2001 Flow alignment in nematic liquid crystals in flows with cylindrical symmetry
R. van der Hout
Differential Integral Equations 14(2): 189-211 (2001). DOI: 10.57262/die/1356123352


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.


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R. van der Hout. "Flow alignment in nematic liquid crystals in flows with cylindrical symmetry." Differential Integral Equations 14 (2) 189 - 211, 2001. https://doi.org/10.57262/die/1356123352


Published: 2001
First available in Project Euclid: 21 December 2012

zbMATH: 1021.35028
MathSciNet: MR1797386
Digital Object Identifier: 10.57262/die/1356123352

Primary: 76A15
Secondary: 35J20 , 35J25

Rights: Copyright © 2001 Khayyam Publishing, Inc.


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Vol.14 • No. 2 • 2001
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