In the first part of the presentation, we introduce a lattice Boltzmann model for miscible gases. In this model, the standard lattice Boltzmann algorithm is employed for each species composing the mixture. First, the diffusion between species is modeled by means of a force derived from kinetic theory of gases, and the complex diffusion dynamics predicted by the Maxwell-Stefan equations is recovered for a purely diffusive flow. Second, the model relies on transport coefficients calculated by an approximation of the relations obtained from kinetic theory. Third, species having different molar masses are simulated using a force term avoiding costly interpolations or an increase in the velocity set. The model is validated against analytical, experimental, and numerical results. One of the advantages of the proposed forcing approach is the easiness of implementation. Since collision is not altered, our method can easily be introduced in any other lattice Boltzmann algorithms in order to take into account complex diffusion among species.
The second part of the talk is dedicated to the simulation of the viscous fingering instability with the aforementioned lattice Boltzmann model. This challenging mixture dynamic takes place when a less viscous fluid displaces a more viscous fluid in a porous medium. Previous studies only consider a binary mixture with Fick-like diffusion behavior. Here, we focus on a mixture composed of three species in different proportions. In this case, the flow may exhibits complex diffusion behavior such as diffusion reversal, diffusion barrier, and osmotic diffusion. These phenomena are not predicted by Fick’s law and their effects on the development of the fingers are presented.