Consistent pseudopotential interactions in lattice Boltzmann models

We outline a systematic procedure on how to construct and derive interactions for nonideal lattice fluids. Using a mesoscopic approach based on exact lattice theories, we prove the consistency of the resulting diffuse interface theory with continuum thermodynamics. Translated in the framework of the so called "Shan-Chen" model for nonideal lattice fluids, this paper shows how to adjust the associated pseudopotentials to reproduce a free energy model based on a square gradient theory of equilibrium interfaces.