Physical Chemistry of Foods

ongoing aggregation leads to the formation offractal aggregates. Figure
13.7a shows an example: it is seen that the aggregate has an open structure,
for the most part consisting of fairly long and branched strands of particles.
If aggregation occurs under the same conditions, while the number of
particles in an aggregate is varied (for instance by varying the duration of
aggregation), it turns out that a simple relation is found between the size
of an aggregate and the number of particlesNpthat it contains:

Np¼

R

a

D

ð 13 : 12 Þ?

as illustrated in Figure 13.7b. Hereais the particle radius andRany type of
radius that characterizes the aggregate. The constantDis called thefractal

FIGURE13.7 Fractal aggregates. (a) Side view of a simulated aggregate of 1000

identical spherical particles of radiusa(courtesy of Dr. J. H. J. van Opheusden). (b)

Example of the average relation between the number of particles in an aggregateNp

and the aggregate radiusRas defined in (a). The fractal dimensionalityD¼tany;its

value is 1.8 in this example. The region between the dotted lines indicates the

statistical variation to be encountered (about 2 standard deviations).