FIGURE 9.12 The turbidity of an emulsion depends on the droplet size and wavelength.

These equations have to be modified for polydisperse emulsions to take into account the fact that each droplet has its own scattering profile (Hernandez and Baker 1991). It should be noted that Equation 9.31 is only applicable to emulsions in which the relative refractive index is close to unity and the size of the droplets is greater than the wavelength of light.

The variation of emulsion turbidity with droplet size and wavelength is illustrated in Figure 9.12. The dependence of scattering on droplet size can be conveniently divided into three regions: long-wavelength regime (r<< X), intermediate-wavelength regime (r~ X), and short-wavelength regime (r >> X). The turbidity is greatest in the intermediate-wavelength regime, where the size of the droplets is similar to that of the wavelength. The wavelength of light varies from about 0.3 to 0.7 |im, and therefore droplets of this size would be expected to scatter most strongly.

Experiments with citrus oil-in-water emulsions have shown that there is a maximum in their turbidity (at 650 nm) when the droplets have a diameter of just under 1 | m (Hernandez and Baker 1991). This has important implications for the formulation of food beverages because it means that the characteristic turbidity of a product can be obtained using a lower concentration of oil when the droplet diameter is optimized to give the maximum amount of scattering. Nevertheless, other factors which depend on particle size also have to be considered, such as the stability of the product to creaming or sedimentation.

The influence of the relative refractive index on the scattering cross-section of an emulsion is illustrated in Figure 9.13. The scattering is minimum when the droplets have a refractive index equal to the surrounding liquid, but increases as the refractive index moves to higher or lower values. The refractive index of pure water is 1.33 (Walstra 1968), while that of most food oils ranges between 1.4 and 1.5 (Formo 1979).* The refractive index of aqueous solutions depends on the type and concentration of solutes present (e.g., proteins, sugars, alcohols, and salts) (Figure 9.14). At high concentrations of these components, it is possible for the refractive index of the droplets to be matched to that of the surrounding liquid, which greatly reduces the degree of scattering by the droplets and therefore causes the emulsion to appear transparent (Taisne et al. 1996). This effect can clearly be observed by diluting an oil-in-water emulsion in a series of aqueous solutions that contain different concentrations of sucrose. An emulsion which appears optically opaque when the droplets are dispersed in water becomes transparent when they are dispersed in a concentrated sugar solution (~60%), even though the droplet size and concentration are unchanged.

* It should be noted that the refractive indices of substances vary with wavelength (Walstra 1968).

FIGURE 9.12 The turbidity of an emulsion depends on the droplet size and wavelength.

FIGURE 9.13 Influence of refractive index on the degree of scattering from emulsions. The scattering is smallest in the region where the droplet and continuous phase have similar refractive indices, but increases at lower or higher values. Absorption and Scattering in Concentrated Emulsions

The optical characteristics of concentrated emulsions can be described by the Kubelka-Munk theory (Francis and Clydesdale 1975, Hutchings 1994). This theory enables one to determine the relative amounts of scattering and absorption in a concentrated emulsion from measurements of the light reflected from it:

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