Angle Youngs Equation

In Eqn (3.14), dA represents small incremental increases/decreases in the surface or interface area. Changes in the interfacial areas are given by Eqns (3.15) and (3.16), because any increase in the solid-—liquid interface is countered by a decrease in the solid—vapor interface. Substitution from these two equations in Eqn (3.14) will yield Young s equation (Eqn (3.12)). 

Most surfaces have heterogeneous composition and are not perfectly smooth. Wetting of such a surface may reach equilibrium or remain in a metastable state. In the case of an ideal surface, the addition or removal of a small volume of liquid from the drop will result in the advancement or recession of the drop. The contact 

The spreading coefficient can be measured by a tecbnique developed by Padday. In this method, it has been shown that such a sessile drop, when successively increased in volume, reaches some constant maximum height h) for a given solid-—liquid system, provided the system is aged to reach equilibrium. It has also been shown that this maximum height is related to the spreading coefficient by Eqn (3.19). In this equation, p is the density of the liquid and g is the gravitational acceleration. 

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The second approach is particularly usefid and builds on the theories of interfacial tensions (Chapter 3) and concepts of contact angle/Young equation (Chapter 4) presented previously. When these theories are applied to solid-liquid interfaces and combined with Young s... 

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes... 

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 axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

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]. 

To review briefly, a contact angle situation is illustrated in Fig. XIII-1, and the central relationship is the Young equation (see Section X-4A) ... 

In liquid-phase sintering, densification and microstmcture development can be assessed on the basis of the liquid contact or wetting angle, ( ), fonned as a result of the interfacial energy balance at the solid-liquid-vapour intersection as defined by the Young equation ... 

For the solid-liquid system changes of the state of interface on formation of surfactant adsorption layers are of special importance with respect to application aspects. When a liquid is in contact with a solid and surfactant is added, the solid-liquid interface tension will be reduced by the formation of a new solid-liquid interface created by adsorption of surfactant. This influences the wetting as demonstrated by the change of the contact angle between the liquid and the solid surface. The equilibrium at the three-phase contact solid-liquid-air or oil is described by the Young equation ... 

If Xjj is reduced by adsorption of surfactants and xs is constant, the Young equation predicts that the contact angle will be smaller, i.e., the wetting is... 

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... 

The Attachment of Air Bubbles. Particles are carried upward and are held in the froth if air bubbles can be attached to them. The adhesion of bubbles is only possible if the particle surface is sufficiently hydrophobic. The contact angle (see Appendix Chapter 4) is an important variable related to the adhesion of bubbles to solid surfaces. As shown in Fig. A.4.1, Chapter 4, and by Youngs Equation (Eq. A.4.3, Chapter 4)... 

The liquid-solid or liquidj-solid-liquidz system is both a contact angle (Young s equation) and capillary phenomena (Laplace equation). These two parameters are... 

Apply the Young equation to relate contact angle with surface energies. 

When the surface of a solid is only partially wetted by a liquid, it forms a droplet with a definite contact angle (0). The interaction of the components is expressed by the Young equation ... 

It is worth noting that if 0a and 0r are equal to the equilibrium contact angle 0, then the first component becomes zero, whereas the second component reduces to the above Equation 21.6. For more information on the difference between 0a, 0r and equilibrium contact angle given by the Young equation the reader may refer to the original works [46, 47]. 

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 ... 

Thomas Young for the contact angle of a liquid with a solid. The derivation and reliability of the Young equation has been especially well discussed in recent years (38, 44). Although I do not believe Bikerman s new treatment is sound, it is an interesting approach nevertheless. 

See also - contact angle, -> equilibrium form of crystals and droplets, - Youngs equation, - Young s rule. 

Thorough characterisation of the materials used is essential if the experimental results are to be reproducible and usable by other workers. The prime requirement is a clear specification of their compositions, with particular attention being paid to surface and interface active components that will change the energies and hence the contact angle of the system as defined by the Young equation. 

Contact angles. According to the Young equation (1.16), the equilibrium contact angle, 0Y, is a unique characteristic for each particular materials combination, determined by the surface and interfacial energies of the system... 

Introducing the Young equation into (H. 1) and setting d(<5Fs)/d(dihedral angle is lower than the value a given by ... 

Surface tensions of low-energy surfaces like many polymers are often determined from contact angle measurements. A review of the method and its application to polymer science was written by Koberstein [ 107], In equilibrium, the contact angle of a liquid drop on a solid surface is given by the Young equation ... 

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

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