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Transport Coefficients for Liquid-Vapor Transition

Jean-Marc Simon1, Jing Xu2, Signe Kjelstrup2, Dick Bedeaux2, and Eivind Johannessen3. (1) Chemistry - Laboratoire de Recherches sur la Réactivité des Solides (UMR 5613 CNRS), Université de Bourgogne, 9, avenue Alain Savary, Dijon, 21000, France, (2) Chemistry, Norwegian University of Science and Technology (NTNU), Trondheim, 7491, Norway, (3) Delft University of Technology, Department of Chemical Technology, Julianalaan 136, Delft, 2628BL, Netherlands

In spite of the technical importance of vapor-liquid phase transitions, little is known on the interface resistance to transport. Bedeaux and Kjelstrup [1] showed that it was possible to define transfer coefficients for the interfacial region from the theory of non-equilibrium thermodynamics for surfaces [1]. It was shown, that the commonly used flux-force relations at the surface do not obey the second law. The coupling between heat and mass transport was furthermore large. The coefficient, that describes this coupling, is neglected in most descriptions of evaporation and condensation [2]. The main results of these new developpements will be presented and illustrating using non-equilibrium molecular dynamics (NEMD).

Surface transfer coefficients in general, and coupling coefficients in particular are hardly known. They can be calculated using kinetic theory but practical needs, like modeling of distillation columns, demand realistic coefficients for non-ideal systems. In this study we used non-equilibrium molecular dynamics simulations to obtain them. We simulated n-octane and argon liquid-vapour interfaces at different temperatures and applied constant energy fluxes throughout these systems following the procedure described in [3, 4]. After a short equilibration period of around 100 picoseconds, the system reached a stationnary state with a non-zero gradient of temperature across the simulation cell, see figure 1 for n-octane. A temperature jump is observed inside the surface area on the gas side of the surface that leads to an excess surface heat resistivity.

For these systems the heat, the mass transfer resistivities and the heat of transfer, which quantify the coupling between the transport of heat and mass, were calculated. They all show an increase of their values with the surface tension of the surface. The heat of transfer is particularly large, it is of the order of the heat of vaporization. The contributions to the heat flux from the heats of transfer will then automatically be large as soon as there is a substantial mass flux. When the heat of transfer is neglected in the transport equations, large errors may therefore arise in the heat flux, and consequently in the mass flux.

[1] Bedeaux, D., Kjelstrup, S. Heat, Mass and Charge Transport and Chemical Reactions at Surfaces, Int. J. Thermodynamics, 2005; 8: 25-41.

[2] Taylor, R. and Krishna, R. Multicomponent Mass Transfer, Wiley, New York, 1993.

[3] Simon, J.-M., Kjelstrup, S., Bedeaux, D., Hafskjold, B. Thermal flux through a surface on n-octane. A non-equilibrium molecular dynamics study. J. Phys. Chem. B, 2004; 108: 7186-7195

[4] Xu, J., Kjelstrup, S., Bedeaux, D., Røsjorde, A., and Rekvig, L., Verification of Onsager's reciprocal relations for evaporation and condensation using non-equilibrium molecular dynamics, Journal of Colloid and Interface Science, 2006, in print.

Figure 1- Temperature profile across the simulation box for five n-octane simulated systems with different temperatures and submitted to different heat fluxes. The liquid phase is located on the right side while the gas phase is on the left, the surface extend is located by a rectangle.