Flow-alignment and viscosity rules for single-phase binary mesomorphic mixtures

Abstract

A macroscopic model for incompressible homogeneous (single phase) binary nematic mixtures, under isothermal conditions is given. The rheological model is a generalization of the standard Ericksen's 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. The theory is used to formulate rules for the rotational viscosity and the reactive parameter of nematic mixtures in the presence of weak flows. The predicted mixture rules for the reactive parameter and rotational viscosity are analysed as a function of concentration and rotational viscosity ratio for various monomeric and polymeric mixtures, and for rod-rod, disc-disc, and rod-disc nematic mixtures. The mixture rules are used to compute alignment phase diagrams and alignment transition (orientational instability) thresholds.