Critical exponents of fluid-fluid interfacial tensions near a critical endpoint in a nonwetting gap
Fluid three-phase equilibria, with phases $\alpha, \beta, \gamma$, 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 $\sigma_{\beta\gamma}$ as a function of the deviation of the noncritical interfacial tension $\sigma_{\alpha\gamma}$ from its limiting value at a critical endpoint $\sigma_{\alpha,\beta\gamma}$. 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 $\sigma_{\alpha\beta} = \sigma_{\alpha\gamma}$. When this point is approached along any path with $\sigma_{\alpha\beta} \neq \sigma_{\alpha\gamma}$, or along the neutral line, $\sigma_{\beta\gamma} \propto | \sigma_{\alpha\gamma} - \sigma_{\alpha,\beta\gamma}|^{3/4}$, featuring an anomalous critical exponent $3/4$, which is an exact result derived by analytic calculation and explained by geometrical arguments.