Line tension between two surface phases on a substrate

An upper bound to the line tension of the boundary line separating a thin and a thick liquid film on a substrate is calculated within mean-field theory. The starting point of the analysis is a van der Waals-like form of the free energy in the presence of a wall which is commonly used in describing wetting phenomena. The expression for the free energy is shown to reduce to the form of the free energy in the interface displacement model with explicit expressions for the parameters in the interface displacement model. At the wetting transition the upper bound to the line tension is finite thereby putting the conclusion of the interface displacement model of a finite line tension at the wetting transition on a more fundamental basis.