Physical Chemistry of Foods

Rheological Properties. We have seen that the permeability of a
particle gel is related to the fractal structure in a simple way. This is not the
case for the rheological properties, because these are affected by several
variables, of which the quantitative effect often cannot be readily
established.
There is, however, one basic principle, which derives from the fact that
fractal clusters arescale invariant. When a gel is formed, clusters of sizeRg
make bonds with each other via strands at the periphery of the cluster, and
the average number of the strands involved per cluster willnotdepend on
cluster size. Since the apparent surface area of a cluster scales withR^2 g, the
number of junctions between clusters per unit area of cross section of the gel
will scale withR
g^2. By using the equation forRgwe arrive at the following
equation for the shearmodulusof a fractal particle gel:

G¼K^0 ð

aeff

a

Þ
aja=ð^3 
DÞ ð 17 : 18 Þ

HereK^0 is an unknown constant, which contains among other things the
rheological properties of the primary particles. Other variables being equal
(which they usually are not), the modulus will be larger ifaeffandaare
smaller andDis higher.
The magnitude of a depends on the structure of the gel-forming
clusters, as is illustrated in Figure 17.18. The variables are the length of the
stress-carrying strandsLand their elastic constantC(in N?m
^1 ). According
to the values ofLandC, four regimes can be distinguished.

1. Fractal strands. This is the original, and in principle the most
   accurate, model, which proceeds on the assumption that the stress-carrying
   strands are fractal. The value ofxcan vary between almost 0 and 1. The
   model implies that the clusters are highly rarefied and that the strands are
   relatively long and slender. This means quite a lowjvalue, and alsoD
   should be relatively small. These conditions are rarely met, and if they are,
   the very weak gel obtained is prone to restructuring, invalidating the model.


2. Hinged strands. This model is more realistic. Now the bending
   modulus of the strands, which is relatively small, is a factor in the parameter
   K^0. The value ofawould equal 3, and this is often observed. Casein gels
   formed by slow acidification fit this regime.


3. Stretched strands. When microsyneresis occurs in the gel, this leads
   to local shrinkage and hence to stretching of the originally hinged strands.
   This occurs in rennet casein gels. Stretched strands can be observed in an
   acid gel if it has been made by acidification in the cold (2 8 C), followed by
   slowly heating up: a gel is then formed at, say, 12 8 C, and upon further
   heating the primary particles shrink to a significant degree, causing the