Continuum Free-Energy formulation for a class of Lattice Boltzmann multiphase models

TL;DR

This paper demonstrates that the Shan-Chen lattice Boltzmann model can be aligned with a free-energy principle by adding a gradient force, with minimal impact on phase separation dynamics, offering new theoretical insights.

Contribution

It introduces a continuum-based method to make the Shan-Chen model compliant with a pseudo free-energy principle by adding a specific gradient force.

Findings

Gradient force minimally affects phase separation.

Shan-Chen model can be made free-energy compliant.

New continuum analysis approach developed.

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 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 (X. Shan, {\it Phys Rev E}, {\bf 77} 066702 (2008)) can be envisaged for the future.