Physical Chemistry of Foods

Regime TV. As mentioned, the relation for regime TI can only hold
if Redr>1. Redrcan be obtained by combining Eqs. (11.8) and (5.5). Using
Eq. (11.11) to eliminatee, we obtain

Redr¼

g^1 =^2 r^1 =^2 d^1 =^2

Zc

ð 11 : 12 Þ

This then leads to the condition given in Table 11.2 (d>Zc^2 /gr).
If Redr<1, the flow near a drop is laminar, and it would be broken up
in the regime TV. Now the local flow velocity is needed at the scale of a
dropletd[i.e.,u^0 (d)], and this scale is (much) smaller thanle. According to
the Kolmogorov theory the velocity is given by

u^0 ðdÞ¼e^1 =^2 dZ
^1 =^2 d 5 le ð 11 : 13 Þ

The shear stress acting on the drop is given byZCtimes the velocity gradient
u^0 (d)/d. The flow type is probably close to plane hyperbolic flow, and Figure
11.8 shows that in this case Wecrwill not strongly depend on the viscosity

FIGURE11.9 Examples of the droplet size (distribution) in O–W emulsions

resulting from treatment in a high-pressure homogenizer, at various homogenizing

pressurespH. (a) Volume frequency distributions (f)in%of the oil per 0.1mm class

width versus droplet diameterd;pHindicated in MPa. (b) Average diameterd 32 as a

function ofpHfor various oil volume fractionsj(indicated); the aqueous phase was

a solution containing about 3%protein.