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)

188 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS In a previous paper ( 1 ), the writer argued that if co and Cw in equation 1 could be regarded as nonequilibrium concentrations in a system where the rate of surfactant migration is slow, the initial surfactant location would be a very important factor in determining the type of emulsion formed. More- over, in systems where the surfactant concentration in the oil phase is not in equilibrium wi. th the aqueous phase concentration, from equation 3, the HLB value of the surfactant system should be considered as a dynamic and not a static value. The experimental data presented indicate that the initial surfactant distribution prior to emulsification can affect emulsion viscosity, particle size distribution, emulsion stability, as well as emulsion type. ]•XPERIMENTAI, As in the previous investigation, most of the experiments were carried out in a clear, plastic emulsification vessel. The dimensions of this vessel as well as the experimental procedure have been described in an earlier paper (1). Prior to emulsification, emulsifiers were dissolved or dispersed in each phase with a laboratory propeller mixer at 600 rpm. The liquids were then placed in a constant temperature bath until the temperature reached 24: ñ 0.1øC. The water phase was first placed in the vessel and the oil phase was then very carefully placed on top of it. The mixer, set at 400 rpm, was then turned on to start emulsification. The emulsion was agitated at this speed for 30 sec and the speed was then increased to 750 rpm. After mixing for another 2 • min, the mixer was turned off, and the type of emulsion was determined immediately. For viscosity measurements, a Brookfield Synchrolectric Viscometer Model LVT * was used. Since only the relative viscosities were required, the results were reported in terms of the readings on the 100 scale. For determining the type of emulsion, a laboratory phase tester was used. This meter was uniformly calibrated to 100 and the maximum reading roughly corresponded to the conductivity of a 0.1•) aqueous solution of sodium chloride. The measurement obtained with this meter was called relative conductivity. Manufactured by Brookfield Engineering Lab, Stoughton, Mass.