增大,两者呈较好的二次函数关系。     

Temperature profiles for polymer melts in tube flow. Part II. Conduction and shear heating corrections

A temperature probe system to measure radial temperature profile of polymer flowing in a rod die and a method to systematically correct the conduction and the frictional shear effects were developed. Experimental data obtained on a 1-1/2-inch extruder using a blow molding compound show that both conduction and frictional shear heating effects are significant in melt temperature measurement and that the radial temperature profiles of the melt in the rod die are influenced by the RPM of the screw and the die-wall temperature. The reliability of the temperature data obtained was compared with the solution obtained from the equations of motion and energy. A good agreement between the predicted versus experimental temperature profile exists. For this polymer system, the relationship between local Nusselt number and the velocity parameter could be adequately described with the theory of Van LeeuWen.     

Numerical simulations of annular extrudate swell of polymer melts

Numerical viscoelastic simulations were carried out using a K-BKZ type of separable integral constitutive equation. Both reversible and irreversible models were tried for several types of damping functions to calculate the annular extrudate behavior of high-density polyethylene (HDPE). There are two aims in this study; first, to clarify the properties of these dumping functions, and second, to investigate the influence of rheological characteristics on annular extrudate swell. In these numerical simulations, relaxation spectrum and shear viscosity were fixed, and the other characteristics were varied. The reversional response of the damping function mainly has an effect on the magnitude of the area swell even if the die is straight. The irreversible model expresses the experimental results of annular extrudate swell better than the reversible model. The accurate fitting of N1 by the damping model is important for predicting it. The magnitude of N1 predicted from the Wagner exponential model is lower than that of the PSM model, and the area swell shows the same tendency as N1. A modified PSM model that allows the N1 curve to shift can fit the magnitude of area swell. The relationship between the diameter and thickness of the extrudate depends on N2/N1, and it was estimated by simple linear elasticity of solids. The time dependent viscosity varies with the type of damping function, and it influences the time-dependent swell.     

Extrudate swell of high density polyethylene. Part I: Aspects of molecular structure and rheological characterization methods

Two high density polyethylene (HDPE) resins–samples 801 and 802–both nominally the same material, as they are taken from successive batches of the same commercial grade, are characterized for their molecular structure and rheological properties. Gel permeation chromatography (GPC) and low angle laser light scattering (LALLS) results must be interpreted in combination with rheological data to show the presence of somewhat more high molecular weight material in 802 that in 801. Small amplitude oscillatory shear, steady shear, and capillary shear measurements performed in different laboratories show consistently higher shear viscosity values at low shear rates for sample 802. Extensional viscosity measurements show similar results. The interpretation of rheological data in terms of molecular structure could be complicated by the possible presence of long chain branching (LCB). The zero shear viscosity and discrete relaxation spectrum is estimated for both samples. The small rheological difference between 801 and 802 forms the basic information for understanding their time dependent extrudate swell behavior, as will be described in Part II.     

Elongational flow of polymer melts

A new technique is described whereby the rate of collapse of an air bubble within a molten polymer may be measured without the need for visual observation. The method involves use of a high speed recording dilatometer, From such data it is possible to measure an apparent elongational viscosity of the melt, and such measurements are presented for two polyethylenes (Tennite, a low density PE, and Plaskon, a high density PE), Limitations of the methods are discussed. This is one of a series of papers (1-3) documenting our development of a new experimental technique, and the corresponding mathematical modeling, whereby one may measure the elongational viscosity of polymeric viscoelastic fluids. Previous experimental work was confined to transparent fluids, since the technique depended on high-speed motion picture photography of the collapse of an air bubble within the fluid. In this paper we describe an attempt, largely successful, to develop a new experimental system which permits the study of molten polymers, including opaque fluids. Sample results are presented for both a low and a high density polyethylene.     

聚合物气辅共挤对挤出胀大影响的数值模拟

采用计算流体力学软件建立了二维模型,以低密度聚乙烯和聚苯乙烯为研究对象分析二维模型的有限元.对比了气辅共挤和传统共挤过程中挤出胀大与熔体界面分布,研究了气辅共挤和传统共挤对口模压降、剪切速率分布及剪切应力分布的影响,将气辅共挤、传统共挤时口模压降与挤出胀大率的模拟、实验结果做了对比.结果表明:气辅共挤能有效减小甚至消除...     

Effects of die temperature on extrudate swell in screw extrusion

Extrusion of a hot polymer melt through a cooler die zone substantially increases the extrudate swell of some thermoplastics. This effect was examined for commercial samples of low-density polyethylene, polypropylene, and polystyrene. Two conflicting effects come into play during extrusion of a thermoplastic. Colder melt temperatures promote increased extrudate swell, but the same conditions also facilitate molecular disentanglement and reduced melt elasticity and die swell. Since the extrusion process itself may affect the relation between die swell and melt temperature, laboratory-scale measurements for the design of processes like blow molding are better carried out with small-scale screw extruders than with capillary rheometers. For some applications it may be advantageous to use a polymer whose die swell is particularly responsive or unresponsive to die temperature variations. The procedure described in this article can be used effectively to monitor this characteristic.     

Effect of temperature on polymer migration II: Concentration equation

Polymer migration is a generally well-known phenomenon in a flow field, and it has been verified that the sources of such phenomena are nonhomogeneity of the flow, concentration effects and hydrodynamic interactions between the polymer molecules. In addition, temperature effects were found to be another source of polymer migration. The Langevin equation for a polymer molecule was first derived from single chain dynamics using a kinetic theory for the bead-spring elastic harmonic dumbbell model, as described in part I (reference [1]). In this paper the diffusion equation and concentration profile of the polymer molecules induced by a temperature gradient are obtained from the Fokker-Planck equation. A new differential operator is also introduced to calculate the concentration profile. From the concentration equation obtained in the general flow geometry, we find that in dilute polymer solution there are significant effects on the polymer migration not only due to the nonhomogeneity of the flow field but also due to temperature gradients.     

Effect of acrylic processing aids on PVC die swell

The die swell behavior of PVC melts is a manifestation of melt elasticity and is of considerable commercial as well as fundamental importance. This behavior is a critical issue in extrusion blow molding application where die swell (i.e. parison thickness) needs to be controlled. Advantageously, the addition of high molecular weight acrylic processing aids to PVC provides better die swell control, thus, improving dramatically the processability of PVC. Hence, knowledge of molecular weight variables of such acrylic processing aids is important from both the commercial and rheological point of view. Various acrylic processing aids were prepared by polymerization designed to provide systematic variation of molecular parameters. Molecular weight distribution of the polymers was characterized by GPC, and their die swell behavior in a typical PVC blow molding formulation was determined at 200°C over various range of residence times using different L/D capillary dies. The results are presented showing effects of specific molecular variables.     

熔体层厚对聚合物共挤出胀大的影响

基于流变学理论和Phan-Thien-Tanne本构方程,建立了三维等温黏弹共挤成型流动过程的数值模型。运用有限元方法对数值模型进行了模拟计算,研究了熔体层厚对共挤成型的影响,分析了熔体层厚对挤出胀大率、偏转变形及界面形貌的影响。结果表明:熔体层厚对挤出胀大率和界面形貌的影响较大,随着熔体层厚的增加,挤出胀大率减小;随着共挤出熔体层厚差值的增大,界面形状趋于不稳定;熔体离开口模后产生低黏度熔体向高黏度熔体一侧偏转变形,但变形程度受熔体层厚的影响不大。     

Capillary flow instability of ethylene polymer melts

The capillary flow instability resulting in extrudate distortion has been studied for ethylene polymer melts using a molecular structure approach. It is found that the instability initiates at a critical value of elastic strain energy independent of (average) molecular weight for linear polyethylene. Once the flow breaks down, a slip interface within the melt is formed near the capillary wall, causing an abrupt increase in volumetric throughput. The velocity gradient within the melt remains continuous through the instability, however. Low molecular weight species present in the molecular weight distribution of linear polyethylene tend to suppress slip. Blends of linear and branched polyethylene exhibit instability behavior characteristic of both components throughout the entire range of composition. Results are discussed in terms of specific molecular mechanisms.     

Effect of die wall cooling or heating on extrudate swell

A general purpose finite element program was used to study polymer extrudate swelling. It is shown that viscosity variations due to externally applied cooling or heating have a significant influence on the swelling ratios of axisymmetric and planar extrudates. The effect is more pronounced at high Peclet and Weissenberg numbers. Swelling due to thermal effects and swelling due to viscoelasticity are not additive because of interrelations between the various mechanisms.     

The effect of temperature on the elastic properties of polymer melts

A correlation is developed between the melt elasticity and temperature, the melt elasticity being defined by the normal stress difference. The correlation follows the form of the Arrhenius equation, for the temperature range tested, for high density polyethylene and polypropylene melts. Measurements were taken using the capillary rheometer which is described in detail in the author's earlier publications. The author further presents a correlation between the pressure drop at the entrance of a capillary and the residual pressure at the exit of the capillary (exit pressure). The correlations presented in the paper support the author's earlier contention that the exit pressure is indeed a manifestation of elastic behavior.     

Temperature measurements of polymer melts in the heating barrel during injection molding. Part 2: Three-dimensional temperature distribution in the reservoir

A new method has been developed to measure the three-dimensional temperature distribution of polymer melts in the reservoir of the heating barrel in the dynamic state. The procedure involves the use of a small-sheathed thermocouple in the nozzle of the machine. The tip of the thermocouple can be varied in depth from the surface to the center of the nozzle. The polymer melt of a shot is found to have a three-dimensional temperature distribution dependent on the geometry of the screw and the order of shot. These results reflect clearly the thermal histories of the polymer melt in the channel of the screw during plastication and conveyance, and indicate part of the dynamics of injection molding. Further, these measurements contribute to optimization of the design for the screw and the process conditions.