DIFFERENTIAL GEOMETRIC-THEORY OF CAPILLARITY

Interfacial physics is a rich area of study with many practical manife stations and significant complexity inherent in the underlying two-dim ensional behaviour. For example, structures formed from aggregates of self-assembled amphiphiles may show a variety of forms and properties ranging from ordered arrays of micelles to disordered, bicontinuous mi croemulsions. Any theoretical study of this behaviour must begin with a characterization of both the shape and energetic state of the interf ace. Often one has terms in the energy that depend on both the area (e .g. surface tension) and the curvature. We present a review of the var ious ''curvature measures'' that have historically been employed to ev aluate the degree of surface bending, and their relationship to both t he generalized theory of capillarity and the form of the corresponding equilibrium conditions (e.g. the Young-Laplace equation of capillarit y).