17 - Interfaces

Summary

Whereas phase separation is undoubtedly the most striking aspect of immiscible lattice-gas models, the interfaces that form due to phase separation are themselves an object of at least equal interest. In this chapter, we consider the interfaces formed by the 2D immiscible lattice-gas (ILG) model of Chapter 9.

We first discuss a theoretical calculation of the surface tension. Our calculation of surface tension not only provides a better understanding of ILG interfaces, but it also predicts the phase transition from the mixed to the unmixed phase described earlier in Chapter 16.

We then present a detailed view of interface fluctuations. In real fluids, interfaces fluctuate due to thermal noise. Lattice-gas interfaces, on the other hand, fluctuate due to the statistical noise in the Boolean dynamics. In both cases, the detailed motion of the interfaces results from a combination of surface tension, viscous hydrodynamics, and noisy excitation. We shall see that a study of interface fluctuations provides a delicate probe of the hydrodynamic and statistical properties of the ILG.

Surface tension: a Boltzmann approximation

The calculation of surface tension in ILG's offers neither the elegance nor the accuracy of the analogous calculation for lattice-Boltzmann models that we presented in Chapter 10. It does however yield several interesting results.

As in Section 10.2, we once again consider the surface tension of a flat interface. As we have already indicated in Exercise 11.3, there is no reason to expect that surface tension is isotropic in Boolean models.