Stability and Instability of Planar Layers of Smectic A Liquid Crystals
Abstract
We consider the mathematical modelling of smectic A liquid crystals using the
continuum dynamic theory for smectic A liquid crystals that has been developed by
Stewart [79]. We also examine biaxial nematic liquid crystals using the continuum
theory of Leslie and co-workers [50, 51] and the review by Stewart [80].
The Helfrich-Hurault transition is considered in this thesis to study the influence
of the compression coefficient B0 when an electric field is applied. The molecular
alignment described by the director n and the unit layer normal a of a smectic
A sample is considered to be not coincident, unlike the classical smectic A theory
where they coincide. Stability and instability in various situations with and without
an electric field will be discussed. Finally, the dynamic continuum theory of
biaxial nematic liquid crystals is an integral part of this thesis. This theory will
be applied to incompressible biaxial nematic liquid crystals to study the linear
stability and instability of a planar alignment sample of biaxial nematic under
oscillatory shear flow.