A non-linear lattice-Boltzmann model for ideal miscible fluids

This work is concerned with the construction of a lattice-Boltzmann (LB) model for ideal miscible fluids. In this particular case, the collision term in the LB equation can be modelled by only considering mutual and cross collisions between, respectively, particles of the same and of different kinds. A non-linear LB model with three distinct relaxation times intended to be used in problems with large concentration gradients is presented. The model enables the independent management of the fluid viscosities μ and μ and binary diffusivity D. It is shown that mass and momentum are, always, preserved and that consistent hydrodynamic equations are obtained at 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. © 2003 Elsevier B.V. All rights reserved. PACS: 47.11.+j; 51.20.+d; 66.10.-x; 66.20.+d