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Synopsis A two-phase microstructural constitutive relation is combined with the thin-shell model for the simulation of blown film extrusion. This combination includes equations for momentum conservation, flow-enhanced crystallization, viscoelasticity, and bubble-tube cooling. Consistent with typical blown film operation, the simulations set the bub...
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Context 1
... blown film extrusion, molten polymer is extruded through an annular die while air is fed through an inner concentric bubble tube Fig. 1. This internal air inflates the bubble tube, increasing its radius by stretching it in two directions: the machine or axial direction and the transverse direction. This action increases the bubble-tube radius and decreases film thickness. Simultaneously, the nip rolls above the die flatten the bubble and subject the film to tension in ...
Context 2
... of the bubble-tube radius, y R / Z, with respect to the axial direction the longitudinal or axial gradient, and a value for this variable is unknown at Z = 0. Rather, a boundary condition involving the axial gradient of the bubble-tube radius is set at the end of the spatial domain Z=L, at the top of the bubble, and just below the nip rolls Fig. 1. In earlier work, the boundary condition at Z = L was chosen to be Dr/ D = 0, where Dr/ D is the advection expression for the bubble-tube radius r. The resulting two-point boundary-value problem has been simulated using shooting methods, which can be numerically unstable, or finite-difference methods, which can be computa- tionally ...
Citations
... The ability to account for the effects of these molecular details during industrial processing is highly desirable. Particularly, in blown film processing, the solidification of the material determines the overall geometry for the air bubble and the thickness of the final product [6][7][8]. ...
Polymer crystallization occurs in many plastic manufacturing processes, from injection molding to film blowing. Linear low-density polyethylene (LLDPE) is one of the most commonly processed polymers, wherein the type and extent of short-chain branching (SCB) may be varied to influence crystallization. In this work, we report simultaneous measurements of the rheology and Raman spectra, using a Rheo-Raman microscope, for two industrial-grade LLDPEs undergoing crystallization. These polymers are characterized by broad polydispersity, SCB, and the presence of polymer chain entanglements. The rheological behavior of these entangled LLDPE melts is modeled as a function of crystallinity using a slip-link model. The partially crystallized melt is represented by a blend of linear chains with either free or cross-linked ends, wherein the cross-links represent attachment to growing crystallites, and a modulus shift factor that increases with the degree of crystallinity. In contrast to our previous application of the slip-link model to isotactic polypropylene, in which the introduction of only bridging segments with cross-links at both ends was sufficient to describe the available data, for these LLDPEs, we find it necessary to introduce dangling segments, with cross-links at only one end. The model captures quantitatively the evolution of viscosity and elasticity with crystallization over the whole range of frequencies in the linear regime for the two LLDPE grades.
... Hyun et al. (2004) introduced a viscoelastic Phan-Thien Tanner (PTT) non isothermal model. Doufas and McHugh (2001) and Pirkle and Braatz (2010) introduced flow induced crystallization with a two-phase model. ...
Drawing instabilities and rupture are a serious limitation in polymer fibre and film processing. Draw resonance and fibre or film rupture depend on the processing conditions, heat transfer and on the rheology of the polymer and some of these defects may also be encountered for Newtonian fluids. This paper reviews the different instabilities observed in fibre spinning, cast-film and film blowing. The time dependent equations are presented for the simplified situation of constant width cast-film and two modelling strategies, linear stability analysis and direct simulation, are proposed and then applied to the different fibre and film processes.
... This behavior is due to biaxial stretching of the molten polymer during the tubular extrusion process, different from the uniaxial flat-sheet extrusion present in the thermoplastic extrusion process. The biaxial stretching effects on molecular orientation, conformation, and crystallization result in a higher strength thin plastic film (Pirkle and Braatz, 2010). These results are in agreement with the study of Rodríguez et al. (2006), where a synergistic behavior between the plasticizer and the surfactants in films of potato starch fabricated by casting method was observed. ...
... In tubular film extrusion, molten polymer is extruded through an annular die while air is fed through an inner concentric bubble-tube. This internal air causes the cylindrical film to inflate, increasing the radius of the polymer bubble by stretching it in two directions, and decreasing the film thickness (Pirkle and Braatz, 2010). Golebiewski et al. (2008) reported for tubular film thickness fabricated with LDPE-montmorillonite 0.022 ± 0.002 mm. ...
The objective of this research was to evaluate the effects of processing parameters on functional properties of extruded and tubular films. Four formulations of sorghum starch, with glycerol, and Yucca Schidigera extract, were used to prepare extruded and tubular films. Based on mechanical testing the formulation of 78.5% sorghum starch, 20% glycerol and 1.5% Yucca Schidigera extract, with 20% moisture content, showed the best mechanical properties and was selected to evaluate the effect of barrel temperature and screw speed during the fabrication of tubular films. Films were characterized through mechanical testing, scanning electron microscopy, water vapor permeability, water disintegration index, density and thickness.
... The final bubble dimensions, e.g., blow-up ratio (BUR, the ratio of bubble radii at FLH and the die) and thickness reduction (TR, the ratio of sheet thicknesses at the die and FLH), are mainly controlled by air pressure difference across the bubble and axial drawing (Middleman, 1977; Petrie, 1970a, 1970b). There have been many theoretical attempts and experimental observations on this process over last four decades due to its academic and industrial importance (Han and Park, 1975; Kanai and White, 1984; Cain and Denn, 1988; Ghaneh-Fard et al., 1996; Yoon and Park, 2000; Doufas and McHugh, 2001; Fang et al., 2005; Zhang and Lafleur, 2008; Pirkle and Braatz, 2010 ). Especially , various theoretical issues including stability and sensitivity as well as multiple base flows have been explored for elucidating intricate phenomena occurring in film blowing systems (Hyun et al., 2004; Shin et al., 2007; Pirkle and Braatz, 2010). ...
... There have been many theoretical attempts and experimental observations on this process over last four decades due to its academic and industrial importance (Han and Park, 1975; Kanai and White, 1984; Cain and Denn, 1988; Ghaneh-Fard et al., 1996; Yoon and Park, 2000; Doufas and McHugh, 2001; Fang et al., 2005; Zhang and Lafleur, 2008; Pirkle and Braatz, 2010 ). Especially , various theoretical issues including stability and sensitivity as well as multiple base flows have been explored for elucidating intricate phenomena occurring in film blowing systems (Hyun et al., 2004; Shin et al., 2007; Pirkle and Braatz, 2010). However, there still remain many aspects to be clarified for nonlinear dynamical behavior of this process. ...
Pseudo arc-length continuation scheme has been implemented in Newton’s numerical method for effectively solving complicated
steady-states in viscoelastic film blowing processes. Various steady contours in both isothermal and nonisothermal cases with
fixed freeze-line height have been obtained under constant bubble pressure or constant tension conditions. It turns out that
the incorporation of single continuation equation into governing equation set is very efficient to successively track solutions
with multiplicity.
Keywordsfilm blowing–Newton’s method–pseudo arc-length continuation–PTT viscoelastic fluid
... The resulting biaxial stress can induce further crystallization, an action termed flow-induced crystallization. Although this effect has been included in recent work involving microstructural constitutive relations [2][3][4][5][6][7], it is neglected in earlier models of blown film extrusion [8][9][10]. ...
... For computer simulation, either (i) air bubble inflation pressure and modified machine tension [16] or (ii) bubble air mass and nip-roll speed [7] can be set as constants. In actual physical operation [17,18], either experimental or commercial, the air bubble inflation pressure and modified machine tension are not fixed and are not easy to control tightly. ...
... Unlike the Hoffman-Lauritzen kinetic expression, which has five parameters, this expression has three parameters and allows a finite crystallization rate at the die, rather than restricting crystallization to temperatures below the melting point. Like most past studies of blown-film extrusion, with the exception of recent work [2,[4][5][6][7], flow-induced crystallization is ignored. Extensive calculations performed in examining the effect of flow-induced crystallization indicated that flow-induced crystallization had a moderate effect on results when bubble air mass and take-up speed are held constant [7]. ...
Stable operating regions for blown film extrusion are mapped using a dynamic model that includes the effect of crystallization on the rheological properties of the polymer. In the computations, the bubble air mass and take-up ratio were held constant, and the machine tension and bubble inflation pressure were treated as dependent variables. For a given bubble air mass, the take-up ratio was used as the continuation parameter for mapping steady-state solutions. The take-up ratio varies smoothly, but not necessarily monotonically, with the machine tension. Curves of either blow-up ratio or thickness reduction versus take-up ratio reveal that there are take-up ratios where no, one, or multiple solutions exist. The heat transfer coefficient from the polymer film to the external air and surroundings has a marked influence on the qualitative and quantitative features of the blow-up ratio versus thickness reduction curves. Generalized eigenvalue analysis of the linearized blown film equations indicates that increasing the heat transfer rate increases the stability of operations. A corresponding decline occurs, however, in the thickness reduction of the blown film for a given blow-up ratio.
A numerical simulation of the film blowing process is performed. The Phan–Thien and Tanner (PTT) constitutive equations with quiescent and flow-induced crystallization effects are considered with proper boundary and initial conditions. The PTT model is employed both for molten and crystallized polymer. Modeling of crystallization is done with nested Schneider rate equations and the Kolmogorov–Avrami model. The current model can predict the shape and size of the bubbles, as well as their temperature, stress, space filling and morphological changes for given process conditions. The study focuses on investigating the impact of process conditions on the mechanical response of the blown film, as well as on the morphological structure of the crystallizing molten polymer. It is observed that the axial stress increases at a faster rate compared to the circumferential stress with increase in draw ratio. The trend is reversed for increasing blow-up ratios. Increasing the draw ratio does not result in significant improvement in the quiescent contribution to the crystalline structure, but it leads to a decrease in the flow-induced contribution. Increasing blow-up ratio leads to increase in total space filling and the flow-induced component of the crystalline structure. Finally, three heat transfer coefficients chosen from the literature are compared. It is observed that the model choice is not critical for higher draw ratio values, but for low and moderate values, detailed investigations are required. The presented model enables accurate prediction of both the morphological structure and mechanical properties of semicrystalline polymers in a film blowing process.
The properties of polymer films cannot be separated from the process by which they are made. The stress and strain history imposed on the polymer as it is melted, extruded through the die, drawn to its final shape and quenched affects the orientation, crystallinity and morphology of the film. These in turn impact the mechanical, optical, barrier and other film properties. Three examples involving blown film are presented that illustrate the importance of processing on flexible packaging films:
•The effect of stress–strain history on film mechanical properties. In particular, the differences in strain history between monolayer and coextruded films and how this translates into property changes are highlighted.
•The impact of quench rate on properties. Key differences between air quench vs water quench blown film and their influence on the properties of barrier coextruded film are discussed.
•The influence of orientation on blend morphology.
Tools are available that can aid the engineer during the design process, starting with the identification of film structures currently being used in the market. Often it is helpful to look at how similar products are packaged; or if the goal is to improve upon the existing structure, understand what it is made of and how it is manufactured. The first section of this chapter briefly describes microscopy, Fourier transform infrared spectroscopy and differential scanning calorimetry techniques that are useful for structure identification.
Several mathematical, statistical and numerical models were introduced in previous chapters that aid in the fundamental understanding of process–structure–property relationships. This chapter summarizes the general approach to modeling for structure design, provides examples of models useful for product development and process optimization, and presents a case study of how they may be used in practice.
An analysis model for the transient viscoelastic flow in the film blowing process was newly developed based on the Galerkin finite element method and incorporating the cooling and crystallization behaviors. Assuming that physical quantities such as temperature and stress are constant in the thickness direction, the process was approximated to be one dimensional in the axisymmetric coordinate system, and the Lagrangian analysis, which involves remeshing and rezoning, was performed. In calculating the air pressure difference, constant air mass in the bubble was assumed and the effect of opening angle of the guide rolls, which lead the blown bubble to the pinch roll, was investigated. The viscoelastic properties were expressed by the multi-mode PTT model. Regarding crystallization characteristics, a phenomenological crystallization model developed by us was used. The model was based on the non-isothermal crystallization characteristics evaluated using a high-speed DSC. Four types of polyethylene, i.e. two LLDPEs, a blend of LLDPE and LDPE, and HDPE, were used and a comparative study of experimental results and results of model analyses for the film blowing process was carried out. Guidelines for appropriate input parameter settings such as the negligibility of the parameter for orientation induced crystallization and the necessity of adopting the heat transfer coefficient functions were obtained. By reflecting these findings in the simulation, the experimental results of polyethylene film blowing, including the unstable film formation behavior, could be predicted well by the developed model.
