Differential and Integral Equations
- Differential Integral Equations
- Volume 14, Number 2 (2001), 189-211.
Flow alignment in nematic liquid crystals in flows with cylindrical symmetry
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.
Differential Integral Equations, Volume 14, Number 2 (2001), 189-211.
First available in Project Euclid: 21 December 2012
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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