Laplace's law for sharp and diffuse interfaces

Abstract

We study both diffuse and sharp liquid-vapor interfaces. The equilibrium equation of fluids is derived by using the principle of virtual work in a domain including the interfaces. For diffuse interfaces, the surface tension coefficient depends on the density profile across the interface. For sharp interfaces, the liquid-vapor layer is mathematically represented by a geometric surface and its specific energy is a Dirac delta function at the surface. We compare the both approaches and find relations between the surface tension coefficient and parameters of the models.