J. Vlachopoulos

Three-dimensional studies on bicomponent extrusion

The present work is concerned with the mathematical modelling and numerical simulation of three-dimensional (3-D) bicomponent extrusion. The objective is to provide an understanding of the flow phenomena involved and to investigate their impact on the free surface shape and interface configuration of the extruded article. A finite element algorithm for the 3-D numerical simulation of bicomponent stratified free surface flows is described. The presence of multiple free surfaces (layer interface and external free surfaces) requires special free surface update schemes. The pressure and viscous stress discontinuity due to viscosity mismatch at the interface between the two stratified components is handled with both a double node (u−v−w−P1−P2−h1−h2) formulation and a penalty function (u−v−w−P−h1−h2) formulation.The experimentally observed tendency of the less viscous layer to encapsulate the more viscous layer in stratified bicomponent flows of side-by-side configuration is established with the aid of a fully 3-D analysis in agreement with experimental evidence. The direction and degree of encapsulation depend directly on the viscosity ratio of the two melts. For shear thinning melts exhibiting a viscosity crossover point, it is demonstrated that interface curvature reversal may occur if the shearing level is such that the crossover point is exceeded. Extrudate bending and distortion of the bicomponent system because of the viscosity mismatch is shown. For flows in a sheath-core configuration it is shown that the viscosity ratio may have a severe effect on the swelling ratio of the bicomponent system.Modelling of the die section showed that the boundary condition imposed at the fluid/fluid/wall contact point is critical to the accuracy of the overall solution.

Controlled Degradation of Polypropylene: A Comprehensive Experimental and Theoretical Investigation

Abstract Experimental and modeling studies of the free-radical-induced degradation of polypropylene (PP) in the melt phase have been carried out. Experiments have been performed in a single-screw plasticating extruder using a peroxide as the free-radical source. Concentration of the peroxide was in the range 0.01–0.6 wt%. Results in the form of melt flow index (MFI) values, viscosity curves, and molecular weight distribution (MWD) of the produced resins are presented here. Based on these results, a constitutive equation describing the shear viscosity of the melt as a function of shear rate, temperature, and molecular weight has been derived. The extensional viscosity of these resins has been determined as a function of strain rate using Cogswells analysis of converging flows. A previously developed kinetic model (plug flow) has been used to simulate the changes of the average molecular weights of the MWD, and a sensitivity analysis of this model has been carried out.

A finite element analysis of laminar flows through planar and axisymmetric abrupt expansions

Abstract Laminar flow of a Newtonian fluid in planar and axisymmetric abrupt expansions is studied by solving the Navier-Stokes equations using the finite element method. The results consolidate information provided in the literature and provide a broader picture of how the expansion ratio and Reynolds number influence the reattachment length, downstream location of the eddy and the relative eddy intensity in both co-ordinate systems.

Three-dimensional non-isothermal extrusion flows

A three-dimensional (3-D) non-isothermal study of viscous free-surface flows with exponential dependence of viscosity on temperature is presented. The effects of non-isothermal conditions and/or geometry on the extrudate shape are investigated with a fully three-dimensional finite element/Galerkin formulation. Apart from the well known thermally induced extrudate swelling phenomenon, bending and distortion of the extrudate may occur because of temperature differences and/or geometric asymmetries. A temperature difference across the die can be imposed by heating or cooling the die walls, but can also arise because of asymmetric viscous heat generation due to the die geometry. Temperature differences affect velocity profiles because of the temperature dependence of viscosity and lead to extrudate bending, an effect known as “kneeing” in the fiber spinning industry. It is also shown numerically and confirmed experimentally that the die geometry induces extrudate bending even in the case of isothermal Newtonian flows.

Boundary conditions for contract lines in coextrusion flows

A bicomponent coextrusion process is modelled using a 3-D finite element formulation. The layer uniformity problem in coextrusion is addressed by examining the effects of the polymer melt/polymer melt/die wall contact line boundary condition. It has been observed that the less viscous polymer layer will tend to displace the more viscous polymer layer near the die wall. The behaviour of the contact lisle is considered to be either a “stick” or “slip” boundary condition. In the “stick” boundary condition, the contact line does not move from its original position after the two polymer layers meet, A slip boundary condition allows the contact line to move along the die wall. The calculated interfaces which result from different contact line assumptions are determined. Results show that if a “stick” boundary condition is appropriate for a given fluid/fluid/solid contact line, then a very thin entrained layer of the more viscous polymer melt will be trapped between the less viscous polymer melt and the die wall. Slip boundary conditions would allow complete displacement of the contact line along the die wall. Both slip and stick boundary conditions produce similar interface profiles far away from the die wall for small viscosity ratios. In certain eases, the displacement of the more viscous material by the less viscous material will cease and a static interface structure is produced regardless of die length. Experimental work with polycarbonate melts is compared with the numerical simulations.

The effect of multiple extrusion passes during recycling of high density polyethylene

High density polyethylene blow modling resins have been identified as a primary material for solid waste minimization and recycling. An experimental study into the effect of multiple extrusion cycles on the properties of a virgin homopolymer, virgin copolymer, natural post consumer, and mixed color post consumer blow molding resin was conducted. Rheological properties such as shear and elongational viscosity and elastic modulus were studied in the context of changes experienced during recycling. The G9–G0 (elastic storage and loss modulus) crossover point was used to measure relative changes in the polydispersity index and molecular weight distribution (MWD). It is also shown that extrudate swell and sag change after multiple extrusion passes. Environmental stress crack resistance was also measured. A rationale for the significant decrease in the environmental stress crack resistance of the virgin copolymer resin is presented. The results are analyzed in terms of known degradation mechanisms such as chain scission and crosslinking, and their relationship to the molecular structure. uf6d9 1997 John Wiley & Sons, Inc. Adv in Polym Techn 16: 11–24, 1997 tend to be application-specific measures. RheologiBackground Information and cal characterization of high density polyethylene Literature Review (HDPE) involves measuring the viscosity and viscoelasticity of the molten polymer. Unlike simple fluP ids, these properties for HDPE have a strong depenolyethylene, like all polyolefins, is described dence on temperature, shear rate, molecular weight, by its density, strength, molecular weight and MWD. There are two primary flow mecha(MW), crystallinity, and melt flow or rheological nisms, shear and elongational flow. Shear flow decharacteristics. Other properties such as environscribes the response of the polymer to an imposed mental stress crack resistance (ESCR) and optics shearing force. Elongational flow is the response of the polymer to an imposed stretching or pulling force. Although not independent of each other, they Correspondence to: A. T. P. Zahavich uf6d9 1997 by John Wiley & Sons, Inc. CCC 0730-6679/97/010011-14 MULTIPLE EXTRUSION PASSES both have their own viscosity measures. At very he 5 9(n 1 1)(DPe) 32hċ2 (4) low shear rates (ċ , 1022 s21), a molten polymer behaves roughly as a Newtonian fluid. Beyond this point the shear stress of molten HDPE has a nonlinand: ear relationship with shear rate. As the shear rate increases the rate of increase in shear stress de« 5 4hċ2 3(n 1 1)DPe (5) creases and this is described as shear thinning. Within the range of typical extrusion shear rates (5 , ċ , 1000 s21) this relationship can be described Similar to the importance of elongational viscosby a power law expression: ity, viscoelasticity manifests itself in the behavior of the molten polymer in the parison. Viscoelasticity h 5 mċn21 (1) determines the elastic recovery of a polymer after a load is applied to cause viscous creep. This pheThe coefficient, m, is a measure of the viscous nature nomenon is time and temperature dependent. As a of the polymer. The power law index, n, is a measure load is applied the molecules tend to disentangle of the effect of shear thinning; as n approaches 1, and align themselves in the direction of the load. the fluid tends to be Newtonian. When the load is removed the molecules relax. The shape of the MWD and the average molecular The time-dependent stress relaxation modulus, weight are directly related to the melt flow properG(t), is defined as the ratio of an applied shear stress, ties and processing performance, in terms of extrut, to the shear strain, c: sion output rate and pressure.1 As the length of the molecule increases the resistance to flow increases. G(t) 5 t c (6) As the breadth of the distribution increases there is a greater tendency to shear thinning.2 In a blow molding process HDPE is extruded into When a sinusoidal rotational shear strain is applied, a molten tube called a parison. After the bottle molds as done in dynamic measurements, G is a function are clamped around the parison air is blown into of the rotational speed, g, and as a complex function the parison which expands it to conform to the mold. can be decomposed: Minimal stretching of the parison prior to clamping and the ability of the parison to expand during blow G(g) 5 G9(g) 1 iG0(g) (7) molding is critical. The elongational flow characteristics, described by the elongational viscosity, he , which results in the following complex function for is a measure of how well the parison will resist the shear stress: stretching and conform to the mold during blowing. By definition: t 5 c [G9sin(gt) 1 G0cos(gt)] (8) The elastic or storage modulus, G9(g), is in phase he 5 Fe/A « (2) with the applied strain and measures the mechanical energy stored during each rotation. The loss moduwhere Fe is the elongational force applied over the lus, G0(g), is out of phase with the applied strain cross-sectional area, A, normal to the flow, and « is and measures the amount of mechanical energy disthe rate of elongation or stretch rate.3 The measuresipated per cycle. ment of he is difficult, but it has been shown by The Relationship between viscoelastic properties Laun and Munstedt4 that, at very low shear rates, and MW characterization has been reported widely.6 where the shear flow is near Newtonian, the Trouton However, it has usually been in the direction of MW relationship holds for LDPE where: predicting visco-elasticity. Within the last 15 years, Tuminello,7 Tuminello and Cudre-Mauroux,8 Yu (3) he 5 3h(ĉ) and Ma,9 and others have successfully used dynamic measurements to describe MW and MWD properties. More specifically, Shang10 used the terminal At higher shear rates, Cogswell5 proposed that he is related to the shear rate, shear viscosity, and enzone crossover point, Gc(g), of G9(g) and G0(g) to predict the polydispersity, the ratio of the weight trance pressure loss, DPe:

Computer Simulation of Film Blowing

The present work is concerned with the numerical simulation of the blown film process and its comparison to experimental data. The bubble formation and the biaxial stretching of the film were studied using a non-isothermal, purely viscous, temperature dependent model. The model is incorporated into a software package called B-FILMCAD. Special attention has been given to the importance of the temperature in the modeling of the blown film process. It was found that temperature is by far the most important modeling parameter. The results show that the majority of the process parameters can be successfully predicted by the employed model, showing a good agreement between experimental data from various investigators and numerical predictions. This was valid for most of the studied cases despite the diversity of the experimental data. With the use of the present model many useful conclusions can be drawn about blown film production lines.

Die swell and melt fracture: Effects of molecular weight distribution

SummaryThe equations for determining die swell of molten polymers are discussed. The critical conditions for melt fracture and die swell results are combined in order to explain the flow behavior at the onset of instability. It is shown that the factorn

Transient finite element analysis of generalized Newtonian coextrusion flows in complex geometries

bar M_z bar M_{z + 1} /bar M_w^2