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Present work is concerned with the construction of a lattice-Boltzmann (LB) model for ideal miscible fluids. In this particular case, collision term in LB equation can be modelled by, only, considering mutual and cross collisions between, respectively, particles of the same and of different kind. A non-linear LB model with three distinct relaxation times intended to be used in problems with large concentration gradients is presented. Model enables the independent management of the fluid viscosities µr and µb and binary diffusivity D. It is shown that mass and momentum are, always, preserved and that the model retrieves consistent hydrodynamic equations in the incompressible limit. Theoretical values, obtained from Chapman-Enskog analysis, for binary diffusivity and mixture viscosity are compared with numerical values, directly obtained from LB simulations.

A Three-Parameter Non-linear Lattice-Boltzmann Model for Ideal Miscible Fluids