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

Abstract

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 ${\sigma }_{\alpha \beta }\ne {\sigma }_{\alpha \gamma }$, 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.

References in corpus (4)

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• Wetting and nonwetting near a tricritical point
• Three-phase equilibria in density-functional theory: interfacial tensions
• Three-component Bose-Einstein condensates and wetting without walls