Skip to main content
SpringerLink
Log in

Time-dependent rheological behavior of branched polymer melts in extensional flows

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

The viscoelastic flow of low-density polyethylene melts in a cross-slot channel is studied numerically for the double convected Pom–Pom (DCPP) and single modified DCPP (S–MDCPP) models. The equal low-order finite elements for velocity–pressure–stress variables are implemented to solve the flow fields using the pressure-stabilized iterative fractional step algorithm. The distributions of axial velocity along the channel centerline and the principal stress difference achieved by numerical predictions are in quantitative good agreement with the reported experimental results. Furthermore, the evolution of backbone stretch of macromolecule with flow time is demonstrated, and then an exponential decay function is proposed linking the microscale stretch relaxation time with the macroscale flow time, in order to reveal the stretch relaxation response of the branched polymer. The effects of the Weissenberg number and several constitutive parameters of the S–MDCPP model on the rheological behavior of polymer melts are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Arratia, P.E., Thomas, C.C., Diorio, J., Gollub, J.P.: Elastic instabilities of polymer solutions in cross-channel flow. Phys. Rev. Lett. 96, 144502 (2006)

    Article  Google Scholar 

  • Auhl, D., Hoyle, D.M., Hassell, D., Lord, T., Harlen, O.G., Mackley, M.R., McLeish, T.C.B.: Cross-slot extensional rheometry and the steady-state extensional response of long chain branched polymer melts. J. Rheol. 55, 875–900 (2011)

    Article  Google Scholar 

  • Brooks, A.N., Hughes, T.J.R.: Streamline upwind/Petrov–Galerkin methods for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput. Methods Appl. Mech. Eng. 32, 199–259 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  • Clemeur, N., Debbaut, B.: A pragmatic approach for deriving constitutive equations endowed with Pom–Pom attributes. Rheol. Acta 46, 1187–1196 (2007)

    Article  Google Scholar 

  • Clemeur, N., Rutgers, R.P.G., Debbaut, B.: On the evaluation of some differential formulations for the Pom–Pom constitutive model. Rheol. Acta 42(3), 217–231 (2003)

    Google Scholar 

  • Coventry, K.D., Mackley, M.R.: Cross-slot extensional flow birefringence observations of polymer melts using a multi-pass rheometer. J. Rheol. 52, 401–415 (2008)

    Article  Google Scholar 

  • Guénette, R., Fortin, M.: A new mixed finite element method for computing viscoelastic flows. J. Non-Newton. Fluid Mech. 60(1), 27–52 (1995)

    Article  Google Scholar 

  • Haward, S.J., Odell, J.A., Li, Z., Yuan, X.-F.: Extensional rheology of dilute polymer solutions in oscillatory cross-slot flow: the transient behaviour of birefringent strands. Rheol. Acta 49(6), 633–645 (2010)

    Article  Google Scholar 

  • Haward, S.J., Oliveira, M.S., Alves, M.A., McKinley, G.H.: Optimized cross-slot flow geometry for microfluidic extensional rheometry. Phys. Rev. Lett. 109(12), 128301 (2012)

    Article  Google Scholar 

  • Haward, S.J., Sharma, V., Odell, J.A.: Extensional opto-rheometry with biofluids and ultra-dilute polymer solutions. Soft Matter 7(21), 9908–9921 (2011)

    Article  Google Scholar 

  • Hoyle, D.M., Huang, Q., Auhl, D., Hassell, D., Rasmussen, H.K., Skov, A.L., Harlen, O.G., Hassager, O., McLeish, T.C.B.: Transient overshoot extensional rheology of long chain branched polyethylenes: experimental and numerical comparisons between filament stretching and cross-slot flow. J. Rheol. 57(1), 293–313 (2013)

    Article  Google Scholar 

  • Li, X.K., Duan, Q.L.: Meshfree iterative stabilized Taylor–Galerkin and characteristic-based split (CBS) algorithms for incompressible N-S equations. Comput. Methods Appl. Mech. Eng. 195, 6125–6145 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Likhtman, A.E., Graham, R.S.: Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation. J. Non-Newton. Fluid Mech. 114(1), 1–12 (2003)

    Article  MATH  Google Scholar 

  • Lord, T.D., Scelsi, L., Hassell, D.G., Mackley, M.R., Embery, J., Auhl, D., Harlen, O.G., Tenchev, R., Jimack, P.K., Walkley, M.A.: The matching of 3D Rolie–Poly viscoelastic numerical simulations with experimental polymer melt flow within a slit and a cross-slot geometry. J. Rheol. 54, 355–373 (2010)

    Article  Google Scholar 

  • Mackley, M.: Stretching polymer chains. Rheol. Acta 49(5), 443–458 (2010)

    Article  Google Scholar 

  • Marchal, J.M., Crochet, M.J.: A new mixed finite element for calculating viscoelastic flow. J. Non-Newton. Fluid Mech. 26(1), 77–114 (1987)

    Article  MATH  Google Scholar 

  • McKinley, G.H., Sridhar, T.: Filament-stretching rheometry of complex fluids. Annu. Rev. Fluid Mech. 34, 375–415 (2002)

    Article  MathSciNet  Google Scholar 

  • McLeish, T.C.B., Larson, R.G.: Molecular constitutive equations for a class of branched polymers: the Pom–Pom polymer. J. Rheol. 42(1), 81–110 (1998)

    Article  Google Scholar 

  • Oñate, E.: A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation. Comput. Methods Appl. Mech. Eng. 182(3), 355–370 (2000)

    Article  MATH  Google Scholar 

  • Peters, G.W.M., Schoonen, J.F.M., Baaijens, F.P.T., Meijer, H.E.H.: On the performance of enhanced constitutive models for polymer melts in a cross-slot flow. J. Non-Newton. Fluid Mech. 82(2), 387–427 (1999)

    Article  MATH  Google Scholar 

  • Pipe, C.J., McKinley, G.H.: Microfluidic rheometry. Mech. Res. Commun. 36(1), 110–120 (2009)

    Article  Google Scholar 

  • Puangkird, B., Belblidia, F., Webster, M.F.: Numerical simulation of viscoelastic fluids in cross-slot devices. J. Non-Newton. Fluid Mech. 162(1), 1–20 (2009)

    Article  MATH  Google Scholar 

  • Remmelgas, J., Singh, P., Leal, L.G.: Computational studies of nonlinear elastic dumbbell models of Boger fluids in a cross-slot flow. J. Non-Newton. Fluid Mech. 88, 31–61 (1999)

    Article  MATH  Google Scholar 

  • Rubio, P., Wagner, M.H.: LDPE melt rheology and the Pom–Pom model. J. Non-Newton. Fluid Mech. 92, 245–259 (2000)

    Article  MATH  Google Scholar 

  • Sadati, M., Luap, C., Lüthi, B., Kröger, M., Öttinger, H.C.: Application of full flow field reconstruction to a viscoelastic liquid in a 2D cross-slot channel. J. Non-Newton. Fluid Mech. 192, 10–19 (2013)

    Article  Google Scholar 

  • Schmidt, M., Wassner, E., Münstedt, H.: Setup and test of a laser doppler velocimeter for investigations of flow behaviour of polymer melts. Mech. Time-Depend. Mater. 3(4), 371–393 (1999)

    Article  Google Scholar 

  • Schroeder, C.M., Shaqfeh, E.S.G., Chu, S.: Effect of hydrodynamic interactions on DNA dynamics in extensional flow: simulation and single molecule experiment. Macromolecules 37, 9242–9256 (2004)

    Article  Google Scholar 

  • Somani, S., Shaqfeh, E.S.G., Prakash, J.R.: Effect of solvent quality on the coil-stretch transition. Macromolecules 43, 10679–10691 (2010)

    Article  Google Scholar 

  • Soulages, J., Schweizer, T., Venerus, D.C., Kröger, M., Öttinger, H.C.: Lubricated cross-slot flow of a low density polyethylene melt. J. Non-Newton. Fluid Mech. 154(1), 52–64 (2008)

    Article  Google Scholar 

  • Tamaddon-Jahromi, H.R., Webster, M.F.: Transient behaviour of branched polymer melts through planar abrupt and rounded contractions using Pom–Pom models. Mech. Time-Depend. Mater. 15(2), 181–211 (2011)

    Article  Google Scholar 

  • Tanner, R.I., Nasseri, S.: Simple constitutive models for linear and branched polymers. J. Non-Newton. Fluid Mech. 116, 1–17 (2003)

    Article  MATH  Google Scholar 

  • Verbeeten, W.M., Peters, G.W., Baaijens, F.: Viscoelastic analysis of complex polymer melt flows using the eXtended Pom–Pom model. J. Non-Newton. Fluid Mech. 108(1), 301–326 (2002)

    Article  MATH  Google Scholar 

  • Verbeeten, W.M.H.: Computational polymer melt rheology. Ph.D. Thesis, Eindhoven University of Technology (2001)

  • Verbeeten, W.M.H., Peters, G.W.M., Baaijens, F.P.T.: Differential constitutive equations for polymer melts: the extended Pom–Pom model. J. Rheol. 45(4), 823–844 (2001)

    Article  Google Scholar 

  • Verbeeten, W.M.H., Peters, G.W.M., Baaijens, F.P.T.: Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model. J. Non-Newton. Fluid Mech. 117(2), 73–84 (2004)

    Article  MATH  Google Scholar 

  • Wang, W., Li, X.K., Han, X.H.: Equal low-order finite element simulation of the planar contraction flow for branched polymer melts. Polym.-Plast. Technol. Eng. 48(11), 1158–1170 (2009)

    Article  Google Scholar 

  • Wang, W., Li, X.K., Han, X.H.: A numerical study of constitutive models endowed with Pom–Pom molecular attributes. J. Non-Newton. Fluid Mech. 165(21–22), 1480–1493 (2010)

    Article  MATH  Google Scholar 

  • Wang, W., Wang, X.P., Hu, C.X.: A comparative study of viscoelastic planar contraction flow for polymer melts using molecular constitutive models. Korea-Aust. Rheol. J. 26(4), 365–375 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China through Contract/Grant numbers 21274072, 11302043, and the State Key Laboratory of Structural Analysis for Industrial Equipment (No. GZ1213) and the Key Laboratory of Rubber–plastics, Ministry of Education (No. KF2010007).

Author information

Authors and Affiliations

  1. Key Laboratory of Rubber–plastics, Ministry of Education/Shandong Provincial Key Laboratory of Rubber–plastics, Qingdao University of Science and Technology, Qingdao, 266042, P.R. China

    Wei Wang, Changxu Hu & Wenwen Li

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, P.R. China

    Wei Wang

Authors
  1. Wei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Changxu Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenwen Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, W., Hu, C. & Li, W. Time-dependent rheological behavior of branched polymer melts in extensional flows. Mech Time-Depend Mater 20, 123–137 (2016). https://doi.org/10.1007/s11043-015-9287-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-015-9287-3

Keywords

Search

Navigation