Slow evaporation and condensation

In a previous paper an explicit condition for the jump coefficients in a one-component fluid was found within the context of non-equilibrium thermodynamics for the occurence of, on the one hand, an inverted temperature profile in the vapor phase between an evaporating and a condensing liquid surface and of, on the other hand, the supersaturation of the vapor close to the evaporating surface. By making comparisons with the kinetic theory description in the vapor phase we obtained explicit expressions for these jump coefficients. Using these expressions, the conditions found using non-equilibrium thermodynamics reduced to those given in the context of kinetic theory for these phenomena. For a fluid that obeys Trouton's rule, as most fluids do, the conditions were found to be satisfied. In the present paper we analyse how a low concentration of dissolved material modifies this situation. For this purpose, the jump conditions for the temperature, the chemical potentials and the pressure are formulated for a multicomponent system in the context of non-equilibrium thermodynamics. Explicit conditions for the occurence of supersaturation and an inverted temperature profile are then given in terms of the jump coefficients. It is found that the inverted temperature profile and supersaturation no longer occur under the same conditions. A comparison is made with the results from kinetic theory, which makes it possible to give explicit expressions for these jump coefficients. We then find that the inverted temperature profile will already disappear for concentrations of dissolved material of the order of the mean-free path divided by the typical size of the system while supersaturation occurs under essentially the same conditions as in the one-component system. The disappearance of the inverted temperature profile is related to the build-up of the concentration of dissolved material near the condensing surface and the corresponding temperature increase.