Lattice Boltzmann simulation methods for boundaries and interfaces in multi component flow.

In this work I shall give details of the development of a two dimensional Lattice Boltzmann algorithm targeting the simulation of immiscible fluids at low Reynolds number and low Capillary number. The Lattice Boltzmann method will be explained along with its multi-component extensions. Key method developments shall first be developed in terms of single component advancements, made in the lattice closure algorithm and in the application of external forces to boundary lattice sites. Having secured single component advancements, I shall present parallel developments made in immiscible flow simulation, considering two immiscible fluids (however extension to larger numbers of immiscible species is mentioned where appropriate). Drop dynamics within shear flow shall be examined with Numerical colour segregation along with attempts for the application of a kinematic condition. Analytic segregation shall then be used and the dynamics of the phase field shall be analysed showing improved drop dynamics. A simple and adaptable method for application of a kinematic condition shall next be shown to be effective when used in conjunction with the analytic diffusion method in improving the quality of the models hydrodynamics. Culmination of all the previously identified improvements to the simulation method shall then be utilised in the simulation of wetting drops in both static and dynamic situations. The final method is qualitatively shown to predict static wetting, rolling contact points, bifurcating contacts and the spreading of films.