Coexistence at critical filling.
At the bulk liquid-gas coexistence the liquid film adsorbed on the corrugated substrate can exhibit a first-order thin-thick transition, provided the corrugation amplitude exceeds the critical value, specific for this kind of corrugation. We study the coexistence of thin and thick layer adsorbed on the sinusoidally corrugated substrate. We evaluate the line tension between these films in the vicinity of the filling critical temperature T(CF) . The line L tension is positive and vanishes at the filling critical point according to the power law L approximately ( T(CF) -T)(3/2) .