Phenomenological theory of flow-alignment in binary nematic mixtures

A macroscopic continuum mechanical model for incompressible homogeneous (single phase) binary nematic mixtures under isothermal conditions is given. The rheological model is a generalization of the standard nematorheological model for single component uniaxial rod-like nematic liquid crystals. Its special cases include single component orthorhombic biaxial nematics and single component uniaxial nematics. Numerical solutions for rectilinear simple shear flow of the model nematic mixture are obtained and analyzed. A complete classification of all the possible shear-alignment modes for binary nematic mixtures is given. Mechanisms and parameter variations leading to alignment transitions are identified. Mixtures of two aligning nematics result in most cases in flow-aligning biaxial nematic mixtures. Mixtures of an aligning nematic with a non-aligning nematic results in a flow-aligning biaxial nematic mixture, only if sufficiently strong dynamic interactions are present. In all cases the predicted degree and type of alignment behavior is shear rate-dependent.