Micromechanical description of curved interfaces, thin films, and membranes: I. Quasistatics

Abstract

Slow quasistatic deformations of a fluid interface or membrane are investigated theoretically from a micromechanical viewpoint. The surface rate-of-strain tensor is characterized by its invariants, α and β, which account for the interfacial dilation and shear, respectively. The macroscopic interfacial stretching and shearing tensions and the bending and torsion moments are expressed through integrals over the components of the pressure tensor. The results are applied to derive the Gibbsian fundamental thermodynamic equations of an arbitrarily curved interface from the fundamental equations of the adjacent bulk phases. Then, by means of a variational principle, the conditions for interfacial mechanical equilibrium are derived.