is the viscosity of the fluid, which depends on the order parameter. The additional term in equation (2) is the chemical force per unit volume of fluid, associated with the gradient of the chemical potential µ ( φ ) . This force is important only where the concentration profile varies significantly, i.e. , at the diffuse interface. In the sharp interface limit this interfacial forcing gives rise to the Young-Laplace condition (see Ref. [27] for details). The dynamics of the order parameter is given by the conservation equation ∂$_{t}$φ + v · ∇ φ = − ∇ · j , where the current, j , is given by j = − M ∇ µ. Hence, φ obeys the convection diffusion equation ∂φ ∂t + v · ∇ φ = M ∇ $^{2}$µ, (3) where M is a mobility. In equilibrium, the state of the system is determined by the free energy functional F [ φ, ρ ] = ∫ d r ( V ( φ, ρ ) + κ 2 ( ∇ φ ) 2 ) . (4) The first term in equation (4) is a volume contribution, V ( φ, ρ ) = Aφ $^{2}$/ 2 + Bφ $^{4}$/ 4 + ρ/ 3 ln ρ , which allows for two phase coexistence via the φ dependent terms, and contains an ideal gas contribution given by the ρ dependent term. The second contribution to the free energy is the squared gradient term, which accounts for the energy cost of spatial variations of the order parameter by a factor κ . From this energy functional one can work out expressions for the chemical potential, µ , the total pressure tensor P , the surface tension of the fluid-fluid interface, γ , the interface width, ξ , and the equilibrium values of the order parameter in the bulk of the phases φ ∗ = ± φ$_{eq}$ . The chemical potential is given by, µ ≡ δF δφ = Aφ + Bφ 3 − κ ∇ $^{2}$φ. In this expression, µ corresponds to the energy cost of varying the concentration φ , hence, it should be understood as the exchange chemical potential of the system. The total pressure tensor, P , is composed of a density dependent contribution arising from the dependence of V on ρ , and a “chemical” contribution, which depends on the order parameter, P = P ( ρ ) δ + ( 1 $_{2}$Aφ 2 + 3 $_{4}$Bφ 4 − κ ( φ ∇ $^{2}$φ + 1 2 | ∇ φ | 2 )) δ + κ ∇ φ ∇ φ, where P = 1 $_{3}$ρ and δ is the diagonal matrix. Thus, by including the ρ dependent term in equation (4) one recovers the behavior of an ideal gas in the case of a single homogeneous fluid 8