Decoupling of the Ericksen–Leslie Equations

We examine the hydrodynamic behaviour of a nematic liquid crystal confined between two parallel electrodes and subject to a non-uniform electric field across the layer. By decoupling the EricksenLeslie equations for the nematic, we are able to derive a dynamic equation for the director orientation which is not explicitly dependent on the fluid velocity, rather a non-local term contains the effects of flow. The flow velocity and electric potential are determined subsequently from the calculated director profile. Our numerical scheme enables us to predict an effective rotational viscosity which takes account of fluid shear viscosities and allows us to establish the behaviour in special symmetry cases. Significantly, our calculations also demonstrate how kickback can be avoided, and the switch-off time optimised, by restricting the applied voltage to an appropriate range.