Generalized curvature expansion for the surface internal energy

In this paper a generalized Taylor series expansion of the surface internal energy about zero mean and Gaussian curvature is presented. The static equilibrium of an isolated system is studied, substituting this expanded version of the surface internal energy. From the set of necessary conditions that follows from the equilibrium analysis, a sequence of subsequent approximations to the normal and tangetial components of the jump momentum balance at the interface is extracted. The first four members of this sequence are presented, and the result obtained by Boruvka and Neumann [J. Chem. Phys. 66 (1977) 5464] for the normal component of the jump momentum balance, are shown to be a special case of the third order approximation for this balance. The results are also compared with the expansions used by Blokhuis and Bedeaux [J. Chem. Phys. 95 (1991) 6986; Physica A 184 (1992) 42; HCR Adv.-Education Rev. 1 (1994) 55].