A lattice model for the line tension of a sessile drop

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.