This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multi-component model used in the subsequent chapters. Commonly used single component LB methods use a non-physical equation of state, in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multi-component systems containing gases of differing molecular masses that are modelled with the ideal gas equation of state. Also, existing methods for implementing boundary conditions are unsuitable for extending to novel boundary conditions, such as diffusion slip. Therefore, a new single component LB derivation and a new method for implementing boundary conditions are developed, and validated against Poiseuille flow. However, including a physical equation of state reduces stability and time accuracy, leading to longer computational times, compared with 'incompressible' LB methods. The new method of analysing LB boundary conditions successfully explains observations from other commonly used schemes, such as the slip velocity associated with 'bounce-back'.The new model developed for multi-component gases avoids the pitfalls of some other LB models, a single computational grid is shared by all the species and the diffusivity is independent of the viscosity. The Navier-Stokes equation for the mixture and the Stefan-Maxwell diffusion equation are both recovered by the model. However, the species momentum equations are not recovered correctly and this can lead to instability. Diffusion slip, the non-zero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple one-dimensional model for channel flow. To increase the accuracy of the scheme a second order numerical implementation is needed. This can be achieved using a variable transformation method which does not result in an increase in computational time. Simulations were carried out on hydrogen and water diffusion through a narrow channel, with varying total pressure and concentration gradients. For a given value of the species mass flux ratio, the total pressure gradient was dependent on the species concentration gradients. These results may be applicable to fuel cells where the species mass flux ratio is determined by a chemical reaction and the species have opposing velocities. In this case the total pressure gradient is low and the cross-channel average mass flux of hydrogen is independent of the channel width. Finally, solutions for a binary Stefan tube problem were investigated, in which the boundary at one end of a channel is permeable to hydrogen but not water. The water has no total mass flux along the channel but circulates due to the slip velocity at the wall. The cross-channel average mass flux of the hydrogen along the channel increases with larger channel widths. A fuel cell using a mixture of gases, one being inert, will experience similar circulation phenomena and, importantly, the width of the pores will affect performance. This thesis essentially proves the viability of LB models to simulate multi-component gases with diffusion slip boundaries, and identifies the many areas in which improvements could be made.

This research investigates the effect of feed composition on the separation performance of pure polyethersulfone (PES) and different types of PES based mixed matrix membranes (MMMs) in order to develop high performing membranes for CO2/CH4 separation. MMMs were prepared by solvent evaporation method using PES as the polymer matrix with SAPO-34 particles as fillers, and 2-hydroxy 5-methyl aniline (HMA) as the low molecular weight additive. Four types of membranes were used throughout the study, namely pure PES membrane, PES/HMA (4, 10%w/w) membrane, PES/SAPO-34 (20%w/w) MMM, PES/SAPO-34 (20%w/w)/HMA (4, 10%w/w) MMM. The effect of CO2 composition on the performance of the membranes was investigated in detail with a wide feed composition range changing between 0 and 100%. In addition to separating CO2/CH4 binary gas mixtures, the separation performances of these membranes were determined by measuring single gas permeabilities at 35&ordm / C, with a feed pressure of 3 bar. Moreover, the membranes were characterized by scanning electron microscopy (SEM), differential scanning calorimetry (DSC) and thermal gravimetric analyzer (TGA). The separation selectivities of all types of membranes generally observed to be independent of feed composition. The composition independency of these membranes eliminates the need of investigating at which feed gas composition the prepared membranes are best performing for practical applications. PES/SAPO-34/HMA MMMs with HMA loading of 10% and SAPO-34 loading of 20% demonstrated the highest separation selectivity of about 40, and the ideal selectivity of 44, among the used membranes.