Physical Chemistry of Foods

Theparticle Reynolds number, given bydvrc=Zc, must be smaller than

about 0.1, since otherwise turbulence will develop in the wake of the

sedimenting particle, decreasing its velocity. Puttingv¼vS, it turns

out that for an oil drop in water, the critical particle size is 140mm.

The particle must not be subject toother forcescausing their motion.

This can involve Brownian motion or weak convection currents.

These will disturb sedimentation for particles smaller than about

0.2mm (assumingC4 0 :1s
^1 ).

The continuous phase should be aNewtonianliquid. This is often not

the case.

Non-Newtonian Liquids. If the shear stresssin a liquid is less
than proportional to the velocity gradientC, the liquid is said to bestrain
rate–thinningand the viscosity is an apparent one; see Section 5.1.3. The
magnitude ofZathen will depend on the strain rate, or the shear stress,
applied; examples are in Figure 13.10. The stress acting on a sedimenting
particle is equal toFBover the particle surface area and is thus given by
Drgd/6. For an oil drop in water of 5mm size this stress would then be
6? 10
^4 Pa. The viscosity to be used in the Stokes equation should thus be
determined at this value ofs. Many rheometers cannot give results at a
shear stress below 0.1 or even 1 Pa, and the viscosity measured then may
be far from relevant, as seen in Figure 13.10. In other words, the
sedimentation rate so calculated would be greatly overestimated.

Polydispersity. In practice, we are often interested in the amount
of material arriving in the sediment (or cream) layer per unit time. An
instrumental relation results ifvis divided by the maximum sedimentation
distance (height of the liquid)H; by using the Stokes velocity we obtain

Q¼

vS

H

¼

gDr<d^2 >

18 ZcH

ð 13 : 24 Þ

whereQis the volumetric proportion of the particles reaching the sediment
per unit time. Since the particles vary in size, an average should be taken.
See Section 9.3.1 for an explanation of size distributions. The volume of
particles in each size classiis proportional tonidi^3 , and to obtain its
contribution toQit has to be multiplied by the particle velocity, which is
proportional todi^2. Summing over the size classes and dividing by the total