OIL-IN-WATER NANOEMULSIONS 339 The degree of pseudoplasticity can also be indicated by the power index (n), which de- creases when pseudoplasticity increases. The applicability of the Power Law model exhib- ited n values ranging between 0.14 (for emulsions prepared with ultrasonic cavitation) and 0.18 (for emulsions prepared with rotor–stator homogenizer) with the regression coeffi cients (r2) ranging between 0.9912 and 0.9973 (Table II). The emulsion prepared with ultrasonic cavitation was found to be more pseudoplastic with the lowest fl ow index. In terms of the consistency coeffi cient (k), the emulsions prepared with ultrasonic cavitation showed the higher consistency. The consistency is an indicator of the viscous nature of the emulsion. At high shear rates, there is some discernible departure from linearity, with the curvature suggesting the attainment of a constant viscosity at high shear rates. Such behavior is expected for shear-thinning systems. Shear-thinning behavior in emulsions can be inter- preted as indicating the presence of weak attractive forces between the emulsion droplets, which give rise to the formation of a weak elastic gel-like network (20). The dependence of the viscosity on the shear rate indicated that the emulsions were typical non- Newtonian in behavior. RHEOLOGICAL CHARACTERIZATION 2: SHEAR STRESS VERSUS SHEAR RATE PLOT Figure 4 is a log/log plot indicating how increasing energy input affects the functional relationship between shear stress and shear rate. It also shows that the data can be ade- quately fi tted to the Herschel–Bulkeley model. The Herschel–Bulkeley model takes the form (21): τ = τ0 + kHBỳα (4) Figure 3. Rheological characterization of 30% w/w palm oil esters-in-water emulsions prepared using rotor–stator homogenizer ( ) and ultrasonic cavitation ( ). Table II Power Law Parameters Obtained From the Data Shown in Figure 3 Fitting to the Power Law Equation Emulsifi cation n k r2 Rotor–stator 0.18 10.6 0.9973 Ultrasonic 0.1378 13.84 0.9912

JOURNAL OF COSMETIC SCIENCE 340 where τ is the shear stress (Pa), τ0 is the apparent yield stress, ỳ is the shear rate (s-1), and kHB and α are model constants. The model accounts for the fact that for any system that possess a network structure, the initial application of shear results in distortion of the network. Once the applied stress is greater than the yield stress, non-Newtonian fl ow will occur. The apparent yield stress values for the emulsions were obtained from the fi tting process and are shown in Table III. The attractive force is one of the colloidal interactions and plays an important role in the increase in yield stress. This is because the magnitude of yield stress depends on the strength of the attractive force between the droplets (22). The decrease of droplet size resulting from the increase in the disperse phase volume fraction causes an increase in the total droplet surface area. When the total droplet surface area increases, the strength of the attractive force increases accordingly. Thus, greater stress is required to initiate fl ow when a high attractive force is holding the droplets resulting in high yield stress (22). A very low yield stress may indicate a tendency to separation. RHEOLOGICAL CHARACTERIZATION 3: FREQUENCY DEPENDENCE OF DYNAMIC MODULI The viscous and elastic responses of viscoelastic systems can be quantifi ed by dynamic oscillatory measurements. Profi les showing frequency dependence of dynamic moduli for emulsions prepared with rotor–stator homogenizer and ultrasonic cavitation are given in Figures 5 and 6, respectively. The data show how the storage modulus, G′ and loss mod- ulus, G″ change as a function of frequency. These ω dependence of dynamic moduli sug- gest that G′ response of these samples is dominant over G″ response throughout the entire measured ω domain, implying that solid-like (elastic) property dominates over liquid-like (viscous) property in these emulsion samples. This indicates the presence of a Table III Herschel–Bulkeley Parameter Obtained From the Data Shown in Figure 4 Emulsifi cation Yield stress (Pa) Rotor–stator 7.29 Ultrasonic 10.98 Figure 4. A plot of shear stress as a function of shear rate for 30% w/w palm oil esters-in-water emulsions prepared using rotor–stator homogenizer ( ) and ultrasonic cavitation ( ).