Extrudate Swell Research Articles

Melt rheology and extrudate swell of titanium (IV) oxide nanoparticle-filled isotactic polypropylene: Effects of content and surface characteristics

Melt rheology and extrudate swell of isotactic polypropylene (iPP) filled with titanium (IV) oxide (TiO 2) nanoparticles of varying content (i.e., 5–30 wt.%) and surface characteristics [i.e., uncoated, silica (SiO 2)-coated, and stearic acid-coated] during capillary melt-extrusion were investigated. The wall shear stress of both the iPP melt and the melts that contained nanoparticles increased in a non-linear, decreasing-rate manner with increasing apparent shear rate. The incorporation of the nanoparticles generally increased the wall shear stress of the melts, with stearic acid-coated ones exhibiting the least variation in the property values. The shear viscosity, when plotted with the real shear rate on a log–log scale, exhibited a linear, decreasing function with the real shear rate. Clearly, the iPP melts containing stearic acid-coated TiO 2 nanoparticles exhibited the lowest shear viscosity values. Lastly, the extrudate swell of the iPP melt and the melts that had been filled with nanoparticles was found to increase with increasing apparent shear rate, while it was found to decrease generally with the addition and increasing amount of nanoparticles.

Rolling of bread dough: Experiments and simulations

Bread dough (a flour–water system) has been rheologically characterized using shear rheometry at room temperature. Its flow curve shows a viscoplastic shear-thinning material, which obeys the Herschel–Bulkley model. In addition, substantial wall slip is exhibited by the material, and an appropriate slip law has been formulated. The material has been rolled using the Sentmanat Extensional Rheometer (SER) (Xpansion Instruments) with an aspect ratio of radius to minimum gap of R/ H 0 = 4.3. Rolling experiments have been performed for different feed thickness ratios and roll speeds. The exit thickness ratios and the torques to roll the samples have been measured. They have been found to increase substantially with roll speed and initial sample thickness. Two-dimensional finite-element simulations based on the rolling geometry and the rheological data with slip provide a wealth of information regarding yielded/unyielded zones, pressure and stress distributions along the rolls. The results from the simulations are in good agreement with the experimental torque values although underestimate the thickness of the exiting sheets. It is argued that the latter is a consequence of viscoelasticity of the bread dough, which manifests itself in a free-surface flow, where (extrudate) swell becomes significant.

Prediction of extrudate swell in polymer melt extrusion using an Arbitrary Lagrangian Eulerian (ALE) based finite element method

Accurate prediction of extrudate (die) swell in polymer melt extrusion is important as this helps in appropriate die design for profile extrusion applications. Extrudate swell prediction has shown significant difficulties due to two key reasons. The first is the appropriate representation of the constitutive behavior of the polymer melt. The second is regarding the simulation of the free surface, which requires special techniques in the traditionally used Eulerian framework. In this paper we propose a method for simulation of extrudate swell using an Arbitrary Lagrangian Eulerian (ALE) technique based finite element formulation. The ALE technique provides advantages of both Lagrangian and Eulerian frameworks by allowing the computational mesh to move in an arbitrary manner, independent of the material motion. In the present method, a fractional-step ALE technique is employed in which the Lagrangian phase of material motion and convection arising out of mesh motion are decoupled. In the first step, the relevant flow and constitutive equations are solved in Lagrangian framework. The simpler representation of polymer constitutive equations in a Lagrangian framework avoids the difficulties associated with convective terms thereby resulting in a robust numerical formulation besides allowing for natural evolution of the free surface with the flow. In the second step, mesh is moved in ALE mode and the associated convection of the variables due to relative motion of the mesh is performed using a Godunov type scheme. While the mesh is fixed in space in the die region, the nodal points of the mesh on the extrudate free surface are allowed to move normal to flow direction with special rules to facilitate the simulation of swell. A differential exponential Phan Thien Tanner (PTT) model is used to represent the constitutive behavior of the melt. Using this method we simulate extrudate swell in planar and axisymmetric extrusion with abrupt contraction ahead of the die exit. This geometry allows the extrudate to have significant memory for shorter die lengths and acts as a good test for swell predictions. We demonstrate that our predictions of extrudate swell match well with reported experimental and numerical simulations.

A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows

This work presents a numerical method for solving three-dimensional (3D) viscoelastic unsteady free surface flows governed by the Oldroyd-B constitutive equation. It is an extension of the two-dimensional (2D) technique introduced by Tomé et al. [M.F. Tomé, N. Mangiavacchi, J.A. Cuminato, A. Castelo, S. McKee, A numerical technique for solving unsteady viscoelastic free surface flows, J. Non-Newt. Fluid Mech. 106 (2002) 61–106]. The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing both visualization and the location of the free surface. The numerical technique is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a 3D-pipe. Numerical results include the simulation of the transient extrudate swell and jet buckling.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5].

Rheological properties, flow visualization and extrudate swell of NR compound by rotating‐die rheometer

AbstractAn experimental apparatus coupled with a rotating die system was especially designed and manufactured to study the rheological properties, flow patterns and swelling behavior of natural rubber (NR) compound for different shear rates and die rotating speeds at a test temperature of 110°C, the results being compared with those by the static capillary die. It was found that NR compound used exhibited psuedoplastic non‐Newtonian behavior. The rotation of the capillary die could reduce the extrusion load. The wall shear stress for any given shear rates increased with increasing die rotating speed. The fluctuation of the entrance pressure drop increased with increasing die rotating speed. The flow pattern development in the rotating‐die rheometer was different from that observed in the static die. The flow patterns in the rotating die were clearly unstable and contained two flow components which included axial flow along the barrel and circumferential flow at the die entrance. The size and shape of the axial and circumferential flows were more dependent on the piston displacement. It was found that the swelling ratio of the NR compound decreased with increasing die rotating speed. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.

Melt rheology and extrudate swell of organobentonite-filled polypropylene nanocomposites

Melt rheological properties and extrudate swell of organobentonite-filled polypropylene nanocomposites were studied by using a capillary rheometer in a shear rate range of 50–8000 s −1 and a temperature range of 190–210 °C. The nanocomposites exhibited shear-thinning behavior and the viscosity was well-described by the power law in this shear rate region. The addition of organobentonite enhanced the pseudoplasticity, i.e. increased the shear thinning behavior. With increasing organobentonite concentration, the shear stress/viscosity increased, while the power law index ( n) decreased, and this effect is more significant at higher filler concentrations (>3 wt%). The dependence of shear viscosity on temperature obeyed the Arrhenius–Eyring expression, and the activation energy ( E a) decreased with increasing shear rate. Extrudate swell is a non-linear function of shear rate, while it is a linear function of shear stress or temperature. With increasing organobentonite concentration (>3 wt%), the extrudate swell clearly decreased, which is attributed to the limitation of the elastic recovery of the polymer chains by oriented silicate layers.

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

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

Rheological Evaluation and Observations of Extrusion Instabilities of Biodegradable Polyesters

Abstract The rheological properties of two commercially available biodegradable polyesters – poly(lactic acid) (PLA) and aliphatic-aromatic co-polyester Ecoflex™ – have been investigated. The rheological study was focused on measuring the viscosity and examining sharkskin, melt fracture, and extrudate swell phenomena, which are crucial in industrial applications. The experiments show that the two biodegradable polyesters exhibit shear-thinning behavior similar to other polymers and the Cox-Merz rule is obeyed. It was observed that with increasing shear rate PLA exhibits sharkskin and gross melt fracture while Ecoflex™ exhibits only gross melt fracture. Experimental results indicate that both biodegradable polyesters exhibit small extrudate swell, up to 28% for PLA and up to 34% for Ecoflex™.

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

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

A marker-and-cell approach to viscoelastic free surface flows using the PTT model

This work is concerned with the development of a numerical method capable of simulating two-dimensional viscoelastic free surface flows governed by the non-linear constitutive equation PTT (Phan-Thien–Tanner). In particular, we are interested in flows possessing moving free surfaces. The fluid is modelled by a marker-and-cell type method and employs an accurate representation of the fluid surface. Boundary conditions are described in detail and the full free surface stress conditions are considered. The PTT equation is solved by a high order method which requires the calculation of the extra-stress tensor on the mesh contour. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. In order to validate the numerical method fully developed flow in a two-dimensional channel was simulated and the numerical solutions were compared with known analytic solutions. Convergence results were obtained throughout by using mesh refinement. To demonstrate that complex free surface flows using the PTT model can be computed, extrudate swell and a jet flowing onto a rigid plate were simulated.

Annular Extrudate Swell of Newtonian Fluids: Effects of Compressibility and Slip at the Wall

Numerical simulations have been undertaken for the benchmark problem of annular extrudate swell present in pipe extrusion and parison formation in blow molding. The effects of weak compressibility and slip at the wall are studied through simple linear laws. The finite element method is used to provide numerical results for different inner/outer diameter ratios κ under steady-state conditions for Newtonian fluids. The present results provide the shape of the extrudate, and, in particular, the thickness and diameter swells, as a function of the dimensionless compressibility and slip coefficients, B and Bsl, respectively. The pressures from the simulations have been used to compute the excess pressure losses in the flow field (exit correction). Weak compressibility slightly affects the thickness swell (about 1% in the range of simulations 0⩽B⩽0.02) mainly by a swell reduction, while slip drastically reduces the swelling to 1–2% for obvious slip (Bsl≈1) and to 0 for perfect slip (Bsl>10). The exit correction increases with increasing compressibility levels and is highest for the tube (κ=0) and lowest for the slit (κ=1). It decreases monotonically to 0 as the dimensionless slip coefficient reaches its asymptotic limit of perfect slip. All results are ordered with the diameter ratio κ, between the limits of tube (κ=0) and slit (κ=1).

The effect of molar mass distribution on extrudate swell of linear polymers

Extrudate swell is an important viscoelastic feature of polymer melt processing. Experimental work with linear polymers has identified extrudate swell to depend strongly on average molar mass and molar mass distribution. Unfortunately there was no method identified to distinguish the relative effects of average mass and polydispersity. This paper revisits previously published experimental data on high-density polyethylenes and proposes a model to understand the coupled effect of these two molecular variables. The model connects findings from double reptation models via the recoverable compliance to extrudate swell. The reported results provide support to the model and lead to a better understanding of the important role of high-mass fractions in polydisperse polymers.

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

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

Effect of molecular structure on extrudate swell behavior for different thermoplastic melts in an electro‐magnetized die

AbstractThe extrudate swell ratio of five different thermoplastic melts flowing in a constant shear rate rheometer having a capillary die with and without application of magnetic field was studied. The effects of the magnetic flux direction and density, die temperature, and wall shear rate on the extrudate swell and flow properties were investigated. The experimental results suggested that an increasing wall shear rate increased the swelling ratio for the polystyrene (PS), LLDPE, and PVC melts, but the opposite effect was observed for the ABS and PC melts. The extrudate swell ratio for the PS, ABS, PC, and LLDPE melts decreased with increasing die temperature, the effect being reversed for the PVC melt. Thermoplastic melts having high benzene content in the side‐chain and exhibiting anisotropic character were apparently affected by the magnetic field, the extrudate swell ratio increasing with magnetic flux density. The effect of the magnetic field on the extrudate swell ratio decreased in the order of PS → ABS → PC. The extrudate swell ratio for the co‐parallel magnetic field system was slightly higher than that for the counter‐parallel magnetic field system at a high magnetic flux density. POLYM. ENG. SCI., 47:270–280, 2007. © 2007 Society of Plastics Engineers.

Die‐swell behavior during the short‐tube flow of rubber compounds

AbstractIn this study, the flow properties and die‐swell ratios (B's) of two kinds of rubber compounds (SI was a calcium carbonate filled natural rubber compound, and SII was a carbon‐black‐filled natural rubber/butadiene–styrene rubber/cis‐1,4‐butadiene rubber compound) in a short‐tube extrusion flow were measured by means of a capillary rheometer under test conditions with a temperature of 90°C and an apparent shear rate varying from 10 to 4000 s−1 to identify the effects of extrusion conditions on the rheological behavior of the materials and to estimate B. The shear flow roughly obeyed the power law, whereas B increased nonlinearly with increasing extrusion rate. Under the same shear rates, the viscosity of SII was higher than that of SI, whereas the values of B of SI were higher than those of SII. Furthermore, B of the rubber compounds was estimated by means of an extrudate swell equation published in a previous work. The results show that the predictions of B were close to the measured data from the experiments. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007

Annular extrudate swell of pseudoplastic and viscoplastic fluids

Numerical simulations have been undertaken for the benchmark problem of annular extrudate swell present in pipe extrusion and parison formation in blow molding. The finite element method (FEM) is used to provide numerical results for different inner/outer diameter ratios κ under steady-state conditions. The Herschel-Bulkley model of viscoplasticity is used with the Papanastasiou regularization, which reduces with appropriate parameter choices to the Bingham–Papanastasiou, power-law and Newtonian models. The present results provide the shape of the extrudate, and in particular the thickness and diameter swells, as a function of the dimensionless power-law index (in the case of pseudoplasticity) and the dimensionless yield stress (in the case of viscoplasticity). The pressures from the simulations have been used to compute the excess pressure losses in the system (exit correction). While shear-thinning leads to reduced swelling relative to the Newtonian values for all κ-values, the opposite is true for shear-thickening fluids, which exhibit considerable swelling. Viscoplasticity leads to decreased extrudate swell as the dimensionless yield stress goes from zero (Newtonian behaviour) to an asymptotic value of fully plastic behaviour. The exit correction decreases to zero with a decrease in the power-law index to zero and an increase in the dimensionless yield stress to its asymptotic limit. However, the decrease is not monotonic: for power-law fluids it has maxima in the range of power-law indices between 0.8 and 0.6, while for viscoplastic fluids it has maxima around Bingham number values of 5.

Effect of filler treatments on rheological behavior of calcium carbonate and talc‐filled polypropylene hybrid composites

AbstractCommercial stearic acid treated calcium carbonate (CaCO3) was used to make a comparative study on rheological behavior of the CaCO3 and talc‐filled polypropylene (PP) hybrid composites with nontreated filler. Apparent shear viscosity and extrudate swell were investigated with variation of filler ratio and temperature with 30% by weight total of filler was used in PP composite. The Shimadzu capillary rheometer was used to evaluate shear viscosity and shear rate of the composite. It was found that the shear viscosities decrease with increasing shear rate. The apparent shear viscosity of the composite containing the stearic acid treated is slightly lower than untreated filler. Shear thickening behavior at higher shear rate has also shown by 15/15 treated composites at higher temperature about 220°C and investigation by SEM has proved that filler being densely packed at that condition. Treated composites also exhibit lower swelling ratio value than untreated composite, and swelling ratio also decreases linearly with increasing temperature and the die length–diameter ratio. It is believed that dispersion of filler play an important role not only on shear viscosity but also on swelling ratio of PP composite. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 5421–5426, 2006

Solving viscoelastic free surface flows of a second‐order fluid using a marker‐and‐cell approach

AbstractThis work is concerned with the numerical simulation of two‐dimensional viscoelastic free surface flows of a second‐order fluid. The governing equations are solved by a finite difference technique based on the marker‐and‐cell philosophy. A staggered grid is employed and marker particles are used to represent the fluid free surface. Full details for the approximation of the free surface stress conditions are given. The resultant code is validated and convergence is demonstrated. Numerical simulations of the extrudate swell and flow through a planar 4:1 contraction for various values of the Deborah number are presented. Copyright © 2006 John Wiley & Sons, Ltd.

Melt rheology and extrudate swell of low-density polyethylene/ethylene–octene copolymer blends

The melt rheological and extrudate swelling behavior of neat low-density polyethylene (LDPE) and blends of LDPE and ethylene–octene copolymer (EOC) was investigated using capillary rheometry at 185.0±0.5 °C. Dies having different length-to-inner diameter ( L/D) ratios were used (i.e., 5/1, 10/11, 10/2, and 30/2 mm/mm, respectively). For a given sample material, the real shear stress was observed to increase with increasing real shear rate, and, for a given real shear rate, the real shear stress was generally observed to increase with the addition and increasing amount of EOC. All of the sample materials exhibited the shear-thinning behavior. Both the tensile stress and the elongational viscosity were found to decrease with increasing elongational rate. Generally, both the tensile stress and the elongational viscosity increased with the addtion and increasing amount of EOC, with an exception for the 85/15 and 80/20 LDPE/EOC blends which exhibited a reversed order. Lastly, the extent of extrudate swelling of the sample materials in the small dies (i.e., inner diameter=1 mm) was greater than that in the larger ones (i.e., inner diameter=2 mm) and the use of a longer die also helped suppress the extent of the extrudate swelling.