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Stability of the tumbled state in shear flow of a nematic liquid crystal

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Abstract

In shear flow of a nematic liquid crystal withα 3 ≧ 0 flow alignment cannot occur. The stability of the stationary in-plane solution, “the tumbled state”, is investigated using abstract techniques. Employing the existence of an elastic energy a sufficient criterion for stability is formulated. This criterion depends on the in-plane solution which is obtainable as a quadrature that is non-elementary except in special cases. It is shown that the tumbled state is stable and asymptotically stable for some physical configurations. The criterion presented is not a necessary condition for stability and thus only gives a lower bound.

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References

  1. Anzelius A (1931) Bewegung der anisotropen Flüssigkeiten. Uppsala Univ Årsskr, Mat och Naturvet 1

  2. Oseen CW (1929) Fortschr Chemie Phys und Phys Chemie 20:25

    Google Scholar 

  3. Leslie FM (1968) Arch Rat Mech Anal 28:265

    Google Scholar 

  4. Ericksen JL (1960) Arch Rat Mech Anal 4:231

    Google Scholar 

  5. Cladis PE, Torza S (1975) Phys Rev Lett 35:1283

    Google Scholar 

  6. Kneppe H, Schneider F, Sharma NK (1981) Ber Bunsenges Phys Chem 85:784

    Google Scholar 

  7. Skarp K, Carlsson T, Lagerwall ST (1981) Mol Cryst Liq Cryst 66:199

    Google Scholar 

  8. Cladis PE, Torza S (1976) Flow instabilities in Couette flow in nematic liquid crystals. Colloid and interface science, Vol IV, Academic Press, New York

    Google Scholar 

  9. Manneville R (1981) Mol Cryst Liq Cryst 70:223

    Google Scholar 

  10. Carlsson T (1985) Theoretical investigation of shear flow of nematic liquid crystals with Leslie viscosityα 3 < 0. Mol Cryst Liq Cryst (in the press)

  11. Carlsson T, Högfors C (1984) Shear flow of nematic liquid crystals withα 3 < 0. Div Mech, Chalmers University of Technology

  12. de Gennes PG (1975) The physics of liquid crystals. Clarendon, Oxford

    Google Scholar 

  13. Thurston RN (1981) J Appl Phys 52:3040

    Google Scholar 

  14. Parodi O (1970) J Phys 31:581

    Google Scholar 

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Authors and Affiliations

  1. Division of Mechanics, Chalmers University of Technology, S-412 96, Göteborg, Sweden

    Ch. Högfors

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  1. Ch. Högfors
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Högfors, C. Stability of the tumbled state in shear flow of a nematic liquid crystal. Rheol Acta 24, 469–473 (1985). https://doi.org/10.1007/BF01462493

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  • DOI: https://doi.org/10.1007/BF01462493

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