The Role of Inertia and Dissipation in the Dynamics of the Director for a Nematic Liquid Crystal Coupled with an Electric Field

We consider the dynamics of the director in a nematic liquid crystal when under the influence of an applied electric field. Using an energy variational approach we derive a dynamic model for the director including both dissipative and inertial forces.A numerical scheme for the model is proposed by extending a scheme for a related variational wave equation. Numerical experiments are performed studying the realignment of the director field when applying a voltage difference over the liquid crystal cell. In particular, we study how the relative strength of dissipative versus inertial forces influence the time scales of the transition between the initial configuration and the electrostatic equilibrium state.