MINIMIZATION OF THE FREE-ENERGY OF ARBITRARILY CURVED INTERFACES

The minimization of the free energy of a two-phase system with an inte rface of arbitrary curvature leads to an extremum (Laplace) condition containing the pressure difference, Delta P, between the two sides of the interface. The expression for Delta P is a function of the normal curvatures and of the resulting bending moments which are themselves f unctions of the normal curvatures, the mathematical form of which depe nds on the particular model for the interfacial bending energy that ha s been employed, On this basis, conclusions can be drawn about the equ ilibrium shape and curvatures of an interface, e.g., for bicontinuous microemulsions and vesicles. In addition, the pressure difference betw een the inside and the outside of surfactant-laden interfaces can be c alculated. This pressure difference influences the work of formation o f microemulsion droplets. A section devoted to the boundary conditions has also been included where in particular the case of a liquid menis cus attached. to a cylindrically shaped solid surface is treated. (C) 1997 Academic Press.