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.
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