Rheology of polymer melts in high shear rate

Little is known of the rheology of polymer melts in the high shear rate up to 10⁶ s^?1 or more. A specially designed high-shear-rate rheometer was developed, by which the rheology of polymer melts for shear rates up to 10⁸ s^?1 can be investigated. Two non-Newtonian regions and a transition or the second Newtonian region were observed in the wide range of shear rates up to 10⁷ s^?1. The observed flow curves for various polymer melts are classified into three typical patterns. One is the flow curve typically shown of high-density polyethylene in which a clear second Newtonian region appears after the first non-Newtonian region. The second is the typical flow curve of polystyrene in which a “transition region” appears instead of the second non-Newtonian region. The third is the flow curve shown of acrylonitrile-styrene copolymer, which exhibits behavior between the two types. A generalized flow curve is proposed to explain the observed flow behaviors of various polymers over a wide range of shear rates. The flow behavior in high shear rate results from high orientation and scission of polymer molecules.     

Capillary and slit flow behavior of concentrated solutions of a rod-like polymer

This paper is concerned with the flow behavior of isotropic solutions of the rod-like polymer, poly(p-phenyleneterephthalamide) (PPT), in 100 percent sulfuric acid. Studies include entry flow visualization in a slit die and solution fracture, and die swell in capillaries and a slit die. It was observed that solutions of PPT exhibit nearly negligible die swell, a slip-stick type of fracture that disappears at high shear rates, and radial entry flow patterns similar to Newtonian fluids. Fracture was associated with the plateau in the shear stress vs shear rate curve. Because values of the wall shear stress (τ_w.) obtained from capillary measurements were in good agreement with those obtained from a cone-and-plate rheometer and values of the loss modulus (G″) obtained from small-strain dynamic oscillatory measurements, it is believed that the rheological properties lead to the flow instability. These results are in agreement with the predictions of a recent theory by Doi and Edwards for concentrated solutions of rod-like molecules. Data are also presented for a flexible chain polyamide, nylon 6,6, in 100 percent H₂SO₄ for the purpose of comparing the flow characteristics of rigid and flexible chain polymers.     

压出过程中混炼胶锥口型流动的研究

本文讨论了聚合物熔体在圆锥口型中的流动问题。应用改进的二阶流体的本构方程,建立起描述熔体入口流动中流速分布、剪切应力分布和法向应力差分布的数学模型,在此基础上,对熔体椎入口流动进行了数值模拟,并以混炼胶为试样,作了相应的实验研究。     

Influence of inertia and viscoelasticity in entry flows through an abrupt annular contraction

A numerical simulation of entry flows in an annular die has been undertaken for Newtonian and power-law fluids as well as viscoelastic fluids that exhibit normal stresses in shear flow. Experimentally measured normal stress and viscosity data are included in a simple rheological model. The influence of inertia and viscoelasticity are examined separately as functions of the Reynolds (Re) and Weissenberg (Ws) numbers. It is found that inertia decreases the size of the corner vortices in the reservoir corners which tend to increase rapidly with elasticity level in the absence of inertia. The combined effect of inertia and elastic forces is to first increase the vortex size followed by a decrease at higher Re numbers. The numberical simulations are in qualitative agreement with experimental studies available in the literature.     

Simulation of Vortex growth in planar entry flow of a viscoelastic fluid

A numerical simulation of entry flow in a slit die has been undertaken for a fluid that is Newtonian in shear but exhibits normal stresses (Boger fluid). Experimentally measured normal stress and viscosity data are included in a simple rheological model. Flow patterns reveal the existence of vortices in the reservoir corners. Vortex size and intensity increase rapidly with elasticity level.     

AN EXPERIMENTAL STUDY OF HOLE PRESSURES FOR POLYMER MELTS

A slit die apparatus is used to measure hole pressures for two polymer melts.Hole pressures up to 110kPa are determined and shear rates reach 200 s~(-1).Viscosity data obtained from the same apparatus agreewell with the values obtained from a cone-and-plate rheometer or a capillary rheometer.The hole pressuresobtained by direct measurements are all positive and increase with increasing shear stress.The values of the firstnormal stress difference obtained from hole pressures according to the Higashitani-Pritchard(HP)theory are ofthe right order of magnitude,but appear to be on the low side when compared with values obtained from a cone-and-plate rheometer or with values obtained via exit pressures.It is believed that the hole pressure is a measureof fluid elasticity,but cannot yield accurate values of the first normal stress difference according to the HP theory.     

What is the role of “pressure” in the use of capillary and slit flows to determine the shear‐rate dependent viscosity of a viscoelastic fluid?

The purpose of this review article is to clear the confusion created by some investigators, who erroneously thought that the pressure transducers mounted on the wall of a capillary or slit die measured a quantity that could meaningfully be called “pressure,” accurately stated “indeterminate isotropic contribution to the total stress,” and then reported on the effect of “pressure” on the shear‐rate dependent viscosity of a viscoelastic fluid. On the other hand, reference to such a quantity is not needed to calculate the wall shear stress and thus shear viscosity in fully developed flow of incompressible, viscoelastic polymer melts in a capillary or slit die; instead only information on the gradient of the total wall normal stress is needed. Further, it is pointed out that much of the literature discussing “pressure shift factor” to describe the effect of “pressure” on the viscosity of polymer melts in flow through a capillary or slit die is based on an erroneous belief that there exists a physically meaningful isotropic “pressure” that can be measured. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

Capillary viscometry: A complete analysis including pressure and viscous heating effects

Capillary viscometers have been used extensively, because of their simplicity and reliability, to measure the viscosity of fluids over a wide range of shear rates. However, in capillary flow, the shear rate is not uniform throughout the capillary, a pressure gradient is established in the direction of flow, and the temperature of the fluid is nonuniform due to viscous dissipation. In the present work, a general, simple and practical method is proposed for correcting for the effects of pressure variation and viscous dissipation in determining the viscosity of polymer melts at high pressures. The method essentially involves the estimation of temperature, pressure, shear rate, and shear stress under a variety of experimental conditions at a predetermined point in the capillary. As such, it may be considered as a generalized extension of the classical Rabinowitsch-Mooney method for estimating true viscosity in capillary flow.     

黏弹性表面活性剂溶液中颗粒沉降特性研究

黏弹性表面活性剂溶液悬浮颗粒流广泛存在于自然界和工业生产中,黏弹性表面活性剂溶液的非线性流变性质及应力松弛效应对其中颗粒沉降有着显著影响。采用FENE-P和Giesekus黏弹性本构模型对表面活性剂溶液中颗粒沉降特性进行研究,发现两种本构模型不仅表现出剪切稀化,而且出现拉伸硬化。颗粒在沉降初期的不稳定性主要是由溶液自身的弹性效应引起,弹性效应越强,颗粒沉降速度不稳定性越强,而剪切稀化效应会减弱颗粒沉降速度的不稳定。颗粒沉降过程中在其尾部形成一个“负尾迹”,随着剪切稀化和拉伸硬化效应增强,负尾迹区增大,弹性效应增加,负尾迹增强,负尾迹区流体内部反向速度分布导致的表面活性剂溶液中微观胶束的拉伸断裂和重构可能是引起颗粒沉降速度持续波动的原因。     

Effect of die temperature on the flow of polymer melts. Part II: Extrudate swell

The effect of die wall temperature on the extrudate swell of polymer melts flowing through dies with single and dual circular channels was studied. Extrudate swell was measured at constant flow rates using an Instron capillary rheometer with a modified die section. It was found that under isothermal conditions, extrudate swell plotted against the average wall shear stress gave rise to a temperature independent correlation for polystyrene. Under non-isothermal conditions, such a correlation did not exist, which might be due to the change of wall shear stress in the axial direction. The extrudate swell in the non-isothermal cases can be better correlated with the wall shear stress at die exit. For the two-hole die, changes of die wall temperature varied both the flow rate ratio and the extru date swell ratio. The latter is, however, much less sensitive to the die wall temperature than the former.     

The flow of polymer melts through the clearance over a barrier flight in extruders

The flow of polymer melts through the clearance over a barrier flight in extruders involves high, rapidly changing shear rates. Polymer melts, being viscoelastic, are expected to exhibit a high elasticity when they flow through the clearance, so the flow through the clearance may not be predictable or stable. The flow through the clearance over a barrier flight was investigated using a shear refining (SR) module connected to an extruder. Three polymers with different melt properties were tested: branched low density polyethylene (BLDPE), high‐density polyethylene (HDPE), and polystyrene (PS). The measured drag flow rate through the clearance was found to be equal to the prediction for a purely viscous fluid, which gives a linear velocity profile in the clearance. At the threshold rotor speed of the SR module whereupon the predicted drag flow rate through the clearance is the same as the extruder output rate, the melt pressures at the inlet and the outlet of the SR module were nearly equal and stable. Below the threshold rotor speed, the inlet pressure was higher than the outlet pressure. Above the threshold rotor speed, the inlet pressure was nearly zero and the outlet pressure fluctuated. The magnitude of the pressure fluctuation increased with increasing rotor speed and decreased with increasing melt temperature. HDPE, which had a higher melt elasticity, showed more pressure fluctuation than BLDPE and PS. The pressure fluctuation probably results from the flow instability through the clearance caused by the melt elasticity.     

Flow of polymer melts through a well-lubricated,conical die

The concept of gross melt fracture of polymer melts as a tensile failure in the die entry region was supported in this work by the observation of a dramatic increase in the melt fracture of poly-ethylene extrudates upon lubricating thoroughly a conical, converging extrusion die. This flow, according to an analysis using a Fromm viscoelastic model, was found capable of producing axial tensile stresses in the extrudate in excess of 10⁶ dynes/cm² at the very moderate exit shear rate (no lubricant) of 100 sec^?1. A calculated stress level of about 5 × 10⁶ dynes/cm² caused sharp, deep transverse cuts to appear in the extrudate. The ability of tensile stresses of this magnitude to fracture melts was demonstrated by separate experiments run in simple tension on molten rods, using similar rates and total deformations. A large qualitative difference between high and low-density polyethylene in both these experiments was noted.     

A mechanism for extrusion instabilities in polymer melts

A mechanism for explaining some of the instabilities observed during the extrusion of polymer melts is further explored. This is based on the combination of non-monotonic slip and elasticity, which permits the existence of periodic solutions in viscometric flows. The time-dependent, incompressible, one-dimensional plane Poiseuille flow of an Oldroyd-B fluid with slip along the wall is studied using a non-monotonic slip equation relating the shear stress to the velocity at the wall. The stability of the steady-state solutions to one-dimensional perturbations at fixed volumetric flow rateis analyzed by means of a linear stability analysis and finite element calculations. Self-sustained periodic oscillations of the pressure gradient are obtained when an unstable steady-state is perturbed, in direct analogy with experimental observations.     

The numerical simulation of boger fluids: A viscometric approximation approach

A general-purpose finite element program has been used to simulate the flow of nonshear-thinning, highly elastic polymer solutions (Boger fluids). In particular, the creeping flow through an abrupt 4:1 circular and planar contraction is studied, as well as the flow at the exit of a capillary die for the determination of extrudate swell. Experimentally measured normal stress and viscosity data are included in a simple rheological model, based on the viscometric simplification of the CEF constitutive equation. Vortex size and intensity in the die entry and extrudate swell at the die exit increase rapidly, with elasticity level, in general agreement with experimental findings. It is shown that despite the limitations of the model, the viscometric approximation can be used to study the effect of normal stresses in cases where a main flow direction can unambiguously be defined. In die exit Flows, it can also provide an upper limit for the determination of extrudate swell, while Tanner's theory of elastic recovery provides the lower limit.     

Experimental investigation of flow induced molecular weight fractionation during extrusion of HDPE polymer melts

In this work, two different HDPEs with virtually identical number, M_n, and weight, M_w, average molecular weights were investigated from rheological as well as die drool phenomenon point of view. It has been revealed that long-chain branching, low polymer melt elasticity and shear viscosity significantly reduce die drool phenomenon at the die exit region. It has been concluded that die drool phenomenon of HDPE polymer melts can be explained by the flow induced molecular weight fractionation.     

The steady flow shear modulus of polymer melts

Relaxation times of polyethylene melts have been measured by Aloisio, Matsuoka, and Maxwell. One implication regarding their observations is that the elastic properties of polymer melts must be time-dependent. In particular, the steady-flow shear modulus depends on the strain rate. Some interpretations of data in the literature have been based on concepts in rubber elasticity where the steady-flow modulus is an equilibrium value, independent of strain rate. We have used Pao's theory for viscoelastic flow together with measurements of relaxation times to discuss the strain rate dependence of the steady-flow shear modulus of melts. The existence of a strain rate-dependent shear modulus leads naturally to a nonlinear relation between shear stress and recoverable shear strain. The conclusions regarding the molecular weight dependence of the modulus also differ from interpretations based on rubber elasticity.     

Observations on the Melt Rheology of Thermotropic Aromatic Polyesters

Rheological measurements were made on a variety of substantially aromatic copolyesters. All of them differ from flexible chain polymers in having unusually long relaxation times, estimated from shear rate dependence of viscosity and from melt elasticity. This behaviour is not accounted for by an unusual molecular weight distribution (MWD); limited measurements indicate that the MWD is somewhat narrower than that of conventional condensation polymers. Numerous anomalous flow phenomena have been observed, though not necessarily with all samples. These include the occurrence of a yield stress, large secondary shear stress maximum after start-up of steady shear, transient negative normal stress, and shear-thickening of melt viscosity. Although the melts are highly elastic, they do not exhibit swelling after extrusion from a capillary. The melt rheology is often very sensitive to temperature and dependent upon thermal history. In one material this dependence has been linked to the destruction and/or growth of crystallites formed from blocks of one comonomer.     

Kinematics of the stick-slip capillary flow of high-density polyethylene

A study of the kinematics of the stick-slip capillary flow of high-density polyethylene has been carried out in this work by using particle image velocimetry (PIV). The experiments covered a wide range of shear rates and the velocity maps and profiles across the die were obtained for the different regimes of the discontinuous flow curve. In the low shear rate region, the melt exhibited shear thinning without slip. In the unstable stick-slip regime, an alternating behavior between full adhesion and slip was observed, whereas both, the maximum velocity and the slip velocity of the melt, changed continuously during pressure oscillations. In addition, non-homogenous slip, characterized by regions with and without slip at the die wall, was occasionally observed during the oscillations. In contrast to the general assumption, the flow in the high shear rate region was found to be unstable, and characterized by high frequency pressure oscillations. A steep rise of the slip velocity took place from the onset of the stick-slip regime and reached values higher than 70% of the maximum velocity for the profiles in the high shear rate branch. However, a true plug flow was never observed due to shear thinning of the melt. Finally, a direct proof of the Mooney hypothesis to account for slip in polymer melts is given on the basis of the comparison of velocity profiles measured in the low and high shear branch.     

Predicting melt flow instability from a criterion based on the behavior of polymer solutions

A criterion, based on the behavior of polymer solutions, is developed and applied for the prediction of the onset of flow anomalies observed at the capillary entrance for polymer melts. It is shown that a direct correspondence exists between the flow anomalies observed for polymer solutions and polymer melts. The onset of these anomalies can be correlated with a critical Weissenberg number which is consistent with the equality of the shear wave velocity and friction velocity. This critical condition can be employed to derive expressions useful for predicting the critical recoverable shear and critical shear stress for melt fracture.