Transfer coefficients for the Gibbs surface in a two-phase mixture in the non-equilibrium square gradient model

In this paper we calculate the transfer coefficients for evaporation and condensation of mixtures. We use the continuous profiles of various thermodynamic quantities through the interface, obtained in our previous works using the square gradient model. Furthermore we introduce the Gibbs surface and obtain the excess entropy production for a surface. Following the traditional non-equilibrium thermodynamic approach we introduce the surface transfer coefficients which we are able to determine from the continuous solution. The knowledge of these coefficients is important for many industrial applications which involve transport through a surface, such as for instance distillation. In our approach the values of the local resistivities in the liquid and the vapor phases are chosen on the basis of experimental values. In the interfacial region there are small peaks in these resistivities. Three amplitudes control the magnitude of these peaks. Possible values of these amplitudes are found by matching the diagonal transfer coefficients to values predicted by kinetic theory. Using these amplitudes we find that the value of the cross resistivities is 1-2 orders of magnitude higher then the one from kinetic theory. The results of both kinetic theory and molecular dynamics simulations support the existence of small peaks in the local resistivities in the interfacial region. The square gradient approach gives an independent way to determine the transfer coefficients for surfaces. The results indicate that kinetic theory underestimates the interfacial transfer coefficients in real fluids.