A lattice model for the line tension of a sessile drop

TL;DR

This paper develops a lattice gas model to analyze the line tension at the contact line of a sessile drop, revealing its temperature dependence and providing a convergent series expression at low temperatures.

Contribution

It introduces a lattice model and cluster expansion method to compute the line tension of a sessile drop, a novel approach in this context.

Findings

Line tension is negative at low temperatures.

Line tension approaches zero as temperature approaches zero.

The series expansion for line tension converges at low temperatures.

Abstract

Within a semi--infinite thre--dimensional lattice gas model describing the coexistence of two phases on a substrate, we study, by cluster expansion techniques, the free energy (line tension) associated with the contact line between the two phases and the substrate. We show that this line tension, is given at low temperature by a convergent series whose leading term is negative, and equals 0 at zero temperature.