Microscale theory of surface tension

A phenomenological model of capillarity, which accounts for the structure of the liquid-vapor layer, is successively derived assuming that the entropy of a particle depends on the internal energy, the density, and the gradient of the density. Employing classical thermodynamic principles in combination with the balance of mass, momentum, and energy, a rheological expression for capillary stresses is obtained in terms of the free energy of a liquid-vapor system. It is demonstrated that this model admits potential solutions, provided that external forces are potential and the effects of viscous dissipation of energy and heat conductivity are neglected. Moreover, it is shown that a variational principle can be formulated for potential flows, which generalizes Luke's variational principle for free-boundary inviscid flow. This model can bk applied to flows involving a topological change of the capillary interface, such as those associated with the spontaneous growth, coalescence and breakup of vaporous bubbles in a liquid.