Nematodynamics equations in two dimensions

A discussion is provided of the combined influence of the elastic torques, boundary conditions and magnetic torque on the hydrodynamical behaviour of a nematic liquid crystal in two dimensions. A partial differential equation for the dependence in time and space of the director orientation is obtained from the constitutive hydrodynamical equations of a nematic phase (Leslie-Ericksen equations). A numerical solution is developed to calculate spatial distributions of the director for a sample in a rotating cylindrical vessel, subjected to a constant magnetic field. Boundary conditions are considered assuming a perfect alignment of the director to the internal walls of the cylinder. From the stationary and transient distributions, we simulate electron spin resonance spectra of a paramagnetic probe immersed in the liquid crystalline phase.