Superimposed effects in high‐shear‐rate capillary rheology of polystyrene melt

During micro‐injection molding, the polymer melt may undergo a shear rate up to 10⁶ s^?1, at which the rheological behaviors are obviously different from those in conventional molding process. Using both online and commercial rheometers, high‐shear‐rate capillary rheology of polystyrene (PS) melt is analyzed systematically in this work. The accurate end pressure drop and pressure coefficient of viscosity are determined via the enhanced exit pressure technique. Experimental and theoretical investigations are conducted on four significant effects, that is, the dissipative heating, end pressure loss, pressure dependence, and melt compressibility in capillary flow. For the PS melt, which exhibits distinct temperature and pressure dependence of viscosity, both dissipation and end effects become pronounced as the shear rate exceeds 2 × 10⁵ s^?1. From lower to higher shear rates (10³–10⁶ s^?1), the competition between dissipation and pressure effects results in the overestimation to underestimation of Bagley‐corrected pressure drop, and finally the comprehensively corrected viscosity becomes about half of the uncorrected one owing to the enhanced superimposed effects. Moreover, the compressibility shows a minor influence on the shear viscosity. Under the shear rate range investigated, the power‐law relationship is sufficient for describing the corrected viscosity curve of PS melt used. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Capillary flow of low‐density polyethylene

The capillary flow of a commercial low‐density polyethylene (LDPE) melt was studied both experimentally and numerically. The excess pressure drop due to entry (Bagley correction), the compressibility, the effect of pressure on viscosity, and the possible slip effects on the capillary data analysis have been examined. Using a series of capillary dies having different diameters, D, and length‐to‐diameter L/D ratios, a full rheological characterization has been carried out, and the experimental data have been fitted both with a viscous model (Carreau‐Yasuda) and a viscoelastic one (the Kaye—Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko, or K‐BKZ/PSM model). Particular emphasis has been given on the pressure‐dependence of viscosity, with a pressure‐dependent coefficient β_p. For the viscous model, the viscosity is a function of both temperature and pressure. For the viscoelastic K‐BKZ model, the time‐temperature shifting concept has been used for the non‐isothermal calculations, while the time–pressure shifting concept has been used to shift the relaxation moduli for the pressure‐dependence effect. It was found that only the viscoelastic simulations were capable of reproducing the experimental data well, while any viscous modeling always underestimates the pressures, especially at the higher apparent shear rates and L/D ratios. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Start-up pressure transients in a capillary rheometer

The “rise time” required to achieve a steady pressure reading in a capillary rheometer operated at constant piston speed can be very long, up to several hours under certain circumstances. This phenomenon can pose a serious problem in the measurement of melt viscosity, and it would be useful to be able to estimate the rise time in the planning of experiments. Based on experiments involving several types of polyethylene, we found that the rise time increases with L/D and the amount of polymer initially in the reservoir and decreases with diameter and piston speed. When the rise time is short, melt viscoelasticity contributes to the rise time, but when it is long, melt compressibility is the dominant factor. A model was developed for the latter case, and this was found to give an accurate prediction of the rise time, given the viscosity and compressibility. The model can also be used to determine the power-law parameters from the start-up pressure trace, P(t), for a single experiment. Alternatively, if the viscosity is known, the compressibility can be inferred from a single pressure trace.     

Experimental investigation of the rheological behaviors of polypropylene in a capillary flow

The rheological characterization of polymer melts is strongly related to their material properties. In this study, we focused on the rheological behaviors of a polypropylene (PP) melt through a capillary die. With an advanced twin‐bore capillary rheometer with dies measuring 1.0, 0.5, and 0.25 mm in diameter, experiments were performed over a shear‐rate range of 3 × 10² to 5 × 10³ s^?1 at three temperatures, 210, 220, and 230 °C. The results demonstrate that the geometry dependence of the PP viscosity relied on the die diameter and the temperature of the PP melt. The viscosity values of the PP melt in the 0.25‐mm diameter die were higher than were those in the 0.5‐ and 1.0‐mm dies at 220 and 230 °C. However, the viscosity values in all of the tested dies were similar at 210 °C. The tendency for the viscosity to decrease as the temperature of the polymer melt increased weakened in the 0.25‐mm diameter die. As a result, the pressure applied to the PP melt in the 0.25‐mm diameter die increased; this caused a decrease in the free volume between molecules. On the basis of the Barus equation, the contribution of pressure to the changed viscosity in each die at each of the tested temperatures was calculated and was found to be as high as 32.86% in the 0.25‐mm die at 230 °C. Additionally, the effect of the wall slip on the geometry dependence of the PP viscosity in the tested dies was investigated with a modified Mooney method. The values of the slip velocity revealed that wall slip occurred only in the 0.25‐mm die at 210 °C. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43459.     

Modeling of three‐dimensional flow and heat transfer in polystyrene foam extrusion dies

A three‐dimensional mathematical model was developed to investigate the nonisothermal, non‐Newtonian polymer flow through the dies used in the polystyrene foam extrusion process. The model, based on the computational fluid dynamics (CFD) code, Polyflow, allowed for the shear rate and temperature dependence of the shear viscosity of the blowing agent laden polystyrene melt. The model also accounted for viscous heating. The shear viscosity of the polystyrene‐blowing agent mixture was measured experimentally at several temperatures. The model was used to calculate pressure, flow, and temperature distributions in two different dies used for industrial‐scale extrusion of polystyrene foams. The article presents a selection of computed results to illustrate the effect of die design on uniformity of flow at the die exit, the overall pressure drop in the die, relative magnitudes of pressure drop in the land section versus the rest of the die, and temperature distribution in the die. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

A study of the effect of the extrusion variables and screw design on the thermal and rheological characteristics of acetal and nylon 66

A detailed study of the effect of several extrusion variables was made on the rheological and thermal properties of Delrin II acetal homopolymer and Zytel 42 polyamide 66 materials. A 63.5 mm Davis Standard extruder was used to measure the effect of screw design, screw rpm, die and head pressure, and melt temperature on the rheology of acetal and nylon 66 resins. A single stage metering screw was used to determine the effect of screw geometry and viscous heating on the melt viscosity breakdown and the rate of degradation of each polymer. The melt temperature was measured in the melt stream in the channel and correlations are shown between ideal melt temperature predicted from the rheology data and the actual loss of properties of each polymer due to viscous heating. The paper also discusses how to measure the melt temperature accurately in extrusion, and to use it as a key indicator to optimize the extrusion process, and to control the rheology, thermal stability, and the molecular weight of a polymer during processing.     

Viscous dissipation in capillary flow of rigid PVC and PVC degradation

The steady state, non-isothermal behavior of rigid polyvinyl chloride melt, flowing in capillaries of circular cross-section, was investigated by solving, with the aid of a digital computer, the momentum and energy balance equations. It was assumed that the polymer melt can be described by the “Power Law” constitutive equation. The shear rate, temperature and pressure dependent properties of the fluid were obtained experimentally. The effects of the thermal degradation of PVC on its viscosity, were also introduced in the equations of momentum and energy. The velocity, temperature and pressure profiles, obtained for both adiabatic flow and flow through a tube of constant wall temperature, indicate that considerable heating of the melt, due to viscous dissipation, can be achieved at moderate flow rates. Thermal degradation occurs in the capillary under certain conditions of temperature history and residence time of the fluid. The results of this work are in fair agreement with experimental results in this area.     

The effect of viscous heating on the observed temperature dependence of mechanochemical reactions

The temperature dependence of mechanochemical reactions of high polymers is investigated in light of viscous dissipation in the flow field. The viscosity of the polymer melt is assumed to depend exponentially upon temperature, and the power-law model is used to describe the shear stress–shear rate relationship. Using equations previously reported in in the literature for the temperature profile generated in capillary flow, evidence that such an experimental system operates under decidedly nonisothermal conditions is presented. These equations, together with the classical Arrhenius equation for the temperature dependence of chemical reactions, predict that the average reaction rate in a capillary decreases, passes through a minimum, and increases as the capillary wall temperature is increased. Good agreement exists between the temperature at the minimum rate found in this work and that found experimentally for polystyrene, natural rubber, and polyisobutylene.     

Numerical simulation of the post-filling stage in injection molding with a two-phase model

A two-phase model is presented for simulating the post-filling stage of injection molding of amorphous and semicrystalline materials. A finite-element scheme with quadratic shape function for the pressure is proposed. The melt is considered in terms of Hele-Shaw flow for a non-Newtonian fluid using a modified-Cross model with either an Arrhenius-type or WLF-type functional form to describe the viscosity under nonisothermal conditions; the compressible behavior of the polymer is assumed to obey either a double-domain Tait or single-domain Spencer Gilmore equation of state. The interfacial energy balance equation including the latent-heat effect for semicrystalline materials is coupled with the transient energy equation for the solid and melt phases in order to predict the solidified layer and temperature profile. Two well-characterized materials, namely a commercial-grade PP and PS, were used in the present work. Good agreement is obtained between the present simulation and experimental pressure traces from this study and from previous investigation in the literature. The effects of compressibility, viscosity model, and thermal properties upon the predicted pressure field are also considered.     

Transient modeling of viscosity

Capillary and parallel plate rheological characterization was conducted for a low‐density polyethylene. In contrast with conventional rheological analysis, steady conditions were not assumed. Transient data, with time steps between 0.0001 and 0.2 s, were analyzed with a nonlinear, viscoelastic constitutive model in which the relaxation time was modeled as a function of the applied stress. The fit model explained more than 99% of the observed transient variation in the capillary and parallel plate rheometers. The model coefficients for the capillary and parallel plate were compared directly to conventional linear viscoelastic analysis of the same parallel plate data. The results indicate that the described constitutive model closely predicts the observed viscoelastic behavior of the polymer melt tested in the parallel plate rheometer. Furthermore, the results indicate that the relaxation spectrum modeled with the transient analysis of the capillary rheological data correlate closely to the results predicted by the same transient analysis of parallel plate rheological data. The conclusion is that described constitutive modeling describes the viscoelastic behavior in both capillary and parallel plate rheometers. Moreover, the analysis and results suggest that the viscoelastic behavior of the polymer melt is a significant factor during the rheological characterization and the modeling of the transient response should be taken into consideration during rheological analysis to provide high fidelity models. POLYM. ENG. SCI., 57:1110–1118, 2017. © 2017 Society of Plastics Engineers     

Geometrical dependence of viscosity of polymethylmethacrylate melt in capillary flow

The shear viscosity of polymethylmethacrylate (PMMA) melt is particularly investigated by using a twin‐bore capillary rheometer at four temperatures of 210, 225, 240, and 255°C with different capillary dies. Experimental results show that the geometrical dependence of shear viscosity is significantly dependent on melt pressure as well as melt temperature. The measured shear viscosity increases with the decrease of die diameter at lower temperatures (210 and 225°C) but decreases with the decrease of die diameter at higher temperatures (240 and 255°C). Based on the deviation of shear viscosity curves and Mooney method, negative slip velocity is obtained at low temperatures and positive slip velocity is obtained at high temperatures, respectively. Geometrical dependence and pressure sensitivity of shear viscosity as well as temperature effect are emphasized for this viscosity deviation. Moreover, shear viscosity curve at 210°C deviates from the power law model above a critical pressure and then becomes less thinning. Mechanisms of the negative slip velocity at low temperatures are explored through Doolittle viscosity model and Barus equation, in which the pressure drop is used to obtain the pressure coefficient by curve fitting. Dependence of pressure coefficient on melt temperature suggests that the pressure sensitivity of shear viscosity is significantly affected by temperature. Geometrical dependence of shear viscosity can be somewhat weakened by increasing melt temperature. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3384–3394, 2013     

高分子材料动态成型过程中熔体非线性行为的研究

借助流变测量和连续介质理论,不依赖已有的本构关系,对平行叠加正弦振动条件下高分子熔体经毛细管的动态挤出过程进行了理论分析。以低密度聚乙烯(LDPE)为原材料,实验测量LDPE熔体在一定振动频率和振幅下毛细管入口压力、体积流量和挤出胀大的瞬态值,即可得到动态成型过程中高分子熔体剪切应力、剪切速率和表观粘度的变化规律:随振幅和频率的变化,LDPE熔体的表观粘度呈非线性变化趋势;在不同的振幅和频率下动态挤出LDPE熔体,跟稳态挤出时一样,壁面剪切应力与壁面剪切速率也成非线性比例关系。     

Measurements of slip velocity and frictional heating in the capillary extrusion of linear‐low‐density polyethylene with a fluoropolymer processing aid

The slip velocity and frictional or slip heating of linear‐low density polyethylene with a fluoropolymer processing aid in capillary flow were measured by rheo‐particle image velocimetry and thermal imaging. The pure polymer did not show slip before the stick‐slip regime but exhibited strong slip when blended with the processing additive. However, for shear stresses beyond the stick‐slip regime, the pure polymer and the blend exhibited the same flow behavior with slip. The slip velocity increased with the shear stress at two different rates before and after the stick‐slip and the contribution of slip to the total flow rate exhibited a minimum. Significant rises in temperature were measured under slip and no slip conditions, being these much higher than the values predicted by the adiabatic flow assumption. Clear difference was made between viscous and frictional heating before the stick‐slip regime, even though they could not be distinguished from one another at higher stresses. Overall, in the presence of slip, frictional and viscous heating act synergistically producing higher temperature rises in the melt. Finally, in contrast to predictions by numerical simulations of viscous heating, measured velocity profiles did not evidence the heating effects in the shear stress range analyzed in this work. POLYM. ENG. SCI., 56:837–845, 2016. © 2016 Society of Plastics Engineers     

圆管聚合物热流中黏性耗散分析的无网格模拟

以与温度相关的指数定律作为本构方程,应用无网格方法模拟了外表面为恒温时的圆管内具有黏性耗散的聚合物流动热传导问题,给出了离入口不同位置处的温度分布。计算结果表明：根据黏性耗散模型计算的温度比无黏性耗散模型高出64℃,从而说明了黏性耗散在聚合物流动热传导问题中具有举足轻重的作用。并且, 无论是无黏性耗散模型,还是黏性耗散模型,其极限温度与壁面温度有很大的关系,但与入口温度无关。     

The Formula for Apparent Viscosity of Polymer Melt Extruding Through a Capillary Under a Superimposed Vibration

The apparent viscosity of a polymer melt within a capillary was analyzed based on experimental measuring when a sine vibration of small amplitude was superimposed in a parallel manner on the extruding direction of polymer melt. The theoretical model for apparent viscosity of polymer melt under an superimposed vibration was set up independent of any existing constitutive equations. Meanwhile, the calculating steps for previously apparent viscosity were established by making use of novel rheological measurement equipment that was designed by the author. Through collecting and analyzing the instantaneous data of a polymer melt dynamic extruding through a capillary under definite frequency and amplitude of vibration, the apparent viscosity of a polymer melt within a capillary was then calculated.     

Rheological properties of molten polymers. II. Two-phase systems

A study is carried out for characterizing two-phase systems of molten polymers by their viscous and elastic properties. The two-phase systems chosen for study are blends of polystyrene and polypropylene, and blends of polystyrene and high-density polyethylene. For the study, measurements of wall normal stresses are made by use of a capillary melt rheometer described in part I of this series. The concept of the “exit pressure” is used to determine the elastic properties of the two-phase polymer systems. The present study shows anomalous viscous and elastic properties of two-phase systems, which are difficult to predict from knowing the viscous and elastic properties of their individual components. A detailed discussion is given on the state of dispersion of two incompatible polymer systems in the molten state, by presenting pictures of the microstructure of the extrudate samples. The state of dispersion appears to vary depending on the blending ratio, extrusion temperature, melt viscosities of individual components, and blending method.     

A basic experimental study of sandwich injection molding with sequential injection

An experimental study of sandwich injection molding is reported which involves sequential injection of polymer melts with differing melt viscosity into a mold. In isothermal injection molding the relative viscosity of the two melts is the primary variable determining the phase distribution in the mold. Generally the most uniform skin-core structure occurs when the second melt entering the mold has a slightly higher viscosity than the first melt injected. Large viscosity inequalities lead to nonuniform skin thicknesses. The influence of blowing agents and non-uniform temperature fields on the extent of encapsulation is described. Temperature fields are very important especially if the first polymer melt injected has a greater activation energy of viscous flow (or a greater temperature dependence of the viscosity function).     

振动力场下聚合物熔体流变行为的响应与分析 Ⅰ.毛细管压力降和熔体表观粘度

在自行设计的恒速型毛细管动态流变装置上 ,对聚合物熔体进行动态挤出实验。借助已建立的振动力场下聚合物熔体流变行为的表征公式 ,分别计算振动力场下聚合物熔体在毛细管壁处的剪切应力、剪切速率和表观粘度。与稳态挤出时相比 ,引入振动力场后 ,发现毛细管压力降、表观粘度均显著降低 ,且随着振动频率和振幅的改变呈非线性变化趋势 ,作者对此进行了深入分析。     

Rheological equation for polymer melt under the action of vibration

Abstract

The entire extrusion process of a polymer melt within a capillary was analyzed thoroughly when a sinusoidal vibration of small amplitude was superimposed in parallel on the flow direction of the polymer melt. On the basis of rheological measurement, an equation for a polymer melt under parallel vibration, i.e. the apparent viscosity, was obtained. Calculation of the apparent viscosity was established by making use of novel experimental equipment. After collecting and analyzing the instantaneous data of capillary entry pressure, capillary volume flux and their phase difference in a superimposed vibration, the apparent viscosity of low-density polyethylene (LDPE) within a capillary was calculated. Meanwhile, the relationship of shear stress vs. shear rate for a LDPE melt with and without imposed vibration was presented.     

Pressure effects in polymer melt rheology

Wide ranges of pressure and temperature are encountered in polymer processing operations, as, for example, in injection molding. While the temperature dependence of viscosity has been widely studied, the pressure dependence has not. The present work focuses on the measurement of the melt viscosity of polystyrene at high pressures (up to 124 MPa or 18,000 psi) and high shear rates (1–100 s^?1) at 180°C. The apparatus was a capillary rheometer with the downstream chamber being held at a high back pressure by means of a needle valve. The data so obtained were combined with zero shear viscosity data from the literature; and then correlated with a shear-dependent rheological model of the authors, using a shift factor suggested by Utracki (based on the Simha–Somcynsky equation of state). The final correlation calls for making both the elastic modulus and the time constant dependent on pressure, with the modulus being the dominant factor at high shear rates.