Computer Simulation of the Pre-Heating, Gelation, and Rheology of Acid Skim Milk Systems - Food Colloids: Self-Assembly and Material Science - page 280

2000

low pH

1800

1600

medium pH

1400

1200

reference sample

1000

800 high pH

600

400

200

0

0 20 40 60 80 100 120 140

Time
Figure 8 Number of whey proteins bound to casein micelles as a function of time during
the gelation process for pre-heated samples at different pH. The low pH system
shows a rapid binding in the first few time steps. Eventually in both low pH and
medium pH systems about 30% of the whey particles are directly bound to the
casein micelles, as against 15% in the high pH system and the untreated
reference sample

approached by another whey protein. Though initially the high pH and
untreated systems have very few bonds, they rapidly catch up, and even slightly
overtake the low and medium pH systems. This is due to the effect of the whey
proteins attached to the surface of the casein micelles, which can form fewer
bonds with other whey proteins. The differences in the end are, however, very
small. We note that a bond between two particles is only counted once, so that
a value of 2.5 in Figure 9 implies that, on average, a whey particle has five
bonds with neighbouring particles. The networks in all the systems are heavily
branched at the particle level, but they still form open structures, as could be
concluded from the fractal dimensionalities. In Figure 10 we have plotted the
average number of neighbouring particles within a sphere of radius r of a
central particle for the whey proteins only. All the systems at the end of the
gelation phase as calculated show a linear regime on a double logarithmic scale
with a slope of about 1.7, the fractal dimension D. On extrapolating the linear
regime between r ¼ 4andr ¼ 10 down to r ¼ 2, we find an effective
coordination number of ca. 5, in accordance with the number of bonds
(Figure 9). Extrapolating the fractal regime upwards leads to a crossover to
the homogeneous regime at a correlation length of r 12. That is rather larger

than the size assumed for the casein micelles in this model, and considerably
less than the average distance (

E

B 30) between them at the given volume

fraction.
The other two parameters indicative of the gelation behaviour of the system
are the largest and the average cluster sizes. These are plotted in Figures 11