186 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS played a significant role in deciding the type of emulsion formed (1). By varying the initial distribution of surfactants in the oil phase and aqueous phase, while keeping all other factors constant, it was possible to prepare emulsions having different physical properties. The purpose of this work is to extend the original exploratory findings further and to determine precisely how the initial surfactant location affects the emulsion type. More specifically, the per cent volume of the internal phase at the inversion point, 4, was studied as a function of the initial distribution of surfactants in the oil and aqueous phases. THEORETICAL CONSIDERATIONS The simple phase volume theory of Ostwald (2) proposes that an emulsion will invert when the internal volume exceeds 74.02%. This volume is geometrically derived from the volume occupied by an internal phase consisting of closely-packed, uniform spherical droplets. Although this theory is reported to be applicable to some systems (3), it does not provide a realistic picture for many practical emulsions having wide droplet size distribution or distorted droplets. It is known, for example, that stable O/W emulsions can be prepared with the oil phase well above 90%. It has been recognized for many years that, in addition to the volume of the internal phase, the type of emulsifying agent also has a marked effect on the emulsion type (4). In 1913, Bancroft (5) pointed out an important relationship between the solubility of an emulsifying agent and the type of emulsion. A general rule, derived from Bancroft's work, states that the continuous phase of an emulsion will be the phase in which the emulsifier is most soluble. In terms of the modern HLB (hydrophile-lipophile balance) concept, it has been shown that low HLB surfactants tend to form W/O emulsions and high HLB surfactants tend to form O/W emulsions (6). It has not been until recent years, however, that the concentration of surfactants has been recognized as an important factor in determining the type of emulsion formed. Sherman (7) studied a serie:, of emulsions stabilized with sorbitan sesquioleate and found that 4, the phase volume at which inversion occurs, increases with the amount of the surfactant until its concentration reaches 3.5%. Later, Becher (8) also reported that both the surfactant type as well as the surfactant concentration have significant influence on 4. The importance of the surfactant concentration was also pointed out by Griffin et al. (9) who conducted a series of experimental work with various types o[ oils stabilized with nonionic surfactants.

EMULSION PHASE INVERSION 187 A more quantitative theory relating the surfactant concentration to the emulsion type was developed by Davies (10, 11). He reasoned that the type of emulsion formed as the result of shaking a mixture of oil and water with a surfactant was determined by the relative coalescence rates indicated below: O/W emulsion preferentially stable if Rate 2 Rate 1 ' 1 and, W/O emulsion preferentially stable if Rate 2 Rate I where' Rate 1 = coalescence rate of an O/W emulsion Rate 2 -- coalescence rate of a W/O emulsion From thermodynamic considerations, Davies further suggested that the ratio of coalescence rates was related to the partition coefficient of the surfactant by the following equation: C• Rate2 __ (Cw• 0'75 t:) (1) __ C 2 Rate I \c,, 7 where: C• = collision factor for Rate 1 Cs = collision factor for Rate 2 C,v = surfactant concentration in water Co -- surfactant concentration in oil t3 = fraction of interface covered Furthermore, Davies suggested the following relationship between the coalescence rates and the HLB number' in (C• Rate 2) -- 2.20 (HLB-7) (2) (C2 Rate 1) Combining equation': 1 and 2 the following relationship is obtained' (HLB_7) = 0.36 in (c•) _• (3)