330 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS HLB IO CASTOR OIL ON I% EMULSIFIER IN H• o/ 4 -28 -24 -20 -16 -12 -8 -4 0 4 8 Si Figure &--The correlation between spreading coefficient S• for castor oil and aqueous solu- tions of varying HLB. Examination of these data lead to the conclusion that (within the admit- tedly wide limits imposed by the estimation of emulsion stability by visual observation) the most stable O/W emulsions are found when S• has a value which is only slightly negative, i.e., 0 to ca. - 5. The reason for this is not too difficult to find. Although the primitive view which correlated emulsion stability with low interfacial tension has largely been abandoned (7), the effect of the interfacial free energy on the energetics of emulsion formation cannot wholly be disregarded. A low inter- facial tension may thus be classed in the category of what the mathe- maticians call a "necessary but not sufficient" condition for stability. We may therefore modify the requirement in terms of the spreading coefficient to be the most negative spreading coejficient consistent with a low interfacial tension. In practice, this means for O/W emulsions, a value which is barely negative, i.e., ca. - 1, as exemplified by the data of Table 1. We have ob- tained only a limited amount of similar data for the stability of W/O emulsions, but the indications are that here the requirement is the largest negative value of S2. The same conclusion would be drawn by comparison of known required HLB numbers with the spreading coefficient-HLB correlation of various oil phases. Now, how may these conclusions be put to practical use? One may, of course, given a particular emulsion system, systematically vary the ernulsi-

SPREADING, HLB, AND EMULSION STABILITY 331 HLB -- •'• DISTILLED WATER ON I% • EMULSIFIER IN CASTOR OIL --..... IO 8 6 4 2 o -30 -34 -38 -42 -46 -50 -54 -58 -62 -6E Sm Figure 4.--The correlation between spreading coefficient S2 for water and castor oil solutions of varying HLB. tier HLB, and, by means of what are after all quite simple measurements, determine the HLB at which the appropriate negative spreading coeffi- cient appears. On the other hand, let us realize that the spreading coefficient describes a physically realizable process. The spreading of one liquid on another can be observed by anyone with a shallow dish, two liquids, and some sort of dropping pipette. For example, Fig. 5 is a diagrammatic representation of what one ob- serves with a number of 31/2-inch Petri dishes filled with solutions of emulsifiers of varying HLB after one drops onto each liquid surface ap- proximately 0.5 mi. of toluene. Clearly, at about an HLB of 9 we have gone from a spread to a no-spread situation. Thus, HLB = 9 is very closely the required HLB for the formation of a stable toluene-in-water emulsion. It is inter.esting to note that in this particular case, at least, if the nonspreading droplet is left in contact with the substrate for a short time, a cloud of spontaneously-formed emulsion may be seen surrounding it. A similar type of observation could be made on a series of dishes filled with solutions of the same emulsifier by dropping a graded set of liquids of varying required HLB. This would perinit a definition of the HLB of the surface active agent. Similarly, if it is desired to establish the conditions for stability for a