Development of a rheological model for polymeric fluids based on FENE model

Document Type : Original research

Authors

1 Polymer Group, Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

2 Soft Tissue Engineering Research Center, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

Rheological models for polymer solutions and melts based on the finitely extensible non-linear elastic (FENE) dumbbell theory are reviewed in this study. The FENE-P model that is a well-known Peterlin approximation of the FENE model, indicates noticeable deviation from original FENE predictions and also experimental results, especially in the transient flow. In addition, both FENE and FENE-P models have some shortcomings from the point of view of theory. To overcome these shortcomings, a new approximation of the FENE spring force has been established. It has been used to develop a modified constitutive rheological model for polymeric fluids. In the procedure of modeling, the effect of non-affine deformation is introduced into the new model. Comparison between the model predictions and experimental data presented in the literature for transient and steady shear flow of polystyrene indicates that this modified model can predict the rheological behavior of polymeric fluids with a great accuracy. The newly developed modified model could predict different slopes that can cover the behavior of most of the polymeric fluids.

Keywords

Main Subjects


  1. Ait-Kadi A, Ramazani A, Grmela M, Zhou C (1999) “Volume preserving” rheological models for polymer melts and solutions using the GENERIC formalism. J Rheol 43: 51–72
  2. Eslami H, Ramazani S. A. A, Khonakdar HA (2004) Predictions of Some Internal Microstructural Models for Polymer Melts and Solutions in Shear and Elongational Flows. Macromol Theory Simul 13: 655–664
  3. Venkataramani V, Sureshkumar R, Khomami B (2008) Coarse-grained modeling of macromolecular solutions using a configuration-based approach. J Rheol 52: 1143–1177
  4. Zhiyu M, Wei C, Changyu S (2008) Numerical study of dilute polymer solutions using FENE bead-spring chain model. Polym-Plast Technol Eng 47: 630–634
  5. Ommati M, Ahmadi IF, Davachi SM, Motahari S (2011) Erosion rate of random short carbon fibre/phenolic resin composites: Modelling and experimental approach. Iran Polym J 20: 943–95
  6. Mousavi SM, Ramazani A, Najafi I, Davachi SM (2012) Effect of ultrasonic irradiation on rheological properties of asphaltenic crude oils. Pet Sci 9: 82–88
  7. Larson RG, Desai PS (2015) Modeling the rheology of polymer melts and solutions. Annu Rev Fluid Mech 47: 47–65
  8. Warner Jr HR (1972) Kinetic theory and rheology of dilute suspensions of finitely extendible dumbbells. Ind Eng Chem Fundam 11: 379–387
  9. Pishdad A, Kaffashi B, Davachi SM (2012) Investigation of Dispersion, Interaction and Superstructure Formation in PTMEG/MWCNT Nanocomposites. Sci Technol 25: 289–300
  10. Sahraeian R, Davachi SM, Heidari BS (2019) The effect of nanoperlite and its silane treatment on thermal properties and degradation of polypropylene/nanoperlite nanocomposite films. Compos Part B Eng 162:103–111
  11. Herrchen M, Öttinger HC (1997) A detailed comparison of various FENE dumbbell models. J Non-Newton Fluid Mech 68: 17–42
  12. Wiest JM, Tanner RI (1989) Rheology of bead-nonLinear spring chain macromolecules. J Rheol 33: 281–316
  13. Wedgewood LE, Bird RB (1988) From molecular models to the solution of flow problems. Ind Eng Chem Res 27: 1313–1320
  14. Lielens G, Halin P, Jaumain I, et al (1998) New closure approximations for the kinetic theory of finitely extensible dumbbells. J Non-Newton Fluid Mech 76: 249–279
  15. Lielens G, Keunings R, Legat V (1999) The FENE-L and FENE-LS closure approximations to the kinetic theory of finitely extensible dumbbells. J Non-Newton Fluid Mech 87: 179–196
  16. Hyon Y, Carrillo JA, Du Q, Liu C (2008) A maximum entropy principle based closure method for macro-micro models of polymeric materials. Kinet Relat Models 1: 171–184
  17. Ahmad A, Vincenzi D (2016) Polymer stretching in the inertial range of turbulence. Phys Rev E 93: 052605
  18. Wedgewood LE, Ostrov DN, Bird RB (1991) A finitely extensible bead-spring chain model for dilute polymer solutions. J Non-Newton Fluid Mech 40: 119–139
  19. Zhou Q, Akhavan R (2004) Cost-effective multi-mode FENE bead-spring models for dilute polymer solutions. J Non-Newton Fluid Mech 116: 269–300
  20. Lhuillier D (2001) A possible alternative to the FENE dumbbell model of dilute polymer solutions. J Non-Newton Fluid Mech 97: 87–96
  21. Vincenzi D, Perlekar P, Biferale L, Toschi F (2015) Impact of the Peterlin approximation on polymer dynamics in turbulent flows. Phys Rev E 92: 053004
  22. Herrchen M, Öttinger HC (1997) A detailed comparison of various FENE dumbbell models. J Non-Newton Fluid Mech 68: 17–42
  23. Keunings R (1997) On the Peterlin approximation for finitely extensible dumbbells. J Non-Newton Fluid Mech 68: 85–100
  24. Bird RB, Curtiss CF, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, Vol 2: Kinetic theory, Wiley
  25. Schneggenburger C, Kröger M, Hess S (1996) An extended FENE dumbbell theory for concentration dependent shear-induced anisotropy in dilute polymer solutions. J Non-Newton Fluid Mech 62: 235–251
  26. Ammar A (2016) Effect of the inverse Langevin approximation on the solution of the Fokker– Planck equation of non-linear dilute polymer. J Non-Newton Fluid Mech 231: 1–5
  27. Renardy M (2013) On the eigenfunctions for Hookean and FENE dumbbell models. J Rheol 1978-Present 57: 1311–1324
  28. Heidari BS, Cheraghchi V-S, Motahari S, et al (2018) Optimized mercapto-modified resorcinol formaldehyde xerogel for adsorption of lead and copper ions from aqueous solutions. J Sol-Gel Sci Technol 88: 236–248
  29. Warner Jr HR (1972) Kinetic theory and rheology of dilute suspensions of finitely extendible dumbbells. Ind Eng Chem Fundam 11: 379–387
  30. Larson RG (1999) The structure and rheology of complex fluids, 1st Ed, Oxford University Press, New York, p.114
  31. Stephanou PS, Baig C, Mavrantzas VG (2009) A generalized differential constitutive equation for polymer melts based on principles of nonequilibrium thermodynamics. J Rheol 53: 309–337
  32. Van Heel APG, Hulsen MA, Van den Brule B (1998) On the selection of parameters in the FENE-P model. J Non-Newton Fluid Mech 75: 253–271
  33. Heidari BS, Davachi SM, Moghaddam AH, et al (2018) Optimization simulated injection molding process for ultrahigh molecular weight polyethylene nanocomposite hip liner using response surface methodology and simulation of mechanical behavior. J Mech Behav Biomed Mater 81: 95–105
  34. Heidari BS, Oliaei E, Shayesteh H, et al (2017) Simulation of mechanical behavior and optimization of simulated injection molding process for PLA based antibacterial composite and nanocomposite bone screws using central composite design. J Mech Behav Biomed Mater 65: 160–176
  35. Gordon RJ, Schowalter WR (1972) Anisotropic fluid theory: a different approach to the dumbbell theory of dilute polymer solutions. Trans Soc Rheol 16: 79–97
  36. Öttinger HC (2005) Beyond equilibrium thermodynamics. John Wiley & Sons
  37. Huang S, Lu C, Fan Y (2006) Time-dependent viscoelastic behavior of an LDPE melt. Acta Mech Sin 22: 199–206
  38. Bhat PP, Pasquali M, Basaran OA (2009) Beads-on-string formation during filament pinch-off: Dynamics with the PTT model for non-affine motion. J Non-Newton Fluid Mech 159: 64–71
  39. Larson RG (2013) Constitutive equations for polymer melts and solutions. In: Butterworths series in chemical engineering, Elsevier Science
  40. Binetruy C, Chinesta F, Keunings R (2015) Multi-scale Modeling and Simulation of Polymer Flow. In: Flows in polymers, reinforced polymers and composites, Springer International Publishing, pp 1–42
  41. Parsa P, Paydayesh A, Davachi SM (2019) Investigating the effect of tetracycline addition on nanocomposite hydrogels based on polyvinyl alcohol and chitosan nanoparticles for specific medical applications. Int J Biol Macromol 121: 1061–1069
  42. Davachi SM, Shekarabi AS (2018) Preparation and characterization of antibacterial, eco-friendly edible nanocomposite films containing Salvia macrosiphon and nanoclay. Int J Biol Macromol 113: 66–72
  43. Bird RB, Curtiss CF, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, Vol. 2: Kinetic theory. Wiley
  44. Cook LP, Rossi LF (2004) Slippage and migration in models of dilute wormlike micellar solutions and polymeric fluids. J Non-Newton Fluid Mech 116: 347–369
  45. Öttinger HC (2005) Beyond equilibrium thermodynamics. John Wiley & Sons
  46. Balali S, Davachi SM, Sahraeian R, et al (2018) Preparation and characterization of composite blends based on polylactic acid/polycaprolactone and silk. Biomacromolecules 19: 4358–4369
  47.  Schweizer T, van Meerveld J, Ottinger HC (2004) Nonlinear shear rheology of polystyrene melt with narrow molecular weight distribution-Experiment and theory. J Rheol 48:1345–1364
  48. Laun HM (1986) Prediction of elastic strains of polymer melts in shear and elongation. J Rheol 1978-Present 30: 459–501
Volume 6, Issue 1 - Serial Number 11
January 2019
Pages 95-106
  • Receive Date: 15 October 2018
  • Revise Date: 14 November 2018
  • Accept Date: 23 November 2018
  • First Publish Date: 01 January 2019