The present work introduces a method to treat interfaces in a multiphase flow with phase changes using the socalled Second Gradient theory introduced by Van Der Waals (1789) and later extended by Cahn and Hilliard (1958). In the prospect of simulating a full cryogenic rocket-engine ignition, the model is intrinsically designed so as to treat such flows with real gas thermodynamics for a wide range of regimes, from a subcritical two-phase flow where the capillary dynamics pilot the system through the surface tension to a supercritical fluid where such effects disappear. Its thermodynamic consistency, a key element, has been thoroughly investigated and demonstrated using canonical mono-dimensional cases. In order to reach a reasonable grid resolution, an interface thickening method has been developed, inspired by the work of Jamet et al. (2001). It allows to keep a typical direct numerical simulation (from the turbulence point of view) resolution for the interface. This method has been implemented in the code AVBP, jointly developed by CERFACS and IFPEN, and validated on two-dimensional simulations of out-of-equilibrium plane interfaces. The model has been used to simulate liquid-gas mixing layer and is currently applied to non isothermal liquid jet injection.