Nematic liquid crystal in oscillatory Poiseuille flow

The orientational behavior of a nematic liquid crystal under the periodically time-varying pressure gradient is studied theoretically. The director motion in the flow plane is analyzed in the case that the distributions of the director and velocity throughout the bulk of nematic liquid crystal depend on the time and the z-coordinate (the z-axis is normal to the nematic liquid-crystal layer). The approximate analytical solutions of the nematodynamic equations for a liquid crystal are obtained at small amplitudes of the director oscillations and at oscillation frequencies, when the viscous hydrodynamic torque on the director is larger than the elastic torque. The pretransitional processes are considered in detail by using the numerical simulation of a full set of nematodynamic equations at various amplitudes and frequencies of the pressure gradient and at different boundary conditions for the director. It is found that the specified ranges of frequencies and amplitudes of the oscillatory flow satisfy the approximate analytical solutions obtained.