Interfacial tension of fluids near critical points and two-scale-factor universality

Data for the surface tension of pure fluids near critical points and for the interfacial tension between coexisting liquid phases of binary mixtures near consolute points are reviewed using recent theoretical values for the critical exponents and the concept of two-scale-factor universality [D. Stauffer, M. Ferer, and M. Wortis, Phys. Rev. Lett. 29-->, 345 (1972)]. The data are used to estimate the universal amplitude ratios relating the interfacial tension amplitude σ₀ to the specific-heat divergence and to the correlation length near T_c. The amplitude ratios for a wide variety of fluid systems including polymer solutions are consistent and, in the most favorable cases, have an accuracy approaching +/-5% of σ₀. The experimental amplitude ratios do not agree with recent theoretical estimates from either Monte Carlo simulations of the Ising model or the ɛ expansion. The theoretical values of σ₀ are about 65% of the experimental values. I have no explanation for this inconsistency. In the process of reviewing surface-tension data for pure fluids, it was observed that the capillary-length data for many fluids deviate by less than 2% from the expression a²=a²₀(1-T/T_c)^{0.93 5} when T varies from the triple point to 0.99T_c. (The exponent 0.935 is expected to be accurate only asymptotically close to T_c.) This observation implies that the scale factors for the critical anomaly in the free energy of these liquid-vapor systems can be estimated from measurements of the densities of the coexisting phases at all temperatures and a measurement of the capillary rise near the triple point.