Model for line tension in three-phase equilibrium

Abstract

We propose a model free-energy functional of two order parameters with which to calculate the interfacial and line tensions in three-phase equilibrium. The Euler-Lagrange equations for the free-energy minimum are solved exactly, yielding the spatial variation of the order parameters analytically. In terms of a parameter b 2 in the model the three interfacial tensions, in dimensionless form, are 1 2 (1+ b 2), 1 2 (1+ b 2) and 2. When b 2=3 the three phases play symmetrical roles and the line tension, again in the appropriate units, is calculated to be −6/π + 2 √3 = −0.755… . A wetting transition, where the sum of two of the interfacial tensions becomes equal to the third, occurs as b 2 → 1+. A quantity that approximates the line tension is found to vanish proportionally to the first power of the vanishing contact angle as the wetting transition is approached.