Effect of wall slip on the uniformity of flow from sheeting extrusion dies

A theoretical study for analyzing the uniformity of flow from sheeting extrusion dies is presented. In this study it is assume that a slip condition exists at the wall of the die, the magnitude of slip velocity is proportional to the shear stress at the wall, the flow is isothermal and steady state, and a power law model is valid for viscosity. Two extrusion dies, T-dies and coat-hanger dies, are examined. The flow uniformity at the exit of the die is calculated and compared with that for a nonslip analysis. The discrepancies between the slip and nonslip models imply that the wall slip condition induces a significant nonuniform flow distribution. Traditional design criticism based on the nonslip model are invalid for flow with the wall slip condition, and it is necessary to increase the length of the die land to even the flow distribution at the exit of the die.     

A new design procedure for profile extrusion dies

A new design procedure for complex profile extrusion dies is presented. This method applies to multiple channel dies, i.e. dies provided with melt flow independent channels in the land. The approach is based on the resolution of the flow inverse problem, which consists of finding the channel topology (channel land lengths, approach angles in the transition region), which gives a balanced flow at the die orifice from the knowledge of the die contour. The methodology uses a blend of the network approach and the cross-section method. The procedure is used to design an industrial die that has been tested in a manufacturing environment, showing the performance of the proposed approach.     

Practical interpretation of laboratory die swell behavior of PVC extrudates—through correlating circular with non-circular die performance

Laboratory die swell measurements are routinely measured on many viscoelastic polymer extrudates to characterize thier ability to maintain a specified shape during extrusion operations. The diameters of downstream extrudates obtainable through selected round dies can then be routinely scanned by optical or laser type devices to compare the degree of swell relative to the die diameter itself. Such measurements, while yielding good relative die swell performance between compounds, frequently do not predict the actual die swell levels observed later when the same compound is extruded through production dies of different cross-sectional shapes and land lengths. This study discusses an alternate method of correlating die swell between dies of different shapes by using a technique derived from fluid mechanics. This concept, used to characterize fluid velocity through non-circular channels with that observed through circular pipes and ducts, involves the inclusion of a shape factors known as the “Hydraulic Radius” in fluid flow comparisons. When this technique was applied to die swell measurements for extrudates of both a flexible PVC wire jacket compound and a rigid PVC pipe compound, good agreement in actual die swell measurements through both round dies and dies with non-circular cross sections was obtained. This approach can lend credibility to laboratory die swell measurements and greatly expand their use in predicting production extrusion performance.     

Development of microlayer blown film technology by combining film die and layer multiplication concepts

Many polymers are extruded through blown film dies to produce both monolayer and multilayer films. A common type of die in use today to produce blown films is the spiral mandrel die. This type of die can be used effectively for many polymers in structures containing up to approximately ten layers. This paper will discuss the development of new technology using a feedblock and layer multipliers in combination with encapsulation technology and a unique film die to produce microlayer blown film structures with significantly larger numbers of layers than can be produced using conventional blown film technology. POLYM. ENG. SCI., 56:598–604, 2016. © 2016 Society of Plastics Engineers     

The onset of wall slip and sharkskin melt fracture in capillary flow

The capillary die flow of high density and linear low density polyethylenes is simulated under slip conditions to investigate the origin of sharkskin melt fracture. As suggested in the literature, it is shown that sharkskin originates at the exit of the die and is due to the acceleration (high stretching rate) of the melt as it exits the die. It is also shown that both adhesion and slip promoters eliminate surface defects by decreasing the stretching rate of the polymer melt at the exit region of the die. The effect of length-to-diameter ratio of the die on the sharkskin melt fracture is also examined. It is found that sharkskin is more pronounced in short dies which is in accord with experimental observations. Finally, it is suggested that applied pressure at the capillary exit suppresses surface defects.     

Flow behaviour of rubber in capillary and injection moulding dies

This study is concerned with the flow behaviour of a rubber compound in capillary and injection moulding dies in the temperature range of 80–120°C. The injection moulding die designs had a tapered angle ranging from 40° up to 150°. The rheological characterisation of the rubber compound in the capillary dies showed that rubber slips at the wall, and this was modelled with an appropriate slip law. The pressure drops in the system were measured for all tapered dies. Numerical simulations were then carried out with a purely viscous (Carreau) model and a multimode viscoelastic (K-BKZ) model. The results showed a good agreement with the experiments for both the capillary and the injection moulding dies, provided that slip is included in the simulations as determined experimentally.     

Improved interfacial surface generator for the co‐extrusion of micro‐ and nanolayered polymers

Two dies for polymer co‐extrusion layer multiplication are evaluated experimentally and computationally in terms of pressure drop and layer uniformity. The first design is that of the original die, is compact, and has successfully been used to co‐extrude low elasticity polymers with closely matched rheological properties. The second die design, the one that is being modified, achieves a more balanced flow path with constant cross‐sectional area. Flow visualization experiments and computational simulations show matched performance between the dies when layering similar viscosity materials and better layering performance of rheologically dissimilar materials with the improved dies compared to the original die design. Furthermore, the improved die has a much lower pressure drop. This facilitates decreased energy consumption or the allowance of additional multiplier dies to be added resulting in an increased total number of layers. POLYM. ENG. SCI., 54:636–645, 2014. © 2013 Society of Plastics Engineers     

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.     

Experimental investigation of the rheological behaviors of polypropylene in a capillary flow

The rheological characterization of polymer melts is strongly related to their material properties. In this study, we focused on the rheological behaviors of a polypropylene (PP) melt through a capillary die. With an advanced twin‐bore capillary rheometer with dies measuring 1.0, 0.5, and 0.25 mm in diameter, experiments were performed over a shear‐rate range of 3 × 10² to 5 × 10³ s^?1 at three temperatures, 210, 220, and 230 °C. The results demonstrate that the geometry dependence of the PP viscosity relied on the die diameter and the temperature of the PP melt. The viscosity values of the PP melt in the 0.25‐mm diameter die were higher than were those in the 0.5‐ and 1.0‐mm dies at 220 and 230 °C. However, the viscosity values in all of the tested dies were similar at 210 °C. The tendency for the viscosity to decrease as the temperature of the polymer melt increased weakened in the 0.25‐mm diameter die. As a result, the pressure applied to the PP melt in the 0.25‐mm diameter die increased; this caused a decrease in the free volume between molecules. On the basis of the Barus equation, the contribution of pressure to the changed viscosity in each die at each of the tested temperatures was calculated and was found to be as high as 32.86% in the 0.25‐mm die at 230 °C. Additionally, the effect of the wall slip on the geometry dependence of the PP viscosity in the tested dies was investigated with a modified Mooney method. The values of the slip velocity revealed that wall slip occurred only in the 0.25‐mm die at 210 °C. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43459.     

Effect of wall slip on blown film thickness distribution

One of the most important materials for blown film is high‐density polyethylene (HDPE) with wide molecular weight distribution. First, we computed a wall stress at the entrance of a spiral groove in a particular die during blown film processing on a particular condition, to which a similar condition is widely utilized in a film works. The computed value is about 170 kPa, while the HDPE melt slips at die wall at stresses above approximately 50 kPa. The stress of 170 kPa is sufficiently large for the slip occurrence of the melt. Then, we investigated the effects of wall slip and melt visosity on film thickness distribution in the circumferential direction; the distribution tends to decrease with decreasing wall slip and melt viscosity. This tendency is explained by considering flow distribution in a spiral mandrel die and polymer melt flow characteristics.     

Experimental study and modeling of wall slip of polymethylmethacrylate considering different die surfaces

Wall slip of polymethylmethacrylate (PMMA) was studied on different flow channel surfaces using a rheological slit die and a high pressure capillary rheometer. As die surfaces polished steel, ground steel, and Si doped Diamond like carbon (DLC) were used. A new wall slip model is presented in this paper which assumes a lubricating film between the polymer melt and the die surface. The slip velocity has a power law dependency on wall shear stress. In the double logarithmic plot the wall slip curves are linear and can be parallel shifted to higher values with increasing temperature. The predicted dependencies of the wall slip velocity could be confirmed with experiments conducted with PMMA on polished steel. Furthermore, the die surface influences the flow behavior of PMMA. No wall slip was found on ground steel and on DLC. No complete film could be established by the lubricant on the ground steel die wall. The DLC‐coating exhibits a similar surface roughness and surface energy to polished steel, but the chemical composition is different. It is a metastable form of amorphous carbon containing sp² and sp³ bonds. As a consequence slip additives have a low ability to bond to this material. POLYM. ENG. SCI., 58:1391–1398, 2018. © 2017 Society of Plastics Engineers     

The synergistic effect of boron nitride particle and die on the capillary extrusion processability of mLDPE

The synergistic effects of boron nitride (BN) powder and die on the rheology and processability of metallocene‐catalyzed low density polyethylene (mLDPE) were investigated. The processability in the extrusion process is closely related to the interfacial properties between the polymer melts and the die wall. BN powder was added to mLDPE to reduce the friction coefficient and surface energy. Adding 0.5 wt% BN powder to mLDPE was very effective in improving the processability and the extrudate appearance. To study the effect of die surface property, three different dies were applied in capillary extrusion. One was conventional tungsten carbide (TC) die, and the others were hot‐pressed BN (hpBN) die and hot‐pressed BN composite (hpBNC) die. The applications of these BN dies were quite effective in delaying surface melt fracture (sharkskin) and postponing gross melt fracture to higher shear rate compared to the TC die. These improvements result from the fact that BN dies reduce the wall shear stress significantly and promote slip. The synergistic effect of processability could be obtained when both BN powder and hpBN die were used together.     

The Finite Element Simulation of Polymer Coextrusion Based on the Slip Boundary

The three-dimensional flow of Non-Newtonian polymer melts in coextrusion dies was analyzed based on finite element simulations. The analysis considered the slip both die wall-polymer and polymer-polymer interface. The slip boundary condition is founded based on the Generalized Navier slippage model. The effects of die wall roughness on the interface were examined farther. It is found that decreasing the roughness of the fluid path can make the velocity field more uniform and the interfacial offset less. If consider the interface alip of two melts, the homologous of interface-slip coefficient and die-wall slip coefficient may ensure the stabilization of the interface.     

聚合物挤出口模设计的数值研究进展

综述了国内外数值研究聚合物挤出口模设计的进展。在壁面无滑移条件下,早期数值模拟了聚乙烯、硬质聚氯乙烯、聚丙烯、丙烯腈-丁二烯-苯乙烯、聚苯乙烯、橡胶等聚合物口模挤出过程,优化设计了棒材、管材、板材和异型材的挤出口模。近年来,数值研究壁面滑移条件和工艺条件对口模流道内熔体流场的影响,深入研究制品的离模膨胀行为。研究表明,改善壁面条件有助于减小聚合物制品的离模膨胀比,有利于提高制品品质。     

Compensating for die swell in the design of profile dies

Because of the effects of die swell, the final shape of an extrudate is often substantially different from that of the exit opening of the die. As a result, the design of profile dies producing complex shapes often involves more than just “balancing” the die but also compensating for the effects of die swell. Typically, a successful design of such dies is achieved only through much “cut and try,” However, with the use of a fully three‐dimensional finite element flow algorithm along with quick mesh generating capabilities, the usual cut and try involved in the design of many profile dies can be greatly reduced, if not eliminated. This paper demonstrates how the effects of die swell can be compensated for in the design of profile dies. For profiles with one plane of symmetry, this includes compensating for the sideways translation of the extrudate as well as the change in shape that the extrudate experiences. Completely asymmetric profiles undergo a “twisting” downstream of the die. This twisting, which appears not to have been reported in the literature (at least for isothermal extrusion), is also accounted for here, along with the change in shape that the extrudate undergoes. The translation or twisting of profiles downstream of a die is often attributed to non‐Newtonian or non‐isothermal effects. Only isothermal Newtonian examples are considered here. These results clearly show that asymmetry of the profile will result in a translation and twisting of the extrudate even in the isothermal Newtonian case.     

Sharkskin and oscillating melt fracture: Why in slit and capillary dies and not in annular dies?

The sharkskin and stick‐slip polymer extrusion instabilities are studied primarily as functions of the type of die geometry. Experimental observations concerning the flow curves, the critical wall shear stress for the onset of the instabilities, the pressure and flow rate oscillations, and the effects of geometry and operating conditions are presented for linear low‐density polyethylenes. It is found that sharkskin and stick‐slip instabilities are present in the capillary and slit extrusion. However, annular extrusion stick‐slip and sharkskin are absent at high ratios of the inside‐to‐outside diameter of the annular die. This observation also explains the absence of these phenomena in other polymer processing operations such as film blowing. These phenomena are explained in terms of the surface‐to‐volume ratio of the extrudates, that is, if this ratio is high, sharkskin and stick‐slip are absent. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers     

Co-extrusion of unfilled and TiO2-filled polyethylene: Influence of viscosity and die cross-section on interface shape

An experimental study of the co-extrusion of polyethylene and TiO₂-filled polyethylene through capillary and rectangular cross-section dies has been carried out. The influence of viscosity ratio, cross-section type, die length and duration of flow has been studied. Low viscosity melts will encapsulate high viscosity melts during flow through cylindrical and rectangular dies. Low viscosity unfilled melts can encapsulate higher viscosity filled melts and low vicosity filled melts can encapsulate higher viscosity unfilled melts. However, the rate and extent of encapsulation seems to be greater for the former case. This may be due to differences in the viscosity-shear stress behavior of the filled and unfilled melts. In rectangular dies, the extent of encapsulation for any pair is greater when the interface is initially perpendicular to the shorter cross-section dimension. The results are consistent with the idea that encapsulation primarily depends upon the ratio of die length to initial interface length.     

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.     

Finite difference solution for flow from a slit die

A finite difference solution for an isothermal viscoelastic liquid flowing through a film forming die is investigated. The fluid is described by a Maxwell model in which the time derivative has been replaced by an Oldroyd's convective derivative and the numerical technique used combines features of the Solution Algorithm (SOLA), Simplified Marker and Cell method (SMAC), and SOLASMAC. The numerical scheme was tested with a Newtonian fluid and high density polyethylene (HDPE). Two slit dies with gap-to-length ratios 4 and 16 were used. In the two cases, die swell has occurred: A maximum of 4.5% swell was observed for the Newtonian fluid, while up to 77% swell was attained with HDPE. The simulated flow behavior of HDPE exhibited high amplitude oscillations at dimensionless time greater than 0.18. These oscillations are thought to be related to the nature of sheet flow, which can be unstable. This study shows that with some improvement the finite difference method can be used for studying the extrusion of polymer through slit and capillary dies.     

Slip effects in tapered dies

Approximate analytical equations are derived for the calculation of pressure drop of power‐law fluids for viscous flow through tapered dies for a wide range of wall‐slip conditions. The predicted pressure drop values are compared with two‐dimensional (2D) finite element calculations to identify contraction angles for which the analytical equations can be used. It is found that the disagreement increases with increase of the contraction angle and with increase of wall slip. At a given flow rate, the pressure drop from the analytical equations is found to decrease continuously with contraction angle, which agrees with the 2D calculations only at small contraction angles. At larger contraction angles, the 2D calculations show that pressure drop increases with contraction angle as opposed to the no‐slip case where pressure drop saturates. The existence of a minimum pressure at a specific taper angle depends on the rheological parameters of the fluid and the degree of slip (slip‐law exponent), and has scientific importance for the die designer. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers