MICROSCALE THEORY OF SURFACE-TENSION

A phenomenological model of capillarity, which accounts for the struct ure of the liquid-vapor layer, is successively derived assuming that t he entropy of a particle depends on the internal energy, the density, and the gradient of the density. Employing classical thermodynamic pri nciples 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 t his model admits potential solutions, provided that external forces ar e potential and the effects of viscous dissipation of energy and heat conductivity are neglected. Moreover, it is shown that a variational p rinciple can be formulated for potential flows, which generalizes Luke 's variational principle for free-boundary inviscid flow. This model c an bk applied to flows involving a topological change of the capillary interface, such as those associated with the spontaneous growth, coal escence and breakup of vaporous bubbles in a liquid.