A wavelet-Galerkin method for simulating the Doi model with orientation-dependent rotational diffusivity

Journal of Non-Newtonian Fluid Mechanics

Volumn 114, Issue 2-3, 2003, Pages 197-228

  Suen, J K ^a   Nayak, R ^b   Armstrong, R C ^a   Brown, R A ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b APPLIED MATERIALS INC   (United States)

Author keywords

Doi model; Liquid crystalline polymers; Wavelet Galerkin method

Indexed keywords

COMPUTER SIMULATION; DIFFUSION IN LIQUIDS; FLUID DYNAMICS; GALERKIN METHODS; LIQUID CRYSTAL POLYMERS;

POLYMER DYNAMICS;

SOLS;

DIFFUSIVITY; LIQUID CRYSTAL; MATHEMATICAL METHOD; NON-NEWTONIAN FLUID; POLYMER SOLUTION; SHEAR FLOW; WAVELET ANALYSIS;

EID: 0141975862     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0257(03)00152-6     Document Type: Article

References (38)

1. Laso M.Öttinger H.C.Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach J. Non-Newtonian Fluid Mech. 47 1993 1-20
2. Hulsen M.A.van Heel A.P.G.van den Brule B.H.A.A.Simulation of viscoelastic flows using Brownian configuration fields J. Non-Newtonian Fluid Mech. 70 1997 79-101
3. Wapperom P.Keunings R.Legat V.The backward-tracking Lagrangian particle method for transient viscoelastic flows J. Non-Newtonian Fluid Mech. 91 2000 273-295
4. Bonvin J.Picasso M.Variance reduction methods for CONNFFESSIT-like simulations J. Non-Newtonian Fluid Mech. 84 1999 191-215
5. Stewart W.E.Sørensen J.P.Hydrodynamic interaction effects in rigid dumbbell suspensions. II. Computations for steady shear flow Trans. Soc. Rheol. 16 1972 1-13
6. Strand S.R.Kim S.Karrila S.J.Computation of rheological properties of suspensions of rigid rods: stress growth after inception of steady shear flow J. Non-Newtonian Fluid Mech. 24 1987 311-330
7. R.C. Armstrong, R. Nayak, I. Ghosh, R.A. Brown, The use of kinetic theory and microstructural models in the analysis of complex flows of viscoelastic liquids, in: A. Ät-Kadi, J.M. Dealy, D.F. James, et al. (Eds.), Proceedings of the XIIth International Congress on Rheology, vol. 1, Chemical Engineering Department, Laval University, Que., 1996, pp. 307-310.
8. R. Nayak, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1998.
9. Doi M.Molecular dynamics and rheological properties of concentrated solutions of rod-like polymers in isotropic and liquid crystalline phases J. Poly. Sci.: Poly. Phys. Ed. 19 1981 229-243
10. M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, New York, 1986.
11. Bhave A.V.Menon R.K.Armstrong R.C.Brown R.A.A constitutive equation for liquid-crystalline polymer solutions J. Rheol. 37 1993 413-441
12. Chaubal C.V.Leal L.G.Fredrickson G.H.A comparison of closure approximations for the Doi theory of LCPs J. Rheol. 39 1995 73-103
13. Chaubal C.V.Leal L.G.A closure approximation for liquid-crystalline polymer models based on parametric density estimation J. Rheol. 42 1999 177-201
14. Ilg P.Karlin I.V.Öttinger H.C.Generating moment equations in the Doi model of liquid crystalline polymers Phys. Rev. E 60 1999 5783-5787
15. Marrucci G.Maffettone P.L.Description of the liquid-crystalline phase of rod-like polymers at high shear rates Macromolecules 22 1989 4076
16. R.G. Larson, A method for calculating orientational distribution functions in flows of nematic polymers, in: D. de Kee, P.N. Kaloni (Eds.), Recent Developments in Structured Continua, vol. 2, Longman Scientific and Technical, 1990.
17. Larson R.G.Arrested tumbling in shearing flows of liquid crystal polymers Macromolecules 23 1990 3983-3992
18. Larson R.G.Öttinger H.C.Effect of molecular elasticity on out-of-plane orientations in shearing flows of liquid crystalline polymers Macromolecules 24 1991 6270-6282
19. T.W. Bell, J.J. de Pablo, M.D. Graham, J.D. Schieber, Brownian dynamics simulation of the Doi theory for liquid crystalline polymers, in: Presented at the 71st Annual Meeting of the Society of Rheology, Madison, WI, 1999 (unpublished).
20. T.W. Bell, Ph.D., University of Wisconsin, Madison, 1998.
21. Hua C.C.Schieber J.D.Application of kinetic theory models in spatiotemporal flows for polymer solutions, liquid crystals and polymer melts using the CONNFFESSIT approach Chem. Eng. Sci. 51 1996 1473-1485
22. R.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, Dynamics of polymeric liquids, in: Kinetic Theory, vol. 2, second ed., Wiley/Intersciences, New York, 1987.
23. Onsager L.The effect of shape on the interactions of colloidal particles Ann. N. Y. Acad. Sci. 51 1949 627-659
24. Maier W.Saupe A.Eine einfache molekulare-statisticsche theory der nematischen kristallinflussingen phase Z. Naturforsch. A. 14a 1959 882-889
25. I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
26. G. Strang, T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, Cambridge, 1997.
27. Sweldens W.The lifting scheme: a construction of second-generation wavelets SIAM J. Math. Anal. 29 1998 511-546
28. A. Latto, E. Tannenbaum, Compactly supported wavelets and the numerical solution of Burgers' equation, C. R. Acad. Sci. Paris, T:311, Serie I (1990) 903-909.
29. Qian S.Weiss J.Wavelets and the numerical solution of partial differential equations J. Comp. Phys. 106 1993 155-175
30. Wong G.C.K.Wong S.C.A wavelet-Galerkin method for the kinematic wave model of traffic flow Comm. Num. Meth. Eng. 16 2000 121-131
31. Liu Y.Cameron I.T.A new wavelet-based method for the solution of the population balance equation Chem. Eng. Sci. 56 2001 5283-5294
32. A. Latto, H.L. Resnikoff, E. Tannenbaum, The evaluation of connection coefficients of compactly supported wavelets, in: Proceedings of the USA-France Workshop on Wavelets and Turbulence, Springer, Verlag, 1992.
33. C.W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1971.
34. Simo J.C.Armeo F.Unconditional stability and long-term behavior of transient algorithms for the incompressible Navier-Stokes and Euler equations Comp. Meth. Appl. Mech. Eng. 111 1994 111-154
35. Saad Y.Schultz M.H.GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems SIAM J. Sci. Stat. Comp. 7 1986 856-869
36. Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston, 1996.
37. Y. Saad, A basic tool-kit for sparse matrix computations, version 2, 1998.
38. Faraoni V.Grosso M.Crescitelli S.Maffettone P.L.The rigid-rod model for nematic polymers: an analysis of the shear flow problem J. Rheol. 43 1999 829-843