Shear and elongational rheology of polyethylenes with different molecular characteristics. II. Elongational rheology

The elongational viscosities of polyethylenes with different molecular characteristics were measured at different Hencky strains and temperatures with a capillary rheometer by the replacement of the capillary cylindrical die with a hyperbolic converging die. The hyperbolic shape of the die established a purely elongational flow field at a constant elongational strain rate throughout the die. The effects of molecular characteristics such as the molecular weight, molecular weight distribution, and long‐chain branching and processing conditions such as the temperature and Hencky strain on the elongational rheology of the polyethylene samples were studied. Good master curves were generated for temperature and Hencky strain shifting and simultaneous shifting with respect to both the temperature and Hencky strain. Both the molecular weight distribution and long‐chain branching seemed to promote strain rate thinning and reduce the elongational viscosity. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1184–1194, 2007     

Converging flow analysis,entrance pressure drops,and vortex sizes: Measurements and calculated values

The use of converging flows for the determination of the elongational behavior of polymer melts is interesting provided that the solving of the inverse problem is fast. For this purpose, this paper shows that the entrance pressure drops that occur during the axisymmetric flow of a polymer melt from the reservoir of a capillary rheometer into a cylindrical die with flat entry can be rapidly calcylated using a Wagner constitutive equation and Protean coordinates. This calculation technique performs particle tracking, which is absolutely necessary when using integral constitutive equations. In turn, the method also enables the determination of the particle path in the entrance zone and gives the boundary of the vertex. The appropriate solution is obtained through the minimization of the power consumption in the entrance zone. Calculation results are compared with experimental pressure drops and vortex pictures using two well‐characterized polyethylenes and show good agreement.     

Shear and extensional flow of a thermotropic liquid crystalline polymer

The flow of a thermotropic liquid crystalline polymer (unfilled and glass fiber filled) was studied using a capillary rheometer and an instrumented injection molding machine. Despite different thermal histories, the techniques gave similar results. From 330 to 350°C, viscosity was independent of temperature. At 340°C, where most measurements were carried out, pronounced shear-thinning occurred and the shear flow curves were nonlinear, the power law exponent decreasing from 0.51 at a shear rate of 10 s⁻¹ to 0.35 at 10⁴ s⁻¹. A previously reported model was used to derive elongational flow curves from die entry pressure data. Because of the nonlinearity of the flow curves, quadratic log-stress vs. log-strain rate plots were needed to model behavior over the strain rate region studied. The elongational flow curves were similar in shape to the shear flow curves, with an effective Trouton ratio of 30. Despite orientation and structure present in the melt, the extensional viscosities and Trouton ratios were within the range found with normal thermoplastic melts. The results suggest that extensional flow may be inhomogeneous, the flowing units possibly being partially ordered domains.     

Experimental and theoretical investigation of extrudate swell of polymer melts from small (length)/(cross-section) ratio slit and capillary dies

An experimental and theoretical study is presented of extrudate swell from short capillary and slit dies. The polymer melts studied were polystyrene and polypropylene. The swell from slit dies is greater than the swell from capillaries. Decreasing die entry angle for capillary dies decreases swell. The argument is made that elongational How existing in the die entry region and for short dies determines extrudate swell. Dimensional analysis arguments are used to relate extrudate swell to a Weissenberg number based on elongational flow at the die entrance and the detailed die geometry. Correlations are developed. The theoretical study is based on unconstrained elastic recovery following elongational How through the die entrance region.     

Gross melt fracture mitigation in converging dies: A singular behavior due to polymer wall slip

This work focuses on mitigating the gross melt fracture defect of polymer flowing through axisymmetrical and two‐dimensional dies. The die entrance angle is considered as well as the influence of the converging wall roughness. Singular results are obtained with a random styrene butadiene rubber (SBR) copolymer, as the gross melt fracture defect cannot be eliminated or mitigated by reducing the die entrance angle. Other experiments carried out with rough converging dies do not give better results. Indeed, the polymer essentially slips along the walls, as shown from capillary rheometer and birefringence experiments. Thus, these results point out the importance of elongational stresses and interfacial conditions in the die entrance region on flow instabilities and the gross melt fracture defect.     

In process measurement of apparent extensional viscosity of low density polyethylene melts using flow visualisation

Abstract

Flow visualisation has been used to study the in process flow behaviour of a low density polyethylene melt as it is processed through planar hyperbolic and abrupt entry slit dies on a commercial scale extruder. The former die profile consisted of a planar hyperbolic section that gradually merged with a parallel slit and was designed to promote constant extensional strain rates at the centreline of flow. The melt was processed through these dies at several flowrates. Extensional strain rates were determined by performing particle velocimetry at the centreline of melt flow in the contraction regions of each die. Constant extensional strain rate conditions were approached at low flowrates in the hyperbolic die. Constant strain rates were not attained for the hyperbolic die at high flowrates nor, as expected, for the abrupt entry die. Analysis of flows using birefringence showed significant shear boundaries developed at the wall of the hyperbolic die at high flowrates. Such boundaries, in combination with the non-Newtonian behaviour of the viscoelastic polymer melt, lead to non-constant strain rates along the centreline of the die at higher flowrates. Stress, strain, and strain rate data for the low density polyethylene melt are presented which, although derived under flow conditions that are not strictly steady in the Lagrangian sense, are experimentally accessible and informative. Stresses and strains derived from the flow visualisation technique are compared with constant strain rate data obtained from a Rheometrics RME elongation rheometer. Close agreement was found between data from the two techniques.     

Equibiaxial elongational viscosity measurements of commercial polymer melts

The equibiaxial elongational viscosity of six commercially available polymer melts is measured using a novel technique known as continuous lubricated squeezing flow. This technique is a modification of simple lubricated squeezing flow. The systems were chosen in order to investigate the dependence of equibiaxial elongational viscosity on molecular structure. Three of the melts are polyethylene with long chain branching, two are polyethylene with short chain branching, and one is polyisobutylene with linear chains. Each polymer was subjected to strain rates ranging from 0.003 to 0.1 s^?1 and compared to the linear viscoelastic prediction so that the degree of strain hardening could be determined. For a modestly branched polymer, comparison of rheological behavior in both uniaxial and equibiaxial deformations was possible. POLYM. ENG. SCI., 55:1012–1017, 2015. © 2014 Society of Plastics Engineers     

Short fiber reinforced thermoplastics. I. Rheological properties of glass fiber reinforced Noryl

An experimental study on the flow behavior of glass fiber reinforced Noryl (a commercial poly(phenyleneoxide)/polystyrene blend) using a capillary rheometer is described. The effect of fiber concentration on shear viscosity and die swell was studied at various temperatures. Breakage of glass fibers during flow through the rheometer is discussed; it was found that the average fiber length (about 230 μm) was not significiantly altered, except at the highest shear rate (575 s⁻¹) studied. The incorporation of short fibers into thermoplastic polymer melts increases their viscosity without changing the basic rheological character-shear rate dependency. No discernible viscosity changes were measured by incorporating 10 weight percent fibers, and upon further increase of fiber concentration from 20 to 30 weight percent no appreciable increase in viscosity was noted. It is shown that short glass fibers cause a large reduction in extrudate swell. The presence of voids and fiber orientation contribute to the decrease of the die swell, an effect greater than expected from volumetric considerations alone.     

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。     

Rheology of wood plastics melt,part 3: Nonlinear nature of the flow

The nonlinear rheology of HDPE/maple melt in both shear and extensional flow was studied using a rotational parallel plate rheometer and the hyperbolic die technique, respectively. Nonlinear features were found in oscillatory shear tests at strain levels far below the values for neat polymer melt. The shear stress relaxation tests revealed the time–strain factorizability, and the damping function was found to follow the sigmoidal‐type relation. The nonlinear nature of the shear flow was further observed as the shear stress growth function from step rate tests as compared to the prediction based on linear viscoelasticity. Extensional stress growth functions of the filled HDPE was build through the viscosity data based on hyperbolic dies with different Hencky strain. The comparison with prediction based on linear viscoelasticity and the Trouton's law further indicated significant damping owing to the particulate suspension nature of the wood plastics melts. POLYM. ENG. SCI., 46:114–121, 2006. © 2005 Society of Plastics Engineers     

Determination of capillary entrance pressure losses and first normal stress difference in polystyrene and high impact polystyrene melts

In industrial polymer processing, polymeric melts give rise to shear stresses above 10⁵ dynes/cm². For the determination of rheological properties and particularly melt elasticity, only the capillary type instrument is applicable to this range. In this paper, a comparative experimental study of the first normal stress difference, obtained from end pressure losses, entrance pressure losses and die swell is reported for polystyrene and high impact polystyrene. Good agreement between results from the three methods of measurement was obtained. The results are in accordance with literature data obtained using a capillary rheometer. It is seen that the values of first normal stress difference are greater in polystyrene than in high impact polystyrene.     

Elongational rheology of polymer melts and solutions

Elongational rheological properties of polymer melts and solutions may be measured using nonlubricated flow characteristics through a semihyperbolic converging die. The effects of body forces related to developing orientation in the fluid during converging extensional flow are so strong that the shearing contribution become negligible in comparison, eliminating the need for lubrication to achieve an essentially pure elongational flow. The effective elongational viscosities of polypropylene melts and lyocell solutions correlated with shear-flow determinations were used to estimate the enthalpy and entropy changes as function of processing conditions. The flow of lyocell solutions through a converging die had, as a result, not only phase separation and cellulose crystallization, but also microfibers formation and high orientation. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 69: 2357–2367, 1998     

Modeling of nonlinear extensional and shear rheology of low-viscosity polymer melts

The hierarchical multi-mode molecular stress function (HMMSF) model developed by Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheol. 60, 625–636 (2016)] for linear and long-chain branched (LCB) polymer melts were used to analyze the set of transient elongational and shear viscosity data of two LCB low-density polyethylenes (1840H and 2426 k), and a linear poly-(ethylene-co-α-butene), PEB A-780090 as reported by [Li et al. J. Rheol. 64, 177 (2020)], who had developed a new horizontal extensional rheometer to extend the lower limits of elongational viscosity measurements of polymer melts. Comparison between model predictions and elongational stress growth data reveals excellent agreement within the experimental window, and good consistency with shear stress growth data, based exclusively on the linear-viscoelastic relaxation spectrum and only two nonlinear model parameters, the dilution modulus G_D for extensional flows, and in addition a constraint release parameter for shear flow.     

Development of an in-line viscometer in an extrusion molding process

In this work, an in-line viscometer to measure the viscosity of polymer melts under extrusion molding processes was developed. The in-line viscometer contains a stress sensor and a shear rate sensor which were installed between the screw and the die of an extruder. In this way, the flow line after the screw cannot be changed, unlike the present in-line capillary rheometer which can change the diameter of the pipe of the flow line and hence influence the throughput. All data acquisition is done by a computer such that the melt viscosity can be calculated automatically. The shear-thinning behavior of a low-density polyethylene (LDPE) under three different temperatures is presented in all experiments. It is concluded that the melt viscosity can be effectively monitored. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 919–924, 1997     

Swell and distortions of high-density polyethylene extruded through capillary dies

The effect of varying the die entrance angle and the die length on extrudate swell and on the onset of extrudate distortion in capillary extrusion has been studied. Using theory from the literature, we have analyzed the contribution to the total pressure drop from the elongational and shear deformation in the entrance region, and from the capillary pressure drop in the land region of the die. From the contribution of the elongational deformation, we obtained an estimate for the elongational viscosity of the polymer. The same analysis was used to study the influence of the die geometry on the stick-slip instability. It is found that the elongational component at the inlet region mainly influences the extrudate distortions. The onset of the stick-slip instability occurs within 10% at a wall stress τ_w of 0.3MPa, where τ_w is calculated from expressions assuming fully developed flow. The variation around this average value is systematic with changes in die geometry, and the observed variations are probably due to the non-homogeneous pressure field in the die. We also propose a model for predicting extrudate swell. Input to the model are material parameters obtainable from oscillatoric measurements of the loss and storage modulus and residence times calculated from the geometry of the die. The swell model includes a fitting parameter that sets the overall scale of the swell.     

Analysis on Composite Flow of Polymer Melts in Sandwich Sheeting Die

Abstract

A broken section method for analyzing the two-phase flow of polymer melts in a sandwich sheeting die under a pressure gradient, is presented. The method assumes that the laminar flows are isothermal and the incompressive materials are power-law fluids. Two polymer melts having different flow behaviors are extruded from two extruders respectively into a coaxial manifold and simultaneously, flow into slits perpendicular to the manifold axis, and then contact with each other in the final slit of the sheeting die for laminating the sandwich sheet. The immiscible interface of these adjacent flows in this final slit is determined by a method of variation. Simultaneous equations in many broken sections are analyzed by computerized successive approximation. Uniformity is defined for both core and skin layers.     

Elongational rheology of polyethylene melts

Effective elongational viscosities were measured for high‐ and low‐density polyethylene samples using a capillary rheometer fitted with semihyperbolic dies. These dies establish a purely elongational flow field at constant elongational strain rate. The effective elongational viscosities were evaluated under the influence of the process strain rate, Hencky strain, and temperature. Enthalpy and entropy changes associated with the orientation development of semihyperbolic‐processed melts were also estimated. The results showed that elongational viscosities were primarily affected by differences in the weight‐average molecular weight rather than in the degree of branching. This effect was process‐strain‐rate‐ as well as temperature‐dependent. An investigation of the melt‐pressure relaxation and the associated first decay time constants revealed that with increasing strain rate the molecular field of the melt asymptotically gained orientation in approaching a limit. As a result of this behavior, molecular uniqueness became much less distinct at high process strain rates, apparently yielding to orientation development and the associated restructuring of the melt's molecular morphology. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 2170–2184, 2001     

Determination of steady-state elongational viscosity for rubber compounds using bell-mouthed dies

A bell-mouthed die geometry was designed to cause convergent flow at a constant, uniform, elongational strain rate. An equation was derived, which showed that steady-state elongational viscosity could be calculated from a plot of pressure drop due to elongation against a simple function of die length. To obtain values of pressure drop due to elongation, it was necessary to correct the total pressure drop measured across the bell-mouthed dies for the contribution from shear occurring near the die wall. For this purpose, a simplified shape for the bell-mouthed dies was assumed, comprising several parallel sided segments. Applying a formula to pressure drop data measured across straight dies corresponding to these segments gave an estimate of the pressure drop due to shear across the bell-mouthed dies. Pressure drops due to elongation were determined by subtracting the pressure drop due to shear from the total pressure drop measured across the bell-mouthed dies. Measurements were also carried out with lubrication to validate the shear correction method. The results indicate that for the compound used in this study, a combination of bell-mouthed and straightsided dies can be used in a conventional capillary rheometer to determine steady-state elongational viscosity. An elongational viscosity of 190 kPa s at 90°C and at a strain rate of 10 s⁻¹ was determined for a simple styrene-butadiene rubber compound. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1139–1150, 1997     

Correlation between entry pressure losses and elongation viscosity of polyethylene melts

The correlation between the entry pressure drop and elongation viscosity during entry converging flow of polymer melts was discussed in this article. The entry pressure drop during extrusion of a low density polyethylene (LDPE) melt and a linear low density polyethylene (LLDPE) melt was measured by means of a capillary rheometer under test conditions with temperature of 170 °C and shear rate varying from 10 to 300 s⁻¹. The results showed that the entry pressure drop increased nonlinearly with an increase of the shear stain rate, and the variation of entry pressure drop of the two melts was close to each other. The melt elongation viscosity of the two resins was estimated using Cogswell equation from the measured entry pressure drop data, and the predictions were compared with the melt extension viscosity measured by using a melt spinning technique published in literature. It was found that the melt extension viscosity from entry converging flow was slightly lower than that from melt spinning technique under the same temperature and extension strain rate.     

Polymer blend containing a thermotropic polyester with long flexible spacer in the main chain

Polymer blends of nylon 66 and thermotropic polyester with long flexible spacers in the main chains were prepared by melt mixing. The samples were made as single filaments by passing the polymer blend through a small and round die of a capillary rheometer. Mechanical properties of blends showed that the modulus and strength of nylon 66 could be improved without reduction of extensibility. The morphology of fractured surfaces was observed by a scanning electron microscope (SEM). It showed that the microfibrillar structure of a thermotropic polyester was formed by extensional flow while the spherical and ellipsoidal particles in the nylon 66 (matrix polymer) were produced by shear flow. The polyester particles were occasionally covered with adhering matrix polymer because of good adhesion between these two polymers. They were highly elongated by tensile stress without loss of elongational characteristics of blends. This fact was explained by very good adhesion between the two phases.