Simulations of flow-induced director structures in nematic liquid crystalsthrough 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 rot ating planar nematic sample subjected to a constant magnetic field. The dyn amics 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 spa tial and time derivatives. Time-dependent patterns of the director are obta ined using a finite-difference scheme in a spatial polar grid. Several expe rimental situations are analyzed, corresponding to common experimental setu ps: continuously rotating samples for different values of the rotational sp eed; 30 degrees and 90 degrees step-rotation experiments. A comparison is m ade to existing approximate treatments. Dependence upon the sample dimensio n is also discussed.