A symposium held in Durham in July 1995 brought together an international collection of key mathematicians, theoretical physicists and experimentalists in the areas of liquid crystals and polymeric systems. Many of the participants met together for the first time, and the symposium stimulated new collaborative interactions among applied mathematicians and others who, prior to this meeting, were working separately on either liquid crystals or polymer fluids. The symposium also enhanced further interchanges of ideas between industry and academia. The flavour of this meeting is captured by the contents of this special issue which resulted from presentations given by invited speakers.

We give a review of theoretical studies of Freedericksz transitions in smectic C liquid crystals due to the application of magnetic and electric fields. The relevance of these results and their connection with experimentation is also discussed.

We consider a chiral smectic C liquid crystal confined between parallel plates in the bookshelf geometry. Using a recently proposed continuum theory for such materials the behaviour of the cell is discussed when an electric field is applied and subsequently removed from the cell. We examine both symmetric and asymmetric boundary conditions for the director.

We present a continuum theory for smectic liquid crystals which allows variable molecular tilt and layer spacing by relating the two. This compressible theory is employed to predict the effect of ‘homeotropic’ type ordering at the plates on a planar Sm C sample. Such a boundary condition induces dilation of individual Sm C layers near the bounding plates.

The static electro-optic behaviour of achiral smectic C samples in the chevron geometry have been modelled using the continuum theory of Leslie et al. [1]. The model assumes that the layer tilt and smectic C director tilt angle are constant, and treats the layers at the chevron interface as an infinitely bound surface. Comparison of the predicted electro-optic behaviour with experimental results gives values for the bend (B1) and splay (B2) c-director elastic constants. However, more detailed optical studies show that surface and chevron interface terms become important at high values of applied electric field.

We review the main outcomes of a continuum theory for the equilibrium of the interface between a nematic liquid crystal and an isotropic environment, in which the surface free energy density bears terms linear in the principal curvatures of the interface. Such geometric contributions to the energy occur together with more conventional elastic contribution, leading to an effective azimuthal anchoring of the optic axis, which breaks the isotropic symmetry of the interface. The theory assumes the interface to be fixed, as for a rigid cavity filled with liquid crystal, and so it does not apply to drops. It should be appropriate when the curvatures of the interface are small compared to that of the molecular interaction sphere. Also, interfaces bearing a sharp edge are encompassed within the theory; a line integral expresses the energy condensed along the edge: we see how it affects the equilibrium equations.

A model for Poiseuille flow of nematic liquid crystals is examined where a layered structure of defects parallel to the flow is present. Constant gradient flows are discussed, together with symmetric and chevron configurations for such flow problems.