Definition of Contact Angle

Fig. 4. Definition of contact angle showing the derivation of Young s equation, Eq.. 8, using a balance of horizontal forces at the three-phase interline.

Fig. 2. Definition of contact angle c of a liquid droplet on a solid surface.

As mentioned in Section 6.1a, surface tension and contact angle determine wetting phenomena we examine this in Section 6.6. We take a closer look at the definition of contact angle and some complications associated with it in Section 6.7. 

A quantity that is closely related to surface tension is the contact angle. The contact angle 0 is defined as the angle (measured in the liquid) that is formed at the junction of three phases, for example, at the solid-liquid-gas junction as shown in Figure 6.2b. Although the surface tension is a property of the two phases that form the interface, 0 requires that three phases be specified for its characterization, as mentioned above. The above definition of contact angle is, however, highly simplified, and we take a more in-depth look at the concept later in this chapter. 

Definition of contact angle at the solid-liquid interface. 7ig denotes the liquid-the solid-liquid interfacial energy, and 7., denotes the... 

Figure 12 3. Definition of contact angle d and the interfacial surface tensions 75/ (solid / liquid), 7/v (liquid/vapor), and 75V (solid/vapor).

Derivation of Young s Equation and Definition of Contact Angle... 

Fig. 1. Definition of contact angle for wetting tests of adhesives.

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 angle will return to its equilibrium value. In the case of a surface that may contain roughness and heterogeneity, there is a delay in the movement of the liquid drop in response to the addition or removal of liquid. This phenomenon, called hysteresis, requires a revision of the definition of contact angle. 

FIGURE 13.7 Definition of contact angle (6 ) for liquid droplet on a surface. 

Measurement of contact angles hysteresis. The experimental determination of contact angles is complicated by two factors first, that the angle depends on the surface tension of the liquid surface second, that the angle is rarely definite, but may have any value between two extremes, according as the liquid is tending to advance over a dry surface, or to recede from a previously wetted one. 

The variation of contact angle with orientation of surface planes can be understood by considering the Young-Dupre equation and the definition of Wa based on the simple model of Section 1.1 ... 

Definition, Young s Equation and Use of Contact Angles in Industry... 

Figure 14-1. Definition of the angle of incidences and angle of refraction j8 for light incident on a homogeneous plate with plane parallel sides, and if the two sides are in contact with the...

Figure 7.12. Definitions of different types of contact angles (a) intrinsic contact angle, Om , (b) actual contact angle, 0ac (c) apparent contact angle, 0ap (from ref. (8)), with permission from Elsevier Science...

According to the definition of line tension (2.222), it is determined by the equilibrium liquid profile in the transition region from the thin flat liquid interlayer to the bulk surface of bubbles. Note that in the case of partial wetting, which is under consideration, the static hysteresis of contact angle (see Chapter 3, Section 3.10) is unavoidable. The latter phenomenon can substantially influence the comparison. 

It is observed that in most instances a liquid placed on a solid will not wet it but remains as a drop having a definite angle of contact between the liquid and solid phases. The situation, illustrated in Fig. X-2, is similar to that for a... 

The preceding definitions have been directed toward the treatment of the solid-liquid-gas contact angle. It is also quite possible to have a solid-liquid-liquid contact angle where two mutually immiscible liquids are involved. The same relationships apply, only now more care must be taken to specify the extent of mutual saturations. Thus for a solid and liquids A and B, Young s equation becomes... 

There are some subtleties with respect to the physicochemical meaning of the contact angle equation, and these are taken up in Section X-7. The preceding, however, serves to introduce the conventional definitions to permit discussion of the experimental observations. 

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