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

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 analyzed. The mean-field critical exponent is obtained for the vanishing of the critical interfacial tension σβγ as a function of the deviation of the noncritical interfacial tension σαγ from its limiting value at a critical endpoint σα,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 σαβ = σαγ. When this point is approached along any path with σαβ ≠ σαγ, or along the neutral line, σβγ ∝|σαγ - σα,βγ|3/4, featuring an anomalous critical exponent 3/4, which is an exact result derived by analytic calculation and explained by geometrical arguments.