The Youngs Equation

There is another aspect to the fact that water forms a high contact angle on hydrophobic surfaces one cannot put a thin layer of water on a hydrophobic surface. Thin films are not stable and will spontaneously rupture (see Section 7.6.2). 

Practically, this is a pain when trying to coat hydrophobic surfaces with an aqueous solution. 

The concept of contact angle gives a notion of wettability. Zisman [2] defined spreading when 0 =0° and wetting when 0 180°. In oflier words, partial wetting occurs in most of the cases we encounter. 

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The importance of the solid-liquid interface in a host of applications has led to extensive study over the past 50 years. Certainly, the study of the solid-liquid interface is no easier than that of the solid-gas interface, and all the complexities noted in Section VIM are present. The surface structural and spectroscopic techniques presented in Chapter VIII are not generally applicable to liquids (note, however. Ref. 1). There is, perforce, some retreat to phenomenology, empirical rules, and semiempirical models. The central importance of the Young equation is evident even in its modification to treat surface heterogeneity or roughness. ... 

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 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 parameter should be unity if molecular diameters also obey a geometric mean law [193] and is often omitted. Equation X-44, if applied to the Young equation with omission of leads to the relationship [192]... 

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... 

Connected with the parameter surface tension is the wetting process of the surface, e.g. fabrics or hard surfaces. The wetting process can be described by the Young equation ... 

This wetting process may be described in terms of a balance of specific surface energies —the Young equation ... 

This equation, called the Young Equation, is in accord with the concept that the various surface forces can be represented by surface tensions acting in the direction of the surfaces. Eq. (A.4.3) results from equating the horizontal components of these tensions. 

It is clear that the above mode of computation suffers from the defect pointed out at the start of this section, in the discussion of the force proof of the Young equation (1). If the forces are supposed to cancel each other along a vertical, rather than a horizontal, projection, then the relation obtained... 

The third relation needed is Eq. (73) the carbide was immersed in liquid uranium metal. The fourth was a compromise between the Young equation (1) and Eq. (75) in that cos a of the latter was implicitly equated to unity, so that... 

This important result is called the Young equation. It can also be derived by simply considering the horizontal resolution of the three surface tensions (i.e. as forces per unit distance), via standard vector addition (Figure 2.18). However, what becomes of the vertical component This force is actually balauced by the stresses in the solid around the drop perimeter (or TPL), which can actually be visually observed on a deformable substrate, such as paraffin wax. 

Figure 2.18 Balance of energies at the TPL gives the Young equation directly.

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

The Young Equation. The principle of balancing forces used in the derivation of the Laplace equation can also be used to derive another important equation in surface thermodynamics, the Young equation. Consider a liquid droplet in equilibrium... 

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. 

Figure 1.4. Displacement of a triple line around its equilibrium position that allows derivation of the Young equation. Only a small region close to the triple line is taken into account to neglect the...

The actual TL configuration observed after a certain time of contact between the solid and liquid phases depends on the scale of observation and on the relative rates of two processes (i) the movement of TL over large distances to satisfy the Young equation and (ii) the distortion of TL to satisfy locally the more general Smith equation. The kinetics of the two movements may be very different. 

Real solid surfaces never satisfy completely the conditions for the Young equation to be valid, namely chemical homogeneity and perfect smoothness. Several phenomena result from this deviation, most importantly ... 

The quantity (surface energy change when a S/V surface of unit area is replaced by a S/L interface of equal area by immersion of a solid in a liquid. In both the immersion and capillary rise processes, S/V and S/L areas change but the total L/V surface remains constant. Using the Young equation (1.16), Wf and ze can be written ... 

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... 

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