Scitation | Help | Feedback
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 
Journal of Rheology / Volume 49 / Issue 2

J. Rheol. 49, 501 (2005); http://dx.doi.org/10.1122/1.1849180 (22 pages)

Constriction flows of monodisperse linear entangled polymers: Multiscale modeling and flow visualization

M. W. Collis, A. K. Lele, and M. R. Mackley

Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom

R. S. Graham, D. J. Groves, A. E. Likhtman, T. M. Nicholson, and T. C. B. McLeish

IRC in Polymer Science and Technology, Department of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom

O. G. Harlen

IRC in Polymer Science and Technology, Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

L. R. Hutchings

Department of Chemistry, University of Durham, Durham DH1 3LE, United Kingdom

C. M. Fernyhough and R. N. Young

Department of Chemistry, University of Sheffield, Sheffield S3 7HF, United Kingdom

View MapView Map
Full Text: Read Online (HTML) | Download PDF FREE | View Cart
We explore both the rheology and complex flow behavior of monodisperse polymer melts. Adequate quantities of monodisperse polymer were synthesized in order that both the materials rheology and microprocessing behavior could be established. In parallel, we employ a molecular theory for the polymer rheology that is suitable for comparison with experimental rheometric data and numerical simulation for microprocessing flows. The model is capable of matching both shearand extensional data with minimal parameter fitting. Experimental data for the processing behavior of monodisperse polymers are presented for the first time as flow birefringence and pressure difference data obtained using a Multipass Rheometer with an 11:1 constriction entry and exit flow. Matching of experimental processing data was obtained using the constitutive equation with the Lagrangian numerical solver, FLOWSOLVE. The results show the direct coupling between molecular constitutive response and macroscopic processing behavior, and differentiate flow effects that arise separately from orientation and stretch.

© 2005 The Society of Rheology

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support of EPSRC (UK) under the “Microscale Polymer Processing” consortium grant, and the essential additional support of BP Chemicals, DuPont Films, DuPont Teijin, Dow Chemical, BASF, DSM, and Lucite International. Helpful discussions with Nat Inkson, Ralph Colby, and Daniel Read assisted the preparation of the manuscript, as did helpful comments from referees.

Article Outline

  1. INTRODUCTION
  2. EXPERIMENTAL METHOD
    1. Synthesis and characterization
      1. Polymerization of butadiene
      2. Polymerization of styrene
      3. Characterization
    2. RHEOLOGICAL MEASUREMENTS
      1. Sample preparation
      2. Shear rheology
      3. Linear rheology
      4. Nonlinear rheology
      5. Elogational rheology
    3. FLOW VISUALIZATION
  3. THEORY AND MODELING
    1. Tube theory in fast flow
    2. Nonlinear constitutive equation
    3. Flow computation
  4. RESULTS AND DISCUSSION
    1. Viscometric flows
    2. Constriction flows
      1. Steady-state flow fields
      2. PS262 melt
      3. PS485 melt
      4. PB 210k melt
      5. Transient flows and pressure drops
  5. CONCLUSIONS

KEYWORDS and PACS

Keywords

polymer melts, shear flow, flow visualisation, flow simulation, rheology, flow birefringence, Entanglements, Entry flow, Numerical methods, Constitutive equations

PACS

  • 83.80.Sg

    Polymer melts

  • 83.50.Ax

    Steady shear flows, viscometric flow

  • 47.11.-j

    Computational methods in fluid dynamics

  • 47.50.-d

    Non-Newtonian fluid flows

  • 47.80.-v

    Instrumentation and measurement methods in fluid dynamics

  • 78.20.Fm

    Birefringence

  • 61.25.H-

    Macromolecular and polymers solutions; polymer melts

PUBLICATION DATA

ISSN

0148-6055 (print)  

Publisher

The Society of Rheology

RELATED DATABASES

Web of Science

View this record in Web of Science

View Web of Science related articles

ARTICLE DATA

History
Received 29 Jul 04
Revised 01 Nov 04
Digital Object Identifier
http://dx.doi.org/10.1122/1.1849180

  1. Baaijens F. P. T., S. H. A. Seelen, H. P. W. Baaijens, G. W. M. Peters, and H. E. H. Meijer, "Viscoelastic flow past a confined cylinder of a low density polyethylene melt," J. Non-Newtonian Fluid Mech. 68, 173–203 (1997). [Inspec] [ISI]
  2. Bent J., L. R. Hutchings, R. W. Richards, T. Gough, R. Spares, P. D. Coates, I. Grillo, O. G. Harlen, D. J. Read, R. S. Graham, A. E. Likhtman, D. J. Groves, T. M. Nicholson, and T. C. B. McLeish, "Neutron-mapping polymer flow: Scattering, flow visualization, and molecular theory," Science 301, 1691–1695 (2003). [MEDLINE]
  3. Bishko G. B., O. G. Harlen, T. M. Nicholson, and T. C. B. McLeish, "Numerical simulation of the transient flow of branched polymer melts through a planar contraction using the `pom-pom' Model," J. Non-Newtonian Fluid Mech. 82, 255–273 (1999). [Inspec] [ISI]
  4. Doi, M., and S.F. Edwards , The Theory of Polymer Dynamics (Oxford University Press, Oxford, UK, 1986).
  5. Graham, R. S., A. E. Likhtman, S. T. Milner, and T. C. B. McLeish, "Microscopic theory of linear entangled polymer chains under rapid deformation including chain stretch and convective constraint release," J. Rheol. 47, 1171–1200 (2003)JORHD2000047000005001171000001.
  6. Ianniruberto, G., and G. Marrucci, "A simple constitutive equation for entangled polymers with chain stretch," J. Rheol. 45, 1305–1318 (2001)JORHD2000045000006001305000001. [ISI]
  7. Janeschitz-Kriegl, H. , Polymer Melt Rheology and Flow Birefringence (Springer, New York, 1983).
  8. Larson, R. G., T. Sridhar, L. G. Leal, G. H. McKinley, A. E. Likhtman, and T. C. B. McLeish, "Definitions of entanglement spacing and time constants in the tube model," J. Rheol. 47, 809–818 (2003)JORHD2000047000003000809000001. [ISI]
  9. Laso, M., and H. C. Öttinger, "Calculation of viscoelastic flow using molecular models: The CONFFESSIT approach," J. Non-Newtonian Fluid Mech. 47, 1–20 (1993). [Inspec] [ISI]
  10. Lee, C. S., B. C. Tripp, and J. J. Magda, "Does N1 or N2 control the onset of edge fracture?" J. Rheol. 31, 306–308 (1992).
  11. Lee, K., and M. R. Mackley, "The application of the multipass rheometer for precise rheooptic characterisation of polyethylene melts," Chem. Eng. Sci. 56, 5653–5661 (2001). [ISI]
  12. Lee, K., M. R. Mackley, T. C. B. McLeish, T. M. Nicholson, and O. G. Harlen, "Experimental observation and numerical simulation of transient stress fangs within flowin molten polyethylene," J. Rheol. 45, 1261–1277 (2001)JORHD2000045000006001261000001. [ISI]
  13. Likhtman, A. E., and T. C. B. McLeish, "Quantitative theory for linear dynamics of linear entangled polymers," Macromolecules 35, 6332–6343 (2002). [ISI]
  14. Likhtman, A. E., and R. S. Graham, "Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie-Poly equation," J. Non-Newtonian Fluid Mech. 114, 1–12 (2003). [ISI]
  15. Mackley, M. R., Marshall, R. T. J., and Smeulders, J. B. A. F., "The multipass rheometer," J. Rheol. 39, 1293–1309 (1995)JORHD2000039000006001293000001.
  16. McLeish, T. C. B., "Tube theory of entangled polymer dynamics," Adv. Phys. 51, 1379–1527 (2002).
  17. McLeish, T. C. B., and S. T. Milner, "Entangled dynamics and melt flow of branched polymers," Adv. Polym. Sci. 143, 195–256 (1999). [ISI]
  18. Mead, D. W., R. G. Larson, and M. Doi, "A molecular theory of fast flows of linear polymers," Macromolecules 31, 7895–7914 (1998).
  19. Meissner J., and J Hostettler, "A new elongational rheometer for polymer melts and other highly viscoelastic liquids," Rheol. Acta 33, 1–21 (1994). [Inspec] [ISI]
  20. Milner, S. T., T. C. B. McLeish, and A. E. Likhtman, "Microscopic theory of convective constraint release," J. Rheol. 45, 539–563 (2001)JORHD2000045000002000539000001.
  21. Morton, M., and Fetters, L. J., "Anionic polymerization of vinyl monomers," Rubber Chem. Technol. 48, 359–409 (1975).
  22. Pangborn, A. B., M. A. Giardello, R. H. Grubbs, R. K. Rosen, and F. J. Timmers, "Safe and convenient procedure for solvent purification," Organometallics 15, 1518–1520 (1996). [ISI]
  23. Peters, E. A. J. F., A. P. G. van Heel, M. A. Hulsen, and B. H. A. A. van den Brule, "Generalization of the deformation field method to simulate advanced reptation models in complex flow," J. Rheol. 44, 811–829 (2000)JORHD2000044000004000811000001. [ISI]
  24. Rajagopalan, D., R. C. Armstrong, and R. A. Brown, "Comparison of computational efficiency of flow simulations with multimode constitutive equations: Integral and differential models," J. Non-Newtonian Fluid Mech. 46, 243–273 (1993). [Inspec] [ISI]
  25. Schulze, J. S., T. P. Lodge, C. W. Macosko, J. Hepperle, H. Munstedt, H. Bastian, D. Ferri, D. J. Groves, Y. H. Kim, M. Lyon, T. Schweizer, T. Virkler, E. Wassner, and W. Zoetelief, "A comparison of extensional viscosity measurements from various RME rheometers," Rheol. Acta 40, 457–466 (2001). [Inspec] [ISI]
  26. Tanner R. I., and M. Keentok, "Shear fracture in cone-plate rheometry," J. Rheol. 27, 47–57 (1983)JORHD2000027000001000047000001.
  27. Verbeeten, W., G. W. M. Peters, and F. P. T. Baaijens, "The extended pom-pom model," J. Rheol. 45, 823–843 (2001)JORHD2000045000004000823000001. [ISI]
  28. Wischnewski A., M. Monkenbusch, L. Willner, D. Richter, A. E. Likhtman, T. C. B. McLeish, and B. Farago, "Molecular observation of contour-length fluctuations limiting topological confinement in polymer melts," Phys. Rev. Lett. 88, 058301 (2002). [MEDLINE]

Figures (10) Tables (2)

Figures (click on thumbnails to view enlargements)

FIG.1
(a) Schematic layout of MPR and (b) cross section of slit flow cell.

Export Figure to PowerPoint

FIG.2
Linear rheology of (a) 250k (filled symbols) and 485k PS (open symbols) melts and (b) PB 48 (squares), 156 (triangles), and 210k (circles) melts with comparison to predictions from the tube theory, parameterized by a chemistry- and temperature-dependent entanglement modulus Ge and Rouse relaxation time of an entanglement segment τe, and the material dependent number of entanglements Z.

Export Figure to PowerPoint

FIG.3
Nonlinear shear and extensional (485k PS only) transients (rates from 0.01–3 s−1) rheology of 250k (a) and 485k PS (b) melts at 170 °C (the extensional data were time-temperature shifted from 160 °C). Comparison curves are predictions from the full tube theory of Eq. ( 2 ), parameterized by plateau modulus GN(0), entanglement time τe, and the number of entanglements Z.

Export Figure to PowerPoint

FIG.4
RoliePoly model predictions and comparison to shear transients for (a) PS 262, and (b) PS 485. Strain rates and temperatures are as for Fig. 3.

Export Figure to PowerPoint

FIG.5
PS 262 at a piston speed of 0.5 mm/s (wall shear rate of 29 s−1). The flow is marginally within Regime (3). Observed stress field is on the left, predicted on the right.

Export Figure to PowerPoint

FIG.6
Experiment and calculation of stress fields for the PS485 monodisperse melt. Piston speeds are (a) 0.05 mm/s, (b) 0.2 mm/s, (c) 5 mm/s, giving wall shear rates of (a) 2.9 s−1, (b) 12 s−1, and (c) 290 s−1. Flows (a) is in Regime (2), flow (b) on the threshold of regime (3) and (c) (calculated only) deeply into Regime (3).

Export Figure to PowerPoint

FIG.7
Experimental and simulated stress field from the PB210 melt in the 11:1 contraction at a wall shear rate of 29 s−1 at a temperature of 80 °C. The mean dimensionless (by reptation) shear rate is 3.6.

Export Figure to PowerPoint

FIG.8
Simulated (solid curve) and experimental data (crosses) on the pressure drop transient for flow start up in an 11:1 contraction of the PS485 melt at 170 °C. The effect of melt compressibility in the upstream piston is marked. The dashed curve shows the modified simulations of the pressure drop when the upstream boundary velocity condition was modulated with a single exponential growth.

Export Figure to PowerPoint

FIG.9
PS262 K at 200 °C—Evolution of flow birefringence at piston speed of 0.5 mm/s (steady-state wall shear rate of 29 s−1): (a) t = 0.25 s, (b) t = 0.5 s, (c) t = 0.75 s, (d) t = 1.0 s, (e) t = 1.25 s, and (f) t = 1.5 s (fully developed).

Export Figure to PowerPoint

FIG.10
Observed and simulated steady-state pressure drops as a function of piston speed for the PS485 melt. Above 0.5 mm/s (wall shear rate of 29 s−1), the observed values fall markedly below the predicted values, but this is also the regime in which the experiment showed flow instabilities, which are suppressed in the simulations.

Export Figure to PowerPoint

Tables

Table I. Labels and descriptions of materials used in this study.

View Table
Table II. Physical parameters of melt material used in this study.

View Table


Close
   

Your Recent History Recent History Help

Recently Viewed

  1. Constriction flows of monodisperse linear entangled polymers: Multiscale modeling and flow visualization
  2. Slip and flow in pastes of soft particles: Direct observation and rheology
  3. Effects of shear flow on a polymeric bicontinuous microemulsion: Equilibrium and steady state behavior
  4. Slip at polymer–polymer interfaces: Rheological measurements on coextruded multilayers
  5. Rheology and nuclear magnetic resonance measurements under shear of sodium dodecyl sulfate/decanol/water nematics
©  The Society of Rheology
close