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.

184 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Quantitative Comparison o[ Emulsion Stability It would be of great practical value if an accelerated test could be devised for quantitative comparison of the stability of emulsion systems to aid in rapid screening of the effect of changes in emulsification pro- cedures, concentration of surfactants, phase volume ratio, type of emul- sifier, etc., without the need for tedious observation of shelf stability. Ultracentrifugal methods may be useful in this connection, although they suffer from two major handicaps and ultimately must be checked by more conventional methods in any case. The first of these, already discussed, is the difference in the physical state of the emulsion in the ultracentri- fuge as contrasted with standing undisturbed in the natural state. The second is the problem of selection of the most meaningful centrifugal criterion for purposes of comparison. The more important of these parameters in terms of which the emul- sions can be compared quantitatively are: (a) the amount of oil which has separated after t minutes of centrifugation (b) the limiting amount of oil which will separate at infinite time, either from an experimental determination or as the extrapolated % 0ilmax Of the empirical eq 1 (c) the value of the constant b in the empirical equation, the larger values corresponding to less stable emulsions (d) the rate of separation of oil after t minutes of centrifugation and (e) the rate of separation of oil after a given constant fraction of that initially present has separated. Illustra- tive values of these parameters for some of the variety of emulsions studied in this work are given in Tables I, II, and III. In addition, use might be made of the quantity of oil separated rapidly at the beginning of centrifugation (extrapolated per cent oil separated at zero time), the length of the induction period in cases where such is present, or the cal- culated value of the rate constant for the process of oil separation in cases where the data fit one of the standard kinetic equations, as may be the case with the Nujol-water-SDS emulsion data. Criteria based on the quantity of oil separated may be of practical interest but are perhaps of less theoretical value since the value includes rather large and variable quantities of oil separated under nonequilib- rium conditions at the beginning of centrifugation. Moreover, because of differences in the steady-state rate of separation of oil, the order of sta- bility found will depend on the time chosen at which to make compari- sons. This is apparent from the tabulation in Table IV based on the data given in Table I. The results with cetyl pyridinium chloride are not included in Table IV because at the same concentration o1• surfac-