Three-dimensional lattice-Boltzmann model of van der Waals fluids.

A three-dimensional lattice-Boltzmann model is developed for the simulation of nonideal fluids under static and flow conditions. The van der Waals formulation of quasilocal thermodynamics for nonuniform fluids is used, and the interfacial stress tensor for nonideal fluids appears explicitly in the hydrodynamic equations. The continuity and flow equations are fully recovered, and Galilean invariance is restored through appropriate manipulations of the pressure tensor. Although applied here to the D3Q15 lattice, the methodology of Galilean restoration can be easily modified for use with other three-dimensional lattices as well. The Laplace law and Gibbs-Thomson equations are satisfied with excellent accuracy by the model, as demonstrated by droplet equilibrium simulations. Spinodal decomposition and droplet coalescence simulations are also carried out, revealing a direct proportionality of the characteristic times to the viscosity, as expected. A wettability adjustment was made possible through the prescription of a chemical potential profile along the fluid-wall interface, and used for the simulation of droplet formation from a conical orifice.