The Statics of Fluid Films with Bending Stiffness

Abstract

Based on the principles of rational mechanics, a general formulation for the bending of a fluid monolayer is given. The internal forces of the surface turn out to be by far more copious than for the classical theory of capillarity, in which case the energy density is independent of the local curvature. There are two striking consequences of the investigation: the membrane forces are not isotropic and hence cannot be characterized by one single surface tension and the tangential component of the surface force must vanish if no torque density acts on the surface. The results should be noted in the study of amphiphiles.