Contact angles definitions

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. 

Roll-up. The principal means by which oily soil is removed is probably roU-up. The appHcable theory is simply the theory of wetting. In briefest outline, a droplet of oily soil attached to the substrate forms at equiUbrium a definite contact angle at the oil-sohd-air boundary line. This contact angle (Fig. 4) is the result of the interaction of interfacial forces in the three phase boundaries of the system. These interfacial forces, expressed in mN/m(= dyn/cm), or interfacial free energy values expressed in mj/m (erg/cm s) are conveniently designated 1SA iSlj subscripts relate to the Hquid-air,... 

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.

Figure 6.10 Contact angle 0of a liquid drop resting on a solid surface. The definition of the forces used in the figure eliminates the contribution from gravity.

If, when a liquid drop is placed on a smooth surface, the forces of adhesion between the solid and the liquid are greater than the forces of cohesion of the liquid, then the liquid will spread and will perfectly wet the surface spontaneously. If the forces reach an intermediate balance determined by the interfacial energies ylv, ysj and ysv, then the liquid drop will form a definite contact angle (0) with the solid surface (Figure 4.12). 

Note that the cos J = - cos 9, hence. Equation 6 differs from References 14-16 due to the definition of the contact angle. 

Figure 4.6. Definition of the contact angle 0 for a particle adsorbed at the water-oil interface. Case where the particle is preferentially wetted by (a) water and by (b) oil.

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 ... 

To rate the wetting of powders by water i.e. their hydrophilicity. A definite value can be assigned even in cases where the contact angle is zero. ... 

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. 

Bond failure may occur at any of the locations indicated in Fig. 1. Visual determination of the locus of failure is possible only if failure has occurred in the relatively thick polymer layer, leaving continuous layers of material on both sides of the fracture. The appearance of a metallic-appearing fracture surface is not definite proof of interfacial failure since the coupling agent, polymer films, or oxide layers may be so thin that they are not detectable visually. Surface-sensitive techniques such as X-ray photoelectron spectroscopy (XPS) and contact angle measurements are appropriate to determine the nature of the failure surfaces scanning electron microscopy (SEM) may also be helpful if the failed surface can be identified. 

Since the fiber is heavier than the liquid, it would sink when placed on the liquid if it were not sustained by an upward force caused by the surface tension of the liquid. This force is exerted at the three-phase air-liquid-fiber boundary lines. If the contact angle 0 and the surface tension y are high enough, this upward force can become sufficient to balance the sinking force, and the fiber will come to rest when the two forces become equal, at an equilibrium depth corresponding to a definite value of < . In this situation, as shown in Figure 1, the force exerted vertically upward on a unit length (1 cm.) of fiber, measured in dynes, will be ... 

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 ... 

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