Theoretical and numerical calculations for the dynamics of nematic liquid crystals with consideration of flow

Abstract

Most of the studies about dynamics of liquid crystals rely on the approximation of zero flow. One of the reasons for this is that the dynamical equations are quite complicated and difficult to study due to the coupling between the orientation motion and the translation motion of molecules. The extra effort, the slow computation and the modelling equations with some approximations and ignorance of physical effects needed to solve them have not always seemed warranted for giving accurate calculation results. In this paper, we present the coupled director equations and flow equations for nematic liquid crystals, as well as the general theoretical and numerical calculation methods for solving these equations. These equations and calculation methods can be further simplified for some director configurations, such as homogeneous and homeotropic cells without twist. These described theoretical and numerical calculation methods show the generality of calculation for various director configurations. They are also computational efficient and easy to implement and can be widely used in studies of nematic liquid crystal dynamics including flow.

Keywords:

• director
• flow
• molecular field
• integration constants
• discrete form
• linear system