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Theoretical study of electrorheological behavior of a nematic liquid crystal confined by two cylindrical surfaces with different anchoring energies

G. Rivas, J. A. Reyes, and D. Martínez
Phys. Rev. E 103, 012706 – Published 22 January 2021
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  • INTRODUCTION
  • BASIC EQUATIONS
  • NLC DIRECTOR'S ORIENTATION, VELOCITY…
  • AVERAGED APPARENT VISCOSITY
  • CONCLUDING REMARKS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Electrorheological response of a nematic liquid crystal confined in the region between two coaxial and rotating circular cylinders is studied theoretically. Utilizing weak anchoring conditions, the physical properties of 4-n-pentyl-4-cyanobiphenyl (5CB), nonslip boundary conditions, and contrasting surface anchoring energies, we numerically obtain the equilibrium configurations for the nematic director under the influence of an external low-frequency radial electric field and the corresponding (angular) velocity profiles. The Fréedericksz transition is parametrized by the cylinders' radii ratio for different values of the surface energies. The averaged apparent viscosity of the nematic is calculated also.

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    • Received 7 September 2020
    • Revised 18 November 2020
    • Accepted 6 January 2021

    DOI:https://doi.org/10.1103/PhysRevE.103.012706

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Rheological propertiesSlip boundary effects
    Condensed Matter, Materials & Applied PhysicsFluid Dynamics

    Authors & Affiliations

    G. Rivas and J. A. Reyes2

    • Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364 01000, Ciudad de México, México

    D. Martínez*

    • Universidad Autónoma de la Ciudad de México, Campus Cuautepec, Av. La Corona 320, Col. Loma la Palma, Alcaldía Gustavo A. Madero, 07160, Ciudad de México, México

    • *dmartinezs77@yahoo.com.mx

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    Issue

    Vol. 103, Iss. 1 — January 2021

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    Images

    • Figure 1
      Figure 1

      Longitudinal section of the coaxial circular cylinders. A nematic liquid crystal between two coaxial cylinders which rotate at different angular velocities Ω1 and Ω2. Also, the radial AC electric field applied to the nematic and the angle of inclination θ(r) of the director n=sinθ(r)êr+cosθ(r)êϕ are shown.

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    • Figure 2
      Figure 2

      Orientation of the NLC 5CB as a function of x. In panels (a) and (b), it is shown the plots for σa=5 and σa=15, respectively, and for different values of q. Dashed lines are the configurations at the Fréedericksz transition q=qc where qc∼7.8 in panel (a) and qc∼13.3 in panel (b).

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    • Figure 3
      Figure 3

      Orientation of the NLC 5CB as a function of x. It is shown the plots for σa=10 of the inclination angle θ(x) for q corresponding to β=0.1,1,10 for panels (a), (b), and (c), respectively. For each value of β, qc has a different value.

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    • Figure 4
      Figure 4

      Threshold field for the NLC 5CB as a function of σa for different values of β=τ0a/τ01.

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    • Figure 5
      Figure 5

      (Angular) velocity profile Δω as a function of x for the NLC 5CB. In panel (a) the values of the parameters q and σa are fixed at q=20 and σa=50. In panel (b) we show the plots of Δω as a function of x for σa=50, ΔΩ=20rads−1 and different values of q, including the plot for qc∼17.6(−−).

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    • Figure 6
      Figure 6

      Apparent viscosity 〈η〉q,σa corresponding to the case β=1 and ΔΩ=20rads−1. In panel (a) we show 〈η〉q as a function of q for different values of σa. In panel (b) we show 〈η〉σa as a function of σa for different values of q; for the case q=15, dotted line corresponds to the viscosity for the NLC undistorted configuration.

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