Single and multi-mode modelling for filament stretching flows

Journal of Non-Newtonian Fluid Mechanics

Volumn 146, Issue 1-3, 2007, Pages 92-113

  Matallah, H ^a   Sujatha, K S ^a   Banaai, M J ^a   Webster, M F ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Body forces; Filament stretching; Linear and exponential stretching; Multi mode; Strain hardening; Surface tension

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PLASTIC FILAMENTS; POLYMER SOLUTIONS; RHEOLOGY; STRAIN; STRAIN HARDENING; SURFACE TENSION;

FILAMENT STRETCHING FLOWS; RHEOLOGICAL VARIATION; STRAIN-HARDENING FLUIDS;

FLOW OF FLUIDS;

COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; FLOW OF FLUIDS; MATHEMATICAL MODELS; PLASTIC FILAMENTS; POLYMER SOLUTIONS; RHEOLOGY; STRAIN; STRAIN HARDENING; SURFACE TENSION;

EID: 34548440197     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2007.04.021     Document Type: Article

References (41)

1. Sridhar T., Tirtaatmadja V., Nguyen D.A., and Gupta R.K. Measurement of extensional viscosity of polymer solutions. J. Non-Newtonian Fluid Mech. 40 (1991) 271-280
2. McKinley G.H., and Sridhar T. Filament-stretching rheometry of complex fluids. Annu. Rev. Fluid Mech. 34 (2002) 375-415
3. Matta J.E., and Tytus R.P. Liquid stretching using a falling cylinder. J. Non-Newtonian Fluid Mech. 67 (1990) 47-76
4. Tirtaatmadja V., and Sridhar T. A filament stretching device for measurement of extensional viscosity. J. Rheol. 37 (1993) 1081-1102
5. Goldin M., Yerushalmi J., Pfeffer R., and Shinnar R. Breakup of a laminar capillary jet of a viscoelastic fluid. J. Fluid Mech. 38 (1969) 689-711
6. Chang H., Demekhin E.A., and Kalaidin E. Iterated stretching of viscoelastic jets. Phys. Fluids 11 (1999) 1717-1737
7. Oliveira M.S.N., Yeh R., and McKinley G.H. Iterated stretching, extensional rheology and formation of beads-on-a-string structures in polymer solutions. J. Non-Newtonian Fluid Mech. 137 (2006) 137-148
8. Sizaire R., and Legat V. Finite element simulation of a filament stretching extensional rheometer. J. Non-Newtonian Fluid Mech. 71 (1997) 89-107
9. Bach A., Rasmussen H.K., Longin P.-Y., and Hassager O. Growth of non-axisymmetric disturbances of the free surface in the filament stretching rheometer: experiments and simulation. J. Non-Newtonian Fluid Mech. 108 (2002) 163-186
10. Hassager O., Kolte M.I., and Renardy M. Failure and nonfailure of fluid filaments in extension. J. Non-Newtonian Fluid Mech. 76 (1998) 137-151
11. Rasmussen H.K., and Hassager O. Three-dimensional simulations of viscoelastic instability in polymeric filaments. J. Non-Newtonian Fluid Mech. 82 (1999) 189-202
12. Yao M., McKinley G.H., and Debbaut B. Extensional deformation, stress relaxation and necking failure of viscoelastic filaments. J. Non-Newtonian Fluid Mech. 79 (1998) 469-501
13. Langouche F., and Debbaut B. Rheological characterisation of high density polyethylene with a multi-mode differential viscoelastic model and numerical simulation of transient elongational recovery experiments. Rheol. Acta 38 (1999) 48-64
14. Giesekus H. A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J. Non-Newtonian Fluid Mech. 11 (1982) 69-109
15. Li J.M., Burghardt W.R., Yang B., and Khomami B. Flow birefringence and computational studies of a shear thinning polymer solution in axisymmetric stagnation flow. J. Non-Newtonian Fluid Mech. 74 (1998) 151-193
16. Matallah H., Banaai M.J., Sujatha K.S., and Webster M.F. Modelling filament stretching flows with strain-hardening models and sub-cell approximations. J. Non-Newtonian Fluid Mech. 134 (2006) 77-104
17. Sujatha K.S., Matallah H., Banaai J., and Webster M.F. Computational predictions for viscoelastic filament stretching flows: ALE methods and free-surface techniques (CM and VOF). J. Non-Newtonian Fluid Mech. 137 (2006) 81-102
18. Webster M.F., Tamaddon-Jahromi H.R., and Aboubacar M. Transient viscoelastic flows in planar contractions. J. Non-Newtonian Fluid Mech. 118 (2004) 83-101
19. Webster M.F., Matallah H., and Sujatha K.S. Sub-cell approximations for viscoelastic flows-filament stretching. J. Non-Newtonian Fluid Mech. 126 (2005) 187-205
20. Noh W.F. A time dependent two space dimensional coupled Eulerian Lagrangian code. Meth. Comput. Phys. 3 (1964)
21. Hirt C.W., Amsden A.A., and Cook J.L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14 (1974) 227-253
22. Hughes T.J.R., Liu W.K., and Zimmermann T.K. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput. Methods Appl. Mech. Eng. 29 (1981) 329-349
23. Foteinopoulou K., Mavrantzas V.G., and Tsamopoulos J. Numerical simulation of bubble growth in Newtonian and viscoelastic filaments undergoing stretching. J. Non-Newtonian Fluid Mech. 122 (2004) 177-200
24. Koplik J., and Banavar J.R. Extensional rupture of model non-Newtonian fluid filaments. Phys. Rev. E67 (2003) 1-12
25. Phan-Thien N., and Tanner R.I. A new constitutive equation derived from network theory. J. Non-Newtonian Fluid Mech. 2 (1977) 353-365
26. Phan-Thien N. A non-linear network viscoelastic model. J. Rheol. 22 (1978) 259-283
27. Larson R.G. Constitutive Equations for Polymer Melts and Solutions (1988), Butterworths, Boston, USA
28. Matallah H., Townsend P., and Webster M.F. Recovery and stress-splitting schemes for viscoelastic flows. J. Non-Newtonian Fluid Mech. 75 (1998) 139-166
29. Levich V.G. Physicochemical Hydrodynamics (1962), Pentice-Hall, Englewood Cliffs, NJ
30. Keunings R. An algorithm for the simulation of transient viscoelastic flows with free surfaces. J. Comput. Phys. 62 (1986) 199-220
31. Spiegelberg S.H., Ables D.C., and McKinley G.H. The role of end-effects on measurements of extensional viscosity in filament stretching rheometers. J. Non-Newtonian Fluid Mech. 64 (1996) 229-267
32. Szabo P. Transient filament stretching rheometer I: force balance analysis. Rheol. Acta 36 (1997) 277-284
33. Chandio M.S., Matallah H., and Webster M.F. Numerical simulation of viscous filament stretching flows. Int. J. Num. Meth. Heat Fluid Flow 13 (2003) 899-930
34. Hawken D.M., Tamaddon-Jahromi H.R., Townsend P., and Webster M.F. A Taylor-Galerkin based algorithm for viscous incompressible flow. Int. J. Num. Meth. Fluids 10 (1990) 327-351
35. Baloch A., Townsend P., and Webster M.F. On two and three dimensional expansion flows. J. Comput. Fluids 24 (1995) 863-882
36. Baaijens F.P.T., Selen S.H.A., Baaijens H.P.W., Peters G.W.M., and Meijer H.E.H. Viscoelastic flow past a confined cylinder of a LDPE melt. J. Non-Newtonian Fluid Mech. 68 (1997) 173-203
37. Yao M., Spiegelberg S.H., and McKinley G.H. Dynamics of weakly strain-hardening fluids in filament stretching devices. J. Non-Newtonian Fluid Mech. 89 (2000) 1-43
38. McKinley G.H., Brauner O., and Yao M. Kinematics of filament stretching in dilute and concentrated polymer solutions. Korea-Australia Rheol. J. 13 (2001) 29-35
39. G.H. McKinley, Visco-Elasto-Capillary Thinning and Break-up of Complex Fluids, Hatsopoulos Microfluids Laboratory Report 05-P-04 (2005).
40. Yao M., and McKinley G.H. Numerical simulation of extensional deformations of viscoelastic liquid bridges in filament stretching devices. J. Non-Newtonian Fluid Mech. 74 (1998) 47-88
41. van Nieuwkoop J., and Muller von Czernicki M.M.O. Elongation and subsequent relaxation measurements on dilute polyisobutylene solutions. J. Non-Newtonian Fluid Mech. 67 (1996) 105-123