Rheological models with microstructural constraints

Rheologica Acta

Volumn 42, Issue 1, 2003, Pages 64-72

  Edwards, B J ^a   Dressler, M ^b   Grmela, M ^c   Ait Kadi, A ^c  

^a University of Tennessee Knoxville   (United States)

^b ETH ZURICH   (Switzerland)

^c ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

Constrained microstructure; Polymer blends; Rigid rod polymers; Volume conservation

Indexed keywords

FLUID FLOW; MICROSTRUCTURE; MODEL; POLYMER; RHEOLOGY;

EID: 0037283537     PISSN: 00354511     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00397-002-0256-9     Document Type: Article

References (33)

1. Ait-Kadi A, Ramazani A, Grmela M, Zhou C (1999) "Volume preserving" rheological models for polymer melts and solutions using the GENERIC formalism. J Rheol 43:51-72
2. Almusallam AS, Larson RG, Solomon MJ (2000) A constitutive model for the prediction of ellipsoidal droplet shapes and stresses in immiscible blends. J Rheol 44:1055-1083
3. Beris AN, Edwards BJ (1990a) Poisson bracket formulation of incompressible flow equations in continuum mechanics. J Rheol 34:55-78
4. Beris AN, Edwards BJ (1990b) Poisson bracket formulation of viscoelastic flow equations of differential type: a unified approach. J Rheol 34:503-538
5. Beris AN, Edwards BJ (1994) Thermo- dynamics of flowing systems. Oxford University Press, New York
6. Bird RB, Curtiss CF, Armstrong RC, Hassager O (1987) Dynamics of polymeric fluids, vol 2, 2nd edn. Wiley, New York
7. Doi M (1981) Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and liquid crystalline phases. J Polym Phys Polym Phys Ed 19:229-243
8. Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon Press, Oxford
9. Dressler M, Edwards BJ, Öttinger HC (1999) Macroscopic thermodynamics of flowing polymeric fluids. Rheol Acta 38:117-136
10. Edwards BJ (1998) An analysis of single and double generator formalisms for the macroscopic description of complex fluids. J Non-Equilib Thermodyn 23:301-333
11. Edwards BJ, Beris AN (1991a) A unified view of transport phenomena based on the generalized bracket formulation. Ind Eng Chem Res 30:873-881
12. Edwards BJ, Beris AN (1991b) Non- canonical Poisson bracket for nonlinear elasticity with extensions to viscoelasticity. J Phys A Math Gen 24:2461-2480
13. Edwards BJ, Beris AN, Grmela M (1990) Generalized constitutive equation for polymeric liquid crystals. Part 1. Model formulation using the Hamiltonian (Poisson bracket) formulation. J Non- Newtonian Fluid Mech 35:51-72
14. Edwards BJ, Beris AN, Grmela M (1991) The dynamical behavior of liquid crystals: a continuum description through generalized brackets. Mol Cryst Liq Cryst 201:51-86
15. Edwards BJ, Beris AN, Öttinger HC (1998) An analysis of single and double generator formalisms for complex fluids. II. The microscopic description. J Non- Equilib Thermodyn 23:334-350
16. Grmela M (1985) Stress tensor in generalized hydrodynamics. Phys. Lett A 111:41-44
17. Grmela M (1988) Hamiltonian dynamics of incompressible elastic fluids. Phys. Lett A 130:81-86
18. Grmela M (1989) Hamiltonian mechanics of complex fluids. J Phys A Math Gen 22:4375-4394
19. Grmela M (2002) Reciprocity relations in thermodynamics. Physica A (in Press)
20. Grmela M, Carreau PJ (1987) Conformation tensor rheological models. J Non-Newtonian Fluid Mech 23:271-294
21. Grmela M. Öttinger HC (1997) Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys Rev E 56:6620-6632
22. Grmela M, Bousmina M, Palierne JF (2001) On the rheology of immiscible blends. Rheol Acta 40:560-569
23. Hand GL (1962) A theory of anisotropic fluids. J Fluid Mech 13:33-46
24. Hinch EJ. Leal LG (1976) Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations. J Fluid Mech 76:187-208
25. Jongschaap RJJ (1990) Microscopic modeling of the flow properties of polymers. Rep Prog Phys 53:1-55
26. Jongschaap RJJ (2001) The matrix model: a driven state variables approach to non-equilibrium thermodynamics. J Non-Newtonian Fluid Mech 96:63-77
27. Leonov AI (1976) Nonequilibrium thermodynamics and rheology of viscoelastic polymer media. Rheol Acta 15:85-98
28. Leslie FM (1979) Theory of flow phenomena in liquid crystals. In: Brown GH (ed.) Advances in liquid crystals, vol. 4. Academic Press, New York, pp 1-81
29. Maffetone PL, Minale M (1998) Equations of change for ellipsoid drops in viscous flow. J Non-Newtonian Fluid Mech 78:227-241
30. Marrucci G, Maffettone PL (1989) Description of the liquid-crystalline phase of rodlike polymers at high shear rates. Macromolecules 22:4076-4082
31. Marsden J, Weinstein A (1974) Reduction of symplectic manifolds with symmetry. Rep Math Phys 5:121-130
32. Öttinger HC, Grmela M (1997) Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism. Phys Rev E 56:6633-6655
33. Rayleigh, Lord (1945) The theory of sound, vol 1, 2nd edn. Dover Publications, New York.