Lattice Boltzmann method for Q-tensor nemato-dynamics in liquid crystal display devices.

Nematic liquid crystals are fluids whose anisometric molecules show long range orientational order but no positional order. The orientational order gives rise to anisotropic properties that have widely been exploited as the basis for liquid crystal display devices. The Ericksen-Leslie director theory has successfully been used to describe many dynamic properties of liquid crystals however there are situations in which a more complete description may be given in terms of the second rank traceless symmetric Q-tensor. The development of a liquid crystal device solver is described. The solver calculates the flow, director and order parameter fields in three-dimensions through the Q-tensor equations of nemato-dynamics. The solver includes elastic, electric, magnetic, thermotropic, flexoelectric, dielectric and surface anchoring effects. Coupled lattice Boltzmann algorithms are used with anisotropic forcing terms included in order to reproduce the governing equations. A Chapman-Enskog analysis demonstrates that the algorithm recovers the target macroscopic equations.The method is successfully validated against analytical results for the effect of temperature, external electric fields, flow alignment and Miesowicz viscosities. Further validation is given against numerical solutions of a one-dimensional model of a liquid crystal display device proposed by Davidson.The switching behaviour of a Zenithal Bistable Display is then investigated. It is shown how flexoelectric properties of nematics produce bistability within this device. Defect creation and annihilation processes are shown during device switching for which it is necessary to use a method with variable order parameter. An approach to determine the flexoelectric coefficients is discussed. Results are presented for the preliminary characterisation and operation of this display that may enable optimisation for use in the display industry.