Two-dimensional hydrodynamical description of a rotating nematic sample in a magnetic field

Nematodynamic equations are applied to the description of a cylindrical nematic sample, rotating around its axis with constant angular velocity, in the presence of a perpendicular magnetic field. The system is described by the director orientation n and by the velocity vector v fields in the cylinder volume. Equations are simplified by considering the director orientation n constrained in a planar section of the cylinder and by neglecting coupling with the velocity field, which is completely determined by the angular speed rate. Boundary conditions for perfect alignment of the director n perpendicularly to the walls are assumed. It is shown that a dynamical equation can be obtained which is amenable to numerical analysis for the spatial and time dependence of the director orientation. Transient distributions and stationary solutions are found and discussed.