The second gradient theory: a tool for the direct numerical simulation of liquid-vapor flows with phase-change

In several numerical methods dedicated to the direct numerical simulation of two-phase flows, the concept of a continuous enlarged interfacial zone is used. In this communication, it is shown that for liquid-vapor systems, it is possible to use this concept in a thermodynamic coherent way. Indeed, if it is considered that the energy of the system depends on the density gradient, this theory being called the Van der Waals or Cahn-Hilliard or more generally the second gradient theory, then it is possible to derive the equations that characterize the fluid motion within a 3-D liquid-vapor interfacial zone. Modifying the thermodynamic behavior of the fluid, it is shown that it is possible to increase the thickness of an interface, so that it can be captured by a 'standard' mesh without changing the surface tension nor loosing the thermodynamic coherence of the model. Several examples of application show that this method can be applied to study various physical problems, including contact line phenomena