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Stability of Couette flow in nematic liquid crystals

Published online by Cambridge University Press:  19 April 2006

E. Dubois-Violette  and
P. Manneville
E. Dubois-Violette
Affiliation:
Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France
P. Manneville
Affiliation:
DPh.G/S.P.S.R.M., Orme des Merisiers, C.E.N. Saclay, B.P. 2, 91190 Gif-sur-Yvette, France
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Abstract

We study the stability of the cylindrical Couette flow in nematics when the director is parallel to the rotation axis. The contribution of the inertial coupling of velocity fluctuations (responsible for the Taylor instability in isotropic liquids) is shown to be destabilizing when the inner cylinder rotates faster than the outer one. However, the instability remains driven by the mechanisms first discovered by Pieranski & Guyon for the plane shear case and quite specific to nematics. This mechanism couples the different orientation fluctuations via viscous torques and the corresponding threshold is given by \[ s\tau_0\sim 1, \] where τ0 is the time constant for the diffusion of orientation fluctuations. The contribution of inertia terms is measured by 2ωm τv, where τv is the time constant for the diffusion of velocity fluctuations. In usual nematics one has τv/τ0 ∼ 10−5 so that corrections due to rotation are small in general. At different stages of the discussion differences between the case of nematics and that of isotropic liquids are pointed out. We also study the possibility of an oscillatory instability when α3 is positive and large, where no stationary instability can occur.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 2 , 28 November 1978 , pp. 273 - 303
Copyright
© 1978 Cambridge University Press

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References

Atkin, R. J. & Leslie, F. M. 1970 Quart. J. Mech. Appl. Math. 23 (2), 83.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press.
Cladis, P. E. & Torza, S. 1975 Phys. Rev. Lett. 35, 1283.
Cladis, P. E. & Torza, S. 1976 Bell. Labs. preprint (July 21).
Currie, P. K. 1970 Arch. Rat. Mech. Anal. 37, 222.
Dubois-Violette, E., Guyon, E., Janossy, I., Pieranski, P. & Manneville, P. 1977 J. Méc. 16 (5), 734.
Ericksen, J. L. 1960 Arch. Rat. Mech. Anal. 4, 231.
Ericksen, J. L. 1966 Quart. J. Mech. Appl. Math. 19, 455.
Frank, F. C. 1958 Discuss. Faraday Soc. 25, 19.
Gähwiller, Ch. 1973 Mol. Cryst. Liq. Cryst. 10, 301.
Gennes, P. G. De 1972 Phys. Lett. A 41, 479.
Gennes, P. G. De 1974 The Physics of Liquid Crystals. Clarendon Press.
Jeffreys, H. 1928 Proc. Roy. Soc. A 118, 195.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Lekkerkerker, H. N. W. 1977 J. Phys. Lettres (Paris), 38, L 277.
Leslie, F. M. 1968 Arch. Rat. Mech. Anal. 28, 265.
Leslie, F. M. 1976 J. Phys. D (Appl. Phys.) 9, 925.
Manneville, P. 1977 Ph.D. thesis, no. 1912, Université Paris-Sud, Orsay, France.
Manneville, P. & Dubois-Violette, E. 1976 J. Phys. (Paris) 37, 285.
Miezowicz, 1946 Nature 158, 27.
Parodi, O. 1970 J. Phys. (Paris) 31, 581.
Pieranski, P. & Guyon, E. 1973 Sol. St. Comm. 13, 435.
Pieranksi, P. & Guyon, E. 1974a Phys. Rev. A 9, 404.
Pieranksi, P. & Guyon, E. 1974b Phys. Rev. Lett. 32, 924.
Pieranksi, P. & Guyon, E. 1975 Adv. Chem. Phys. 32, 151.
Pieranksi, P. & Guyon, E. 1976 Comm. Phys. 1, 45.
Pieranksi, P., Guyon, E. & Pikin, S. A. 1976 J. Phys. (Paris) Coll. 37, C1, C1.
Pikin, S. A. 1973 Zh. Eksp. Teor. Fiz. 65, 2495 (Engl. transl.: Sov. Phys. J. Exp. Theor. Phys. 38, 1246 (1974)).
Stephen, M. J. & Straley, J. P. 1974 Rev. Mod. Phys. 46, 617.