Fingerprinting the processing behavior of polyethylenes from transient extensional flow and peel experiments in the melt state

The flow curves of linear (linear-low and high density) and branched polyethylenes are known to differ significantly. At increasing shear rates, the linear polymers exhibit a surface melt fracture or sharkskin region that is followed by an unstable oscillating or stick-slip flow regime when a constant piston speed capillary rheometer is used. At even higher shear rates, gross melt fracture appears. Unlike their linear counterparts, branched polyethylenes rarely exhibit sharkskin melt fracture and although gross melt fracture appears at high shear rates there is no discontinuity in their flow curve. The various flow regimes of these two types of polyethylenes are examined by performing experiments in the melt state using a unique extensional rheometer (the SER by Xpansion Instruments) that is capable of performing accurate extensional flow and peel experiments at very high rates not previously realized. The peel strength curves of these linear and branched polyethylenes exhibit all of the distinct flow regimes exhibited in their respective flow curves, thereby providing a fingerprint of their melt flow behavior. Moreover, these extensional flow and peel results in the melt state provide insight into the origins and mechanisms by which these melt flow phenomena may occur with regard to rapid tensile stress growth, melt rupture, and adhesive failure at the polymer wall interface.     

Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear

 This contribution presents a survey on the influence of long-chain branching on the linear viscoelastic properties zero shear-rate viscosity and steady-state recoverable compliance of polyethylene melts. The materials chosen are linear and slightly long-chain branched metallocene-catalyzed polyethylenes of narrow molecular mass distribution as well as linear and highly long-chain branched polyethylenes of broad molecular mass distribution. The linear viscoelastic flow properties are determined in shear creep and recovery experiments by means of a magnetic bearing torsional creep apparatus. The analysis of the molecular structure of the polyethylenes is performed by a coupled size exclusion chromatography and multi-angle laser light scattering device. Polyethylenes with a slight degree of long-chain branching exhibit a surprisingly high zero shear-rate viscosity in comparison to linear polyethylenes whereas the highly branched polyethylenes have a much lower viscosity compared to linear samples. Slightly branched polyethylenes have got a higher steady-state compliance in comparison to linear products of similar polydispersity, whereas the highly branched polyethylenes of broad molecular mass distribution exhibit a surprisingly low elasticity in comparison to linear polyethylenes of broad molecular mass distribution. In addition sparse levels of long-chain branching cause a different time dependence in comparison to linear polyethylenes. The experimental findings are interpreted by comparison with rheological results from literature on model branched polymers of different molecular topography and chemical composition. Received: 12 July 2001 Accepted: 30 October 2001     

Influence of molecular structure on secondary flow of polyolefin melts as investigated by laser-Doppler velocimetry

Laser-Doppler velocimetry (LDV) is applied to investigate velocity profiles in the entrance region of a slit die. Due to the high spatial resolution of the device and the accuracy of the velocity measurements the secondary flow patterns of different polyolefins have quantitatively been analyzed for the first time. A linear polyethylene is compared with two long-chain branched polyethylenes and a conventional linear polypropylene with a long-chain branched one. All materials are rheologically characterized with respect to their viscosity functions, elasticity, and elongational properties. For the two linear materials no indication of secondary flow is found, but the three long-chain branched polymers (two polyethylenes and one polypropylene) exhibit pronounced vortices. Neither viscosity nor elasticity seem to be decisive for the occurrence of secondary flow. The viscosity has an influence, however, on the size of the vortices and the velocities within them. All of the three long-chain branched polymers are strongly strain hardening which gives rise to the conclusion that this behavior may be a necessary condition for the formation of vortices. The linear polypropylene does not show any indication of strain hardening. The linear polyethylene, surprisingly, is significantly strain hardening, but it becomes less pronounced with higher strain rates. As most of the deformation in the entrance region takes place at elongational rates at which the strain hardening of the linear polyethylene is not significant, the findings on the linear polyethylene do not contradict the hypothesis that strain hardening and vortex formation in entrance flow may be related to each other. Received: 27 April 2000 Accepted: 30 November 2000     

Pressure effects on viscosity and flow stability of polyethylene melts during extrusion

In the present work, the effects of pressure on the viscosity and flow stability of four commercial grade polyethylenes (PEs) have been studied: linear-low-density polyethylene copolymer, high-density polyethylene, metallocene polyethylenes with short-chain branches (mPE-SCB), and metallocene polyethylenes with long chain branching (mPE-LCB). The range of shear rates considered covers both stable and unstable flow regimes. “Enhanced exit-pressure” experiments have been performed attaining pressures of the order of 500×10⁵ Pa at the die exit. The necessary experimental conditions have been clearly defined so that dissipative heating can be neglected and pressure effects isolated. The results obtained show an exponential increase in both shear and entrance-flow pressure drop with mean pressure when shear rate is fixed and as long as flow is stable. These pressure effects are described by two pressure coefficients, β_S under shear and, β_E under elongation, that are calculated using time–pressure superposition and that are independent of mean pressure and flow rate. For three out of four PE, pressure coefficient values can be considered equal under shear and under elongation. However, for the mPE-LCB, the pressure coefficient under elongation is found to be about 30% lower than under shear. Flow instabilities in the form of oscillating flows or of upstream instabilities appear at lower shear rates as mean pressure increases. Nevertheless, the critical shear stress at which they are triggered remains independent of mean pressure. Moreover, it is found that the β_S values obtained for stable flows do not differ much from the values obtained during upstream instability regimes, and differ really from pressure effects observed under oscillating flow and slip conditions.     

Pressure drop caused by flow area changes in capillaries under low flow conditions

Single-phase and two-phase flow pressure drops caused by flow area expansion and contraction were measured using air and water. The test section consisted of two capillaries with 0.84 mm and 1.6 mm diameters. For single-phase flow, the Reynolds numbers defined based on the smaller diameter capillary covered the range 160–11,000. For two-phase flow, the all-liquid Reynolds number based on the smaller capillary varied in the 410–1020 range, and the flow quality varied in the 0.018–0.2 range. The single-phase flow loss coefficients for both flow area expansion and contraction were empirically correlated. For two-phase flow, the data indicated the occurrence of significant velocity slip, and the one-dimensional homogeneous flow model utterly disagreed with the data. For flow area expansion the one-dimensional slip flow model along with an Armand-type slip ratio correlation could predict the data well. For flow area contraction, the one-dimensional slip flow model along with the slip ratio expression of Zivi agreed with the data very well, provided that no vena-contracta was considered.     

Bagley correction: the effect of contraction angle and its prediction

The excess pressure losses due to end effects (mainly entrance) in the capillary flow of a branched polypropylene melt were studied both experimentally and theoretically. These losses were first determined experimentally as a function of the contraction angle ranging from 10° to 150°. It was found that the excess pressure loss function decreases for the same apparent shear rate with increasing contraction angle from 10° to about 45°, and consequently slightly increases from 45° up to contraction angles of 150°. Numerical simulations using a multimode K-BKZ viscoelastic and a purely viscous (Cross) model were used to predict the end pressures. It was found that the numerical predictions do agree well with the experimental results for small contraction angles up to 30°. However, the numerical simulations under-predict the end pressure for larger contraction angles. The effects of viscoelasticity, shear, and elongation on the numerical predictions are also assessed in detail. Shear is the dominant factor controlling the overall pressure drop in flows through small contraction angles. Elongation becomes important at higher contraction angles (greater than 45°). It is demonstrated in abrupt contractions (angle of 180°) that both the entrance pressure loss and the vortex size are strongly dependent on the extensional viscosity for this branched polymer. It is suggested that such an experiment (visualisation of entrance flow) can be useful in evaluating the validity of constitutive equations and it can also be used to fitting parameters of rheological models that control the elongational viscosity.     

An experimental investigation of the shear behaviour of polyethylenes with different structures

Rheological properties in shear flow are presented for four different polyethylene samples: a high density, a linear low density and two low density polyethylenes manufactured using different techniques. Tests have been performed with the aid of capillary types of instrument equipped with capillaries of various lengths at three different temperatures. End correction factors have been determined and true flow curves obtained. Swelling ratios for both unannealed and annealed samples have been determined as well as the shear rate and shear stress at which irregularities begin. In some cases generalized plots have been prepared and in all cases the rheological response is discussed in terms of molecular characteristics, in particular the average molecular weight, molecular weight distribution and degree of branching.     

A linear model of the stick-slip phenomena in polymer flow in rheometers

A linear approach was employed for the qualitative theoretical study of the stick-slip phenomena in polymer flows in rheometers. For this purpose, the familiar three-constant rheological equation and a linear wall friction law (i.e. wall stress — slip velocity dependence) were used with some additional hypotheses about the onset of the stick-slip behaviour. The friction law used was derived from a crude molecular approach. On the basis of these equations the inertialess stickslip behaviour of a viscoelastic liquid flowing through a capillary at a constant flow rate was considered. To be able to describe some transient phenomena in this problem, inertial effects (as an example) were taken into account. Furthermore, the distortions on the extrudate surface due to the slip phenomena inside the capillary were described theoretically within the framework of a linear approximation. In the final part of the study the possibility of rapid stochastization was discussed for rotational stick-slip flow of polymers in a cone-plate rheometer.     

Enhanced melt strength and stretching of linear low-density polyethylene extruded under strong slip conditions

The influence of extrusion under strong slip conditions on the extensional properties of linear low-density polyethylene was studied in this work. The material was extruded at two different temperatures under strong slip and no slip conditions, and was subsequently subjected to uniaxial elongational flow by means of a Rheotens device. Strong slip was evident through the elimination of sharkskin distortions and the stick-slip instability, as well as by the electrification of the extrudates. The extrudate swell was smaller in the presence of slip when comparing with no slip conditions at constant apparent shear rate, but it was found to be a unique function of the shear stress if comparison was performed at constant stress. The draw ratio and melt strength of the filaments obtained under slip conditions were larger compared to those without slip. In addition, draw resonance was postponed to higher draw ratios during the extrusion with strong slip at constant apparent shear rate. It is suggested that slip of the polymer at the die wall decreases the shear stress in the bulk, and therefore, restricts the disentanglement and orientation of macromolecules during flow, which subsequently produces the increase in draw ratio and melt strength during stretching.     

Investigation of a combustion driven oscillation in a refinery flare: Part B: Visualisation of a periodic flow instability in a bifurcating duct following a contraction

A flow visualisation study was performed to investigate a periodic flow instability in a bifurcating duct within the tip of the flares at the Shell refinery in Clyde, NSW, to verify the trigger of a combustion-driven oscillation proposed in Part A of this study, and to identify its features. The model study assessed only the flow instability, uncoupled from the acoustic resonance and the combustion that are also present in the actual flare. Three strong, coupled flow oscillations were found to be present in three regions of the fuel line in the flare tip model. A periodic flow separation was found to occur within the contraction at the inlet to the tip, a coupled, periodic flow oscillation was found in the two transverse “cross-over ducts” from the central pipe to the outer annulus and an oscillating flow recirculation was present in the “end-cap” region of the central pipe. The dimensionless frequency of these oscillations in the model was found to match that measured in the full-scale plant for high fuel flow rates. This, and the strength of these flow oscillations, gives confidence that they are integral to the full-scale combustion-driven oscillation and most likely the primary trigger. The evidence indicates that the periodic flow instability is initiated by the separation and roll-up of the annular boundary layer at the start of the contraction in the fuel section of the flare tip. The separation generates an annular vortex which interacts with the blind-ended pipe downstream, leading to a pressure wave which propagates back upstream, initiating the next separation event and repeating the cycle. The study also investigated flow control devices with a view to finding a practical approach to mitigate the oscillations. The shape of these devices was constrained to allow installation without removing the tip of the flare. This aspect of the study highlighted the strength and nature of the coupled oscillation, since it proved to be very difficult to mitigate the oscillation in this way. An effective configuration is presented, comprising of three individual components, all three of which were found to be necessary to eliminate the oscillation completely.     

Comparison of the melt fracture behavior of metallocene and conventional polyethylenes

The influence of sparse long-chain branching and molecular weight distribution on the melt fracture behavior of polyethylene melts was investigated. Four commercial polyethylene resins were employed for this study: a conventional low-density polyethylene, a conventional linear low-density polyethylene, a linear metallocene polyethylene, and a sparsely branched metallocene polyethylene. Rheological measurements were obtained for both shear and extensional deformations, and melt fracture experiments were carried out using a controlled rate capillary rheometer. A single capillary geometry was used to focus on the effects of material properties rather than geometric factors. For the linear polyethylenes, surface melt fracture, slip-stick fracture, and gross melt fracture were all observed. Conversely, the branched PE resins did not exhibit a slip-stick regime and the degree of gross fracture was observed to be much more severe than the linear resins. These variations can be explained by the effects that long-chain branching has on the onset of shear-thinning behavior (slip-stick fracture) and the degree of extensional strain hardening (gross melt fracture). Although there is some indication that the breadth of molecular weight distribution indirectly influences surface melt fracture, the results remain inconclusive.     

The effect of slip in the flow of a branched PP melt: experiments and simulations

In this paper visualisation and direct velocity profile measurement experiments for a branched polypropylene melt in a 10:1 axisymmetric contraction demonstrate the onset of wall slip. Video processing of the flow shows the formation of vortices and their diminution with increasing flow rate. Numerical simulations using a multimode K-BKZ viscoelastic and a purely viscous (Cross) model—both of them incorporating a nonlinear slip law—were used to predict the flow kinematics and dynamics as well as to deduce the slip velocity function by performing fitting to the velocity profiles. It was found that the numerical predictions agree well with the experimental results for the velocity profiles, and vortex formation, growth and reduction. It is suggested that such experiments (visualisation of entrance flow and direct velocity profile measurement) can be useful in evaluating the validity of constitutive equations and slip laws in the flow of polymer melts through processing equipment.     

Effect of pressure-dependent slip on flow curve multiplicity

Various microstructural pictures for slip at polymer/solid interfaces lead to relations which have a region where multiple values of slip velocity are predicted for the same shear stress. This leads to the expectation of multivalued flow curves, which has been verified in specific cases by numerous researchers. We study the effect of pressure dependence on flow curve multiplicity using a simple multivalued slip relation to model the phenomena of hysteresis and spurt flow in polymer extrusion. A continuation technique is used to trace out the boundaries of the region of flow curve multiplicity as pressure drop and die length to diameter (L/D) ratio are changed. Results for Newtonian, shear thinning and viscoelastic constitutive equations show that, despite the multivalued nature of the slip model, multiplicity (and thus hysteresis) is absent at high L/D.  For the sake of completeness, we also carry out time-dependent simulations at constant piston speed taking fluid compressibility into account. These simulations show that oscillations in the pressure drop and exit volumetric flow rate result only if the system is operated in the multiplicity region of the steady state flow curve, in agreement with the results of similar simulations by researchers using various multivalued slip models without pressure dependence. The results demonstrate that a multivalued slip model does not guarantee multiplicity in the flow curve for the constant pressure drop operation, nor oscillations for constant piston speed operation. Received: 18 August 1997 Accepted: 30 March 1998     

Elastic response from pressure drop measurements through planar contraction–expansion geometries by molecular dynamics: structural effects in melts and molecular origin of excess pressure drop

In this work, we use nonequilibrium molecular dynamics to simulate a contraction–expansion flow of various systems, namely melts with molecules of various conformations (linear, branched, and star), linear molecules in solution, and a reference Lennard–Jones fluid. The equations for Poiseuille flow are solved using a multiple time scale algorithm extended to nonequilibrium situations. Simulations are performed at constant temperature using the Nose–Hoover dynamics. The main objective of this analysis is to investigate the molecular origin of pressure drop along planar contraction–expansion geometry, varying the length of the contraction, and the effect that different molecular conformations have on the resulting pressure drop along the geometry. Pressure drop is closely related to mass distribution (in neutral and gradient directions) and branching index of molecules. Also, it is shown that remarkable increases of pressure drops are also possible in planar geometries, provided large extensional viscosities combined with moderate values of the first normal stress difference in shear are considered, in addition to considerable reductions of the flow area at the contraction region.     

Two‐phase pressure drop caused by sudden flow area contraction/expansion in small circular pipes

Theoretical studies have been made to determine the pressure drops caused by abrupt flow area expansion/contraction in small circular pipes for two‐phase flow of air and water mixtures at room temperature and near atmospheric pressure. Two‐phase computational fluid dynamics (CFD) calculations, using Eulerian–Eulerian model (with the air phase being compressible for pipe contraction case) are employed to calculate the pressure drop across sudden expansion and contraction. The pressure drop is determined by extrapolating the computed pressure profiles upstream and downstream of the expansion/contraction. The larger and smaller tube diameters are 1.6 and 0.84 mm, respectively. Computations have been performed with single‐phase water and air, and two‐phase mixtures in a range of Reynolds number (considering all‐liquid flow) from 1000 to 12 000 and flow quality from 1.2 × 10^?3 to 1.6 × 10^?2. The numerical results are validated against experimental data from the literature and are found to be in good agreement. The expansion and contraction loss coefficients are found to be different for single‐phase flow of air and water, and they agreed reasonably well with the commonly used theoretical predictions. Based on the numerical results as well as experimental data, correlations are developed for two‐phase flow pressure drops caused by the flow area contraction as well as expansion. Copyright © 2010 John Wiley & Sons, Ltd.     

Three-dimensional flow of Newtonian and Boger fluids in square–square contractions

The flow of a Newtonian fluid and a Boger fluid through sudden square–square contractions was investigated experimentally aiming to characterize the flow and provide quantitative data for benchmarking in a complex three-dimensional flow. Visualizations of the flow patterns were undertaken using streak-line photography, detailed velocity field measurements were conducted using particle image velocimetry (PIV) and pressure drop measurements were performed in various geometries with different contraction ratios. For the Newtonian fluid, the experimental results are compared with numerical simulations performed using a finite volume method, and excellent agreement is found for the range of Reynolds number tested (Re₂ ≤ 23). For the viscoelastic case, recirculations are still present upstream of the contraction but we also observe other complex flow patterns that are dependent on contraction ratio (CR) and Deborah number (De₂) for the range of conditions studied: CR = 2.4, 4, 8, 12 and De₂ ≤ 150. For low contraction ratios strong divergent flow is observed upstream of the contraction, whereas for high contraction ratios there is no upstream divergent flow, except in the vicinity of the re-entrant corner where a localized atypical divergent flow is observed. For all contraction ratios studied, at sufficiently high Deborah numbers, strong elastic vortex enhancement upstream of the contraction is observed, which leads to the onset of a periodic complex flow at higher flow rates. The vortices observed under steady flow are not closed, and fluid elasticity was found to modify the flow direction within the recirculations as compared to that found for Newtonian fluids. The entry pressure drop, quantified using a Couette correction, was found to increase with the Deborah number for the higher contraction ratios.     

Onset of flow instability in a heated capillary tube

We study the stability of flow in a heated capillary tube with an evaporating meniscus. The behavior of the vapor/liquid system, which undergoes small perturbations, is analyzed by linear approximation, in the frame of a one-dimensional model of capillary flow, with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes, on the flow stability is studied. The velocity, pressure and temperature oscillations in a capillary tube with a constant wall heat flux or a constant wall temperature are determined. A scenario of a possible process at small and moderate Peclet numbers corresponding to the flow in capillaries is considered. The boundaries of stability, subdividing the domains of stable and unstable flows, are outlined, and the values of geometrical and operating parameters corresponding to the transition from stable to unstable flow are estimated. It is shown that the stable capillary flow occurs at relatively small wall heat fluxes, whereas at high ones, the flow is unstable, with continuously growing velocity, pressure and temperature oscillations.     

Effect of radial flow in the die entrance region on gross melt fracture of PDMS extrudate

The gross melt fracture defect is related to the flow instabilities developed in the contraction region. To mitigate these upstream instabilities, a convergent radial flow in the die entrance has been created. In fact, the ultimate objective of the present work is to examine the effect of the clearance width of radial flow on the appearance and development of gross melt fracture defect. So, capillary rheometer experiments were performed with linear polydimethylsiloxane (PDMS) oil.As for the influence of radial flow width on the morphology of gross melt fracture defect, extrudate photographs show that this imperfection can be mitigated since its frequency is higher and amplitude smaller when the gap of radial flow decreases. Such results may be related both to shear and elongational components of radial flow. Actually, when gap width is very small compared to the external diameter of radial flow, shear deformations become more enhanced with respect to the elongational deformations and thus the helical gross melt fracture becomes more like a surface defect than volume defect.     

Fast flow behavior of highly entangled monodisperse polymers

A systematic experimental investigation is carried out to clarify the nature of a well-known capillary flow phenomenon in linear monodisperse polybutadienes (PBd). By varying the surface condition and the die diameter, it is alluded that a spurt-like stick-slip transition actually results from a breakdown of chain entanglement between adsorbed and next-layer unbound chains. In other words, the transition is not a manifestation of any constitutive properties, as previously asserted by Vinogradov and coworkers (1984). The melt viscosity dependence of the transition amplitude agrees with a Navier-de Gennes type analysis of wall slip. A comparison between the capillary flow and dynamic shear behavior of the same monodisperse PBd reveals that the interfacial stick-slip transition occurs at a stress level that is only a third of the plateau stress given by the elastic plateau modulus G _N ⁰=1.0 MPa at 40°C. The molecular weight independence of the critical stress for the transition provides a striking contrast with the transition characteristics observed in linear polyethylenes and suggests a different state of PBd chain adsorption on steel surfaces. Received: 2 April 1998 Accepted: 1 June 1998     

双自由面溶质?热毛细液层的不稳定性

溶质?热毛细对流是流体界面的浓度和温度分布不均导致的表面张力梯度驱动的流动, 它主要存在于空间微重力环境、小尺度流动等表面张力占主导的情况中, 例如晶体生长、微流控、合金浇筑凝固、有机薄液膜生长等. 对其流动进行稳定性分析具有重要意义. 本文采用线性稳定性理论研究了双自由面溶质?热毛细液层对流的不稳定性, 得到了两种负毛细力比(η)下的临界Marangoni数与Prandtl数(Pr)的函数关系, 并分析了临界模态的流场和能量机制. 研究发现: 溶质?热毛细对流和纯热毛细对流的临界模态有较大的差别, 前者是同向流向波、逆向流向波、展向稳态模态和逆向斜波, 后者是逆向斜波和逆向流向波. 在Pr较大时, Pr增加会降低流动稳定性; 在其他参数下, Pr增加会增强流动稳定性. 在中低Pr, 溶质毛细力使流动更加不稳定; 在大Pr时, 溶质毛细力的出现可能使流动更加稳定; 在其他参数下, 溶质毛细力会减弱流动稳定性. 流动稳定性不随η单调变化. 在多数情况下, 扰动浓度场与扰动温度场都是相似的. 能量分析表明: 扰动动能的主要能量来源是表面张力做功, 但其中溶质毛细力和热毛细力做功的正负性与参数有关.