Critical exponents of fluid-fluid interfacial tensions near a critical endpoint in a nonwetting gap

Abstract

Fluid three-phase equilibria, with phases $α, β, γ$, are studied close to a tricritical point, analytically and numerically, in a mean-field density-functional theory with two densities. Employing Griffiths' scaling for the densities, the interfacial tensions of the wet and nonwet interfaces are analysed. The mean-field critical exponent is obtained for the vanishing of the critical interfacial tension $σ_{βγ}$ as a function of the deviation of the noncritical interfacial tension $σ_{αγ}$ from its limiting value at a critical endpoint $σ_{α,βγ}$. In the wet regime, this exponent is $3/2$ as expected. In the nonwetting gap of the model, the exponent is again $3/2$, except for the approach to the critical endpoint on the neutral line where $σ_{αβ} = σ_{αγ}$. When this point is approached along any path with $σ_{αβ} \neq σ_{αγ}$, or along the neutral line, $σ_{βγ} \propto | σ_{αγ} - σ_{α,βγ}|^{3/4}$, featuring an anomalous critical exponent $3/4$, which is an exact result derived by analytic calculation and explained by geometrical arguments.