In the previous chapters we have restricted our discussion to models of simple fluids such as water. But what if the water contains some dye? Thus we now consider models of fluid mixtures.

In this chapter we consider the simplest mixtures—those composed of two miscible fluids. We will construct models of miscible fluids from straightforward extensions of the models of the previous chapters. To illustrate an application of these miscible-fluid models, we will close this chapter with a summary of a study of passive scalar dispersion in a slow flow.

A discussion of miscible lattice gas mixtures is the first step toward an understanding of lattice gas models of immiscible fluids, a subject which we shall take up in the following chapter.

Boolean microdynamics

Miscible lattice-gas mixtures are constructed by adding a second type of particle and letting it evolve passively. This is roughly equivalent to injecting a fluid with a colored dye that allows one to see the fluid motions but does not affect the flow itself.

For convenience, we usually distinguish between particle type by assuming that the particles are colored. Our favorite mixtures are red and blue. (Aside from a certain aesthetic appeal, this choice also nicely avoids the political pitfalls of black and white.) In a miscible lattice-gas mixture the color of the particles is a property that is carried with them, but the evolution of the particles is no different than it would be if they were not colored.