Vapour Interface

The direct measurement of adsorption in this case is not always easy. Thus for a system containing a liquid/vapour interface the two terms in equation (AIII.5) arc nearly equal and a very highly precise analytical technique is needed to obtain reasonably accurate results. One way in which this problem can be reduced is seen by rewriting equation (AIII.5), for a binary solution, and neglecting the concentration in the vapour phase  

If fT/ is very small, then, since for a given intcrfacial area nfu is independent of the amount of liquid taken, the term in square brackets must be proportionally larger and hence rneasurcable 

Similar considerations apply to the liquid/liquid interface. 

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Surface waves at an interface between two innniscible fluids involve effects due to gravity (g) and surface tension (a) forces. (In this section, o denotes surface tension and a denotes the stress tensor. The two should not be coiifiised with one another.) In a hydrodynamic approach, the interface is treated as a sharp boundary and the two bulk phases as incompressible. The Navier-Stokes equations for the two bulk phases (balance of macroscopic forces is the mgredient) along with the boundary condition at the interface (surface tension o enters here) are solved for possible hamionic oscillations of the interface of the fomi, exp [-(iu + s)t + i V-.r], where m is the frequency, is the damping coefficient, s tlie 2-d wavevector of the periodic oscillation and. ra 2-d vector parallel to the surface. For a liquid-vapour interface which we consider, away from the critical point, the vapour density is negligible compared to the liquid density and one obtains the hydrodynamic dispersion relation for surface waves + s>tf. The temi gq in the dispersion relation arises from... 

The non-consen>ed variable (.t,0 is a broken symmetry variable, it is the instantaneous position of the Gibbs surface, and it is the translational synnnetry in z direction that is broken by the inlioinogeneity due to the liquid-vapour interface. In a more microscopic statistical mechanical approach 121, it is related to the number density fluctuation 3p(x,z,t) as... 

Holcomb C D, Clancy P and Zollweg J A 1993 A critical study of the simulation of the liquid-vapour interface of a Lennard-Jones fluid Mol. Phys. 78 437-59... 

As with all thermodynamic relations, the Kelvin equation may be arrived at along several paths. Since the occurrence of capillary condensation is intimately, bound up with the curvature of a liquid meniscus, it is helpful to start out from the Young-Laplace equation, the relationship between the pressures on opposite sides of a liquid-vapour interface. 

Hua Li, Nai-Ben Ming. Significance of many-body interactions in Monte Carlo simulation of crystal-vapour interface. Solid State Commun 707 351, 1997. 

In the design of a cooler-condenser for a mixture of vapour and a permanent gas, the method of Colburn and Hougen(66) is considered. This requires a point-to-point calculation of the condensate-vapour interface conditions T( and P . A trial and error solution is required of the equation ... 

Kxnv Nucleus edge-vapour interface tension... 

Figure 2.10 Schematic diagram showing that the equilibrium vapour pressure changes with the curvature of the liquid-vapour interface.

For some applications flat heat pipe panels (HPP) have advantages over conventional cylindrical heat pipes, such as geometry adaptation, ability for localized heat dissipation and the maintenance of an entirely flat isothermal surface (Fig. 14). The liquid-vapour interface formed in capillary channels inside the heat pipe panel is capable to generate self-sustained thermally driven oscillations. Thin layer (several mm) of the sorbent between mini-fins on the outer side of the heat pipe panel ensures an advanced heat and mass transfer during the cycle adsorption/de sorption. 

The ratio dA/dN is a geometric quantity, determined by the curvature of the adsorbate/vapour interface. When dealing with a concave hemispherical meniscus of the capillary condensed liquid in a cylindrical tube, it can easily be calculated that... 

Two intermediate levels deserve consideration, depending on the pre-coverage of the solid surface. If the solid surface has adsorbed less than a liquid film, then the surface excess energy is located at the solid-vapour interface, Ua (SG), and it can be written (always assuming the adsorbent to be inert) ... 

Spreading wetting is a process in which a drop of liquid spreads over a solid substrate (the liquid and solid being previously in equilibrium with the vapour). Here, the solid-vapour interface is replaced by two new interfaces (solid-liquid and liquid-vapour) of same area. 

The few investigators who have attempted to use the original Harkins-Junt method have encountered a number of inherent difficulties. A major problem is that it is virtually impossible to avoid some interparticle capillary condensation as p/p° —+ 1. This inevitably reduces the extent of the available liquid-vapour interface (Wade and Hackerman, 1960), Moreover, the thickness of a pre-adsorbed film as p/p° — 1 is highly dependent on the shape, size and roughness of the particles. 

The question of the constancy of the surface tension in porous media has been under consideration for many years and has been taken up again recently by Grown et al. (1997). Formerly, it was thought that for a concave liquid-vapour interface the surface tension should increase with increased curvature. The experimental findings that the hysteresis critical temperature is generally appreciably lower that the bulk critical temperature (see Section 7.5) is considered to be a strong indication that the surface tension of a capillary-condensate is reduced below the bulk value. More work on model pore structures is evidently required to settle this question. 

With a drop of liquid in contact with a solid (Figure C2-7), there are three interfaces the solid/liquid the solid/vapour and the liquid/vapour interfaces. Each of these has its own interface tension. For a drop that partially wets a solid, the horizontal components of the interface tensions must be in equilibrium. This determines the value of the contact angle 0... 

A small contact angle implies that the drop spreads over the surface if the contact angle is zero, the surface will be wetted completely (Figure C2-8). This happens when the solid/vapour tension is much larger than the solid/liquid tension the system then avoids any solid/vapour interface. If the contact angle is equal to Jt, there is no wetting. This happens when the solid/liquid tension is much higher than the solid/vapour tension. The system then minimizes the liquid/vapour interface, as with a drop of mercury on paper. 

The substrate also has a role to play in the evaporation of a droplet, with the evaporation rate of droplets being limited by the substrate s thermal properties this is especially the case for high evaporation rates. When a droplet is deposited onto a substrate, two extreme cases can occur. If the substrate is a perfect thermal insulator then the evaporation rate is altered by changes in the droplet-vapour interface area. However, if the substrate is a perfect thermal conductor then the evaporation rate is also affected by a second mechanism, namely the heat transfer between the substrate and the droplet. In this second situation, the evaporation rate is higher than that of a droplet sitting on a thermal insulator. 

In the case of a liquid/vapour interface it is straightforward to reduce the above procedure of approximating the inhomogeneous direct correlation functions Cayivi, F2) given by Equations (19)-(20) and (23)-(26) to the non-linear interpolation between two phases, vapour and liquid. 

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