strands to stretch. We now havea¼2, and the parameterK^0 includes the
Young modulus of the primary particles. Its value tends to be much higher
than that of the bending modulus.
- Weak link. Here the clusters are considered to be rigid. Upon
deformation of the gel, the clusters remain undeformed, and only the
relatively weak links between the clusters are strained. This generally means
that bothjandDwill be high, and that the primary particles are quite rigid.
Such systems have rarely been observed in foods.
It may be concluded that the value ofawill generally be 2 or 3,
although intermediate values, or values slightly larger than 3, may also
occur. The dependence of the modulus onjis strong; forD¼2.35, anda
values of 2 and 3, the exponent ofjequals 3.1 and 4.6, respectively. Such
relations are shown in Figure 17.13c (page 716). Because of the uncertainties
in the relation between modulus and volume fraction, it is better to deriveD
values from permeability results.
FIGURE17.18 Various regimes, based on structural models, for the scaling
relations between rheological parameters (especiallyG^0 ) and the volume fraction of
particlesjmaking up the gel network. The circles schematically denote the clusters
forming the gel (of radiusRg); inside only the stress-carrying strands (of lengthL) are
shown. It is assumed that the stress on the system is in the horizontal direction.Cis
the elastic constant of the strands; the parameterais given in Eq. (17.18). Highly
schematic.