Our discussion of lattice-gas models now takes a qualitative turn. We continue to study fluid mixtures as in the previous chapter, but now they will exhibit some surprising behavior—they won't like to mix!

This change in direction also steers us towards the heart of this book: models for complex hydrodynamics. The particular kind of complexity we introduce in this chapter relates to interfaces in immiscible fluids such as one might find in a mixture of oil and water. We are all familiar with the kind of bubbly complexity that that can entail. So it seems all the more remarkable that only a revised set of collision rules are needed to simulate it with lattice gases. Indeed, the models of immiscible fluids that we shall introduce are so close to the models of the previous chapters that we call them immiscible lattice gases.

This chapter, an introduction to immiscible lattice-gas mixtures, is limited to a discussion of two-dimensional models. In the next chapter, we introduce a lattice-Boltzmann method that is the “Boltzmann equivalent” of the immiscible lattice gas. That then sets the stage for our discussion of three-dimensional immiscible lattice gases in Chapter 11.

Color-dependent collisions

In the miscible lattice gases of the previous chapter, the collision rules were independent of color. The diffusive behavior derived instead from the redistribution of color after generic colorblind collisions were performed. Aside from some diffusion, the color simply went with the flow.