ANZIAM J. 46(E) ppC320--C335, 2005.

Prediction of chain length effects in elongational flows of dilute polymer solutions by successive fine graining

P. Sunthar

J. Ravi Prakash

(received 25 October 2004, revised 8 March 2005)

Abstract

A new computational tool for predicting the rheological properties of a dilute solution of polymers in q-conditions is presented. Within this approach, the polymer is modelled as a bead spring chain with finitely extensible springs and fluctuating hydrodynamic interactions incorporated. The novelty of the method lies in obtaining predictions for a very large Kuhn step chain by extrapolating results of a series of bead-springs representations to the bead-rod limit. This provides the computational advantage of using smaller number of modes in a coarse grained description and better accuracy in the extrapolated result. The effect of chain length in the unraveling dynamics of a polymer in elongational flow is examined using this approach.

Download to your computer

Authors

P. Sunthar
J. Ravi Prakash
Department of Chemical Engineering, Monash University, Melbourne, Victoria 3800, Australia. mailto:Ravi.Jagadeeshan@eng.monash.edu.au

Published May 3, 2005. ISSN 1446-8735

References

  1. R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager. Dynamics of Polymeric Liquids --- Volume 2: Kinetic Theory. John Wiley, New York, second edition, 1987.
  2. M. Doi and S. F. Edwards. The Theory of Polymer Dynamics. Clarendon Press, Oxford, New York, 1986.
  3. P. S. Doyle and E. S. G. Shaqfeh. Dynamic simulations of freely draining, flexible bead-rod chains: {S}tart-up of extensional and shear flow. J. Non-Newtonian Fluid Mech., 76:43--78, 1998. http://dx.doi.org/10.1016/S0377-0257(97)00112-2.
  4. M Fixman. Construction of {L}angevin forces in the simulation of hydrodynamic interaction. Macromolecules, 19:1204--1207, 1986. http://dx.doi.org/10.1021/ma00158a043.
  5. C.-{C}. Hsieh, L. Li, and R. G. Larson. Modeling hydrodynamic interaction in {B}rownian dynamics: {S}imulations of extensional flows of dilute solutions of {DNA} and polystyrene. J. Non-Newtonian Fluid Mech., 113:147--191, 2003. http://dx.doi.org/10.1016/S0377-0257(03)00107-1.
  6. R. M. Jendrejack, M. D. Graham, and J. J. de Pablo. Hydrodynamic interactions in long chain polymers: {A}pplication of the {C}hebyshev polynomial approximation in stochastic simulations. J. Chem. Phys., 113(7):2894--2900, 2000. http://dx.doi.org/10.1063/1.1305884.
  7. M. Kr{o}ger, A. Alba-P{{e}}rez, M. Laso, and H. C. {O}ttinger. Variance reduced {B}rownian simulation of a bead-spring chain under steady shear flow considering hydrodynamic interaction effects. J. Chem. Phys., 113(11):4767--4773, 2000. http://dx.doi.org/10.1063/1.1288803.
  8. H. C. {O}ttinger. A model of dilute polymer solutions with hydrodynamic interaction and finite extensibility. {I}. {B}asic equations and series expansions. J. Non-Newtonian Fluid Mech., 26(2): 207--246, 1987. http://dx.doi.org/10.1016/0377-0257(87)80005-8.
  9. H. C. {O}ttinger. Stochastic Processes in Polymeric Fluids. Springer, Berlin, 1996.
  10. R. Prabhakar 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. http://dx.doi.org/10.1016/S0377-0257(03)00155-1.
  11. R. Prabhakar, 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. http://dx.doi.org/10.1122/1.1807841.
  12. J. Rotne and S. Prager. Variational treatment of hydrodynamic interaction in polymers. J. Chem. Phys., 50:4831--4837, 1969. http://dx.doi.org/10.1063/1.1670977.
  13. P. E. Rouse. A theory of the linear viscoelastic properties of dilute polymer solutions of coiling polymers. J. Chem. Phys., 21(7):1271--1280, 1953. http://dx.doi.org/10.1063/1.1699180.
  14. Douglas E. Smith and Steven Chu. Response of flexible polymers to a sudden elongational flow. Science, 281:1335--1340, 1998. http://dx.doi.org/10.1126/science.281.5381.1335.
  15. P. Sunthar and J. Ravi Prakash. Parameter free prediction of dna conformations in elongational flow by successive fine graining. Macromolecules, 38:617--640, 2005. http://dx.doi.org/10.1021/ma035941l.
  16. B. H. Zimm. Dynamics of polymer molecules in dilute solution: {V}iscoelasticity, flow birefringence and dielectric loss. J. Chem. Phys., 24(2):269--281, 1956. http://dx.doi.org/10.1063/1.1742462.