Skip to main content
Log in

Nonequilibrium fluctuations from a nematic under a thermal gradient and a gravity field

I. Hydrodynamic modes

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Grinstein, D.H. Lee, S. Sachdev, Phys. Rev. Lett. 64, 1927 (1990)

    Article  ADS  Google Scholar 

  2. D. Ronis, I. Procaccia, J. Machta, Phys. Rev. A 22, 714 (1980)

    Article  ADS  Google Scholar 

  3. J.R. Dorfman, T.R. Kirkpatrick, J.V. Sengers, Ann. Rev. Phys. Chem. 45, 213 (1994)

    Article  ADS  Google Scholar 

  4. D. Beysens, Y. Garrabos, G. Zalczer, Phys. Rev. Lett. 45, 403 (1980)

    Article  ADS  Google Scholar 

  5. B. Law, M.P.N. Segrè, R.W. Gammon, J.V. Sengers, Phys. Rev. A 41, 816 (1990)

    Article  ADS  Google Scholar 

  6. L.D. Landau, E.M. Lifshitz, in Fluid Mechanics (Addison-Wesley, Reading, 1959), Chap. XVII

  7. R.F. Fox, G.E. Uhlenbeck, Phys. Fluids 13, 1893 (1970)

    Article  ADS  MathSciNet  Google Scholar 

  8. R.F. Fox, Phys. Rep. 48, 179 (1978)

    Article  ADS  Google Scholar 

  9. L. Onsager, Phys. Rev. 37, 405 (1931)

    Article  ADS  Google Scholar 

  10. L. Onsager, Phys. Rev. 38, 2265 (1931)

    Article  ADS  Google Scholar 

  11. L. Onsager, S. Machlup, Phys. Rev. 91, 1505 (1953)

    Article  ADS  Google Scholar 

  12. P.N. Segré, R. Schmitz, J.V. Sengers, Physica A 195, 31 (1993)

    Article  ADS  Google Scholar 

  13. H. Pleiner, H.R. Brand, Phys. Rev. A 27, 1117 (1983)

    Article  ADS  Google Scholar 

  14. H. Pleiner, H.R. Brand, J. Phys. Lett. 44, L23 (1983)

    Article  Google Scholar 

  15. R.F. Rodríguez, J.F. Camacho, Rev. Mex. Fís. 48, 144 (2002)

    Google Scholar 

  16. M. López de Haro, J.A. del Río, F. Vázquez, Rev. Mex. Fís. 48 S1, 230 (2002)

    Google Scholar 

  17. H. Híjar, R.F. Rodríguez, Phys. Rev. E 69, 051701 (2004)

    Article  Google Scholar 

  18. J.F. Camacho, H. Híjar, R.F. Rodríguez, Physica A 348, 252 (2005)

    Article  ADS  Google Scholar 

  19. 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

  20. R.F. Rodríguez, H. Híjar, Eur. Phys. J. B 50, 105 (2006)

    Article  ADS  Google Scholar 

  21. I. Santamaría-Holek, J.M. Rubí, A. Gadomski, J. Phys. Chem. B 111, 2293 (2007)

    Article  Google Scholar 

  22. J. Bonet-Avalos, J.M. Rubí, R.F. Rodríguez, A. Pérez-Madrid, Phys. Rev. A 41, 1923 (1990)

    Article  ADS  Google Scholar 

  23. 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)

  24. J.F. Camacho, Ph.D. Dissertation, Universidad Nacional Autónoma de Mexico, 2016 (in Spanish)

  25. J.F. Camacho, R.F. Rodríguez, arXiv:1604.08250 [cond-mat.soft] (2016)

  26. K. Miyakawa, J. Phys. Soc. Jpn 39, 628 (1975)

    Article  ADS  Google Scholar 

  27. N.G. Migranov, A.V. Verevochnikov, A.N. Chuvyrov, Mol. Cryst. Liq. Cryst. 319, 31 (1998)

    Article  Google Scholar 

  28. H. Pleiner, H.R. Brand, in Pattern Formation in Liquid Crystals, edited by A. Buka, L. Kramer (Springer-Verlag, Berlin, 1996)

  29. E.I. Kats, V.V. Lebedev, Fluctuational Effects in the Dynamics of Liquid Crystals (Springer-Verlag, Berlin, 1994)

  30. F.M. Leslie, Quart. J. Mech. Appl. Math. 19, 357 (1966)

    Article  MathSciNet  Google Scholar 

  31. J. Ortíz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006)

  32. H.N.W. Lekkerkerker, J.P. Boon, Phys. Rev. A 10, 1355 (1974)

    Article  ADS  Google Scholar 

  33. D. Forster, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions (Benjamin, Reading, 1975)

  34. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon, Oxford, 1961)

  35. P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1998)

  36. B.M. Law, J.V. Sengers, J. Stat. Phys. 57, 531 (1989)

    Article  ADS  Google Scholar 

  37. R.D. Mountain, Rev. Mod. Phys. 38, 205 (1966)

    Article  ADS  Google Scholar 

  38. B.J. Berne, R. Pecora, Dynamic Light Scattering (J. Wiley, New York, 1976)

  39. Groupe d’Etude des Cristaux Liquides (Orsay), J. Chem. Phys. 51, 816 (1969)

  40. P. Pieranski, E. Dubois-Violette, E. Guyon, Phys. Rev. Lett. 30, 736 (1973)

    Article  ADS  Google Scholar 

  41. J.P. Boon, C. Allain, P. Lallemand, Phys. Rev. Lett. 43, 199 (1979)

    Article  ADS  Google Scholar 

  42. J.P. Boon, S. Yip, Molecular Hydrodynamics (Dover, New York, 1991)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jorge F. Camacho.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2016-70327-8

Keywords

Navigation