A Lattice Boltzmann Method for a Binary Miscible Fluid Mixture and Its Application to a Heat-Transfer Problem

A lattice Boltzmann method (LBM) for an isothermal binary miscible fluid mixture is proposed. The binary miscible fluid mixture is assumed to be composed of A and B species where the fraction of B species is much smaller than that of A species. The asymptotic theory proposed by Sone [in Rarefied Gas Dynamics, edited by D. Dini (Editrice Tecnico Scientifica, Pisa, 1971), Vol. 2, p. 737] is applied to the present LBM model and the convection–diffusion equation for component B is obtained. A diffusion problem is calculated and the validity of the proposed model is shown. Also, the present method can be applied to thermal fluid systems, in which the concentration field of component B is regarded as the temperature field of component A, and a buoyancy force proportional to the temperature difference is included. Rayleigh–Bénard convection is numerically simulated. The results indicate that the present LBM is useful for the simulation of fluid flows with heat transfer as well as mass transfer.