Differential and Integral Equations

Flow alignment in nematic liquid crystals in flows with cylindrical symmetry

R. van der Hout

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