Stable dynamic states at the nematic liquid crystals in weak shear flow

Physica D: Nonlinear Phenomena

Volumn 232, Issue 2, 2007, Pages 156-165

  Zhang, Hui ^a   Zhang, Pingwen ^b  

^a BEIJING NORMAL UNIVERSITY   (China)

^b PEKING UNIVERSITY   (China)

Author keywords

Hysteresis phenomenon; Nematic liquid crystals; Stable dynamic states; Theoretical analysis

Indexed keywords

COMPUTER SIMULATION; ELECTRON ENERGY LEVELS; HYSTERESIS; PHASE DIAGRAMS; SHEAR FLOW;

HYSTERESIS PHENOMENON; STABLE DYNAMIC STATES; THEORETICAL ANALYSIS;

NEMATIC LIQUID CRYSTALS;

EID: 34547096289     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.06.011     Document Type: Article

References (30)

1. Archer L., and Larson R.G. A molecular theory of flow alignment and tumbling in sheared nematic liquid crystals. J. Chem. Phys. 103 (1995) 3108-3111
2. Baek S.G., Magda J.J., Larson R.G., and Hudson S.D. Rheological differences among liquid-crystalline polymers. II. Disappearance of negative N1 in densely packed lyotropes and thermotropes. J. Rheol. 38 (1994) 1473-1503
3. Berry G.C. Bingham Award LectureC1990: Rheological and rheo-optical studies on nematic solutions of a rodlike polymer. J. Rheol. 35 (1991) 943-983
4. Bhave A.V., Menon R.K., Armstrong R.C., and Brown R.A. A constitutive equation for liquid-crystalline polymer solutions. J. Rheol. 34 (1993) 413-441
5. Boudreau D.M., Winter H.H., Lillya C.P., and Stein R.S. Conoscopic observations of shear-induced rotations in nematic liquid crystals. Rheol. Acta 38 (1999) 503-513
6. Burghardt W.R. Molecular orientation and rheology in sheared lyotropic liquid crystalline polymers. Macromol. Chem. Phys. 199 (1998) 471-488
7. Constantin P., Kevrekidis I., and Titi E.S. Asymptotic states of a Smoluchowski equation. Arch. Ration. Mech. Anal. 174 (2004) 365-384
8. Constantin P., Kevrekidis I., and Titi E.S. Remarks on a Smoluchowski equation. Discrete Contin. Dyn. Syst. 11 (2004) 101-112
9. Constantin P., and Vukadinovic J. Note on the number of steady states for a 2D Smoluchowski equation. Nonlinearity 18 (2005) 441-443
10. Doi M., and Edwards S.F. The Theory of Polymer Dynamics (1986), Oxford University Press
11. W.N. E, P.W. Zhang, Ericksen-Leslie equation derived from a molecular kinetic equation under small Deborah number, Preprint
12. Faraoni V., Grosso M., Crescitelli S., and Maffettone P.L. The rigid-rod model for nematic polymers: An analysis of the shear flow problem. J. Rheol. 43 (1999) 829-843
13. Fathullin I., and Slastikov V. A note on the Onsager model of nematic phase transitions. Commun. Math. Sci. 3 (2005) 21-26
14. Fathullin I., and Slastikov V. Critical points of the Onsager functional on a sphere. Nonlinearity 18 (2005) 2565-2580
15. Forest M.G., and Wang Q. The rigid-rod model for nematic polymers: An analysis of the shear flow problem. Rheol. Acta 42 (2003) 20-46
16. Forest M.G., Wang Q., and Zhou R. The weak shear kinetic phase diagram for nematic polymers. Rheol. Acta 43 (2004) 17-37
17. Forest M.G., Zhou R., and Wang Q. Full-tensor alignment criteria for sheared nematic polymers. J. Rheol. 47 (2003) 105-127
18. de Gennes P.G., and Prost J. The Physics of Liquid Crystals. 2nd ed. (1993), Oxford Science Publications
19. Gähwiller Ch. Temperature dependence of flow alignment in nematic liquid crystals. Phys. Rev. Lett. 28 (1972) 1554-1556
20. Jordan R., Kinderlehrer D., and Otto F. The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1-17
21. Kuzuu N., and Doi M. Constitutive equation for nematic liquid crystals under weak velocity gradient derived from a molecular kinetic equation. J. Phys. Soc. Japan 52 (1983) 3486-3494
22. Larson R.G., and Mead D.W. Time and shear-rate scaling laws for liquid crystal polymers. J. Rheol. 33 (1989) 1251-1281
23. Larson R.G., and Öttinger H.C. Effect of molecular elasticity on out-of-plane orientations in shearing flows of liquid-crystalline polymers. Macromolecules 24 (1991) 6270-6282
24. Liu H.L., Zhang H., and Zhang P.W. Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential. Commun. Math. Sci. 3 (2005) 201-218
25. Luo C., Zhang H., and Zhang P.W. The structure of equilibrium solutions of the one-dimensional Doi equation. Nonlinearity 18 (2005) 379-389
26. Maffettone P.L., and Crescitelli S. Bifurcation analysis of a molecular model for nematic polymers in shear flows. J. Non-Newtonian Fluid Mech. 59 (1995) 73-91
27. Marrucci G., and Maffettone P.L. Description of the liquid crystalline phase of rodlike polymers at high shear rates. Macromolecules 22 (1989) 4076-4082
28. Onsager L. The effects of shape on the interaction of colloidal particles. Ann. N. Y. Acad. Sci. 51 (1949) 627-659
29. Zhou H., Wang H., Forest M.G., and Wang Q. A new proof on uniaxial equilibria of Smoluchowski equation for rodlike nematic polymers. Nonlinearity 18 (2005) 2815-2825
30. Zhou H., and Wang H.Y. Steady states and dynamics of 2-D nematic polymers driven by an imposed weak shear. Commun. Math. Sci. 5 (2007) 113-132