## 756 727 679 589 223 1x4 28 4 487 83 325 40 840 708 18 5 31

'Critical surface tension for wetting.

where g is the gravitational constant, h the equilibrium height, p the density of the liquid, y is the surface tension, 6 is the contact angle, and r the radius of the capillary. The surface tension is therefore given by:

The surface tensions of various substances are given in Table 7-1. Equation 7-1 may be written:

2y cos 0

The term ghp is the force driving the liquid into the capillary and is called the capillary pressure.

rises in a glass capillary. On the other hand, creation of new surfaces involves an increase in free energy. For example, when a solid is split, chemical bonds are broken and an electrostatic surface charge thereby created. Therefore, work must be supplied to split a solid, or to create new surfaces in other ways.

Spec ific surface energy is defined as the ratio of work to area. Its dimensions are the same as surface tension: it is expressed in dynes/cm, and the values are numerically equal.

A liquid will adhere to a solid if the attraction of the molecules to the solid surface is greater than their attraction to each other. In other words, the work of adhesion must be greater than the work of cohesion. Thermodynamically this criterion may be expressed as follows:3

where Wadh is the work of adhesion; Fs the surface free energy of the solid; Ft that of the liquid; and Fsl that of the newly formed interface. The work of cohesion is the work of a liquid spreading on itself, and is shown by Equat ion 7-6 to be equal to IF,. The criterion for adhesion therefore is:

where W,oh is the work of cohesion. Therefore the liquid will adhere if:

Attractive forces also exist between two solid surfaces but the surfaces do not adhere when pressed together, because the attractive forces are extremely short range (a matter of a few Angstroms), and the area of intimate contact is very small. Even two smooth, highly polished surfaces have microscopic irregularities, and contact is only between highs, as shown in Figure 7 5.

Figure 7-5. Microscopic section of two solid surfaces showing small area of contact (Schematic).

Figure 7-5. Microscopic section of two solid surfaces showing small area of contact (Schematic).

Adhesives bond solid surfaces together because they fill the irregularities while in the liquid state, and then develop sufficient cohesive strength by drying or setting. Solids can also be bonded together if they are ductile enough to be forced into intimate contact. For instance, the oldtime blacksmith welded two steel bars together by heating them white hot, and hammering them together. For the same reason, shales adhere to a bit or to drill collars if they are plastic enough to be forced into intimate contact by the weight of the drill string (see section on Bit Balling in Chapter 9).

### Surfactants

The term surfactant is the standard contraction for surface active agent, so-called because these agents are adsorbed on surfaces and at interfaces, and lower the surface free energy thereof. They are used in drilling fluids as emulsifiers, wetting agents, foamers, defoamers, and to decrease the hydration of clay surfaces.

Surfactants may be either cationic, anionic, or nonionic. Cationics dissociate into a large organic cation and a simple inorganic anion. They are usually the salt of a fatty amine or polyamine, for example, trimethy] dodecyl am monium chloride:

Anionics dissociate into a large organic anion and a simple inorganic cation. The classic example is a soap, such as sodium oleate:

Nonionic surfactants are long chain polymers which do not dissociate, for example, phenol 30-mol ethylene oxide:

C6FF 0-(CH2CH20)30H

which is known in the drilling industry as DMS.4

Since clay minerals and most rock surfaces are negatively charged, the eletrostatic attraction causes the cationic surfactants to be more strongly adsorbed thereon, because of the electrostatic attraction. Anionic surfactants are adsorbed at the positive sites at the ends of clay crystal lattices and at oil/water interfaces. Nonionics, such as DMS, compete with water for adsorption on the basal surfaces of clay crystals,5 thereby limiting the expansion of swelling clays such as bentonite.

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