In the present paper we discuss various forms of the gener-The minimization of the free energy of a two-phase system with alized Laplace equation which are valid for interfaces with an interface of arbitrary curvature leads to an extremum (Laplace) variable curvature and for an arbitrary choice of dividing condition containing the pressure difference, DP, between the two surface between the two bulk phases. This rather complete sides of the interface. The expression for DP is a function of the surface-thermodynamic background is needed, especially normal curvatures and of the resulting bending moments which when considering more exotic forms of surfactant aggregates are themselves functions of the normal curvatures, the mathematifor which the (curvature-dependent) interfacial free energy cal form of which depends on the particular model for the interfaplays a key role. cial bending energy that has been employed. On this basis, conclu-On the basis of earlier works of Buff (1), Murphy (2), sions can be drawn about the equilibrium shape and curvatures of an interface, e.g., for bicontinuous microemulsions and vesicles. Melrose (3), and Eliassen (4), the first rigorous treatment In addition, the pressure difference between the inside and the of this kind was presented by Boruvka and Neumann (5) in outside of surfactant-laden interfaces can be calculated. This pres-1977. Later on Kralchevsky (6) formulated an even more sure difference influences the work of formation of microemulsion general thermodynamics of curved interfaces (encompassing droplets. A section devoted to the boundary conditions has also the effect of elastic surface shear) subsequently commented been included where in particular the case of a liquid meniscus by the present authors (7).
attached to a cylindrically shaped solid surface is treated.