Continuum free-energy formulation for a class of lattice Boltzmann multiphase models

¹  Department of Physics and INFN, University of Tor Vergata - Via della Ricerca Scientifica 1, 00133 Rome, Italy, EU
²  EXA Corporation - 55 Network Drive, Burlington, MA 01803, USA
³  Istituto per le Applicazioni del Calcolo CNR - Viale del Policlinico 137, 00161 Rome, Italy, EU

Corresponding author: sbragaglia@roma2.infn.it

Received: 29 January 2009
Accepted: 30 March 2009

Abstract

It is shown that the Shan-Chen (SC) model for non-ideal lattice fluids can be made compliant with a pseudo-free-energy principle by simple addition of a gradient force, whose expression is uniquely specified in terms of the fluid density. This additional term is numerically simulated and shown to provide fairly negligible effects on the system evolution during phase-separation. To the best of our knowledge, these important properties of the SC model were not noted before. The approach developed in the present work is based on a continuum analysis: Further extensions, more in line with a discrete lattice theory (Shan X., Phys. Rev. E, 77 (2008) 066702), can be envisaged for the future.