A numerical study of the effect of normal stresses and elongational viscosity on entry vortex growth and extrudate swell

A general-purpose finite element program has been used to simulate the flow of a typical polystyrene melt in the entry and exit regions of a slit die. Instead of using a general viscoelastic constitutive equation, simplified models were used that include correlations based on experimental data available in the literature for the shear and elongational viscosities and the normal stresses. With such simple models convergence of the iterative scheme is extended to relatively high Deborah numbers (De ≈ 5). The models predict vortex growth in the entry region and an increase of extrudate swell at the exit in qualitative agreement with experimental observations. It was found that the normal stresses are primarily responsible for these phenomena, while the elongational viscosity tends to increase the end (Bagley) correction and decrease the swelling.     

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.     

Die swell of liquid crystal-forming solutions of hydroxypropyl cellulose through a long capillary die

The die swell and shear viscosity of lyotropic liquid crystal-forming hydroxypropyl cellulose solutions in N,N-dimethylacetamide were determined over a relatively wide range of shear stress or polymer concentration at 30°C by using a long capillary die with an aspect ratio of 114. The dependence of die swell on the concentration was similar to that of shear viscosity: a maximum at a critical concentration C_a and a minimum at another critical concentration C_b (C_a < C_b). The dependence of the swell on shear stress is greatly affected by the solution phase: in an isotropic range (below C_a), the die swell increased monotonously with shear; in the vicinity of C_a, the die swell exhibited a maximum; in a biphasic range (between C_a and C_b), the die swell decreased monotonously; in a single-phase anisotropic range (above C_b), the die swell exhibited a minimum. Above C_b, extrudate distortion was observed and disappeared around the shear where the die swell exhibited a minimum.     

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.     

Competition between textural transitions and pressure effects on the viscosity of thermotropic liquid-crystal polymers

Steady measurements in capillary and slit dies and transient experiments in a cone-plate system are presented for two thermotropic copolyesters, X7G® and Vectra A950, and a thermotropic copolyesteramide, Vectra B950. The wide shear rate range covered, from 10⁻² to 10⁴ s⁻¹, allows us to observe the three regions defined by Onogi and Asada (1). However, the copolyesters on one hand, and the copolyesteramide on the other, show different rheological behavior that can be summarized as follows: For X7G® and Vectra A950: i. higher viscosities in slit than in capillary die flow; ii. upward-concave pressure profiles in slit die flow; iii. overshoot peaks in transient experiments at a shear strain γ_M = 2. For Vectra B950: i. lower viscosities in slit than in capillary die flows; ii. linear or slightly convex pressure profiles in slit die flow; iii. overshoot peaks in transient experiments at a shear strain of γ_M = 180. These seemingly contradictory results are explained by the competition between the texture changes along the flow (a transition from a worm texture to a flow-aligned region) and the pressure effect on viscosity.     

The rheology of polysulfone

The viscosity-shear rate functions for polysulfone (PSF) condensates ranging from 0.4RV to 0.95RV were determined using capillary rheometry, The most probable distribution of molecular weights of these resins allowed facile comparison with the polydisperse Bueche theory for viscosity, The agreement in shape of the viscosity function with theory was good but the data were displaced by a factor of 3 to 4 to higher reduced shear rate, a fairly common occurrence for melts. The high absolute value of PSF viscosity was explained with existing empirical correlations as a combination of low critical molecular weight and strong intermolecular interactions. The temperature dependence of viscosity was found to be close to that for polystyrene in the temperature range, T_g + 90 to T_g + 190°C. The die swell, end corrections, and melt fracture characteristics were also determined. The latter was found to occur at a constant wall shear stress of about 6 × 10⁶ dynes/cm² while the die swell and end corrections were found to be small.     

An analytical model for steady coextrusion of viscoplastic fluids in thin slit dies with wall slip

Coextrusion is widely used to fabricate multilayered products with each layer providing a separate functionality, including barrier resistance to gases, strength, and printability. Here an analytical model of the coextrusion die flow of two incompressible, viscoplastic fluids in a slit die, subject to nonlinear wall slip and under fully developed and isothermal conditions, is developed to allow the prediction of the steady‐state velocity and shear stress distributions and the flow rate versus pressure gradient relationship. The resulting model is applied to the coextrusion of two layers of viscoplastic fluids in a thin rectangular slit die (slit gap, h ? slit width, W). The analytical solution recognizes a number of distinct flow conditions (eleven cases) that need to be treated separately. The solutions for all eleven cases are provided along with an apriori identification methodology for the determination of the applicable case, given the shear viscosity and wall slip parameters of the two viscoplastic fluids, the slit geometry and the flow conditions. Simplifications of the model would provide the solutions for the fully developed and isothermal coextrusion flows of any combination of Hershel‐Bulkley, Bingham, power‐law and Newtonian fluids with or without wall slip at one or both walls of the slit die. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Extrudate swell from slit and capillary dies: An experimental and theoretical study

A comparative experimental study of extrudate swell from long slit and capillary dies is reported for rheologically characterized polystyrene and polypropylene melts. Generally extrudate swell from a slit is greater than that from a capillary die. At low die wall shear rates it goes to a value of about 1.2 as opposed to about 1.1 found for capillary dies. The onset and character of extrudate distortion have been studied. The experimental results are compared with theories of swell based on unconstrained recovery from Poiseuille flow in these geometries. A detailed analysis of such theories of extrudate swell based on the original work of Tanner has been carried out. The analysis is placed in a more general form which should be valid for a range of die cross-sections.     

Experimental studies on extrudate swell behavior of PS and LLDPE melts in single and dual capillary dies

Extrudate swell behavior of polystyrene (PS) and linear low‐density polyethylene (LLDPE) melts was investigated using a constant shear rate capillary rheometer. Two capillary dies with different design configurations were used, one being a single flow channel and the other being a dual flow channel. A number of extrudate swell related parameters were examined, and used to explain the discrepancies in the extrudate swell results obtained from the single and dual flow channel dies, the parameters including output rate and output rate ratio, power law index, wall shear rate, wall shear stress, melt residence time, pressure drop induced temperature rise, flow channel position relative to the barrel centerline, and the flow patterns. It was found in this work that the power law index (n value) was the main parameter to determine the output rate ratio and the extrudate swell between the large and small holes for the dual flow channel die: the greater the n value the lower the output rate ratio and thus decreased extrudate swell ratio. The differences in the extrudate swell ratio and flow properties for PS and LLDPE melts resulted from the output rate ratio and the molecular chain structure, respectively. The extrudate swell was observed to increase with wall shear rate. The discrepancies in the extrudate swell results from single and dual dies for a given shear rate were caused by differences in the flow patterns in the barrel and die, and the change in the melt velocities flowing from the barrel and in the die to the die exit. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1713–1722, 2003     

Die swell from capillary die and slit die: A theoretical study

Assuming polymer fluids obey the CEF equation, equations concerning die swell from capillary die and slit die were derived. The die swell of polymer increased with increasing shear rate and recoverable shear. Our theoretical predictions conformed well with the experimental data of die swell for PP and PS.     

Rheological properties of poly(trimethylene terephthalate) in capillary flow

The shear viscosity, extensional viscosity, and die swell of the PTT melt were investigated using a capillary rheometer. The results showed that the PTT melt was a typical pseudoplastic fluid exhibiting shear thinning and extensional thinning phenomena in capillary flow. There existed no melt fracture phenomenon in the PTT melt through a capillary die even though the shear rate was 20,000 s^?1. Increasing the shear rate would decrease the flow activation energy and decline the sensitivity of the shear viscosity to the melt temperature. The molecular weight had a significant influence on the flow curve. The flow behavior of the PTT melt approached that of Newtonian fluid even though the weight‐molecular weight was below 43,000 s^?1 at 260°C. The extensional viscosity decreased with the increase of the extensional stress, which became more obvious with increasing the molecular weight. The sensitiveness of the extensional viscosity to the melt temperature decreased promptly along with increasing the extensional strain rate. The die swell ratio and end effect would increase along with increasing the shear rate and with decreasing the temperature, which represented that the increase of the shear rate and the decrease of temperature would increase the extruding elasticity of the PTT melt in the capillary die. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 705–709, 2005     

Viscosity,modulus, and die swell of glass bead filled polystyrene-acrylonitrile copolymer

Flow curves were obtained at 190°C over the shear rate range 0.1 to 100 sec^?1 for polystyrene-acrylonitrile copolymer containing up to 36 percent by volume glass beads, using a capillary extrusion rheometer. The addition of glass beads always increased shear stress and viscosity at a given shear rate, with the increase being more pronounced at low shear rates. The addition of glass beads decreased die swell, which also depended on shear-stress and capillary length-to-radius ratio. At low shear rates a lower limiting value of die swell ratio of about 1.1 was achieved. Values of recoverable shear derived from end correction data by the technique of Philippoff and Gaskins and from die-swell data by the method of Bagley and Duffey are compared. A fairly good agreement was found for low concentration blends at low shear, However, the values differed by a factor of up to 3 at higher shear stresses. In all cases, recoverable shear was found to increase with shear stress at a fixed filler loading and to decrease with increased filler loading at a fixed shear stress. Values of shear modulus calculated from the recoverable shear measurements decreased rapidly with increasing shear stress.     

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.     

Extrusion die swell of carbon black-filled natural rubber

Extrusion die swell of natural rubber compounded with a wide variety of carbon blacks has been determined in a capillary rheometer using a long circular die. The range of variation of carbon black loading, surface area, and structure are, respectively, 10 to 60 phr, 44 to 124 m²/g, and 78 to 120 cc/100 g. The effective carbon black volume fraction φ_e not participating in the strain recovery leading to die swell is assumed to be the sum of the actual filler volume fraction and the fraction of unextractable rubber determined experimentally for each compound. Bagley and Duffey's analysis of extrusion die swell of unfilled polymers as unconstrained elastic recovery was adopted for a filled elastomeric system whose relative shear modulus (G/G₀) is assumed to vary as (1 ? φ_e)^?N. The matrix shear modulus G₀, originally introduced by Nakazima and Shida on the basis of a linearized approximation, will depend on the shear stress level because of nonlinear deformation. The power N will vary with shear stress which changes the orientation of carbon black aggregates. Except for these features, die swell data for a wide range of carbon black compounds fall on a single curve when plotted in the manner of the predicted relation between the wall shear stress, die swell, and φ_e. Replacing φ_e by Medalia's φ′ based on an equivalent sphere concept introduces a larger scatter around the mean curve.     

Slit die flow measurements of a liquid crystalline polyesteramide and its blends with polyarylate

A commercial thermotropic polyesteramide and its blends with polyarylate are the object of a slit die flow rheological study. The measurements are carried out at 280°C, a temperature slightly above the melting temperature of the thermotropic, covering a shear rate range 10^?1 s^?1 to 10²s^?1. Except in the case of the thermotropic polymer, the pressure profiles are upward parabolic which is attributed to the dependence of the viscosity on pressure. The most striking result is the observed downward curvature in pressure profiles obtained for the liquid crystalline polyesteramide: no explanation is given for this phenomenon, for the present. The elasticity of the polymer melts is expressed in terms of the exit pressure and the extrudate swell. The thermotropic polyesteramide presents negative values of both parameters (e.g. samples shrink instead of swell). Viscosity and elasticity present negative deviation from linearity when plotted against composition; this reduction in the rheological functions, caused by the addition of liquid crystal, is more pronounced at high shear rates.     

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.     

Rheological properties of phenophthalein poly(ether ether ketone)

The rheological properties of the novel engineering thermoplastic phenophthalein poly(ether ether ketone) (PEK-C) have been investigated using both a rotational and a capillary rheometer. The dependence of the viscosity on the shear rate and temperature was obtained. The activation energy was evaluated both from the Arrhenius and the Williams-Landel-Ferry (WLF) equation. An estimate for the proper E_η (dependent only on the chemical structure of the polymer) has been found from the WLF equation at temperatures about T_g + 200°C. Measurements of the die swell have been performed. The first normal stress differences were evaluated from the die swell results and compared with the values obtained from the rotational rheometer at low shear rates.     

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.     

Numerical investigation of spinneret geometric effect on spinning dynamics of dry‐jet wet‐spinning of cellulose/[BMIM]Cl solution

In this study, the effect of spinneret geometry, including the entrance angle α of the entrance channel, the length L_s, and the diameter D₀ of the exit channel, on the spinning dynamics of dry‐jet wet‐spinning of cellulose/1‐butyl‐3‐methylimidazolium chloride ([BMIM]Cl) solution was simulated by using finite element method. Based on the mathematical model of dry‐jet wet‐spinning established in our previous work (Xia et al., Cellulose 2015, 22, 1963) the radial and axial profiles of velocity, pressure, and shear rate in the spinneret and the profiles of diameter, temperature, and tensile stress in the air‐gap region were obtained. From the simulated profiles, the effect of spinneret geometric parameters on the flow behavior and the pressure drop of polymer solution in the spinneret and the die‐swell ratio near the spinneret was discussed. The entrance angle α of the entrance channel mainly influences the flow behavior of polymer solution in the spinneret and the die‐swell effect near the spinneret. As the decrease of the entrance angle α of the entrance channel, the vortices in the spinneret could be removed and the die‐swell ratio decreases. The increase of the length L_s of the exit channel results in the increase of pressure drop in the spinneret and the decrease of the die‐swell ratio. It is also found that the increase of the diameter D₀ of the exit channel reduces the flow velocity of polymer solution and decreases the pressure drop in the spinneret at a constant mass flow rate. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43962.     

Slit flow of molten polyethylene filled with plastic flakes

The processability of polyethylene in sheet-extrusion or calendering may be improved by the addition of plastic flakes. The effects of plastic flake parameters and flow conditions on the viscosity and the die swell of the suspension were determined, and the structure in flow (morphology or dispersion state) and applications were discussed. Flakes of biaxially oriented polystyrene, high-impact polystyrene, polypropylene, polyamide or polypropylene spheres were dry-blended with polyethylene. The viscosity was determined by means of a slit or a capillary rheometer. The quenched extrudate was annealed and its die swell was measured. Flakes of biaxially oriented polystyrene shrunk into rod-like form during heating, but other plastics retained the flake-form. The relative viscosity and the swell ratio of the suspensions depended on the type of plastic and operating conditions. The rheological behavior of suspensions qualitatively suggested that polypropylene flakes deformed or crowded (including stacking), polyamide flakes deformed slightly, and polystyrene flakes were difficult to buckle, but crowded slightly. The thickness of extrudates can be controlled easily by flake addition due to decreased die swell, while the output would be reduced to some extent.