Vapor-liquid interface, perturbation

Tarazona and Navascues have proposed a perturbation theory based upon the division of the pair potential given in Eq. (3.5.1). In addition, they make a further division of the reference potential into attractive and repulsive contributions in the manner of the WCA theory. The resulting perturbation theory for the interfacial properties of the reference system is constructed through adaptation of a method developed by Toxvaerd in his extension of the BH perturbation theory to the vapor-liquid interface. The Tarazona-Navascues theory generates results for the Helmholtz free energy and surface tension in addition to the density profile. Chacon et al. have shown how the perturbation theories based upon Eq. (3.5.1) may be developed by a series of approximations within the context of a general density-functional treatment. 

As we stated at the beginning of this section, most of the work in this area has focused upon the study of molecular orientation at the liquid-vapor interface and how this is affected by details of the intermolecular forces. Thompson and Gubbins have carried out molecular dynamics simulations of the vapor-liquid interface for homonuclear 12-6 diatomic molecules and for such molecules with point-charge quadrupoles. They find that in the case of the nonpolar molecules, there is a tendency for molecules in the liquid to align perpendicular to the surface and those in the vapor to align parallel to the surface. The addition of a quadrupole to the 12-6 diatomic " reverses this effect. A study of the vapor-liquid interface for an interaction site model of -octance leads to similar conclusions as for the nonpolar diatomic. These effects are reproduced qualitatively by all the theoretical approximations, with the exception of the influence of the quadrupole, which can only be predicted at first order within the context of the perturbation theory based upon division of the Mayer function Eq. (3.5.2). 

The onset of flow instability in a heated capillary with vaporizing meniscus is considered in Chap 11. The behavior of a vapor/liquid system undergoing small perturbations is analyzed by linear approximation, in the frame work of a onedimensional model of capillary flow with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes on the flow stability is studied. A scenario of a possible process at small and moderate Peclet number is considered. The boundaries of stability separating the domains of stable and unstable flow are outlined and the values of the geometrical and operating parameters corresponding to the transition are estimated. 

The wall heat flux is the cause for the liquid evaporation, and perturbation of equilibrium between the gravity and capillary forces. It leads to the offset of both phases (heated liquid and its vapor) and interface displacement towards the inlet. In this case the stationary state of the system corresponds to an equilibrium between gravity, viscous (liquid and vapor) and capillary forces. Under these conditions the stationary height of the liquid level is less than that in an adiabatic case... 

Orientational structure at a liquid vapor-interface of diatomic interaction site fluids has been studied extensively by Gubbins and Thompson using both thermodynamic perturbation theory and molecular dynamics simulation, and by Tarazona and Navascues using perturbation theory. Chacon et al. have applied density-functional theories to these systems. The theoretical methodology and results are reviewed in a comprehensive article by Gubbins, to which the reader is directed for more complete details. 

In a situation compatible with the lubrication approximation, perturbations due to the proximity of a solid surface are weak. In this case, the translational invariance of an unbounded two-phase system is weakly broken, and both the shift of the equilibrium chemical potential due to interactions with the solid surface and the deviation from the zero-order density profile are small. Since molecular interactions have a power decay with a nanoscopic characteristic length, this should be certainly true in layers exceeding several molecular diameters. A necessary condition for the perturbation to remain weak even as the liquid-vapor and liquid-solid interfaces are drawn together still closer, as it should happen in the vicinity of a contact line, is smallness of the dimensionless Hamaker constant % = asps/p — 1- Even under these conditions, the perturbation, however, ceases to be weak when the density in the layer adjacent to the solid deviates considerably from p+. This means that low densities near the solid surface are strongly discouraged thermodynamically, and a... 

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