Advertisement

Microcontinuum Theory of Heat-Conducting Smectic Liquid Crystals

  • M. N. L. Narasimhan
  • T. E. Kelley

Abstract

Balance laws governing the flow of heat-conducting smectic liquid crystals are presented. Appropriate constitutive equations are formulated taking into account thermal gradients on the basis of the micropolar theory of A.C.Eringen. Full material symmetry considerations of the smectic phase are applied to effect simplifications in the constitutive equations. A generalized form of the Clausius-Duhem inequality governing these constitutive equations is obtained and includes the effects of heat-conduction. A complete set of thermodynamical restrictions governing the material coefficients are derived. The resulting constitutive theory is then specialized to the linear case to facilitate its use in practical applications.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Friedel, Ann. Physique 19, 273 (1922).Google Scholar
  2. 2.
    G. H. Brown, Ind. Res. 53, May (1966).Google Scholar
  3. 3.
    J. L. Fergason, Sci. Am. 211, No. 2, 77 (1964).CrossRefGoogle Scholar
  4. 4.
    Groupe d’Etudes des Cristaux Liquides (Orsay), J. Chem. Phys. 51, 816 (1969).CrossRefGoogle Scholar
  5. 5.
    G. W. Gray, Molecular Structure and the Properties of Liquid Crystals, Acad. Press, New York (1962).Google Scholar
  6. 6.
    J. L. Fergason and G. H. Brown, J. Am. Oil Chem. Soc. 45, 120 (1968).CrossRefGoogle Scholar
  7. 7.
    R. S. Porter and J. F. Johnson, eds., “Ordered Fluids and Liquid Crystals”, Adv. in Chem. Series, No. 63, Am. Chem. Soc. (1967).Google Scholar
  8. 8.
    R. S. Porter, E. M. Barrall II, and J. F. Johnson, J. Chem., Phys. 45, 1452 (1966).CrossRefGoogle Scholar
  9. 9.
    R. S. Porter and J. F. Johnson, J. Appl. Phys. 34, 51 (1963).CrossRefGoogle Scholar
  10. 10.
    R. S. Porter and J. F. Johnson, J. Phys. Chem., 66, 1826 (1962).CrossRefGoogle Scholar
  11. 11.
    E. M. Barrall II, R. S. Porter, and J. F. Johnson, J. Phys. Chem., 68, 2810 (1964).CrossRefGoogle Scholar
  12. 12.
    R.S. Porter and J. F. Johnson, J. Appl. Phys. 34, 55 (1963).CrossRefGoogle Scholar
  13. 13.
    R. S. Porter and J. F. Johnson, “The Rheology of Liquid Crystals”, Ch. 5, in “Rheology”, 4, ed., F. R. Eirich, 317 (1967).Google Scholar
  14. 14.
    S. Chandrasekhar, Mol. Cryst. Liquid Cryst. 2, 71 (1966).Google Scholar
  15. 15.
    W. Maier and A. Saupe, Z. Naturforsch. 13A, 564 (1958); 14A, 882 (1959); 15A, 287 (1960).Google Scholar
  16. 16.
    K. K. Kobayashi, Phys. Letters 31A, 125 (1970); J. Phys.Soc. Japan 29, 101 (1970).CrossRefGoogle Scholar
  17. 17.
    A. Saupe, Angew. Chem. International Edit. 7, No. 2, 97 (1968).CrossRefGoogle Scholar
  18. 18.
    A. Saupe, Mol. Cryst. Liquid Cryst. 7, 59 (1969).Google Scholar
  19. 19.
    I. G. Chistyakov, Soviet Physics USPEKHI, 9, No. 4, 551 (1967).CrossRefGoogle Scholar
  20. 20.
    C. W. Oseen, Trans. Faraday Soc. 29, 883 (1933).CrossRefGoogle Scholar
  21. 21.
    H. Zocher, Trans. Faraday Soc. 29, 945 (1933).CrossRefGoogle Scholar
  22. 22.
    A. Anzelius, Uppsala Univ. Arsskr. Mat. Och Naturvet, 1 (1931).Google Scholar
  23. 23.
    F. C. Frank, Discussions Faraday Soc. 25, 19 (1958).CrossRefGoogle Scholar
  24. 24.
    P. C. Martin, P. S. Pershan, and J. Swift, Phys. Rev. Lett., 25, No. 13, 844 (1970).CrossRefGoogle Scholar
  25. 25.
    M. Stephen, Phys. Rev. A2, 1558 (1970).CrossRefGoogle Scholar
  26. 26.
    T. C. Lubensky, Phys. Rev. A2, 2497 (1970).CrossRefGoogle Scholar
  27. 27.
    D. Forster, et al, Phys. Rev. Lett., 26, 1016 (1971).CrossRefGoogle Scholar
  28. 28.
    H. Huang, Phys. Rev. Lett., 26, 1525 (1971).CrossRefGoogle Scholar
  29. 29.
    H. Schmidt and J. Jahnig, Annals of Physics, 71, 129 (1972).CrossRefGoogle Scholar
  30. 30.
    J. D. Lee and A. C. Eringen, J. Chem. Phys. 54, 5027 (1971).CrossRefGoogle Scholar
  31. 31.
    J. D. Lee and A. C. Eringen, J. Chem. Phys. 55, 4504 (1971).CrossRefGoogle Scholar
  32. 32.
    J. D. Lee and A. C. Eringen, J. Chem. Phys. 55, 4509 (1971).CrossRefGoogle Scholar
  33. 33.
    J. D. Lee and A. C. Eringen, J. Chem. Phys. 58, 4203 (1973).CrossRefGoogle Scholar
  34. 34.
    A. C. Eringen and J. D. Lee, “Liquid Crystals and Ordered Fluids”, Am. Chem. Soc. Symposium 2, 383 (1973).Google Scholar
  35. 35.
    J. L. Ericksen, Arch. Rat. Mech. Anal. 4, 231 (1960).CrossRefGoogle Scholar
  36. 36.
    J. L. Ericksen, Trans. Soc. Rheol. 5, 23 (1961).CrossRefGoogle Scholar
  37. 37.
    J. L. Ericksen, Arch. Rat. Mech. Anal. 9, 371 (1962).Google Scholar
  38. 38.
    J. L. Ericksen, Arch. Rat. Mech. Anal. 23, 266 (1966).CrossRefGoogle Scholar
  39. 39.
    J. L. Ericksen, Phys. of Fluids, 9, 1205 (1966).CrossRefGoogle Scholar
  40. 40.
    J. L. Ericksen, Quart. J. Mech. Appl. Math., 19, 455 (1966).CrossRefGoogle Scholar
  41. 41.
    J. L. Ericksen, Appl. Mech. Rev., 20, 1029 (1967).Google Scholar
  42. 42.
    J. L. Ericksen, J. Fluid Mech., 27, 59 (1967).CrossRefGoogle Scholar
  43. 43.
    J. L. Ericksen, Mol. Cryst. Liquid Cryst. 7, 153 (1969).Google Scholar
  44. 44.
    J. L. Ericksen, “Liquid Crystals and Ordered Fluids”, Am.Chem. Soc. Symposium, 1, (1970), ed. R. S. Porter and J. F. Johnson.Google Scholar
  45. 45.
    F. M. Leslie, Quart. J. Mech. Appl. Math., 19, 357 (1966).CrossRefGoogle Scholar
  46. 46.
    F. M. Leslie, Arch. Rat. Mech. Anal. 28, 265 (1968).CrossRefGoogle Scholar
  47. 47.
    F. M. Leslie, Proc. Roy. Soc. London A 207, 359 (1968).CrossRefGoogle Scholar
  48. 48.
    F. M. Leslie, Mol. Cryst. Liquid Cryst. 7, 407 (1969).Google Scholar
  49. 49.
    A. C. Eringen, Proc. Eleventh International Congr. Appl. Mech. ed., H. Gortler (Springer, Berlin), 131 (1966).Google Scholar
  50. 50.
    A. C. Eringen, J. Math. Mech. 15, 909 (1966).Google Scholar
  51. 51.
    M.N.L. Narasimhan and A. C. Eringen, Int. J. Eng. Sci., 13, 233 (1975).CrossRefGoogle Scholar
  52. 52.
    M.N.L. Narasimhan and A. C. Eringen, Mol. Cryst. Liquid Cryst. 29, 57 (1974).CrossRefGoogle Scholar
  53. 53.
    M.N.L. Narasimhan, “Continuum Theory of Heat-Conducting Smectic Liquid Crystals”, in Proc. Twelfth Annual Meeting, Soc. Eng. Sci., ed., Morris Stern, 61 (1975).Google Scholar
  54. 54.
    W. Nef, “Linear Algebra”, (Translated from the German by J.C. Ault), McGraw Hill, New York, 212 (1967).Google Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • M. N. L. Narasimhan
    • 1
  • T. E. Kelley
    • 1
  1. 1.Department of MathematicsOregon State UniversityCorvallisUSA

Personalised recommendations