Modeling of the dynamics of a liquid crystal under the action of weak perturbations

We study dynamic processes in liquid crystals using a simplified mathematical model in which a liquid crystal is considered as a finely dispersed continuous medium with rotating particles which has elastic resistance to volume deformation and viscoelastic resistance to relative rotation of the particles. The oscillatory regime of rotational motion described by the Klein–Gordon equation for tangential stress is studied. Moment interactions of particles due to the inhomogeneity of the rotation field are taken into account. The dispersion properties of a subsystem of two equations for tangential stress and angular velocity are investigated. These equations are used to numerically analyze the rotation field in the liquid crystal under the action of tangential stress caused by the thermal expansion of a metal plate at the boundary. We consider the problem of perturbation of an extended layer of a 5CB liquid crystal by means of an electric field generated by charges on capacitor plates located periodically along the layer. Singularities of the electric potential at the ends of the capacitor plates are selected explicitly. Some results of computations simulating the Fréedericksz effect in the liquid crystal layer are presented.