Multi-component interfacial transport as described by the square gradient model: evaporation and condensation.

Abstract

The aim of this thesis is to build a theoretical approach which allows to describe the behavior of fluid during evaporation and condensation in multicomponent systems. We consider isotropic non-polarizable mixtures. We have developed the description of the surface using continuous non-equilibrium thermodynamics and established the link to the macroscopic non-equilibrium thermodynamics of surfaces, which uses excess densities and fluxes. The present analysis for the mixture’s surface generalizes the equilibrium square gradient model and the non-equilibrium description of one-component systems.

The thesis is based on four articles. Within this work we have addressed three major issues. First, we have established an analytical continuous description of an interfacial region between two different phases of a mixture under nonequilibrium conditions. Next, we have verified numerically the possibility to describe the non-equilibrium surface as a separate phase. Finally, we have investigated the connection between transport properties of a mixture inside an interfacial region and those for the whole surface, both analytically and numerically.

Within the continuous approach we have gone through a number of steps. First, the equilibrium thermodynamic behavior in the interfacial region was established. We used the square gradient theory as a model which describes thermodynamic phenomena in the interfacial region. It has been widely used for one-component equilibrium systems and has been extended to mixture interfaces. Next, we extended the description to non-equilibrium. The nonequilibrium Gibbs relation has been postulated and we discussed how the gradient theory motivates the chosen form of this equation. The expression for the entropy production, which gives one information about the measure of the irreversibility everywhere in the interfacial region, has been obtained. We have discussed how the gradient description breaks the three-dimensional  isotropy of a mixture inside the interface. The resulting linear laws relating the forces and the fluxes were given. Having this approach established we have gotten the complete continuous description of a two-phase mixture under nonequilibrium conditions. The theory was applied to and solved for a particular mixture of cyclohexane and were discussed and resulting profiles of various thermodynamic quantities were obtained.

Another focus of the thesis was to make a link to the macroscopic description of transport through a surface. Within this approach a surface in non-equilibrium is treated as a separate phase which has its own thermodynamic properties, such as the temperature or the excess density. This hypothesis is called local equilibrium of a Gibbs surface. This is a simplifying assumption about the behavior of real systems which is physically elegant. With the help of the continuous gradient description we have verified the hypothesis of local equilibrium of a surface for a binary mixture.

The macroscopic approach uses interfacial resistances to heat and mass transfer through the surface as parameters of the theory. The continuous description allowed us to obtain these coefficients directly and gave insight of the nature of these coefficients. With the help of the continuous description we obtained the excess entropy production of the whole surface and the resulting linear laws. The interfacial resistances have been evaluated both numerically and with the help of derived integral relations. By comparison with results from kinetic theory it was shown that the continuous resistivity profiles have a peak in the interfacial region. We have also shown that the interfacial resistances depend among other things on the enthalpy profile across the interface. The enthalpy of evaporation is one of the main differences between liquid and vapor phases and therefore the interface is important for the resistance to heat and mass transfer

n-hexane. The details of the numerical procedure