Abstract
A unified, nonlinear, hydrodynamic theory of liquid crystals is presented. The theory makes use of the balance laws of micropolar continuum mechanics. New strain and rate measures appropriate to liquid crystals and suspensions are introduced. The nonlinear constitutive equations are obtained for the nematic and cholesteric liquid crystals employing these measures and the micro-inertia tensor. The thermodynamic restrictions are studied in detail. The relation of the theory to the director theory is established. The solution is given for the shear flow of nematic liquids in a channel.
The present work was supported by the National Science Foundation.
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References
Oseen, C.W. [ 1929 ]: Die anisotropen Flüssigkeiten. Tatsachen und Theorien, Berlin.
Oseen, C.W. [ 1933 ] Trans. Faraday Soc. 29, 883.
Anzelius, A. [ 1931 ] Arssker, Mat. Ocb. Natl., 1.
Frank, F.C. [ 1958 ] Discussion Faraday Soc. 25, 1928.
Ericksen, J.L. [ 1962 ] Arch. Ration. Mech. Anal. 9, 371–378.
Ericksen, J.L. [ 1967 ] Arch. Ration. Mech. Anal. 23, 266.
Ericksen, J.L. [ 1969 ] Molecular Crystals and Liquid Crystals, 7, 153–164.
Leslie, F.M. [ 1968a ] Arch. Ration. Mech. Anal. 28, 265–283.
Leslie, F.M. [ 1968b ] Proc. Royal Soc. A 307, 359–372.
Davison, L. [ 1967 ] Phys. Fluid, 10, 2333–2338.
Davison, L. [ 1969 ] Phys. Review 180, 232–237.
Martin, P.C., D.S. Pershan and J. Swift [ 1970 ]. Phys. Review 25, 844 – 848.
Helfrich, W.J. [ 1969 ] J. Chem. Phys. 51, 4092.
Helfrich, W.J. [ 1970 ] J. Chem. Phys. 53, 2267.
Helfrich, W.J. [ 1972 ] J. Chem. Phys. 56, 3187.
Aero, E.L. and A.N. Bulygin [ 1970 ] Ikv Akad. Nauk SSR, MZLG, 3.
Aero, E.L. and A.N. Bulygin [ 1971 ] PMM, 35, 879–891.
Lee, J.D. and A.C. Eringen [ 1971a ] J. Chem. Phys. 54, 5027–5034.
Lee, J.D. and A.C. Eringen [ 1971b ] J. Chem. Phys. 55, 4504–4508.
Lee, J.D. and A.C. Eringen [ 1971c ] J. Chem. Phys. 55, 4509–4512.
Eringen, A.C. and J.D. Lee [ 1973 ] Liquid Crystals and Ordered Fluids 2, 315–330, Plenum Publishing Co.
Stephen, M.J. and J.P. Straley [ 1974 ] Reviews of Modern Physics 46, 617–704.
P.G. de Gennes [ 1974 ] The Physics of Liquid Crystals, Clarendon Press, Oxford.
Eringen, A.C. [ 1964a ] Proc. 11th Intern. Congress of Appl. Mech. Munich, Germany.
Lee, J.D. and A.C. Eringen [ 1973 ] Liquid Crystals and Ordered Fluids 2, 315–370, Plenum Publishing Co.
Shahinpoor, M. [ 1975 ] J. Chem. Phys. 63, 1319–1320.
Lee, J.D. and A.C. Eringen [ 1975 ] J. Chem. Phys. 63, 1321–1322.
Eringen, A.C. and C.B. Kafadar [ 1976 ] Continuum Physics Vol. 4 (edit. A.C. Eringen) Academic Press, New York.
Eringen, A.C. [ 1970 ] “Foundations of Micropolar Thermoelasticity” Springer-Verlag, Vienna.
Kafadar, C.B. and A.C. Eringen [ 1971 ] Int. J. Engng. Sci. 9, 271–305.
Eringen, A.C. [ 1966 ] J. Math. and Mechanics 16, 1–18.
Eringen, A.C. [ 1964b ] Int. J. Engng. Sci. 2, 205–217.
Eringen, A.C. [1967] Int. J. Engng. Sci. 5, 191–204.
Wang, C.C. [1970] Arch. Ration. Mech. Analysis 36, 166–197, 198–223.
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Eringen, A.C. (1978). Micropolar Theory of Liquid Crystals. In: Johnson, J.F., Porter, R.S. (eds) Liquid Crystals and Ordered Fluids. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8888-7_30
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DOI: https://doi.org/10.1007/978-1-4615-8888-7_30
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