A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip

This paper describes the development of a lattice Boltzmann (LB) model for a binary gas mixture, and applications to channel flow driven by a density gradient with diffusion slip occurring at the wall. LB methods for single component gases typically 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. Substantial variations in the species densities and pressures may exist even at low Mach numbers; hence, the usual linearized equation of state for small fluctuations is unsuitable. Also, existing methods for implementing boundary conditions do not extend easily to novel boundary conditions, such as diffusion slip. 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 NavierStokes equation for the mixture and the StefanMaxwell diffusion equation are both recovered by the model. 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 may be achieved using a variable transformation method that does not increase the computational time. Simulations were carried out on hydrogen and water diffusion through a narrow channel for varying total pressure and concentration gradients. Copyright (c) 2011 John Wiley & Sons, Ltd.