THEORY OF CURVED INTERFACES AND MEMBRANES - MECHANICAL AND THERMODYNAMICAL APPROACHES

The mechanical and thermodynamical approaches to the theory of the gen eral curved interfaces are presented and compared. In the mechanical a pproach a curved interface or membrane is characterized by the tensors of surface stresses and moments. They are connected by the surface ba lances of the linear and angular momentum. On the other hand, in the t hermodynamical approach the surface is characterized by the scalar dil ation and shear tensions as well as by the bending and torsion moments . In this review we investigate the problem about the relationships co nnecting the mechanical and thermodynamical approaches. We find that t hese two approaches are in a good agreement, that they are complementa ry to each other and represent the two parts of a self-consistent theo ry. The latter can be applied to any system where curved interfaces, t hin films or membranes are present: microemulsions, lamellar and spong e phases, lipid vesicles and cell membranes, capillary waves at interf aces, undulation and peristaltic surface forces, lateral capillary for ces between particles in thin liquid films, etc.