In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the Laplace-Young relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.

FIU's Applied Research Center is assisting the Department of Energy's Hanford Site by developing a computational program based on the lattice Boltzmann method in order to generate computer simulations of engineering problems involving multiphase flows.

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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.

In this paper, a lattice Boltzmann (LB) model is presented for axisymmetric multiphase flows. Source terms are added to a two-dimensional standard lattice Boltzmann equation (LBE) for multiphase flows such that the emergent dynamics can be transformed into the axisymmetric cylindrical coordinate system. The source terms are temporally and spatially dependent and represent the axisymmetric contribution of the order parameter of fluid phases and inertial, viscous and surface tension forces. A model which is effectively explicit and second order is obtained. This is achieved by taking into account the discrete lattice effects in the Chapman-Enskog multiscale analysis, so that the macroscopic axisymmetric mass and momentum equations for multiphase flows are recovered self-consistently. The model is extended to incorporate reduced compressibility effects. Axisymmetric equilibrium drop formation and oscillations, breakup and formation of satellite droplets from viscous liquid cylindrical jets through Rayleigh capillary instability and drop collisions are presented. Comparisons of the computed results with available data show satisfactory agreement.