182 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS rive adsorbability of the surfactants with resultant differences in the ex- tent of surface coverage of the oil-water interface in the different cases. One of the questions to which an unambiguous answer still cannot be given is whether the differences in the rates at which free oil appears in the different emulsions are due to differences in intrinsic probability of coalescence or in rate of drainage of residual water from between the deformed oil drops. Another is whether the separation of oil is occur- ring throughout the body of the emulsion or solely at the interface be- tween flocculated emulsion and separated oil. The available evidence is not conclusive (2, 12, 17) on either of these points. However, in all cases, as oil separates the total area of oil-water inter- face decreases, with release of previously adsorbed surfactant to the aque- ous lamellae separating the deformed oil drops. Whether this is trans- ported rapidly to the underlying bulk aqueous phase, thus increasing its concentration throughout, or, more likely, some is readsorbed directly from the lamellae at the residual oil-water interface, the net result would be to increase the coverage of the residual oil-water interface with ad- sorbed surfactant, at least until surface saturation was attained, thereby decreasing the subsequent rate of separation of oil (9). This may well account for the tendency of the rate of separation of oil to decrease with increasing time of centrifugation, approaching zero as a limit, and for the fact that the empirical equation (eq 1) found to describe the behavior of many systems reduces to approximately zero rate of separation of oil at long times of centrifugation. It is useful to identify as many as possible of the processes which must occur during coalescence before free bulk oil appears in the system, since comparison of theoretically calculated rates for such steps with the over- all rate of appearance of oil may succeed in establishing which is the rate- determining step in the sequence, or of transition from one to another rate-determining process as demulsification proceeds. Possible rate-de- termining processes include drainage of solution from the aqueous lamel- lae to the underlying bulk aqueous phase rupture of the adsorbed sur- factant film surrounding the oil globules, presumably dependent on film yield value or viscosity or elasticity desorption of surfactants from the oil-water interface readsorption of surfactants at the oil-water inter- face diffusion of desorbed surfactant from the site .of coalescence through the aqueous lamellae electrostatic effects on the forces of attraction and repulsion between oil globules, affecting the equilibrium distances and the rate of approach and transport of larger oil "drops" through the ttocculated emulsion layer to the site of coalescence to form visible bulk

ULTRACENTRIFUGAL STABILITY OF EMULSIONS 185 oil. Even where absolute rates are uncertain, the relative effect of changes in such operating variables as speed of ultracentrifugation, tem- perature, concentration of surfactant, concentration of added electrolyte, phase volume ratio, drop size as influenced by method of preparation, etc., on possible rate-determining steps can be calculated and compared with its observed effect on the macroscopic rate of oil separation. Earlier stud- ies of this type (9, 17) suggest that interfacial film properties may be more important than the rate of drainage of the residual aqueous phase. Since the flocculated emulsions in the ultracentrifuge resemble foams in their physical structure, it is interesting to test the applicability of foam drainage equations to the present data. Ross (18) considers the following three equations for expressing the rate of drainage of water from foam, and applies them to the reported stability of the emulsions of King et al. (3, 4) equating the volume of oil remaining in the emulsion after a specified length of time with the amount of water remaining in a foam after drainage. Vd = Vo(1 - e -et) (5) Vo - Vd 1 Vo - (bt + 1)I/2 (6) •100 V•N 1/2 + kt = log /100V•/¾ 2 7) where V is the volume of oil remaining in the emulsion after time t, Vo is the initial volume of oil in the emulsion, Va is the volume of oil sepa- rated from the emulsion, and b and k are experimental constants. The problem has also been treated in some detail by Bikerman (19). Ross (18) reports that the behavior of the emulsions described by King (4) is represented over wide limits by eq 6, whereas the behavior of the less stable emulsions reported by King and Mukherjee (3) is described by eq 7. None of these equations describe properly the separation of oil from the present emulsions. This may be taken as further evidence that in all likelihood the rate of drainage of residual water from the flocculated emulsion in the ultracentrifuge is not the rate-determining step govern- ing the rate of demulsification as measured by the appearance of bulk oil.