Young equation interfacial tension

Young-Laplace Equation. Interfacial tension causes a pressure difference to exist across a curved surface, the pressure being greater on the concave side (i.e., on the inside of a droplet). In an interface between phase A in a droplet and phase B surrounding the droplet, the phases will have pressures and If the principal radii of curvature are Ri and R2, then... 

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

The three interfacial tensions at equiHbrium (Fig. 7) conform to Young s equation (eq. 1) where y represents soHd—gas, soHd—Hquid, and Hquid—gas interfacial tension as indicated by subscripts. 

The oil-water dynamic interfacial tensions are measured by the pulsed drop (4) technique. The experimental equipment consists of a syringe pump to pump oil, with the demulsifier dissolved in it, through a capillary tip in a thermostated glass cell containing brine or water. The interfacial tension is calculated by measuring the pressure inside a small oil drop formed at the tip of the capillary. In this technique, the syringe pump is stopped at the maximum bubble pressure and the oil-water interface is allowed to expand rapidly till the oil comes out to form a small drop at the capillary tip. Because of the sudden expansion, the interface is initially at a nonequilibrium state. As it approaches equilibrium, the pressure, AP(t), inside the drop decays. The excess pressure is continuously measured by a sensitive pressure transducer. The dynamic tension at time t, is calculated from the Young-Laplace equation... 

Figure 2 is a representation of the force balance on a Wilhelmy plate that has gone through one phase and has been wetted by a second phase. The three interfacial tensions are related to the contact angle (measured through phase 2) by the familiar Young equation... 

Detergency, or the power of a detergent product to remove soil, depends on the ability of surfactants to lower the interfacial tension between different phases. This can be explained for a typical case where removal of liquid soil is aided by surfactant adsorption onto the soil and substrate surfaces from the cleaning bath (Figure 2) using Young s equation,... 

Wettability Dependence of Detergency. The dependence of Dr on i]/ was described above. The purpose of this section will be to develop an expression for in terms of experimentally accessible interfacial tension quantities. To begin with, the TPL has a geometry as shown in Figure 7. For this system, the Young-Dupre"" equation (14-16) can be written as... 

FIG. 6.6 Components of interfacial tension needed to derive Young s equation. 

Recent theoretical studies indicate that thermal fluctuation of a liquid/ liquid interface plays important roles in chemical/physical properties of the surface [34-39], Thermal fluctuation of a liquid surface is characterized by the wavelength of a capillary wave (A). For a macroscopic flat liquid/liquid interface with the total length of the interface of /, capillary waves with various A < / are allowed, while in the case of a droplet, A should be smaller than 2nr (Figure 1) [40], Therefore, surface phenomena should depend on the droplet size. Besides, a pressure (AP) or chemical potential difference (An) between the droplet and surrounding solution phase increases with decreasing r as predicted by the Young-Laplace equation AP = 2y/r, where y is an interfacial tension [33], These discussions indicate clearly that characteristic behavior of chemical/physical processes in droplet/solution systems is elucidated only by direct measurements of individual droplets. 

This technique is based on the determination of the shape of a pendant drop that is formed at the tip of a capillary. The classical form of the Young and Laplace equation relates the pressure drop (Ap) across an interface at a given point to the two principal radii of curvature, r( and r2, and the interfacial tension (Freud and Harkins, 1929) ... 

The controlled drop tensiometer is a simple and very flexible method for measuring interfacial tension (IFI) in equilibrium as well as in various dynamic conditions. In this technique (Fig. 1), the capillary pressure, p of a drop, which is formed at the tip of a capillary and immersed into another immiscible phase (liquid or gas), is measured by a sensitive pressure transducer. The capillary pressure is related to the IFT and drop radius, R, through the Young-Laplace equation [2,3] ... 

Young s equation is the basis for a quantitative description of wetting phenomena. If a drop of a liquid is placed on a solid surface there are two possibilities the liquid spreads on the surface completely (contact angle 0 = 0°) or a finite contact angle is established.1 In the second case a three-phase contact line — also called wetting line — is formed. At this line three phases are in contact the solid, the liquid, and the vapor (Fig. 7.1). Young s equation relates the contact angle to the interfacial tensions 75, 7l, and 7sl [222,223] ... 

If the interfacial tension of the bare solid surface is higher than that of the solid-liquid interface (7s > Isl), the right hand side of Young s equation is positive. Then cos has to be positive and the contact angle is smaller than 90° the liquid partially wets the solid. If the solid-liquid... 

Young s equation is also valid if we replace the gas by a second, immiscible liquid. The derivation would be the same, we only have to replace 7l and 7sl by the appropriate interfacial tensions. For example, we could determine the contact angle of a water drop on a solid surface under oil. Instead of having a gas saturated with the vapor, we require to have a second liquid saturated with dissolved molecules of the first liquid. 

Young s equation relates the contact angle to the interfacial tensions 7s, 7l, and 7Sl-... 

The Young-Laplace equation forms the basis for some important methods for measuring surface and interfacial tensions, such as the pendant and sessile drop methods, the spinning drop method, and the maximum bubble pressure method (see Section 3.2.3). Liquid flow in response to the pressure difference expressed by Eqs. (3.6) or (3.7) is known as Laplace flow, or capillary flow. 

Wetting can be determined by contact angle measurements. It is governed by the Young equation, which relates the equilibrium contact angle 9 made by the wetting component on the substrate to the appropriate interfacial tensions ... 

Out of the parameters appearing in the Young equation, Eq. (1), only the surface tension of the liquid can be simply and accurately measured. However, the measured value of a/ can be used in the Young equation only under a certain condition, as discussed in the following. Gibbs was the first to note that the Young equation may need to be modified, even for an ideal solid surface. This is so because the three interfacial tensions may be influenced by each other at the three-phase contact line, due to the effect that one phase may... 

The other interfacial tensions appearing in the Young equation, cTs and asi, are not accessible to measurement as yet. The former is of special interest, because it is the solid surface characteristic of interest. In addition, the YCA can be measured only in very few cases that involve solid surfaces, which are close to being ideal. Thus, even if the values of 9y and ct/ are known, Eq. (1) stiU contains two unknowns. In order to elucidate Uj from the Young equation, or predict wetting behavior on a predefined solid surface, the value of asi must be known. 

Contact angles provide a unique means of determining solid-vapor and solid-liquid interfacial tensions because of the Young equation... 

In the classical treatment of surface tensions, it is intuitively assumed that the surface tension of a solid, 7s, can be assigned as if it is a material constant. In a practical sense, Eq. (25.3) is valid if the surface tension of the solid does not change after the contact with the liquid (sessile droplet) is made. While Young s equation describes the force balance at the three-phase line, it does not give information relevant to the true interfacial tension at the interface that is beneath the droplet, which is the major concern of surface dynamics. In general cases, 7s and 7sl are... 

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