On the line tension of curved boundary layers. I. boundary thermodynamics

We present a formally exact thermodynamic treatment of curved boundary layers. Specifically, we extend the boundary layer analysis of Mandell and Reiss [ J. Stat. Phys. 1975 , 13 , 107 ] for a spherical cavity located within a uniform bulk fluid to the case of a cavity intersecting a hard, structureless wall. We derive various expressions for the line tension of an intersecting cavity, all of which can be evaluated for a hard-sphere fluid using existing versions of scaled particle theory. Since the analysis is similar to the standard approach for describing curved interfacial layers, several boundary analogues to conventional interfacial relations appear. In some instances, we obtain results that apparently have not yet been derived either for boundary layers or for their parallel relations in interfacial thermodynamics. Several results offer interesting insights into the behavior of the line tension of a cavity when the cavity approaches macroscopic sizes or in the specific limit where the cavity no longer intersects the wall.