Surface tension and interfacial density profile of fluids near the critical point

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Abstract
Presented is a new procedure for the derivation of the density profile ρ(ξ) along the interface between coexisting liquid and gas phases near the critical point. The fundamental equation used is the invariance throughout the fluid of the component of the stress tensor perpendicular to the interface. A general and physically plausible form is suggested for the pair distribution function ρ(2) across the interface, which allows conversion of the fundamental equation to a differential equation which may be solved for the singlet density ρ(ξ). In the limit (ρL − ρG)/ρc ≫ 1, the result reduces to the classical hyperbolic tangent function, but for any T < Tc is fundamentally different. In addition, the equation obtained for ρ(ξ) allows the derivation of several new formulas for surface tension, which reduce to the square‐gradient theory result in the limit T → Tc.

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