Brownian dynamics simulations of bead-rod and bead-spring chains: Numerical algorithms and coarse-graining issues

Journal of Non-Newtonian Fluid Mechanics

Volumn 108, Issue 1-3, 2002, Pages 227-255

  Somasi, Madan ^a   Khomami, Bamin ^a   Woo, Nathanael J ^b   Hur, Joe S ^b   Shaqfeh, Eric S G ^b  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Algorithm; Bead rod model; Bead spring model; Brownian dynamics; Coarse graining; Dilute polymer solution; Extensional flow; Shear flow

Indexed keywords

ALGORITHMS; BROWNIAN MOVEMENT; COMPUTER SIMULATION; DEGREES OF FREEDOM (MECHANICS); RANDOM PROCESSES;

INVERSE LANGEVIN FUNCTION (ILF);

NON NEWTONIAN FLOW;

ALGORITHM; BROWNIAN MOTION; EXTENSIONAL FLOW; FLUID DYNAMICS; POLYMER SOLUTION; SHEAR FLOW;

EID: 0037203452     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0257(02)00132-5     Document Type: Article

References (24)

1. M.J. Crochet, Numerical simulation of viscoelastic flow: a review, Rubber Chem. Technol. 62 (1989) 426-455.
2. R.A. Brown, M.A. Szady, P.J. Northey, R.C. Armstrong, On the numerical stability of mixed finite element methods for viscoelastic flows governed by differential constitutive equations, Theoret. Comput. Fluid Dyn. (1993) 677-706.
3. B. Khomami, K.K. Talwar, H.K. Ganpule, A comparative study of higher-and lower-order finite element techniques for computation of viscoelastic flows, J. Rheol. 38 (1994) 255-289.
4. P.S.Doyle, E.S.G. Shaqfeh, G.H. Mckinley, S.H. Spiegelberg, Relaxation of dilute polymeric solutions following extensional flow, J. Non-Newtonian Fluid Mech. 76 (1998) 79-110.
5. H.C. Ottinger, M. Laso, Smart polymers in finite element calculations, theoretical and applied rheology, in: P. Moldenaers, R. Keunings (Eds.), Proceedings of the International Congress on Rheology, Elsevier, Brussels, 1992.
6. M. Laso, H.C. Ottinger, Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach, J. Non-Newtonian Fluid Mech. 47 (1993) 1-20.
7. 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-Newtonian Fluid Mech. 70 (1997) 79-101.
8. P. Halin, G. Lielens, R. Keunings, V. Legat, The Lagrangian particle method for macroscopic and micro-macro viscoelastic flow computations, J. Non-Newtonian Fluid Mech. 77 (1998) 153-190.
9. I. Ghosh, G.H. McKinley, R.A. Brown, R.C. Armstrong, An adaptive length scale method for dilute polymer solutions, in: Proceedings of the XIIIth International Congress on Rheology, Cambridge, UK, August 2000.
10. P.S. Doyle, E.S.G. Shaqfeh, A.P. Gast, Dynamic simulation of freely draining flexible polymers in steady linear flow, J. Fluid Mech. 334 (1997) 251-291.
11. H.C. Ottinger, Stochastic Processes in Polymeric Fluids, Springer, Berlin, 1996.
12. R.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, vol. 2, Wiley, New York, 1987, p. 40.
13. J.F. Marko, E.D. Siggia, Stretching DNA, Macromolecules 28 (1991) 3427-3433.
14. A. Cohen, A Pade approximant to the inverse Langevin function, J. Rheol. Acta 30 (1991) 270-272.
15. T.W. Liu, Flexible polymer chain dynamics and rheological properties in steady flows, J. Chem. Phys. 90 (1989) 5826-5842.
16. P.S. Grassia, E.J. Hinch, L.C. Nitsche, Computer simulations of Brownian motion of complex systems, J. Fluid Mech. 282 (1995) 373-403.
17. G.H. Golub, C.V. Loan, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
18. D.E. Smith, H.P. Babcock, S. Chu, Single polymer dynamics in steady shear flow, Science 283 (1999) 1724-1727.
19. J.S. Hur, E.S.G. Shaqfeh, R.G. Larson, Brownian dynamics simulations of single DNA molecules in shear flow, J. Rheol. 44 (2000) 713-742.
20. H.P. Babcock, D.E. Smith, J.S. Hur, E.S.G. Shaqfeh, S. Chu, Relating the microscopic and macroscopic response of a polymeric fluid in a shearing flow, Phys. Rev. Lett. 85 (2000) 2018-2021.
21. J.S. Hur, E.S.G. Shaqfeh, H.P. Babcock, D.E. Smith, S. Chu, Dynamics of dilute and semidilute DNA solutions in the start-up of shear flow, J. Rheol. 45 (2001) 421-450.
22. J.M. Wiest, R.I. Tanner, Rheology of bead-nonlinear spring chain macromolecules, J. Rheol. 33 (1989) 281-316.
23. P.S. Doyle, E.S.G. Shaqfeh, Dynamic simulation of freely draining flexible bead-rod chains: start-up of extensional and shear flow, J. Non-Newtonian Fluid Mech. 76 (1998) 43-78.
24. I. Ghosh, G.H. McKinley, R.A. Brown, R.C. Armstrong, Deficiencies of FENE dumbbell models in describing the rapid stretching of dilute polymer solutions, J. Rheol. 45 (2001) 721-758.