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Analysis of Film Blowing with Flow-enhanced Crystallization

Part 2. Linearized Sensitivity and Stability Behavior
  • L. K. Henrichsen and A. J. McHugh
Published/Copyright: February 28, 2022
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International Polymer Processing
From the journal International Polymer Processing Volume 22 Issue 2

Abstract

An analysis of the transient film blowing process is presented based on the two-phase Giesekus/rigid rod model for flow-enhanced crystallization described in Part 1 [1]. Linearized frequency analysis has been used to explore the effects of system disturbances on the process. Results show that perturbations related to heat transfer and inflation pressure are more significant than the effects of film thickness (die swell). In addition, crystallinity is shown to have a consistent stabilizing effect on the system, with more crystallinity dampening the perturbations. Stability diagrams for each material show relatively wide regions of convergence in the blow-up ratio (BUR) – draw ratio space, however, at higher BURs (≥ ~ 4) the system becomes unstable for all DRs.

* Mail address: A. J. McHugh, Department of Chemical Engineering, Lehigh University, Bethlehem, PA 18015, USA

Acknowledgements

This work was supported in part by the Engineering Research Centers Program of the National Science Foundation under NSF Award Number EEC-9731680. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation. The authors also wish to thank Professor William Schiesser for many helpful discussions regarding the setup and numerical solution of the system of PDEs encountered in solving the transient model.

Nomenclature

a (subscript)

amorphous or ambient

f (subscript)

final quantity (z = ZL)

o (subscript)

initial quantity (z = 0)

sc (subscript)

semi-crystalline

∞ (subscript)

final transformation value

cp

heat capacity

kB

Boltzmann constant

Go

plateau shear modulus

Kav

Avrami temperature-dependent coefficient

U

overall heat transfer coefficient

V

axial velocity

W

mass flow rate

△P

bubble inflation pressure

△Hf

heat of fusion

ξ

two-phase model parameter

α

Giesekus model parameter

λ

relaxation time

ρ

fluid density

σ

rigid-rod model parameter

φ

degree of crystallinity

x=φφ∞

degree of transformation

H*=HHo

dimensionless bubble thickness

R*=RRo

dimensionless bubble radius

t*=tVoRo

dimensionless time

T*=TTo

dimensionless temperature

z*=z/Ro

dimensionless distance from spinneret exit

V*=VVo

dimensionless axial velocity

DR=VfVo

draw ratio

BUR=RfRo

blow up ratio

a*=aGo

dimensionless Helmholtz free energy

c*=cKokBT

dimensionless conformation tensor

S=〈uu〉−13δ

orientation tensor of semi-crystalline phase

u

orientation vector of semi-crystalline phase

⟨ ⟩

averaged quantity

δ

identity tensor

Fz*=Fz2πRoHoGo

dimensionless take-up force

∇*=∇/Ro

dimensionless gradient operator

τ*=τGo

dimensionless stress

C1=TaTo

dimensionless temperature ratio

C2=2πRo2UWcp

dimensionless heat transfer coefficient

C5=ΔHfφ∞cpTo

dimensionless heat of fusion

Dea=VoλaRo

dimensionless group

D6=ΔPGo

dimensionless pressure

Dea=VoλaRo

amorphous phase Deborah number

Desc=VoλscRo

semi-crystalline phase Deborah number

Dx=RoKavVo

dimensionless Avrami coefficient

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References

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Received: 2006-08-26
Accepted: 2006-12-21
Published Online: 2022-02-28
Published in Print: 2022-02-28

© 2007 Walter de Gruyter GmbH, Berlin/Boston, Germany

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https://doi.org/10.1515/ipp-2007-0010

Articles in the same Issue

  1. Contents
  2. Regular Contributed Articles
  3. Functionalization of Low Density Polyethylene with Ricinol-2-oxazoline Methyl Maleate in a Twin-screw Extruder
  4. Modelling of Phase Transitions and Residual Thermal Stress of CTBN Rubber Modified Epoxy Resins during a Pultrusion Process
  5. Real-time Diagnosis of Micro Powder Injection Molding Using Integrated Ultrasonic Sensors
  6. Rheological Behavior of HEUR Mixtures in Aqueous Media
  7. Spinnability and Dyeability for Copolymer/Nano-SiO2 Fiber of Glycol and 1,2-Propanediol with PTA
  8. Development of a Novel Transcription Molding Process to Fabricate Sophisticated Polymer Products with Precise Microstructure and High Transparency Applicable to Display Devices and Bio-chips
  9. Effect of Aspect Ratio of Whisker on the Fibrillation of Liquid Crystalline Polymer in Polysulfone Matrix
  10. Gas Assisted Injection Molding of an Industrial Part: 3D Simulation Provides Virtual Molding Trials
  11. Analysis of Film Blowing with Flow-enhanced Crystallization
  12. Analysis of Film Blowing with Flow-enhanced Crystallization
  13. A Composite Model for Melting, Pressure and Fill Factor Profiles in a Metered Fed Closely Intermeshing Counter-rotating Twin Screw Extruder
  14. Surface Defects of TPO Injected Foam Parts for Automotive Applications
  15. PPS News
  16. PPS News
  17. Seikei-Kakou Abstracts
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