On the Unified Theory for Non-Equilibrium Phenomena in the Isotropic and Nematic Phases of a Liquid Crystal; Spatially Inhomogeneous Alignment

A nonlinear equation is derived which describes the relaxation of the alignment and the flow alignment in the isotropic and nematic phases of a liquid crystal. In addition to the previously treated case, contributions associated with spatial derivatives of the alignment are taken into account which stem from gradient terms occuring in the free energy (elastic energy) and from the flux of the alignment. Some applications are discussed. In particular, the Leslie and Frank coefficients of the nematic phase are expressed in terms of the equilibrium alignment order parameter and coefficients which are meaningful in both phases