The line of contact of three fluid phases

We study the variation of density or chemical composition in the neighborhood of the line in which three phases meet and we determine the associated line tension. Three models are considered: a phenomenological model based on a primitive approximation to the excess free-energy density that arises from the inhomogeneities at the two-phase interfaces and at the three-phase line; a generalized van der Waals approximation, in which the excess free-energy density is the sum of an analytic function of the densities and a quadratic form in the density gradients; and a microscopic model of a three-component, three-phase fluid, for which the properties of the interfaces and of the three-phase line are determined in mean-field approximation as solutions of nonlocal functional equations. Both positive and negative line tensions are found. In the third model, when the nonlocal functional equations for the composition profiles of the two-phase interfaces are approximated by gradient expansions truncated in second order (van der Waals approximation), the resulting profiles are fairly accurate but the surface tensions are not.