Gaussian approximation for finitely extensible beadspring chains with hydrodynamic interaction

Journal of Rheology

Volumn 50, Issue 4, 2006, Pages 561-593

  Prabhakar, R ^b   Ravi Prakash, J ^a  

^a MONASH UNIVERSITY   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BROWNIAN MOVEMENT; MAGNETIC HYSTERESIS; METHOD OF MOMENTS; ORDINARY DIFFERENTIAL EQUATIONS; PROBABILITY DISTRIBUTIONS;

APPROXIMATE MODELS; GAUSSIAN APPROXIMATION; HYDRODYNAMIC INTERACTION; ROUSE CHAINS;

HYDRODYNAMICS;

EID: 33749028177     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.2206715     Document Type: Article

References (60)

1. Bird, R. B., P. J. Dotson, and N. L. Johnson, ";;Polymer solution bheology based on a finitely extensible bead-spring chain model,"; J. Non-Newtonian Fluid Mech. 7, 213-235 (1980).
2. Bird, R. B., C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids - Volume 2: Kinetic Theory, 2nd ed. (Wiley, New York, 1987b).
3. De Gennes, P.-G., ";Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients,"; J. Chem. Phys. 60, 5030-5042 (1974).
4. Doi, M., and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, New York, 1986).
5. Doyle, P. S., E. S. G. Shaqfeh, G. H. McKinley, and S. H. Spiegelberg, ";Relaxation of dilute polymers solutions following extensional flow,"; J. Non-Newtonian Fluid Mech. 76, 79-110 (1998).
6. Fan, X. J., R. B. Bird, and M. Renardy, ";;Configuration-dependent friction coefficients and elastic dumbbell rheology,";; J. Non-Newtonian Fluid Mech. 18, 255-272 (1985).
7. Fixman, M., ";;Polymer dynamics: Boson representation and excluded volume forces,"; J. Chem. Phys. 45, 785-792 (1966).
8. Fixman, M., ";Inclusion of hydrodynamic interaction in polymer dynamical simulations,"; Macromolecules 14, 1710-1717 (1981).
9. Ghosh, I., G. H. McKinley, R. A. Brown, and R. C. Armstrong, ";Deficiencies of FENE dumbbell models in describing rapid stretching of dilute polymer solutions,"; J. Rheol. 45, 721-758 (2001).
10. Gorban, A. N., I. V. Karlin, P. Ilg, and H. C. Öttinger, ";Corrections and enhancements of quasiequilibrium states,"; J. Non-Newtonian Fluid Mech. 96, 203-219 (2001).
11. Hassager, O., ";Kinetic theory and rheology of bead-rod models for macromolecular solutions, 1. Equilibrium and steady flow properties,"; J. Chem. Phys. 60, 2111-2124 (1974).
12. Herrchen, M., and H. C. Öttinger, ";A detailed comparison of various FENE models,"; J. Non-Newtonian Fluid Mech. 68, 17-42 (1997).
13. Hsieh, C.-C., L. Li, and R. G. Larson, ";Modeling hydrodynamic interaction in Brownian dynamics: Simulations of extensional flows of dilute solutions of DNA and polystyrene,"; J. Non-Newtonian Fluid Mech. 113, 147-191 (2003).
14. Jendrejack, R. M., J. J. de Pablo, and M. D. Graham, ";Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions,"; J. Chem. Phys. 116, 7752-7759 (2002).
15. Jendrejack, R. M., M. D. Graham, and J. J. de Pablo, ";Hydrodynamic interactions in long chain polymers: Application of the Chebyshev polynomial approximation in stochastic simulations,"; J. Chem. Phys. 113, 2894-2900 (2000).
16. Keunings, R., ";On the Peterlin approximation for finitely extensible dumbbells,"; J. Non-Newtonian Fluid Mech. 68, 85-100 (1997).
17. Kirkwood, J. G., and J. Riseman, ";The intrinsic viscosities and diffusion constants of flexible macromolecules in solution,"; J. Chem. Phys. 16, 565-573 (1948).
18. Kröger, M., ";Simple models for complex nonequilibrium fluids,"; Phys. Rep. 390, 453-551 (2004).
19. Kröger, M., A. Alba-Pérez, M. Laso, and H. C. Öttinger, ";Variance reduced Brownian simulation of a beadspring chain under steady shear flow considering hydrodynamic interaction effects,"; J. Chem. Phys. 113, 4767-4773 (2000).
20. Kumar, K. S., and J. R. Prakash, ";Universal consequences of the presence of excluded volume interactions in dilute polymer solutions undergoing shear flow,"; J. Chem. Phys. 121, 3886-3897 (2004).
21. Li, L., and R. G. Larson, ";Excluded volume effects on the birefringence and stress of dilute polymer solutions in extensional flow,"; Rheol. Acta 39, 419-427 (2000).
22. Lielens, G., P. Halin, I. Jaumin, R. Keunings, and V. Legat, ";New closure approximations for the kinetic theory of finitely extensible dumbbells,"; J. Non-Newtonian Fluid Mech. 76, 249-279 (1998).
23. Lielens, G., R. Keunings, and V. Legat, ";The FENE-L and FENE-LS closure approximations to the kinetic theory of finitely extensible dumbbells,"; J. Non-Newtonian Fluid Mech. 87, 179-196 (1999).
24. Magda, J. J., R. G. Larson, and M. E. Mackay, ";Deformation- dependent hydrodynamic interaction in flows of dilute polymer solutions,"; J. Chem. Phys. 89, 2504-2513 (1988).
25. Nitsche, L. C., W. Zhang, and L. E. Wedgewood, ";Asymptotic basis of the L closure for finitely extensible dumbbells in suddenly started uniaxial extension,"; J. Non-Newtonian Fluid Mech. 133, 14-27 (2006).
26. Orr, N. V., and T. Sridhar, ";Probing the dynamics of polymer solutions in extensional flow using step strain rate experiments,"; J. Non-Newtonian Fluid Mech. 82, 203-232 (1999).
27. Öttinger, H. C., ";Generalized Zimm model for dilute polymer solutions under theta conditions,"; J. Chem. Phys. 86, 3731-3749 (1987).
28. Öttinger, H. C., ";Gaussian approximation for Rouse chains with hydrodynamic interaction,"; J. Chem. Phys. 90, 463-473 (1989).
29. Peterlin, A., ";Hydrodynamics of macromolecules in a velocity field with longitudinal gradient,"; J. Polym. Sci., Part B: Polym. Lett. 4B, 287-291 (1966).
30. Prabhakar, R., Predicting the rheological properties of dilute polymer solutions using bead-spring models: Brownian dynamics simulations and closure approximations, Ph.D. thesis, Monash University (2005).
31. Prabhakar, R., and J. R. Prakash, ";Viscometric functions for Hookean dumbbells with excluded volume and hydrodynamic interaction,"; J. Rheol. 46, 1191-1220(2002).
32. Prabhakar, R., and J. R. Prakash, ";Multiplicative separation of the influences of excluded volume, hydrodynamic interactions and finite extensibility on the rheological properties of dilute polymer solutions,"; J. Non-Newtonian Fluid Mech. 116, 163-182 (2004).
33. Prabhakar, R., and J. R. Rakash, ";Fast and accurate closure approximations for bead-spring models of dilute polymer solutions,"; Aust N. Z. Ind. Appl. Math. J. 46, C379-C393 (2005).
34. Prabhakar, R., J. R. Prakash, and T. Sridhar, ";A successive fine-graining scheme for predicting the rheological properties of dilute polymer solutions,"; J. Rheol. 48, 1251-1278 (2004).
35. Prakash, J. R., ";The influence of the range of excluded volume interactions on the linear viscoelastic properties of dilute polymer solutions,"; Chem. Eng. Sci. 56, 5555-5564 (2001a).
36. Prakash, J. R., ";Rouse chains with excluded volume interactions: Linear viscoelasticity,"; Macromolecules 34, 3396-3411 (2001b).
37. Prakash, J. R., and H. C. Öttinger, ";Universal viscometric functions for dilute polymer solutions,"; J. NonNewtonian Fluid Mech. 71, 245-272 (1997).
38. Prakash, J. R., and H. C. Öttinger, ";Viscometric functions for a dilute solution of polymers in a good solvent,"; Macromolecules 32, 2028-2043 (1999).
39. Rotne, J., and S. Prager, ";Variational treatment of hydrodynamic interaction in polymers,"; J. Chem. Phys. 50, 4831-4837 (1969).
40. Rouse, P. E., ";A theory of the linear viscoelastic properties of dilute polymer solutions of coiling polymers,"; J. Chem. Phys. 21, 1272-1280 (1953).
41. Schroeder, C. M., E. S. G. Shaqfeh, and S. Chu, ";Effect of hydrodynamic interactions on DNA dynamics in extensional flow: Simulation and single molecule experiments,"; Macromolecules 37, 9242-9256 (2004).
42. Schroeder, C. M., H. P. Babcock, E. S. G. Shaqfeh, and S. Chu, ";Observation of polymer conformation hysteresis in extensional flow,"; Science 301, 1515-1519 (2003).
43. Sizaire, R., G. Lielens, I. Jaumain, R. Keunings, and V. Legat, ";On the hysteretic behaviour of dilute polymer solutions in relaxation following extensional flow,"; J. Non-Newtonian Fluid Mech. 82, 233-253 (1999).
44. Somasi, M., B. Khomami, N. J. Woo, J. S. Hur, and E. S. G. Shaqfeh, ";Brownian dynamics simulations of bead-rod and bead-spring chains: Numerical algorithms and coarse graining issues,"; J. Non-Newtonian Fluid Mech. 108, 227-255 (2002).
45. Spiegelberg, S. H., and G. H. McKinley, ";Elastic and viscous contributions to stress in extensional rheometry of viscous polymer solutions,"; in Proceedings of the XIth International Congress on Rheology, p. 211-212, Quebec City (1996).
46. Sunthar, P., and J. R. Prakash, ";Parameter-free prediction of DNA conformations in elongational flow by successive fine graining,"; Macromolecules 38, 617-640 (2005).
47. Sunthar, P., D. A. Nguyen, R. Dubbelboer, J. R. Prakash, and T. Sridhar, ";Measurement and prediction of the elongational stress growth in a dilute solution of DNA molecules,"; Macromolecules 38, 10200- 10209 (2005).
48. van den Brule, B. H. A. A., ";Brownian dynamics simulation of finitely extensible bead-spring chains,"; J. Non-Newtonian Fluid Mech. 47, 357-378 (1993).
49. Warner, H. R., ";Kinetic theory and rheology of dilute suspensions of finitely extensible dumbbells,"; Ind. Eng. Chem. Fundam. 11, 379-387 (1972).
50. Wedgewood, L. E., ";A Gaussian closure of the second-moment equation for a Hookean dumbbell with hydrodynamic interaction,"; J. Non-Newtonian Fluid Mech. 31, 127-142 (1989).
51. Wedgewood, L. E., and R. B. Bird, ";From molecular models to the solution of flow problems,"; Ind. Eng. Chem. Res. 27, 1313-1320 (1988).
52. Wedgewood, L. E., and H. C. Öttinger, ";A model of dilute polymer solutions with hydrodynamic interaction and finite extensibility. II. Shear flows,"; J. Non-Newtonian Fluid Mech. 27, 245-264 (1988).
53. Wiest, J. M., ";Birefringence in strong flows of polymer solutions,"; Polymer 40, 1917-1922 (1999).
54. Wiest, J. M., and R. I. Tanner, ";Rheology of bead-nonlinear spring chain molecules,"; J. Rheol. 33, 281-316 (1989).
55. Wiest, J. M., L. E. Wedgewood, and R. B. Bird, ";On coil-stretch transitions in dilute polymer solutions,"; J. Chem. Phys. 90, 587-594 (1989).
56. Yamakawa, H., Modern Theory of Polymer Solutions (Harper and Row, New York, 1971).
57. Zimm, B. H., ";Dynamics of polymer molecules in dilute solution: Viscoelasticity, flow birefringence and dielectric loss,"; J. Chem. Phys. 24, 269-278 (1956).
58. Zimm, B. H., ";Chain molecule hydrodynamics by the Monte-Carlo method and the validity of the KirkwoodRiseman approximation,"; Macromolecules 13, 592-602 (1980).
59. Zylka, W., ";Gaussian approximation and Brownian dynamics simulations for Rouse chains with hydrodynamic interaction undergoing simple shear flow,"; J. Chem. Phys. 94, 4628-4636 (1991).
60. Zylka, W., and H. C. Öttinger, ";Calculation of various universal properties for dilute polymer solutions undergoing shear flow,"; Macromolecules 24, 484-494 (1991).