The nonequilibrium van der Waals square gradient model. (II). Local equilibrium of the Gibbs surface

In a first paper we extended the van der Waals square gradient model for the equilibrium liquid–vapor interface to nonequilibrium systems, in which both the density and the temperature depend on position and time. In this paper, we defined and calculated the excess densities for an arbitrary choice of the dividing surface in such nonequilibrium systems. Comparing with the thermodynamic relations given by Gibbs we were then able to define a unique temperature and chemical potential of the surface. From numerical results for stationary state evaporation and condensation, we were then able to verify that the “Gibbs surface” is autonomous, i.e., in local equilibrium. Even for temperature gradients in the vapor of a million degrees per cm and evaporation and condensation fluxes up to 2 m/s, we were able to verify this property and to define a unique surface temperature. This autonomous nature of the Gibbs surface is remarkable in view of the non-autonomous nature of the continuous description in the van der Waals model. Results are presented for both the equimolar surface and the surface of tension. A discussion is given of how to transform the thermodynamic densities for the surface from one choice of the dividing surface to the other in the case that there is heat and mass flow through the surface.