Mesoscopic interparticle potentials in the lattice Boltzmann equation for multiphase fluids.

I introduce a method to derive mesoscopic particle interactions by macroscopic thermodynamics, which is suitable for simulation of multiphase fluids by means of the lattice Boltzmann equation. For van der Waals fluids, the interaction possesses a high-density strong repulsive core and a low-density weak attractive tail, which looks like the Lennard-Jones potential with replacement of the distance between particles with mass density. Numerical results on phase separation show a droplet growth scheme rather than spinodal decomposition, and exhibit accurately the equilibrium phase diagram, a convincing interfacial energy property, and irreversible thermodynamics.