Diffuse Interface in a Critical Fluid Mixture

Abstract

The interface between the two fluids in equilibrium at temperature $T$ below the critical (consolute) temperature $T_c$ of a binary mixture in a gravitational field has been observed to expand into a transition layer that thickens, while the coexisting phases become more similar and the interfacial energy vanishes as ${\mathrm{T\to T}}_c$ . The effective thickness $L$ of the transition layer has been deduced from reflectivity measurements as a function of light wavelength $\lambda$ and temperature. The shape of the interface concentration distribution function has been found from the $\lambda$ dependence of the reflectivity to be close to an error functon and to a function recently proposed by Fisk and Widom and distinguishable from the classical hyperbolic tangent distribution. In the range $\text{0.02\hspace{0.17em}<\hspace{0.17em}Δ\hspace{0.17em}T\hspace{0.17em}<\hspace{0.17em}3.0°}\mathrm{C}{\mathrm{,\; L\propto (\Delta T)}}^{\mathrm{-\nu }}$ where $\text{ν\hspace{0.17em}=\hspace{0.17em}0.67\hspace{0.17em}±\hspace{0.17em}0.02}$ and $\xi$ the appropriately defined thickness ${\text{L′\hspace{0.17em}=\hspace{0.17em}2(Δ\hspace{0.17em}T\hspace{0.17em}/\hspace{0.17em}T}}_c{)}^{\text{−0.67}}$ is comparable with the correlation length of the bulk fluids for corresponding $\mathrm{\Delta T}$ . The critical index $\nu$ , together with the critical index $\beta$ for the coexistence curve, and $\mu$ for the surface tension, can be combined to test various theoretical relations amongst the critical exponents and theories of the critical interface.