Mesoscopic lattice Boltzmann nemato-dynamics.

In this thesis we have developed an anisotropic lattice Boltzmann (LB) model that recovers the incompressible isentropic Ericksen-Leslie-Parodi (ELP) equations of continuum nemato-dynamics in two dimensions with the director confined to the plane. Suitable validations of the developed model against known solutions of the continuum theory are undertaken as. well as investigations into nematic flow in interesting geometries. The model is based upon two coupled LBE schemes, the standard momentum density distribution and a new link angle distribution. To achieve evolution, the link angle distribution undergoes a Bhatnagar-Gross-Krook (BGK) collision step and advects (propagates) in unit time with the momentum densities. Anisotropy is introduced into the momentum density evolution scheme through a linearized Lattice Boltzmann (1LB) collision process which is made anisotropic. Correctly to capture the macroscopic dynamics, 6th order isotropy of the underlying lattice structure is required, accordingly we introduce a new variant on the standard 1LB scheme : a two-dimensional thirteen link (D2Q13) model. Chapmann-Enskog expansions of the momentum and angle evolution schemes are shown, through a suitable selection of equilibrium distribution functions and forcing terms, correctly to map onto the target macroscopic ELP equations of continuum nemato-dynamics. Results are presented which validate the new scheme against known analytical solutions of the governing equations to a high degree of accuracy. The validated scheme is subsequently applied to nemato-dynamic behavior in an applied magnetic field, i.e the Freedericksz transition and velocity back-flow with director kick-back. Finally we simulate the geometrically complex Zenithly Bi-stable Display (ZBD) device to illustrate some of the advantages of the LB schemes.