Solid-vapor interfacial

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

T Solid-vapor interfacial energy dyn/cm dyn/cm z Pow der shear stress kg/cm psf... 

A drop of liquid at rest on a solid surface is under the influence of three forces or tensions. As shown in Fig. 10.2, the circumference of the area of contact of a circular drop is drawn toward the center of the drop by the solid-liquid interfacial tension, 7sl- The equilibrium vapor pressure of the liquid produces an adsorbed layer on the solid surface that causes the circumference to move away from the drop center and is equivalent to a solid-vapor interfacial tension, ygy- The interfacial tension between the liquid and vapor, y y, essentially equivalent to the surface tension y of the... 

The three interfacial surface energies, as shown at the three-phase junction in Figure 2.29, can be used to perform a simple force balance. The liquid-solid interfacial energy plus the component of the liquid-vapor interfacial energy that lies in the same direction must exactly balance the solid-vapor interfacial energy at equilibrium ... 

Fig. 14. Schematic illustration of a drop ofliquid spreading in contact with a solid surface, showing the relations between the relevant parameters the contact angle, 0 the solid/vapor interfacial free energy, Ysv the liquid/vapor interfacial free energy, yLV and the solid/liquid interfacial free energy, ySL. Young s equation describes the relationship between these parameters for a stationary drop at thermodynamic equilibrium [175]...

In this Young s expression, the solid-vapor interfacial tension, ysv is the surface tension of the solid in equilibrium with the vapor of the wetting liquid. If ys is the surface tension of the solid against its own vapor or in vacuum, then [72]... 

Viscous sintering is a process of densification driven by interfacial energy (81). Material moves by viscous flow in such a way as to eliminate porosity and thereby reduce the solid-vapor interfacial area. The rate of viscous sintering is proportional to the surface area and inversely propor-... 

The large surface area of the dried gel. A xerogel has a solid/vapor interfacial area of 100-1000 m /g. Reduction of the surface area provides a driving force for densification. 

The Wenzel Eq. (21) was derived by assuming that the roughness increases the surface solid/liquid and solid/vapor interfacial tensions by the factor r, the surface roughness coefficient, so that the effective interfacial tensions become ry L Tsv and by direct substitution into Young s equation yields,... 

If the densification of liquid-phase sintering is achieved due to the viscous flow of a liquid that is able to fill up the pore spaces between the solid grains, it is called vitrification [112-114]. The driving force for vitrification is the reduction of solid-vapor interfacial energy, because the flow of the liquid covers the surfaces of the solid. Traditional clay-based ceramics are usually densified through vitrification. However, it is very unlikely to be observed in the processing of transparent ceramics, because the content of liquid phase must be controlled to a limited level. 

The analysis shows that the pores in the simple model fill sequentially. If we extend the results to the more complex situation of a powder compact with a distribution of pore sizes, the same behavior of sequential filling of the pores is expected to occur. The pores with the smallest coordination number will be the first to fill because such pores have high surface to volume ratio, so a given volume of liquid eliminates more solid-vapor interfacial area. If there is sufficient liquid, the pores with higher coordination number start to fill. However, the pore filling leads to a percolation problem, and the liquid might not have access to all small pores, so some may be empty while large pores start to fill. 

Liquid/vapor interfacial tension Solid/vapor interfacial tension Curvature ( = 1/r)... 

This appendix presents computation of resultant solid/liquid and solid/vapor interfacial tensions from the methanol/water binary mixture bubble point data from Chapter 4. Governing equations are presented for deriving the Langmuir isotherms for the S/L and S/V data. The goodness of fits are also discussed for both cases. 

FIGURE D.1 Solid/Vapor Interfacial Tension as a Function of Liquid/Vapor Interfacial Tension for Binary Methanol/ Water and Stainless Steel 304 System. 

The bubble point tests conducted in methanol/water mixtures were worked up to show properties of the three-phase interfaces along the complex contact line in SS304 LAD screens. In particular, the variation with F2 of the solid/vapor interfacial tension /sv differed from that of the solid/liquid interface j/sl- The data are consistent with the Langmuir isotherm description of the thermodynamics of adsorption. The result of the analysis is that the co-areas Amin are 0.32 nm /molecule for the SS304— vapor interface and 1.77 nm /molecule for the SS304—solution interface. This implies that that methanol molecules form a dense, liquid-like monolayer at the interface of SS304 with the vapor phase, while the methanol molecules are very dilute in the interface between SS304 and the solution of methanol/water. 

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