Capillary Viscometry of Cholesteric Liquid Crystals

  • Wolfgang Helfrich
Conference paper


A recently proposed model of pluglike capillary flow of liquid crystals is studied in some detail for the case of cholesterics. The emphasis is on outlining the conditions under which pluglike flow may be found in circular capillaries. Numerical examples are given, and comparison with the few existing experimental data is made.


Couple Stress Capillary Wall Orientation Pattern CHOLESTERIC Liquid Crystal Molecular Rotation 
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References and Footnotes

  1. 1.
    R. S. Porter, E. M. Barrall II, and J. F. Johnson, J. Chem. Phys., 45, 1452 (1966).CrossRefGoogle Scholar
  2. 2.
    W. Helfrich, Phys. Rev. Letters, 23, 372 (1969).CrossRefGoogle Scholar
  3. 3.
    J. L. Ericksen, Arch. Rational Mech. Anal., 4, 231 (1960).CrossRefGoogle Scholar
  4. 4.
    F. M. Leslie, Proc. Roy. Soc., A307, 359 (1968).CrossRefGoogle Scholar
  5. 5.
    Ericksen and Leslie use six viscosity coefficients (α or μ). We prefer to distinguish between four viscosity (η) and two shear-torque coefficients (K). (They have already been used in a forthcoming theory of conduction-induced alignment.) The two sets of coefficients are related as follows: Η1 = ½ (μ4 + μ5 − μ2) Η2 = ½ (μ4 + μ6 − μ3) Η12 = μ1 Η3 = ½ μ4 K1 = ½ (μ5 + μ3 − μ2 − μ6) K2 = ½ (μ6 + μ3 − μ5 − μ2) The sum K1 + K2 equals the coefficient –λ1 of Ericksen and Leslie.Google Scholar
  6. 6.
    There are some indications in the older literature of disclinations bound to glass walls.Google Scholar
  7. 7.
    F. C. Frank, Disc. Faraday, 25, 19 (1958) or Ref. 4. A fourth constant occurring in curvature elasticity, k24, is neglected because it affects the distortional energy only through the surface alignment, as was first shown byCrossRefGoogle Scholar
  8. J. L. Ericksen, Arch. Rational Mech. Anal., 10, 189 (1962).CrossRefGoogle Scholar
  9. 8.
    In the considered deformation of the orientation pattern, the deformational torques contain components normal to the capillary wall. These components must also be balanced. With fixed wall alignment, no balancing by shear is required as their integral over 0 < φ < 2π vanishes. An analysis of the orientation pattern at the wall appears difficult. Shear is involved if the wall alignment is unrestrained, complicating the situation even more.Google Scholar
  10. 9.
    R. S. Porter informed us of recent experiments which indicate that pure cholesteryl acetate may have only a smectic but no cholesteric mesophase. However, he is convinced that the impure cholesteryl acetate used in the viscosity measurements of Porter et al. (Ref. 1) was cholesteric.Google Scholar

Copyright information

© Plenum Press, New York 1970

Authors and Affiliations

  • Wolfgang Helfrich
    • 1
  1. 1.RCA LaboratoriesDavid Sarnoff Research CenterPrincetonUSA

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