A deformation tensor model of Brownian suspensions of orientable particles - The nonlinear dynamics of closure models

Journal of Non-Newtonian Fluid Mechanics

Volumn 64, Issue 1, 1996, Pages 43-69

  Szeri, Andrew J ^a   Lin, David J ^a  

^a University of California at Irvine   (United States)

Author keywords

Brownian motion; Fibers; Modelling; Nonlinear dynamics; Suspensions

Indexed keywords

BROWNIAN MOVEMENT; DEFORMATION; DEGREES OF FREEDOM (MECHANICS); DYNAMICS; FIBERS; MATHEMATICAL MODELS; SUSPENSIONS (FLUIDS); TENSORS; THREE DIMENSIONAL; UNSTEADY FLOW;

CLOSURE MODELS; DEFORMATION TENSOR MODELS; EVOLUTION EQUATION; FOKKER-PLANCK EQUATION; GLOBAL ATTRACTOR; ORIENTABLE PARTICLES; ORIENTATION DISTRIBUTION FUNCTION;

PARTICLES (PARTICULATE MATTER);

EID: 0030148007     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0257(95)01427-6     Document Type: Article

References (21)

1. R.B. Bird, C.F. Curtiss, R.A. Armstrong and O. Hassager, Dynamics of Polymeric Liquids, Vol. 2, Kinetic Theory, John Wiley & Sons, New York, 1987.
2. R.G. Larson, Constitutive Equations for Polymer Melts and Solutions, Butterworth, 1988.
3. S.G. Advani and C.L. Tucker, Closure approximations for three-dimensional structure tensors, J. Rheol., 34 (1990) 367-386.
4. A.J. Szeri and L.G. Leal, A new computational method for microstructured fluids. Part 1. Theory, J. Fluid Mech., 242 (1992) 549-576.
5. A.J. Szeri and L.G. Leal, A new computational method for microstructured fluids. Part 2. Inhomogeneous shear flow of a suspension, J. Fluid Mech., 262 (1994) 171-204.
6. A.J. Szeri, A deformation tensor model for liquid crystalline polymers, J. Rheol., 39 (1995) 873-891.
7. F. Folgar and C.L. Tucker, Orientation behavior of fibers in concentrated suspensions, J. Reinf. Plas. Compos., 3 (1984) 98-119.
8. F.P. Bretherton, The motion of rigid particles in a shear flow at low Reynolds number, J. Fluid Mech., 14 (1962) 284-304.
9. A.J. Szeri and L.G. Leal, Microstructure suspended in three-dimensional flows, J. Fluid Mech., 250 (1993) 143-167.
10. P.K. Currie, Constitutive equations for polymer melts predicted by the Doi-Edwards and Curtiss-Bird kinetic theory models, J. Non-Newtonian Fluid Mech., 11 (1982) 53-68.
11. N. Malamataris and T.C. Papanastasiou, Closed-form material functions for semidilute fiber suspensions, J. Rheol., 35 (1991) 449-464.
12. B.N. Rao, L. Tang and M.C. Altan, Rheological properties of non-Brownian spheroidal particle suspensions, J. Rheol., 38 (1994) 1-17.
13. A.J. Szeri, Pattern formation in recirculating flows of suspensions of orientable particles, Philos. Trans. R. Soc. London, Ser. A, 345 (1993) 477-506.
14. E.J. Hinch and L.G. Leal, Constitutive equations in suspension mechanics. Part 2. Approximate forms for suspension of rigid particles affected by Brownian rotations, J. Fluid Mech., 76 (1976) 187-208.
15. G.L. Hand, A theory of anisotropic fluids, J. Fluid Mech., 13 (1962) 33-46.
16. J.S. Cintra and C.L. Tucker, Orthotropic closure approximations for flow-induced fiber orientations, J. Rheol., 39 (1995) 1095-1122.
17. V. Verleye and F. Dupret, Prediction of fiber orientation in complex injection molded parts, Proc. ASME Winter Annual Meeting, 28 Nov.-3 Dec., 1993, New Orleans.
18. J.K. Hale, Asymptotic Behavior of Dissipative Systems, American Mathematical Society, Providence, RI, 1988.
19. C.V. Chaubal, L.G. Leal and G.H. Fredrickson, A comparison of closure approximations for the Doi theory of LCPs, J. Rheol., 39 (1995) 73-103.
20. J.M.T. Thompson and H.B. Stewart, Nonlinear Dynamics and Chaos, J. Wiley & Sons, Chichester, 1986.
21. B.C. Carlson, Computing elliptic integrals by duplication, Numer. Math., 33 (1979) 1-16.