Physical Chemistry of Foods

which is the volume fraction of the material that is in droplets containing
crystals. This is not necessarily the fraction frozen: if the material is a
mixture of components—as is nearly always the case in practice—it will
generally have a melting range, implying that part of each drop can remain
liquid. Ifydoes not increase any more with time, it is assumed that the
maximum valueymaxhas been reached. In a temperature region whereymax
increases with decreasing temperature, nucleation will be predominantly
heterogeneous. Assuming that the distribution of catalytic impurities over
the droplets is random, i.e., obeys Poisson statistics,Ncatcan now be derived
from

ymax¼ 1 
expð
vNcatÞ

v¼

pd 633

6

ð 14 : 14 Þ

wherevis volume-weighted average droplet volume (see Section 9.3 for size
distributions). For very small values ofvNcat, we haveymax¼vNcat; for

FIGURE14.9 Nucleation in oil-in-water emulsions.ymaxis the volume fraction of

droplets containing crystals after 24 hours keeping at temperatureTc;Thomis the

approximate homogeneous nucleation temperature and Teq the equilibrium

temperature (clear point). (a) Tristearate in paraffin oil. 1 and 2, cooling curves of

highly purified and not purified tristearate, respectively; 3, heating curve. (b) Mixture

of triglycerides. Calculated cooling curves for heterogeneous nucleation of emulsions

with various average droplet volumev, indicated inmm^3. S denotes an example of

surface nucleation.