Abstract
We use a fluctuating hydrodynamics (FH) approach to study the fluctuations of the hydrodynamic variables of a thermotropic nematic liquid crystal (NLC)in a nonequilibrium steady state (NESS). This NESS is produced by an externally imposed temperature gradient and a uniform gravity field. We calculate analytically the equilibrium and nonequilibrium seven modes of the NLC in this NESS. These modes consist of a pair of sound modes, one orientation mode of the director and two visco-heat modes formed by the coupling of the shear and thermal modes. We find that the nonequilibrium effects produced by the external gradients only affect the longitudinal modes. The analytic expressions for the visco-heat modes show explicitly how the heat and shear modes of the NLC are coupled. We show that they may become propagative, a feature that also occurs in the simple fluid and suggests the realization of new experiments. We show that in equilibrium and in the isotropic limit of the NLC, our modes reduce to well-known results in the literature. For the NESS considered we point out the differences between our our modes and those reported by other authors. We close the paper by proposing the calculation of other physical quantities that lend themselves to a more direct comparison with possible experiments for this system.
Similar content being viewed by others
References
G. Grinstein, D.H. Lee, S. Sachdev, Phys. Rev. Lett. 64, 1927 (1990)
D. Ronis, I. Procaccia, J. Machta, Phys. Rev. A 22, 714 (1980)
J.R. Dorfman, T.R. Kirkpatrick, J.V. Sengers, Ann. Rev. Phys. Chem. 45, 213 (1994)
D. Beysens, Y. Garrabos, G. Zalczer, Phys. Rev. Lett. 45, 403 (1980)
B. Law, M.P.N. Segrè, R.W. Gammon, J.V. Sengers, Phys. Rev. A 41, 816 (1990)
L.D. Landau, E.M. Lifshitz, in Fluid Mechanics (Addison-Wesley, Reading, 1959), Chap. XVII
R.F. Fox, G.E. Uhlenbeck, Phys. Fluids 13, 1893 (1970)
R.F. Fox, Phys. Rep. 48, 179 (1978)
L. Onsager, Phys. Rev. 37, 405 (1931)
L. Onsager, Phys. Rev. 38, 2265 (1931)
L. Onsager, S. Machlup, Phys. Rev. 91, 1505 (1953)
P.N. Segré, R. Schmitz, J.V. Sengers, Physica A 195, 31 (1993)
H. Pleiner, H.R. Brand, Phys. Rev. A 27, 1117 (1983)
H. Pleiner, H.R. Brand, J. Phys. Lett. 44, L23 (1983)
R.F. Rodríguez, J.F. Camacho, Rev. Mex. Fís. 48, 144 (2002)
M. López de Haro, J.A. del Río, F. Vázquez, Rev. Mex. Fís. 48 S1, 230 (2002)
H. Híjar, R.F. Rodríguez, Phys. Rev. E 69, 051701 (2004)
J.F. Camacho, H. Híjar, R.F. Rodríguez, Physica A 348, 252 (2005)
R.F. Rodríguez, J.F. Camacho, in Recent Developments in Mathematical and Experimental Physics, Statistical Physics and Beyond, edited by A. Macías, E. Díaz, F. Uribe (Kluwer, New York, 2002), Vol. B, p. 209
R.F. Rodríguez, H. Híjar, Eur. Phys. J. B 50, 105 (2006)
I. Santamaría-Holek, J.M. Rubí, A. Gadomski, J. Phys. Chem. B 111, 2293 (2007)
J. Bonet-Avalos, J.M. Rubí, R.F. Rodríguez, A. Pérez-Madrid, Phys. Rev. A 41, 1923 (1990)
H.F. Gleeson, in Handbook of Liquid Crystals, edited by D. Demus, J. Goodby, G.W. Gray, H.W. Spiess, V. Vill (Wiley-Vch, Weiheim, 1998)
J.F. Camacho, Ph.D. Dissertation, Universidad Nacional Autónoma de Mexico, 2016 (in Spanish)
J.F. Camacho, R.F. Rodríguez, arXiv:1604.08250 [cond-mat.soft] (2016)
K. Miyakawa, J. Phys. Soc. Jpn 39, 628 (1975)
N.G. Migranov, A.V. Verevochnikov, A.N. Chuvyrov, Mol. Cryst. Liq. Cryst. 319, 31 (1998)
H. Pleiner, H.R. Brand, in Pattern Formation in Liquid Crystals, edited by A. Buka, L. Kramer (Springer-Verlag, Berlin, 1996)
E.I. Kats, V.V. Lebedev, Fluctuational Effects in the Dynamics of Liquid Crystals (Springer-Verlag, Berlin, 1994)
F.M. Leslie, Quart. J. Mech. Appl. Math. 19, 357 (1966)
J. Ortíz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006)
H.N.W. Lekkerkerker, J.P. Boon, Phys. Rev. A 10, 1355 (1974)
D. Forster, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions (Benjamin, Reading, 1975)
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon, Oxford, 1961)
P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1998)
B.M. Law, J.V. Sengers, J. Stat. Phys. 57, 531 (1989)
R.D. Mountain, Rev. Mod. Phys. 38, 205 (1966)
B.J. Berne, R. Pecora, Dynamic Light Scattering (J. Wiley, New York, 1976)
Groupe d’Etude des Cristaux Liquides (Orsay), J. Chem. Phys. 51, 816 (1969)
P. Pieranski, E. Dubois-Violette, E. Guyon, Phys. Rev. Lett. 30, 736 (1973)
J.P. Boon, C. Allain, P. Lallemand, Phys. Rev. Lett. 43, 199 (1979)
J.P. Boon, S. Yip, Molecular Hydrodynamics (Dover, New York, 1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Camacho, J.F., Rodríguez, R.F. Nonequilibrium fluctuations from a nematic under a thermal gradient and a gravity field. Eur. Phys. J. B 90, 21 (2017). https://doi.org/10.1140/epjb/e2016-70327-8
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2016-70327-8