Stress tensor of liquid-vapor states of inhomogeneous fluids

The theory of the stress tensor of nonuniform fluids by means of density functional theory is reviewed. We present a general, symmetric, stress tensor valid for any free energy density functional with translational and rotational invariance. We specialize to the nonlocal van der Waals free energy density functional of a simple fluid and study inhomogeneous liquid-vapor coexistence states, separated by either a planar or a spherical interface. It is shown that the stress tensor contains all the information regarding the mechanical equilibrium of the state of the system. On the one hand, it leads to the expected expressions and relationships of the interfacial quantities and, on the other, it allows for a correct separation of the bulk and interfacial contributions to the free energy.