Abstract
Interfacial physics is a rich area of study with many practical manifestations and significant complexity inherent in the underlying two-dimensional 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 microemulsions. Any theoretical study of this behaviour must begin with a characterization of both the shape and energetic state of the interface. 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 various “curvature measures” that have historically been employed to evaluate the degree of surface bending, and their relationship to both the generalized theory of capillarity and the form of the corresponding equilibrium conditions (e.g. the Young-Laplace equation of capillarity).
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