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We investigate generalized potentials for a mean-field density functionaltheory of a three-phase contact line. Compared to the symmetrical potentialintroduced in our previous article [1], the three minima of these potentialsform a small triangle located arbitrarily within the Gibbs triangle, which ismore realistic for ternary fluid systems. We multiply linear functions thatvanish at edges and vertices of the small triangle, yielding potentials in theform of quartic polynomials. We find that a subset of such potentials hassimple analytic far-field solutions, and is a linear transformation of ouroriginal potential. By scaling, we can relate their solutions to those of ouroriginal potential. For special cases, the lengths of the sides of the smalltriangle are proportional to the corresponding interfacial tensions. For thecase of equal interfacial tensions, we calculate a line tension that isproportional to the area of the small triangle.

Generalized Potentials for a Mean-field Density Functional Theory of a Three-Phase Contact Line