Physical Chemistry of Foods

situations intermediate between the two mentioned can occur. This greatly
complicates the determination of an aggregation rate. The reader may have
noticed that the graphs in Figure 13.21 do not have a scale for the rate. This
is because it would mean something different in different systems.
Nevertheless, the trends given have been consistently observed.

Conclusion. Whereas O–W emulsions with small globules (say
< 5 mm) that are covered with protein are very stable to coalescence, partial
coalescence may readily occur if the oil in the globules becomes partly
crystalline. The phenomenon is a good example of the complexity of
stability problems that can be encountered in food systems. There are so
many variables that it is generally not possible to predict quantitatively the
rate of partial coalescence. Nevertheless, it is also a good example in that it
shows how systematic research, making use of the fundamentals of colloid
and surface science, can lead to the unraveling of such a complex problem.

13.6 OSTWALD RIPENING

Most dispersions are polydisperse. According to theKelvin equation(10.9),
the solubility of the material making up a particle is greater for a smaller
particle. For convenience, the equations are repeated here:

sðaÞ

s?

¼exp

x^0

a



x^0 ¼

2 gVD

RT

ð 13 : 32 Þ

wheresis solubility,gis interfacial tension, andVDis the molar volume of
the material in the disperse phase (it equals molar mass over density). If the
particle material is at least a little soluble in the continuous phase, part of it
will be transported from a smaller to a larger particle, because its
concentration in the continuous phase will be larger near a small than
near a large particle. The driving force is adifference in chemical potentialof
the particle material caused by the difference in radius. The transport
phenomenon can be calledisothermal distillation, where the molecules move
bydiffusion. The result is adisproportionationof the particle size: large
particles become larger and small ones become smaller or even disappear.
The whole process is calledOstwald ripening.
The rate of the process depends on the driving force, hence on the ratio
of the characteristic lengthx^0 over the particle radius. Some typical examples
are given in Table 10.4. The rate is, moreover, proportional to the bulk
solubility of the material s? and to its diffusion coefficient Din the