Table of Contents Author Guidelines Submit a Manuscript
International Journal of Polymer Science
Volume 2015, Article ID 312839, 8 pages
http://dx.doi.org/10.1155/2015/312839
Research Article

Role of Nonmonotonic Constitutive Curves in Extrusion Instabilities

1College of Computer, National University of Defense Technology, Changsha, Hunan 410073, China
2State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha, Hunan 410073, China
3School of Chemical Engineering and Analytical Science, Manchester Institute of Biotechnology, University of Manchester, Manchester M13 9PL, UK
4National Supercomputer Centre in Guangzhou and Research Institute on Application of High Performance Computing, Sun Yat-Sen University, Guangzhou, Guangdong 510006, China

Received 10 September 2015; Revised 14 December 2015; Accepted 15 December 2015

Academic Editor: Angel Concheiro

Copyright © 2015 Yu Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. G. Larson, “Instabilities in viscoelastic flows,” Rheologica Acta, vol. 31, no. 3, pp. 213–263, 1992. View at Publisher · View at Google Scholar · View at Scopus
  2. D. S. Kalika and M. M. Denn, “Wall slip and extrudate distortion in linear lowdensity polyethylene,” Journal of Rheology, vol. 31, no. 8, pp. 815–834, 1987. View at Google Scholar
  3. J. D. Shore, D. Ronis, L. Piché, and M. Grant, “Theory of melt fracture instabilities in the capillary flow of polymer melts,” Physical Review E, vol. 55, no. 3, pp. 2976–2992, 1997. View at Google Scholar · View at Scopus
  4. K. P. Adewale and A. I. Leonov, “Modeling spurt and stress oscillations in flows of molten polymers,” Rheologica Acta, vol. 36, no. 2, pp. 110–127, 1997. View at Publisher · View at Google Scholar · View at Scopus
  5. W. B. Black, Wall slip and boundary effects in polymer shear flows [Ph.D. thesis], 2000.
  6. M. M. Denn, “Extrusion instabilities and wall slip,” Annual Review of Fluid Mechanics, vol. 33, pp. 265–287, 2001. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Aarts, Analysis of the flow instabilities in the extrusion of polymeric melts [Ph.D. thesis], 1997.
  8. M. M. Fyrillas, G. C. Georgiou, and D. Vlassopoulos, “Time-dependent plane Poiseuille flow of a Johnson-Segalman fluid,” Journal of Non-Newtonian Fluid Mechanics, vol. 82, no. 1, pp. 105–123, 1999. View at Publisher · View at Google Scholar · View at Scopus
  9. D. S. Malkus, J. A. Nohel, and B. J. Plohr, “Dynamics of shear flow of a non-Newtonian fluid,” Journal of Computational Physics, vol. 87, no. 2, pp. 464–487, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. E. Achilleos, G. Georgiou, S. G. Hatzikiriakos, and E. Achilleos, “On numerical simulations of polymer extrusion instabilities,” Applied Rheology, vol. 12, no. 2, pp. 88–104, 2002. View at Google Scholar
  11. C. Chung, T. Uneyama, Y. Masubuchi, and H. Watanabe, “Numerical study of chain conformation on shear banding using diffusive rolie-poly model,” Rheologica Acta, vol. 50, no. 9-10, pp. 753–766, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. J. M. Adams, S. M. Fielding, and P. D. Olmsted, “Transient shear banding in entangled polymers: a study using the rolie-poly model,” Journal of Rheology, vol. 55, no. 5, pp. 1007–1032, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. X.-W. Guo, S. Zou, X. Yang, X.-F. Yuan, and M. Wang, “Interface instabilities and chaotic rheological responses in binary polymer mixtures under shear flow,” RSC Advances, vol. 4, no. 105, pp. 61167–61177, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. X.-W. Guo, W.-J. Yang, X.-H. Xu, Y. Cao, and X.-J. Yang, “Non-equilibrium steady states of entangled polymer mixtures under shear flow,” Advances in Mechanical Engineering, vol. 7, no. 6, pp. 1–10, 2015. View at Publisher · View at Google Scholar
  15. M. W. Johnson Jr. and D. Segalman, “A model for viscoelastic fluid behavior which allows non-affine deformation,” Journal of Non-Newtonian Fluid Mechanics, vol. 2, no. 3, pp. 255–270, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. T. C. Ho and M. M. Denn, “Stability of plane poiseuille flow of a highly elastic liquid,” Journal of Non-Newtonian Fluid Mechanics, vol. 3, no. 2, pp. 179–195, 1977. View at Publisher · View at Google Scholar · View at Scopus
  17. E. Brasseur, M. M. Fyrillas, G. C. Georgiou, and M. J. Crochet, “The time-dependent extrudate-swell problem of an Oldroyd-B fluid with slip along the wall,” Journal of Rheology, vol. 42, no. 3, pp. 549–566, 1998. View at Publisher · View at Google Scholar · View at Scopus
  18. H. Jasak, “Dynamic mesh handling in openfoam in,” in Proceedings of the 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition, Orlando, Fla, USA, January 2009.
  19. H. Jasak and Ž. Tuković, “Automatic mesh motion for the unstructured finite volume method,” Transactions of Famena, vol. 30, no. 2, pp. 1–20, 2006. View at Google Scholar · View at Scopus
  20. E. J. Hinch, “Mechanical models of dilute polymer solutions in strong flows,” Physics of Fluids, vol. 20, no. 10, pp. S22–S30, 1977. View at Publisher · View at Google Scholar · View at Scopus
  21. P. G. De Gennes, “Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients,” The Journal of Chemical Physics, vol. 60, no. 12, pp. 5030–5042, 1974. View at Google Scholar · View at Scopus
  22. S. C. Omowunmi and X.-F. Yuan, “Time-dependent non-linear dynamics of polymer solutions in microfluidic contraction flow-a numerical study on the role of elongational viscosity,” Rheologica Acta, vol. 52, no. 4, pp. 337–354, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. Ž. Tuković and H. Jasak, “A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow,” Computers & Fluids, vol. 55, pp. 70–84, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. W. Yang, Parallel computer simulation of highly nonlinear dynamics of polymer solutions in benchemark flow problems [Ph.D. thesis], 2014.
  25. H. Matallah, P. Townsend, and M. F. Webster, “Recovery and stress-splitting schemes for viscoelastic flows,” Journal of Non-Newtonian Fluid Mechanics, vol. 75, no. 2-3, pp. 139–166, 1998. View at Publisher · View at Google Scholar · View at Scopus
  26. M. A. Ajiz and A. Jennings, “A robust incomplete choleski-conjugate gradient algorithm,” International Journal for Numerical Methods in Engineering, vol. 20, no. 5, pp. 949–966, 1984. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. J. Lee, J. Zhang, and C.-C. Lu, “Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems,” Journal of Computational Physics, vol. 185, no. 1, pp. 158–175, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  28. K. C. Porteous and M. M. Denn, “Linear stability of plane poiseuille flow of viscoelastic liquids,” Transactions of The Society of Rheology, vol. 16, no. 2, pp. 295–308, 1972. View at Google Scholar
  29. H. Palza, S. Filipe, I. F. C. Naue, and M. Wilhelm, “Correlation between polyethylene topology and melt flow instabilities by determining in-situ pressure fluctuations and applying advanced data analysis,” Polymer, vol. 51, no. 2, pp. 522–534, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. J. Barone and S.-Q. Wang, “Flow birefringence study of sharkskin and stress relaxation in polybutadiene melts,” Rheologica Acta, vol. 38, no. 5, pp. 404–414, 1999. View at Publisher · View at Google Scholar · View at Scopus