SPREADING, HLB, AND EMULSION STABILITY 327 If one places a drop of liquid on a surface (and the surface may be either a solid or another liquid) one of two things will happen. Either the drop will take up a more or less hemispherical shape on the surface, or it will spread to cover the surface. The question of which one of these events will occur is a function of the surface and interfacial tensions, and the exact relation is quite readily found. Let us imagine a cylinder of liquid, which for convenience we will assume to be one square centimeter in cross section (Fig. 1 A). Imagine that we may in some way pull it apart at the plane marked s. (Harkins has pointed out that this is exactly the problem of determining the tensile strength of the column of liquid. Unfortunately, there is no convenient way to clamp the liquid into a tensile strength tester.) When we pull apart the column, an additional 2 sq. cm. of surface has been created. From the definition of surface tension, the work (really a free energy) involved is given by /4/e = 25' (1) where///c is called the work of cohesion. Now let us perform a second intellectual experiment. Imagine now a second such column, but this time made up of two different liquids, with an interface at the plane s (Fig. 1 B). If we now pull this column apart at s, we create one square centimeter of surface of each of the liquids, but we lose one square centimeter of interface. Hence the work involved is •f• = w + w - 5'• (2) where 74 and y• are the surface tensions of the liquids, X•B is the inter- facial tension and///4 is known as the work of adhesion. Now, in order for one liquid to spread on another, it is merely necessary that the work of adhesion between the two liquids be greater than the work of cohesion of the liquid to itself. This may be put another way by de- fining a quantity called the spreading coe•cient, defined as 8 =/vA - we (3) Clearly, for spreading to take place, S must be positive. By combining equations. 1, 2 and 3, we can define S in terms of meas- urable quantities (in liquid systems) 8 = vB- va - 5',t• (4) where equation 4 defines the spreading coefficient for the case of liquid •/ spreading on liquid B. Now let us consider the application of this to the problem of the stability of emulsions. Consider the fate of an oil droplet, for example, in an oil- in-water emulsion. Imagine that, as in Fig. 2, this droplet rises through the emulsion (whether through creaming or as the result of random motion)

328 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS until it reaches the surface. At this point, one of two things will happen. In one case, the oil drop will spread on the surface and become a film of oil, losing its identity as a droplet. In the other, it will not spread and will, in due course, return to the body of the emulsion. In the first case, of course, repetition of the process leads to breaking of the emulsion. Clearly then, a negative spreading coefficient between the phases of the emulsion is necessary to ensure the stability of the emulsion. so UNSTABLE STABLE so Figure 2.--The effect of spreading coefficient on the fate of an emulsion droplet at the emulsion-air interface. The validity of this rather simple point of view may be established in a number of ways. For example, we know, as the result of a large number of years of experience, that the HLB number is, in fact, rather intimately related to emulsion stability. This is true in the sense that an emulsion, made up to the so-called "required HLB" for a given oil phase, is afortiori a stable emulsion. Thus any parameter which is a measure of emulsion stability must be correlatable with HLB. In order to perform this correlation two spreading coefficients were de- fined: al = q/ 8oln. aq. -- (Toil -[- Tint.) $2 = q' •oX•. oi, - (3'•q. + •'i•t.) (Sb)