Computer Simulation of the Pre-Heating, Gelation, and Rheology of Acid Skim Milk Systems - Food Colloids: Self-Assembly and Material Science - page 282

5000

reference sample

4500

4000

3500

high pH

3000

2500

2000

low pH

1500

1000

medium pH

500

0

0 20 40 60 80 100 120 140

Time

Figure 11 Number of particles (small and large) in the largest cluster of the gelling
sample as a function of time in the simulations. Only the untreated sample
actually shows the characteristic S-shaped curve of the cluster-cluster aggre-
gation process. The low pH and (especially) the medium pH sample may not
have fully formed a multiply percolating network in the image box

and 12, respectively. Monodisperse samples exhibiting diffusion-limited aggre-
gation have an S-shaped curve that gives a clear indication of the transition
between the initial stage, in which cluster-cluster aggregation is the dominant
phenomenon, and the final stage, in which smaller clusters attach to the gel
backbone. We can identify the gelation time with the symmetry point of the
curve, when about 50% of the particles are part of the largest cluster. In reality
the percolation point will be reached slightly earlier, but that time is more
difficult to assess, and for comparison between the different systems it probably
does not matter very much which is taken. In order to have a sample
with gel-like behaviour, a single percolating strand does not suffice. Actually,
Figure 11 shows that only the untreated sample gives more or less that
distinctive shape, indicating that the pre-heated simulations may not actually
have formed a percolating cluster. The largest cluster in the high pH system
does contain over 50% of the particles. Upon visual inspection of the config-
urations in the simulations with the largest cluster drawn in a different colour, it
could be observed to stretch across the image box - as do the largest clusters in
low and medium pH systems, although they do not actually form a continuous
connection across the box.
The average cluster size in the percolating samples is higher than in the non-
percolating ones, as can be expected; but the difference is much less clear than
for the largest cluster. Most of the particles in all the simulated systems studied
here are part of rather large clusters. Figure 12 shows that the average cluster
size for the low pH system is somewhat lower than that for the medium pH
system, even though the largest cluster is larger (see Figure 11). This apparent