Differential and Integral Equations

Flow alignment in nematic liquid crystals in flows with cylindrical symmetry

R. van der Hout

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Abstract

Using variational techniques, we study the properties of the director field of a nematic liquid crystal in steady cylindrical flow, assuming that such a steady flow exists. In particular, we construct an energy functional of which a steady director field would be a stationary point, and we show that, when strong anchoring is imposed at the boundary, this functional has a lower bound. A minimizing sequence in an appropriate Hilbert space is not necessarily bounded in that space, and we show that, as a consequence, a finite nontrivial line energy density may be found along the axis; it can take only discrete values. In contrast, when weak anchoring is imposed at the boundary, there is a critical shear rate beyond which the associated energy has no lower bound. This may result in a tumbling regime for the liquid crystal.

Article information

Source
Differential Integral Equations, Volume 14, Number 2 (2001), 189-211.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356123352

Mathematical Reviews number (MathSciNet)
MR1797386

Zentralblatt MATH identifier
1021.35028

Subjects
Primary: 76A15: Liquid crystals [See also 82D30]
Secondary: 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations

Citation

van der Hout, R. Flow alignment in nematic liquid crystals in flows with cylindrical symmetry. Differential Integral Equations 14 (2001), no. 2, 189--211. https://projecteuclid.org/euclid.die/1356123352


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