Lattice Boltzmann methods for binary mixtures with different molecular weights

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Abstract
Previous authors have suggested lattice Boltzmann methods for binary mixtures. However, these methods are limited to fluids with nearly the same molecular weight. In this work, two modified methods are proposed for simulating fluids with different molecular weights. The first method is based upon the physical principle that particles with different molecular weights move at different lattice speeds (DLS) when at the same temperature. Therefore, different streaming distances are employed for species with different molecular weights. A second method is developed by selecting constants in the equilibrium distribution function in such a way that the speed of sound can be adjusted for each species. In this approach, the species have the same lattice speed (SLS). Using multiscale expansions, the methods are shown to reproduce the appropriate species continuity equation in the macroscopic limit. The accuracy of the methods is evaluated by studying binary diffusion problems. The DLS method is shown to be able to simulate diffusion in fluids with larger ratios of molecular weights relative to the SLS method.