166 JOURNAL OF COSMETIC SCIENCE 4 nm (and, therefore, the concentration of the polyfructose in this layer is high and this increases the free energy ox mixing according to equation 2) and (iv) enhanced steric stabilization as suggested by Napper (8) for polymers with multi-attachment points. The hydrophobically modified inulin surfactant can also stabilize the emulsions against Ostwald ripening. The latter arises from the difference in solubility between the small and large droplets. During storage, oil molecules will diffuse from the smaller droplets (which have higher solubility due to their higher curvature) to the larger droplets (with lower solubility due to the smaller curvature). This process can be prevented by using polymers that adsorb very strongly at the O/W interface. As discussed by Walstra (12), this strong adsorption results in an increase in dilatational elasticity, thus reducing the process of diffusion from the small to the large droplets. W/O EMULSIONS STABILIZED WITH PHS-PEO-PHS BLOCK POLYMER W/O emulsions (with the oil being Isopar M) can be prepared using PHS-PEO-PHS block copolymer at a very high water volume fraction (0.7). These emulsions have a narrow droplet size distribution, with an average radius, R, of 183 nm. They also remain fluid up to high-volume fraction (0.6), as is illustrated in Figure 13, which shows the viscosity-volume fraction curves for the emulsion (13). The effective volume fraction, 'Peff, was calculated from the relative viscosity, 'llr, using the Douherty-Krieger equation (14): 200 150 100 � 50 0-1------....-------....---------------------t 0.4 0.5 0.6 0.7 0.8 0.9 volume fraction Figure 13. Viscosity-volume fraction curves for W/O emulsions stabilized with PHS-PEO-PHS block copolymer. o, experimental points ■, calculated using equation 4.

EMULSION STABILIZATION 167 (4) where [T)] is the intrinsic viscosity that is equal to 2.5 for hard-spheres and 'P p is the maximum packing fraction that was found to be 0.84 (which is a reasonable value for a polydisperse system). From 'P eff and 'P, the adsorbed layer thickness, 8, was calculated using equation 5: (5) where 8 was found to be -10 nm at 'P = 0.4 and decreased with an increase in 'P as a result of the possible interpenetration and/or compression of the PHS chains. The emulsions remained stable both at room temperature and 50°C for several months, and there was no evidence of flocculation and/or coalescence, as assessed by using rheological measurements for concentrated W/0 emulsions. This stability is expected since the anchor chain (PEO) is soluble in water and insoluble in oil, thus ensuring lack of displacement of the polymer molecules. The PHS chains remained strongly solvated by the oil molecules both at room temperature and at 50°C, and this ensured effective steric stabilization. CONTROL OF CREAMING OR SEDIMENTATION OF EMULSIONS Creaming or sedimentation can be controlled by addition of "thickeners" in the con- tinuous phase. Most of these thickeners are high-molecular-weight polymers such as hydroxyethyl cellulose (or its hydrophobically modified version, referred to as associative thickeners), xanthan gum, alginates, carbomers (e.g., Carbopol), etc. All these materials produce non-Newtonian systems above a critical concentration. This non-Newtonian behavior can be expressed from plots of shear stress, CT (Pa), as a function of shear rate, 'Y (s - \ as is illustrated in Figure 14, referred to as psudopolastic flow. 17/Pa.s cr/Pa y/s-1 y/s-1 Figure 14. Shear stress and viscosity as a function of shear rate for a psudoplastic system.