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A numerical investigation into thermal instabilities in homeotropic nematics heated from below

Published online by Cambridge University Press:  20 April 2006

P. J. Barratt  and
D. M. Sloan
P. J. Barratt
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1
D. M. Sloan
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1
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Abstract

This paper employs continuum theory to examine the onset of a particular type of cellular thermal instability in a sample of nematic liquid crystal confined between two infinite, horizontal flat plates when subjected to a vertical temperature gradient. We consider the case in which the anisotropic axis is initially uniformly aligned perpendicular to the plates. Using Chebyshev polynomials, accurate numerical solutions for the critical temperature gradient are obtained and the variation of this quantity with a uniform magnetic field applied vertically across the plates is investigated. In particular we obtain the value of the magnetic field at which the nature of the instability changes from an oscillatory type to a stationary one.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 389 - 404
Copyright
© 1981 Cambridge University Press

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References

Barratt, P. J. & Sloan, D. M. 1976 J. Phys. A, Appl. Phys. 9, 1987.Google Scholar
Boussinesq, J. 1903 Theorie Analytique de la Chaleur, vol. 2. Paris: Gauthier-Villars.
Chandrasekhar, S. 1977 Liquid Crystals. Cambridge University Press.
Currie, P. K. 1973 Rheol. Acta 12, 165.
de Gennes, P. G. 1974 The Physics of Liquid Crystals Clarendon.
Dubois-Violette, E. 1974 Solid State Comm. 14, 767.
Dubois-Violette, E., Guyon, E. & Pieranski, P. 1973 Mol. Cryst. Liq. Cryst. 22, 359.
Ericksen, J. L. 1961 Trans. Soc. Rheol. 5, 23.
Ericksen, J. L. 1962 Arch. Rat. Mech. Anal. 9, 371.
Ericksen, J. L. 1976 Adv. Liquid Crystals 2, 233.
Frank, F. C. 1958 Discuss. Faraday Soc. 25, 19.
Gähwiller, C. 1971 Phys. Lett. A 36, 311.
Gary, J. & Helgason, R. 1970 J. Comp. Phys. 5, 169.
Guyon, E. & Pieranski, P. 1972 C.R. Acad. Sci. Paris, B 274, 656.
Guyon, E., Pieranski, P. & Salan, J. 1979 J. Fluid Mech. 12, 65.
Haller, I. 1972 J. Chem. Phys. 57, 1400.
Lanczos, C. 1956 Applied Analysis. Prentice-Hall.
Lekkerkerker, H. N. W. 1977 J. Phys. Lett. Paris 38, L277.
Lekkerkerker, H. N. W. 1979 J. Phys. Paris 40, C3–67.
Leslie, F. M. 1968a Arch. Rat. Mech. Anal. 28, 265.
Leslie, F. M. 1968b Proc. Roy. Soc. A 307, 359.
Leslie, F. M. 1969 Mol. Cryst. Liq. Cryst. 7, 407.
Leslie, F. M. 1980 Adv. Liquid Crystals.
Orszag, S. A. 1971 J. Fluid Mech. 50, 689.
Oseen, C. W. 1929 Fortschr. Chemie, Phys. & Phys. Chemie 20, 25.
Parodi, O. 1970 J. Phys. Paris 31, 581.
Pieranski, P., Dubois-Violette, E. & Guyon, E. 1973a Phys. Rev. Lett. 30, 736.
Pieranski, P., Brochard, F. & Guyon, E. 1973b J. Phys. Paris 34, 35.
Stephen, M. J. & Straley, J. P. 1974 Rev. Mod. Phys. 46, 617.
Velarde, M. G. & Zuniga, I. 1979 J. Phys. Paris 40, 725.
Vilanove, R., Guyon, E., Mitescu, C. & Pieranski, P. 1974 J. Phys. Paris 35, 15.
Wilkinson, J. H. & Reinsch, C. 1971 Handbook for Automatic Computation. Vol. 2. Linear Algebra, p. 315. Springer.