Physical Chemistry of Foods

dis much smaller than the wavelength (Rayleigh scattering), the amount of

light scattered by each particle is about proportional tod^6 ,l
^4 and (m
1)^2 ;

since the volume of a particle is proportional tod^3 , the total scattering per

unit volume (or mass) of particles is proportional tod^3. As the particles

become larger, the dependence of scattering ondand onlbecomes weaker,

and finally total scattering decreases with increasingd=l. This is illustrated

in Figure 9.8. It is seen that scattering is at maximum ford?Dn=l& 0 :5. For

visible light (averagel¼ 0 : 55 mm) andDn¼ 0 :1, this yields for the optimum

dabout 3mm. We can now understand that the appearance of an emulsion

of oil in water (jbeing, e.g., 0.03) will depend on droplet size as follows:

d& 0 : 03 mm: grayish, almost transparent

d& 0 : 3 mm: blueish, transmitted light being red

d& 3 mm: white

d& 30 mm: less white, maybe some color

The smallest particles hardly scatter light. For those of about 0.3mm

scattering greatly increases with decreasing wavelength. This means that

blue light (shortl) is scattered far more intensely than red light (longl),

FIGURE9.8 Turbidity or total scattering per unit mass of particles as a function of
particle sized, refractive index differenceDn, and wavelengthl. Approximate results
for smallDn. The arrows denote droplets of 0.03, 0.3, and 3mm for an average oil-in-
water emulsion atl¼ 0 : 55 mm.