In many applications involving materials processing and development, it is necessary to understand and control the morphology of multiphase fluid mixtures and particulate dispersions subject to a complex flow history. These applications often involve free liquid-air boundaries that can respond to flow and phase separation processes, solid boundaries that can be preferentially wet by certain liquid components, thin-film geometries, complex solid substrate geometries, and high Reynolds number flows in which fluid inertia is important. The development of computational methods of sufficient flexibility and generality to treat such realistic fluid dynamics problems is a basic theoretical challenge.
The Lattice Boltzmann (LB) method, and other related computational methods based on cellular-automata ideas (e.g., lattice gas) [1] have emerged as powerful tools for modeling complex fluid dynamics problems. These methods are developing rapidly in response to recent theoretical advances and the availability of resources for large scale computation. Applications of LB to modeling high Reynolds flow [1], the dynamics of fluid phase separation [2,3] , and multicomponent fluid flow in porous media [4,5,6] have proven the potential of LB as a general purpose computational scheme for modeling complex fluid dynamics problems. Many of these exploratory studies have emphasized the development of the LB methodology and have not considered a direct comparison to the properties of real liquids. Therefore, basic characteristics of these computational models of liquids are still largely unknown. In this paper, we characterize the type of critical phenomena observed in two LB models of multicomponent liquids. The first model, due to Shan and Chen [2] modifies the Boltzmann equilibrium distribution to account for fluid-fluid interactions. The second approach, considered in the present paper, incorporates the forcing between two fluids directly into the body-forcing term of the Boltzmann equation [7]. In Appendix A, we show how the second method is related to a density-gradient expansion of a BBGKY collision operator [8,9,10] which should facilitate comparison with the Cahn-Hilliard theory of phase separation [11,12,13,14,15,16] and the Ginzburg-Landau theory of critical phenomena [17,18].
We calculate basic equilibrium properties (coexistence curve, interfacial width and correlation length, surface tension) and express our results in terms of a reduced variables description that allows comparison with real fluid measurements. Asymmetry in the mass and volume of the fluid components is considered in this comparison since this property is characteristic of real liquids. The effect of flow and interacting boundaries on the phase separation process is briefly explored to identify some basic phenomena of experimental interest.