Simulations of flow-induced director structures in nematic liquid crystals through leslie-ericksen equations. I. Computational methodology in two dimensions

A computational treatment of the constitutive equations of nematodynamics, based on the Leslie-Ericksen approach, is presented and discussed for a rotating planar nematic sample subjected to a constant magnetic field. The dynamics of the velocity v and director n fields is taken into account exactly. Coupled partial differential equations suitable to be solved numerically are worked out, in terms of derived functionals of v and n and of their spatial and time derivatives. Time-dependent patterns of the director are obtained using a finite-difference scheme in a spatial polar grid. Several experimental situations are analyzed, corresponding to common experimental setups: continuously rotating samples for different values of the rotational speed; 30 degrees and 90 degrees step-rotation experiments. A comparison is made to existing approximate treatments. Dependence upon the sample dimension is also discussed.

Simulations of flow-induced director structures in nematic liquid crystals through leslie-ericksen equations. II. Interpretation Of NMR experiments in liquid crystal polymers

Computationally exact and approximate solutions of the Leslie-Ericksen equations for nematic liquid crystals in two dimensions are employed to calculate director distributions in cylindrical samples, rotating under the influence of a magnetic field. In particular, the time evolution of systems prepared initially in metastable states with respect to the magnetic field is investigated, and calculated director distributions are used to interpret rheo-NMR experiments in nematic liquid crystal polymers.