Solid vapor interface, contact angle

Equation (10.18) was derived for capillary rise or depression assuming complete wetting, that is, 6 = 180°. In the case of contact angles greater than 0° and less than 180°, equation (10.18) must be modified. As liquid moves up the capillary during capillary rise the solid-vapor interface disappears and the solid-liquid interface appears. The work required for this process is... 

Contact angle — The contact angle is the angle of contact between a droplet of liquid and a flat rigid solid, measured within the liquid and perpendicular to the contact line where three phases (liquid, solid, vapor) meet. The simplest theoretical model of contact angle assumes thermodynamic equilibrium between three pure phases at constant temperature and pressure [i, ii]. Also, the droplet is assumed to be so small that the force of gravity does not distort its shape. If we denote the - interfacial tension of the solid-vapor interface as ysv. the interfacial tension of the solid-liquid interface as ySL and the interfacial tension of the liquid-vapor interface as yLV, then by a horizontal balance of mechanical forces (9 < 90°)... 

Contact angle measurements provide information on the wettability of the sample, the surface energetics of the solid, and the interfacial properties of the solid-liquid interface. The samples were immersed in water and captive air and octane bubbles were determined by measuring the bubble dimensions. By measurement of both air and octane contact angles the surface free energy (.y) of the solid-vapor ( > ) interface may be calculated by use of Young s equation and the narmonic mean hypothesis for separation of the dispersive and polar components of the work of adhesion. This method for determination of surface and interfacial proper-... 

A captive air (or other gas) bubble is formed in the liquid contacting with the solid by means of an inverted micrometer syringe beneath the substrate which is kept in the test liquid. The contact angle is measured by means of a goniometer microscope or video camera. In this method, the solid-vapor interface is in equilibrium with the saturated vapor... 

The shape of the curved surface, in turn, allows one to determine the surface tension of the liquid when it is in equilibrium with its own vapor or to determine the interfacial tension if the droplet is in contact with a different substance (gas, liquid, or solid). The interfacial tension is determined by measuring the contact angles at the liquid-solid and solid-vapor interfaces. The contact angle is defined in Figure 3.11, which shows a typical liquid-solid interface. 

Let us assume that in the absence of surfactant the drop forms an equilibrium contact angle above If the water contains surfactants then three transfer processes take place from the liquid onto all three interfaces surfactant adsorption at both (i) the inner liquid-solid interface and (ii) the liquid-vapor interface, and (iii) transfer from the drop onto the solid-vapor interface just in front of the drop. Adsorption processes (i) and (ii) result in a decrease of corresponding interfacial tensions, and y. The transfer of surfactant molecules onto the solid-vapour interface in front of the drop results in an increase of a local free energy, however, the total free energy of the system decreases. That is, surfactant molecule transfer ii) goes via a relatively high potential barrier and, hence, goes considerably slower than adsorption processes (i) and (ii). Hence, they are "fast" processes as compared with the third process (iii). 

All three surfaetant transfer processes are favorable to spreading, as they result in both an increase of the spreading power, ysv - y- ysi, and, hence, a decrease of the contact angle (Fig. 5). As it was mentioned above, the transfer of surfactant molecules from the drop onto the solid-vapor interface in front of the drop results in an increase of local surface tension, y. Hence, it is the slowest process that will be the rate determining step. Let us define the initial contact angle by... 

For a drop of liquid in equilibrium on a solid surface. Young s equation relates interfacial tensions at the solid/vapor interface yi, Uquid/vapor interface 72, and solid/liquid interface Y12, with the contact angle 0, which is a measure of the degree of wetting and takes a value of zero for ideal wetting... 

Consider now a wet gel with pores that are assumed, for simplicity, to be cylindrical. If evaporation occurs to expose the solid phase, a solid-liquid interface is replaced by a solid-vapor interface. If the liquid wets the solid (i.e., the contact angle 0 < 90°), then as seen from Fig. 5.19, ysv > Isl- The exposure of the solid phase would lead to an increase in the energy of the system. To prevent this, liquid tends to spread from the interior of the gel to cover the solid-vapor interface. (This is analogous to the example of liquid flow up a capillary tube discussed earlier.) Since the volume of the liquid has been reduced by evaporation, the meniscus must become curved, as indicated in Fig. 5.20. The hydrostatic tension in the liquid is related to the radius of curvature r of the meniscus by... 

Surface energy is most commonly quantified using contact angle goniometry. Wetting is quantitatively defined with reference to a liquid droplet resting on a solid surface, as shown in fig. 7.5. The tensions at the three-phase contact point are indicated such that SW represents the solid/vapor interface, LA is the liquid/vapor... 

This expression makes it possible to obtain solid surface information by making independent contact angle measurements using liquids with known dispersive and polar contributions to O. The surface tension of the solid-vapor interface can be calculated from the slope and the ordinate intercept in plots following Equation 5.12. Alternative approaches based on the Wilhelmy plate method (Wilhelmy, 1863) and variations thereof have been reported recently. 

Schematic illustration of heterogeneous nucleation. If the contact angle, B, between the crystal, liquid, and inclusion is small, less energy is expended in creating the surface of the nucleus. Nucleation at the exterior surface is unfavorable, because it requires formation of a solid-vapor interface with a high specific energy (yLv)-...

The unequal adsorption to the liquid-vapor and solid-liquid interfaces has been the subject of several studies [34,36,38]. In contrast to Bemett and Zisman [33], Pyter et al. [34] explained the different wetting characteristics of hydrocarbon surfactants and fluorinated surfactants by low adsorption of fluorinated surfactants on nonpolar solids. The higher contact angles exhibited by solutions of fluorinated surfactants on polyethylene were explained by poor adsorption of fluorinated surfactants instead of the strong adsorption proposed by Bemett and Zisman [33]. 

Adam has listed two additional causes of contact angle hysteresis. One is physical interaction between the fluid and the solid. In the case of water, this would take the form of hydration, dissolution, or possible deposition of soluble contaminants. The other cause is chemical interaction between the liquid and solid. Thus, with water it could be hydrolysis or water-induced decomposition. In both cases, the solid surface in contact with water changes so that the receding contact angle is now defined by a different solid-vapor interface. 

We have shown that the difference between charge densities located at the solid-liquid and solid-vapor interfaces is given by the variation in adhesion tension, or more specifically of the cosine of the contact angle, with respect to the potential difference across the interface ... 

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. 

The fluid phase that fills the voids between particles can be multiphase, such as oil-and-water or water-and-air. Molecules at the interface between the two fluids experience asymmetric time-average van der Waals forces. This results in a curved interface that tends to decrease in surface area of the interface. The pressure difference between the two fluids A/j = v, — 11,2 depends on the curvature of the interface characterized by radii r and r-2, and the surface tension, If (Table 2). In fluid-air interfaces, the vapor pressure is affected by the curvature of the air-water interface as expressed in Kelvin s equation. Curvature affects solubility in liquid-liquid interfaces. Unique force equilibrium conditions also develop near the tripartite point where the interface between the two fluids approaches the solid surface of a particle. The resulting contact angle 0 captures this interaction. 

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