Analysis of shear flow alignment of nematic liquid crystals at low shear stress based on catastrophe theory

The low stress shear flow alignment of a nematic liquid crystal in the presence of strong anchoring at the boundaries is analysed. Layers with pretilted director orientation are taken into account. Two kinds of symmetric deformations are assumed. They differ in the director distribution in the vicinity of the boundaries. The analysis is carried out using an expansion of the free energy of the layer in powers of the maximum deformation angle. The results have qualitative character. The condition for the threshold behaviour and the stability of the solutions are discussed. The deformation may develop continuously or discontinuously. The transition between two kinds of deformation is predicted. The facts already known are confirmed and supplemented.