Die swell ratio of polystyrene melt from an electro‐magnetized capillary die in an extrusion rheometer: effects of barrel diameter,shear rate and die temperature

A constant shear‐rate extrusion rheometer with an electro‐magnetized capillary die was utilized to investigate die swell behavior and flow properties of a polystyrene melt as the application of an electro‐magnetic field to the capillary die was relatively novel in polymer processing. The test conditions such as magnetic flux density, barrel diameter, extrusion rate and die temperature were studied. The results suggest that the maximum swelling of the polystyrene melt with application of the electro‐magnetic field could be enhanced up to 2.6 times (260%) whereas that without the electro‐magnetic field was 1.9 times (190%). The barrel diameter of 30 mm was found to be a critical value in the case of the die swell ratio and flow properties of the polystyrene melt were significantly affected by the magnetic flux density. This involved the number and angle of magnetic flux lines around the barrel part. Under the electro‐magnetic field, there were two mechanical forces influencing the die swell ratio and the flow properties; magnetic torque and shearing force. The die swell at wall shear rates less than 11.2 sec^?1 was caused by the magnetic torque, whereas at higher wall shear rates it was dependent on the shearing force. For a given magnetic flux density, the maximum increase in the die swell ratio as a result of the magnetic torque was calculated to be approximately 20%. Increasing the die temperature from 180 to 200°C reduced the overall die swell ratio and suppressed the effect of the magnetic flux density. Copyright © 2004 John Wiley & Sons, Ltd.     

Extrudate swell behavior of PS and LLDPE melts in a dual die with mixed circular/slit flow channels in an extrusion rheometer

Extrudate swell behaviors of polystyrene (PS) and linear low‐density polyethylene (LLDPE) melts in a dual channel die, having mixed circular/slit flow channels, in a constant shear rate rheometer were examined. The extrudate swell ratio for PS melt was observed to be higher than that for LLDPE melt for all cases, this being associated with the differences in molecular structures that could be described in terms of power law indexes and secondary flows near the die entrance. In single channel die, the extrudate swell of both PS and LLDPE melts in circular flow channel die was greater than that in slit flow channel, whereas, in dual channel die the slit channel exhibited a higher extrudate swell ratio, the results being explained by revealing the flow patterns of the melt in the barrel and die of the rheometer. It was found that the dimensionless size of the vortex flows near the entrance, and the extent of disentanglement of molecular chains on entering the die were the important factors for the differences in the extrudate swell ratios of the melts at the die exit influenced by the die designs used. Copyright © 2003 John Wiley & Sons, Ltd.     

Melt extrudate swell behavior of graphene nano-platelets filled-polypropylene composites

The extrudate swell ratios of polypropylene (PP) composite melts filled with graphene nano-platelets (GNPs) were measured using a capillary rheometer within a temperature range of 180–230 °C and apparent shear rate varying from 100 to 4000 s⁻¹ in order to identify the effects of the filler content and test conditions on the melt die-swell behavior. It was found that the values of the extrudate swell ratio of the composites increased with increasing apparent shear rate, with the correlation between them obeying a power law relationship, while the values of the extrudate swell ratio decreased almost linearly with rise in temperature. The values of the melt extrudate swell ratio increased approximately linearly with increasing shear stress, and decreased roughly linearly with an increase of the GNP weight fraction. In addition, the extrudate swell mechanisms are discussed from the observation of the fracture surface of the extrudate using scanning electronic microscopy. This study provides a basis for further development of graphene reinforced polymer composites with desirable mechanical performance and good damage resistance.     

Melt rheology and morphology of thermoplastic elastomers from polyethylene/nitrile‐rubber blends: The effect of blend ratio,reactive compatibilization,and dynamic vulcanization

A study of the melt‐rheological behavior of thermoplastic elastomers from high‐density polyethylene and acrylonitrile butadiene rubber (NBR) blends was carried out in a capillary rheometer. The effect of the blend ratio and shear rate on the melt viscosity reveals that the viscosity decreases with the shear rate but increases with NBR content. Compatibilization by maleic anhydride modified polyethylene has no significant effect on the blend viscosity, but a finer dispersion of the rubber is obtained, as is evident from scanning electron micrographs. The melt‐elasticity parameters, such as the die swell, principal normal stress difference, recoverable shear strain, and elastic shear modulus of the blends, were also evaluated. The effect of annealing on the morphology of the extrudate reveals that annealing in the extruder barrel results in the coalescence of rubber particles in the case of the incompatible blends, whereas the tendency toward agglomeration is somewhat suppressed in the compatibilized blends. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1104–1122, 2000     

Dynamic Theory of Die Swell for Entangled Polymeric Liquids in Tube Extrusion: Correlations of Total and Ultimate Extrudate Swell Effects to Growth Time,Shear Stress and Aspect Ratio Under the Free States

The dynamic theory of die swell deduced in a previous paper was extensively applied to study the xtrudate swelling behaviors of two entangled polymeric liquids (HDPE and PBD) in a simple shear flow at steady shear stress. The mechanism and dynamics for the recoils and the recoveries of viscoelastic strains in the extrudate were investigated under the free recovery and dynamic states. It was found that in the course of recovery the free recoil and the growth of die swell in the extrudate may be divided into two recovery regions (instantaneous and delayed regions) and three growth stages (instantaneous, delayed, and ultimate extrudate swelling stages). The free recoil and the extrudate swelling behaviors may be expressed as a function of shear stress. The correlations of instantaneous, delayed, total and ultimate extrudate swell effects to the molecular parameters and the operational variables in the simple shear flow at steady shear stress were derived from the dynamic theory of die swell. Also, two sets of new universal equations on the total extrudate swelling effect (TESE) and ultimate extrudate swelling effect (UESE) were deduced. The first is the universal equation of the logarithmic correlation between the TESE and the growth time under the free and dynamic states; the second is the universal equation of the logarithmic correlation between the UESE and the operational variables under the free and equilibrium states. The first equation was verified by experimental data of PBD with different molecular weights at different operational variables. The second equation was verified by experimental data of HDPE at two temperatures and different operational variables. An excellent agreement result was obtained. The excellent agreement shows that the two universal equations can be used directly to predict the correlations of the TESE and UESE to the growth time, the molecular parameters, and the operational variables under the dynamic and equilibrium states.     

The melt elastic behavior of polypropylene/glass bead composites in capillary flow

The melt extrudate swell and entry pressure losses are important characteristics of elastic properties during die extrusion of polymeric fluids. They are usually expressed with die-swell ratio (B) and entry pressure drop (ΔP_o). In the present paper, the die-swell behavior and entrance pressure drop of a polypropylene (PP) filled with A-glass beads were investigated by using a Rosand capillary rheometer to identify the effects of the filler contents and extrusion rate on the elastic behavior of the sample melts. The experiments were carried out under the conditions with an apparent shear rate range of 50–10⁴ s⁻¹ and a temperature of 190 °C. The results showed that B increased nonlinearly with increasing shear rate at the wall (γ_w), and increased linearly with the increase of shear stress at the wall (τ_w). With the increase of the volume fraction of the fillers B decreased nonlinearly. Similarly, the entry pressure drop increased linearly with the increase of τ_w, whereas the influence of the filler concentration on ΔP_o was insignificant in this case. Furthermore, B increased as a linear function of ΔP_o, and extension stress (σ_e) increased nonlinearly with increasing γ_w.     

Flow behaviour of gas-containing LDPE/i-PP melts

An experimental study was conducted to investigate the rheological behaviour and extrudate swell of polyolefin blends based on two grades of low-density polyethylene (LDPE) and an isotactic polypropylene (i-PP). Blending was carried out on a twin-screw extruder “Brabender” at different composition ratios in the temperature range from 140 to 190°C. The LDPE/i-PP blends mixed with 0.5 wt.% blowing agent were extruded by means of “Brabender” extrusiograph at melt temperature of 200°C and different extrusion rates. The influence of composition content on the viscosity and extrudate swell was considered. The foam structure and morphology are discussed in terms of shear rate, molecular characteristics and composition content. The presence of layered structure was observed: an outer smectic layer and an inner partially crystalline layer. The thickness of smectic layer and size of spherulites were determined.     

聚合物熔体挤出胀大的三维数值模拟

采用粘弹性PTT模型对聚合物熔体的矩形口模挤出胀大进行了三维等温数值模拟,得出了不同条件下的口模外流动速度和挤出胀大率沿挤出方向的分布规律.模拟时利用罚函数有限元法和把动量方程转化成椭圆类方程的去耦算法以降低模拟对计算机内存的要求和增加计算收敛的稳定性,采用用路线法对挤出胀大自由表面进行更新迭代.模拟结果表明:We数越大,则挤出胀大率越大,而且对于矩形口模挤出而言,高度方向的挤出胀大率比宽度方向的挤出胀大率大.     

聚合物挤出过程中的数值模拟技术

介绍了计算流体力学中常用的数值计算方法,并从螺杆挤出过程、口模的设计以及挤出胀大等方面综述了数值模拟技术在聚合物挤出过程中的应用,最后针对聚合物挤出过程数值模拟发展的方向作了简要论述。     

Dynamic Theory of Die Swell for Entangled Polymeric Liquids in Tube Extrusions: New Set of Equations for the Growth and Ultimate Extrudate Swelling Ratios under the Free States

A new dynamic theory of die swell for entangled polymeric liquids in a steady simple shear °ow is proposed which can be used to predict the correlation of the time-dependent and time-independent extrudate swelling behaviors to the molecular parameters of polymers and the operational variables. The theory is based on the O-W-F constitutive equation and the free recovery from Poioeuille flow with different ratios. Experimentsshow that the magnitudes of the simple shear in the steady simple shear flow may be resolved into the free recoil resulting from the recoverable elastic strains and the viscous heating resulting from the unrecoverable viscoelastic strains. For distinguishing the recoil from the viscous heating, a partition function and twoexponential fractions of conformation for the recoil and the viscous heating were defined. Thus the instantaneous, delayed and ultimate recoverable strain, and recoil in the free recovery were correlated to the partition function, the fraction of recoverable conformation, the molecular parameters, and the operational variables. Also the dynamics of the growth equation on the delayed viscoelastic strain and the delayed recoil in freestate were deduced. After introducing the condition of uniform two dimensional extensions, the definition ofswell ratio and the operational variables into the above correlation expressions and growth equations, then the correlations of the delayed extrudate swelling effect and the ultimate extrudate swelling effects to the molecular parameters and the operational variables were derived. Finally, two new sets of equations on the growth variables and ultimate extrudate swelling ratios under the dynamic and equilibrium states were also deduced from this dynamic theory of die swell. The first set of equations on the ultimate extrudate swelling ratio under the free and equilibrium states was verified by HDPE experimental data at two temperatures and different operational variables. The second set of equations on the growth extrudate swelling ratios under free and dynamic states was verified by PBD experimental data with different molecular weights and different operational variables. An excellent agreement is obtained, which shows that the two sets of equations for the growth and ultimate extrudate swelling ratios can be used directly to predict the correlation of extrudate swelling ratios to the molecular parameters and the operational variables.     

Rheological characterization of the die swell phenomenon of rubber compounds

The die swell phenomenon of rubber compounds in capillary experiments with various ratios of length to diameter of capillaries is investigated. This knowledge is important for the design of injection heads for the extrusion of rubber profiles. The die swell of viscoelastic rubber compounds depends on the geometry of the capillary dies, on the melt temperature and on the shear strain rate. One empirical relationship will consider all these dependencies. Usage of this equation and identification of only one new material parameter enables the comparison and assessment of the die swell of different materials, independently of the corresponding geometry of the capillary die used. Furthermore, the influence of melt temperature, molecular structure and extrusion process on the die swell can be identified. The investigation was performed with various rubber compounds as well as rubber blends used in industry, mainly EPDM and carbon black in different compositions.     

RHEOLOGICAL PROPERTIES OF LIQUID CRYSTALLINE COPOLY (ρ-HYDR0XYBENZ0ATE/BISPHENOL A TEREPHTHALATE)

Various aspects of the rheological behaviour of liquid crystalline copolyesters, i.e.,samples of copoly (p-hydroxybenzoate / bisphenol A terephthalate), were explored by usingInstron capillary rheometer. The experimental results indicated that the apparent viscositywas affected significantly by shear rate, melt temperature and p-hydroxybenzoate unit con-tent. The flow activation energies △E_η are in the range of 205.1 to 74.5 kJ/mol, dependingon the shear rate of 10-1000 s~(-1), at temperature 568-603K. These copolyesters exhibit ayield phenomenon in the shear flow, and the values of yield stress decrease with increasingtemperature. It is quite unusual that the extrudate of the copolyester shows the smallerswelling ratio even than unity at the lower temperature and lower shear rates.     

Modeling of particle‐dispersed melting mechanism and its application in corotating twin‐screw extrusion

Particle‐dispersed melting is a complex but important melting mechanism in the corotating twin‐screw extruder. In this study, the complex multi‐particle‐dispersed system was simplified into a single‐particle melting model. The finite‐difference method was introduced to solve this problem. The simulation results show that the melting of a particle may involve two steps: the heating stage and melting stage. The heating time and melting time depend on solid concentration, initial melt and solid temperature, and shear rate. Calculations indicate that high solid concentration and solid temperature, low melt temperature and shear rate will result in a more uniform temperature distribution after polymer melting. The model offers valuable information for designing the melting zone in a corotating twin‐screw extruder, especially at high screw speed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2461–2468, 2001     

Fiber spinning from the nematic melt. II. Effect of thermal history on spinning of the copolyester of polyethylene terephthalate and p-oxybenzoate

Fibers were spun from the nematic phase of the copolymer of polyethylene terephthalate having 60 mol % of p-oxybenzoate units. A capillary rheometer was used for spinning with a shear rate at the wall of 6.4 sec^?1, and capillary (length/diameter) ratio of 14.1. The spinning temperature was varied from 250° to 300°C and, at each temperature, the spin-draw ratio was examined as a variable. Spinning was performed under two conditions. When spinning from the melt without preheating, the initial modulus of the fibers increased with spin-draw ratio and increased with increasing spinning temperature for a fixed spin-draw ratio. In the second case, the melt was preheated and then cooled to the desired temperature before spinning the fibers. The preheating temperature was 280°C for spinning at 250°C, and 300°C for spinning at 280°C. Preheating increased the fiber modulus to the value obtained by spinning at the preheating temperature. A reduction of the viscosity due to the melting of poly(p-hydroxybenzoic acid) (PHB) crystallites produces better orientation and higher modulus. However, with increasing spin-draw ratio, the modulus of the preheated fibers decreased to the values expected for the spinning temperature. This decrease in modulus is due to recrystallization of PHB in the threadline.     

Computer‐Aided Optimization of the Extrusion Process of Automobile Rubber Seal

In this work, the extrusion process of a kind of π‐shape automobile rubber seal was considered using computer‐aided simulation technology. The extrusion flow was assumed to be isothermal and steady, and the finite element method was used to analyze the extrusion process. It was found that the velocity profile was quite uneven near the die exit when a straight die, developed strictly according to the desirable product dimension, was used and the local distortion of the extrudate was fairly prominent when compared with the die geometry. We adjusted the structure of the die and predicted the extrudate's swell by the computer simulation in advance. Simulation results confirmed that the distortion of the seal was greatly suppressed if a short enlarged inflow part was added to the upstream of the original straight die. Then, the extrusion experiment, using the newly designed die, was performed under practical conditions and the swell of the rubber seal was reduced to be within the range of acceptable tolerance. The profiles of the acceptable rubber seals were also well predicted by the computer simulation. Finally, the influences of the take‐up imposed on the end of extrudate and flow rate on the final seal shape were also investigated numerically.     

Effect of Interfacial Failure on the Viscosity of High-density Polyethylene

The effect of a processing agent (Dynamar) on the viscosity and surface properties of high-density polyethylene (HDPE) has been studied. A capillary rheometer was used to measure the viscosity of HDPE compounds containing various concentrations of Dynamar as a function of time at constant apparent shear rates. The shear rates used are 250 and 500 sec⁻¹. The addition of a small amount of Dynamar leads to a marked reduction in viscosity. The viscosity decreases dramatically initially, then levels off to an equilibrium. The rate of the viscosity reduction and the equilibrium viscosity value depend upon the Dynamar concentration and the shear rate. This phenomenon can be explained by the migration of Dynamar from the bulk to the interface of HDPE melt and die wall, resulting in the formation of a lubrication layer. X-ray photoelectron spectroscopy and scanning secondary ion mass spectrometry analyses of the extrudates from a slit die reveal a low concentration of Dynamar at the surface. Adhesive failure at the Dynamar and HPDE interface is attributed to a reduction in viscosity. © 1997 John Wiley & Sons, Ltd.     

Capillary extrusion of polypropylene/high-density polyethylene immiscible blends as studied by rheo-particle image velocimetry

The capillary extrusion of polypropylene (PP) and high-density polyethylene (HDPE) immiscible blends was studied in this work by rheo-particle image velocimetry (Rheo-PIV). The PP/HDPE blends were prepared by single screw extrusion and extruded through a transparent capillary die at a temperature of 200 °C and concentrations of 80/20, 60/40, 40/60 and 20/80 wt%, respectively. PIV measurements described accurately the flow behavior of PP/HDPE blends and revealed continuous velocity profiles in the die, without macroscopic phase separation, for all the blends in the resolution range of the PIV technique. The flow behavior of all the blends was shear-thinning (power-law) type and their viscosities laid in between the values corresponding to the neat polymers and increased in an exponential way along with the concentration of the highest viscosity component in the blend (HDPE). Also, it was found that the extruded blends acquired a stratified morphology and that HDPE mitigates extrudate distortions in PP, meanwhile PP eliminates slip and flow instabilities in HDPE by migrating to the region of highest shear stresses in the die. Migration of PP to the capillary wall was corroborated by Raman spectroscopy measurements on the periphery of solid extrudates. Finally, via calculations of the density of the molten blends under flow using the velocity profiles in the die, we show that the homopolymers are compatible in the molten state and follow a simple inverse relation for their density, and an exponential one for their viscosity.     

Experimental investigation of the concept of molecular migration within sheared polystyrene

Several important aspects of the flow in polymer melts through capillaries remain unexplored. This paper examines experimentally one such effect associated with the radial shear-stress gradient in capillaries. During capillary melt flow of a polymer with a wide molecular weight distribution, migration of the large molecules away from the region of highest shear stress, i.e., at the capillary wall, has been predicted but only modestly investigated. This effect has the potential to produce a molecular weight spectrum over the cross section of extruded polymer. Studies of distribution in shear were conducted on a well-characterized wide-distribution polystyrene (M?_w = 234,000). An Instron Rheometer equipped with a long capillary (length/diameter ratio of 66.7) was used to perform the extrusion at temperatures of 160–250°C. A solvent coring procedure was used to dissolve away concentric layers of polymer from the extrudate for molecular weight analyses. The method has been shown to cut clean sections without selective extraction. Values of M?_w, M?_n and M?_w/M?_n were calculated from complete molecular weight distribution data obtained by calibrated gel permeation chromatography. For a wide range of shear rates and temperatures, no evidence for molecular fractionation was observed. Shear degradation of this polymer was found to be small. However, at high shear rates at 250°C, evidence indicating extensive shear-induced thermal degradation was found. No evidence for oxidative degradation at the extrudate surface was found at either low or high shear rates at this temperature.     

Fiber spinning from the nematic melt. VI. Flow instabilities in the 30:70 copolyester of hydroxybenzoic acid and 2-hydroxy-6-naphthoic acid

The rheological behavior and fiber spinning are investigated for the Celanese liquid crystal copolyester 30 mol% p-hydroxybenzoic acid and 70 mol% 2-hydroxy-6-naphthoic acid (designated as 30HBA/70HNA) with inherent viscosity 7.8 dL/g. Shear thinning viscosity, and yield stress are observed at low shear stress, which probably results from the existence of crystallites in the melt. The crystal-nematic melting point of the copolymer, as measured by differential scanning calorimetry, is around 309°C. Extrudates are collected at four different temperatures ranging from 315 to 345°C. Melt fracture and die swell are observed above 335°C at low shear stress. A wide-angle x-ray diffraction (WAXS) study of an annealed sample indicates that the abnormal phenomenon may be due to crystallites arising from blocky units of HNA. Fiber spinning is performed at high shear rate at 325 and 335°C. Flow is stable under these conditions. The spin draw ratio is the ratio of take-up velocity to the velocity of extrudate existing from the capillary. The initial modulus reaches a maximum at a fairly low spin draw ratio. Instron and wide-angle x-ray (WAXS) studies show that the mechanical properties and orientation are poor for the fiber spun near the crystal-nematic melting point. Also, thermal history is found to affect the rheological behavior. Heat treatment offibers, particularly those which are well oriented, brings an improvement of mechanical properties.     

Polyetherether ketone/polyarylethersulfone blends: Thermal and compatibility aspects

The compatibility behavior of polyetherether ketone (PEEK) with poly(ether sulfone) (PES) has been reexamined using differential scanning calorimetry (DSC), scanning electron microscopy (SEM), and extrudate swell measurements. The blends were prepared by both melt‐blending and solution‐blending techniques. The phase behavior of blends is strongly affected by the blending technique used. Blends prepared by solution‐blending are compatible in the entire composition range on the basis of the single composition‐dependent glass transitions and exhibit lower critical solution temperature (LCST) behavior. LCST was near 340 °C around which the crystalline melting point of PEEK exists. Near LCST melting‐induced movement of molecular chains disturbs the initial homogeneous state of the solution blends and leads to a phase‐separated state that is thermodynamically more stable in the absence of strong specific interactions between the homopolymers. Contrary to the solution‐blended samples, melt‐blended samples were in the phase‐separated state even at a lower processing temperature of 300 °C. Two glass transitions corresponding to a PEEK‐rich and a PES‐rich phase were found for all compositions. From the measured glass transition of phase‐separated blends, weight fractions of PES and PEEK dissolved in each phase were determined using the Fox equation. Compatibility is greater in the PEEK‐rich compositions than in the PES‐rich compositions. PEEK dissolves more in PES‐rich phases than does PES in the PEEK‐rich phase. Variation of the specific heat increment (ΔC_p) at the glass transition with composition also supports these inferences. Solution‐blended samples, quenched from 380 °C, also indicated similar behavior but were slightly more compatible. The aforementioned results are consistent with those inferred from SEM studies and extrudate swell measurements that show a greater compatibility in PEEK‐rich compositions than in PES‐rich compositions. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1407–1424, 2002