Dynamic simulation of freely-draining, flexible bead-rod chains: Start-up of extensional and shear flow

Journal of Non-Newtonian Fluid Mechanics

Volumn 76, Issue 1-3, 1998, Pages 43-78

  Doyle, Patrick S ^a   Shaqfeh, Eric S G ^a  

^a Stanford University   (United States)

Author keywords

Bead rod chains; Extensional flow; Shear flow

Indexed keywords

BROWNIAN MOVEMENT; MATHEMATICAL MODELS; OPTICAL PROPERTIES; POLYSTYRENES; RHEOLOGY; SHEAR FLOW; SHEAR STRESS; STRAIN; STRESS ANALYSIS; STRESS RELAXATION; TENSORS; VISCOELASTICITY;

EXTENSIONAL FLOW; FINITELY EXTENSIBLE NONLINEAR ELASTIC (FENE) MODEL; POLYMERIC LIQUIDS; ROUSE MODEL; STRESS OPTIC COEFFICIENTS; STRESS OPTIC LAW; ZIMM RELAXATION SPECTRUM;

COMPUTATIONAL FLUID DYNAMICS;

EID: 0032050232     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0257(97)00112-2     Document Type: Article

References (68)

1. P.S. Doyle, E.S.G. Shaqfeh, A.P. Gast, Dynamic simulation of freely draining, flexible polymers in linear flows, J. Fluid Mech. 334 (1997) 251-291.
2. M. Laso, H.C. Öttinger, Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach, J. Non-Newton. Fluid Mech. 47 (1993) 1-20.
3. K. Feigl, M. Laso, H.C. Öttinger, CONNFFESSIT approach for solving a two-dimensional viscoelastic fluid problem, Macromolecules 28 (1995) 3261-3274.
4. H.C. Öttinger, B.H.A.A. van den Brule, M.A. Hulsen, Brownian configurational fields and variance reduced CONNFFESSIT, preprint, 1997.
5. M.A. Hulsen, A.P.G. van Heel, B.H.A.A. van den Brule, Simulation of viscoelastic flows using Brownian configuration fields, J. Non-Newton. Fluid Mech. (1996), in press.
6. E.J. Hinch, Mechanical models of dilute polymer solutions in strong flows, Phys. Fluids 20 (1977) 22-30.
7. J.M. Rallison, E.J. Hinch, Do we understand the physics in the constitutive equation?, J. Non-Newton. Fluid Mech. 29 (1988) 37-55.
8. E.J. Hinch, Uncoiling a polymer molecule in a strong extensional flow, J. Non-Newton. Fluid Mech. 54 (1994) 209-230.
9. J.M. Rallison, Dissipative stresses in dilute polymer solutions, J. Non-Newton. Fluid Mech. 68 (1997) 61-83.
10. R.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids: Kinetic Theory, Vol. 2, Wiley, New York, 1987.
11. R.G. Larson, Constitutive Equations for Polymer Melts and Solutions, Butterworth, London, 1988.
12. M.D. Chilcott, J.M. Rallison, Creeping flow of dilute polymer solutions past cylinders and spheres, J. Non-Newton. Fluid Mech. 29 (1988) 381-432.
13. J. V. Satrape, M.J. Crochet, Numerical simulation of the motion of a sphere in a boger fluid, J. Non-Newton. Fluid Mech. 54 (1994) 91-111.
14. R.A. Keiller, Entry-flow calculations for the Oldroyd-B and FENE equations, J. Non-Newton. Fluid Mech. 46 (1993) 143-178.
15. J. Azaiez, R. Guenette, A. Ait-Kadi, Numerical simulation of viscoelastic flows through a planar contraction, J. Non-Newton. Fluid Mech. 62 (1996) 253-277.
16. W. Kuhn, H. Kuhn. Helv. Chim. Acta 28 (1945) 1533-1579.
17. C.W. Manke, M.C. Williams, Comparison of a new internal viscosity model with other constrained-connector theories of dilute polymer solution rheology, Rheol. Acta 32 (1993) 418-421.
18. C.W. Manke, M.C. Williams, Transient stress predicted by the internal viscosity model in elongational flow, Rheol. Acta 30 (1991) 316-328.
19. D. Acierno, G. Titomanlio, G. Marrucci, Dilute solution rheology of flexible macromolecules, J. Polymer Sci. 12 (1974) 2177-2187.
20. C.W. Manke, M.C. Williams, Transient stress and strain responses predicted by the internal viscosity model in shear flow, J. Rheol. 33 (1989) 949-978.
21. M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Oxford Science Publications, 1986.
22. D.H. King, D.F. James, Analysis of the Rouse model in extensional flow. II Stresses generated in sink flow by flexible macromolecules and by finitely extended macromolecules, J. Chem. Phys. 78 (1983) 4749-4754.
23. R.G. Larson, The unravelling of a polymer chain in a strong extensional flow, Rheol. Acta 29 (1990) 371-384.
24. P.S. Grassia, E.J. Hinch, Computer simulations of polymer chain relaxation via Brownian motion, J. Fluid Mech. 208 (1996) 255-288.
25. L.R.G. Treloar, The Physics of Rubber Elasticity, 3rd edn., Claredon Press, Oxford, 1975.
26. W. Kuhn, F. Grun, Relationships between elastic constants and stretching double refraction of highly elastic substances, Kolloid Z. 101 (1942) 248.
27. H.R. Warner, Kinetic theory and rheology of dilute suspensions of finitely extendible dumb-bells, Ind. Eng. Chem. Fundam. 11 (1972) 379-387.
28. R.B. Bird, P.J. Dotson, N.L. Johnson, Polymer solution rheology based on a finitely extensible bead-spring chain model, J. Non-Newton. Fluid Mech. 7 (1980) 213-235.
29. G.G. Fuller, Optical Rheometry of Complex Fluids, Oxford University Press, London, 1995.
30. W. Philippoff, Studies of flow birefringence of polystyrene solutions, in: Proc. 4th Int. Cong. Rheology, Vol. 2, 1965, p. 243.
31. W.H. Talbott, J.D. Goddard, Streaming birefringence in extensional flow of polymer solutions, Rheol. Acta 18 (1979) 505-517.
32. C.A. Cathey, G.G. Fuller, The optical and mechanical response of flexible polymer solutions in extensional flow, J. Non-Newton. Fluid Mech. 34 (1990) 63-88.
33. S.H. Spiegelberg, G.H. McKinley, Elastic and viscous contributions to stress in extensional rheometry of viscous polymer solutions, in: XIth Int. Cong. Rheology, Quebec City, Que, Canada, 1996, pp. 211-212.
34. S.F. Smyth, Chen-Hua Liang, M.E. Mackay, G.G. Euller, The stress jump of a semirigid macromolecule after shear: Comparison of the elastic stress to the birefringence, J. Rheol. 40 (1995) 659-672.
35. C.W. Gardiner, Handbook of Stochastic Methods. Springer, Berlin, 1985.
36. W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions, Cambridge University Press, Cambridge, 1989.
37. J.P. Rycksert, G. Ciccotti, J. Berendsen, Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n-aLkanes, J. Comput. Phys. 23 (1977) 327-341.
38. T.W. Liu, Flexible polymer chain dynamics and rheological properties in steady flows, J. Chem. Phys. 90 (1989) 5826-5842.
39. O. Hassager, Kinetic theory and rheology of bead-rod models for macromolecular solutions, (i) Equilibrium and steady flow, J. Chem. Phys. 60 (1974) 2111-2124.
40. E.J. Hinch, Brownian motion with stiff bonds and rigid constraints, J. Fluid Mech. 271 (1994) 219-234.
41. J.L.S. Wales, The Application of Flow Birefringence to Rheological Studies of Polymer Melts, Delft University Press, Delft, 1976.
42. R.M. Kannan, J.A. Kornfield, Stress-optical manifestations of molecular and microstructural dynamics in complex polymer melts, J. Rheol. 38 (1994) 1127-1150.
43. R. Keunings, On the Peterline appoximation for finitely extensible dumbbells, J. Non-Newton. Fluid Mech. 68 (1997) 85-100.
44. M. Herrchen, H.C. Öttinger, A detailed comparison of various FENE dumbbell models, J. Non-Newton. Fluid Mech. 68 (1997) 17-42.
45. H.C. Ottinger, Stochastic Processes In Polymeric Fluids, Springer, Berlin, 1995.
46. P.E. Rouse, A theory for the linear viscoelasticity properties of dilute solutions of coiling polymers, J. Chem. Phys. 21 (1953) 1272-1280.
47. L.E. Wedgewood, D.N. Ostrov, R.B. Bird, A finitely extensible bead-spring chain model for dilute polymer solutions, J. Non-Newton. Fluid Mech. 40 (1991) 199-239.
48. B.H.A.A. van den Brule, Brownian dynamics of finitely extensible bead-spring chains, J. Non-Newton. Fluid Mech. 47 (1993) 357-378.
49. J.H. Fersiger, Numerical Methods for Engineering Application, Wiley, New York, 1981.
50. P.S. Doyle, E.S.G. Sheqfeh, G.H. McKinley, S.H. Spiegelberg, Relaxation of dilute polymer solutions in extensional flow, J. Non-Newton. Fluid Mech. (1997), submitted.
51. B. Berne, R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology and Physics, Krieger, Malabar, FL, 1990.
52. G. Ryskin, Calculation of the effect of polymer additive in a converging flow, J. Fluid Mech. 178 (1987) 423-440.
53. N. Pistoor, K. Binder, Scattering function and the dynamics of phase separation in polymer mixtures under shear flow, Colloid Polym. Sci. 266 (1988) 132-140.
54. F.R. Cottrell, E.W. Merrill, K.A. Smith, Conformation of polyisobutylene in dilute solution subject to a hydrodynamic shear field, J. Polym. Sci. A-2 (7) (1969) 1415-1434.
55. A. Link, J. Springer, Light scattering from dilute polymer solutions in shear flow, Macromolecules 26 (1993) 464-471.
56. M. Zisenis, J. Springer, Rheooptical detection of shear-induced orientation of high molar mass polystyrene in dilute solution, Polymer 35 (1994) 3156-3163.
57. P. Lindner, R.C. Oberthür, Shear-induced deformation of polystyrene colis in dilute solution from small angle neutron scattering 2. Variation of shear gradient, molecular mass and solvent viscosity, Colloid Polym. Sci. 266 (1988) 886-897.
58. J.J.L. Cascales, J.G. de la Torre, Hydrodynamic interaction effects on the conformation of flexible chains in simple shear flow, Macromolecules 23 (1990) 809-813.
59. L.E. Wedgewood, H.C. Öttinger, A model of dilute polymer solutions with hydrodynamic interaction and finite extensibility II. Shear flows, J. Non-Newton. Fluid Mech. 27 (1988) 245-264.
60. S.H. Spiegelberg, G.H. McKinley, Stress relaxation and elastic decohesion of viscoelastic polymer solutions in extensional flow, J. Non-Newton. Fluid Mech. 67 (1996) 49-76.
61. S.H. Spiegelberg, D.C. Ables, G.H. McKinley, The role of end-effects on measurements of extensional viscosity in filament stretching rheometers, J. Non-Newton. Fluid Mech. 64 (1996) 229-267.
62. N.V. Orr, T. Sridhar, Stress relaxation in uniaxial extension, J. Non-Newton. Fluid Mech. 67 (1996) 77-103.
63. P.G. de Gennes, Coil-stretch transition in dilute flexible polymers under ultrahigh velocity gradients, J. Chem. Phys. 60 (1974) 5030-5042.
64. E.J. Hinch, Proc. Symp. Polymer Lubrification, Brest, France, 1974.
65. G.G. Fuller, L.G. Leal, Flow birefringence of dilute polymer solutions in two dimensional flows, Rheol. Acta 19 (1980) 580-600.
66. R.G. Larson, The structure and rheology of complex fluids, 1997, in press.
67. R.G. Larson, T.T. Perkins, D.E. Smith, S. Chu, Hydrodynamics of a DNA molecule in a flow field, Phys. Rev. E 55 (1997) 1794-1797.
68. S.W. Fetsko, P.T. Cummings, Brownian dynamics simulation of bead-spring chains models for dilute polymer solutions in elongational flow, J. Rheol. 39 (1995) 285-299.