many of the properties of natural micelles are significantly changed, but the
particles roughly keep their size and shape. Near the isoelectric pH (4.6), the
protruding chains collapse, and aggregation occurs. If the acidification
proceeds slowly, an ‘‘acid gel’’ is formed. A gel can also be obtained by
dissolving sodium caseinate in a buffer (neutral pH, ionic strength about
0.07 molar), followed by slow acidification. Neither acid nor rennet gels are
formed at temperatures below 10 8 C.
ThepermeabilityB, as defined in the Darcy equation (5.24), is a useful
parameter to characterize the fractal nature of particle gels (apart from
being important in practice). It can be readily measured under conditions
where the flow through the gel does not alter gel structure. The largest holes
in the gel have a radius close toRg. According to Eq. (5.23), the flux through
a pore of that radius would be proportional toR^4 g. The number of these
large pores per unit cross section of the gel will be proportional toRg^2 ,
leading toBbeing proportional toRg^2. Furthermore,Rgis proportional to
aeff, and by use of Eq. (13.15) we obtain
B¼
a^2 eff
Kj^2 =ðD^3 Þ ð 17 : 16 ÞThe value of the proportionality parameterKwill depend on structural
details. It must be larger than unity, since we have taken the largest pores as
a reference; in practice,K¼50–100 is observed.
Linearity between logBand logjis well obeyed for casein gels. From
the slope of the line,Dcan be calculated, and for acid gels, values between
2.35 and 2.4 are observed, in good agreement with simulation results. For
rennet gels, the slope yieldsD¼2.2–2.25.
Short-term rearrangements, i.e., changes in particle arrangement
occurring before gel formation, cause an increase inaeffaccording to Eq.
(13.19) [Np=np¼ðR=aeffÞD, wherenpis the number of primary particles in a
building block] and hence inB. For acid casein gels (about 3%casein), the
extent of rearrangement greatly depends on the temperature of formation.
For instance, at 20 8 C,B¼0.13mm^2 , andnp¼1 was observed, i.e., no
rearrangement; at 30 and 40 8 C,npwas 25 and 45, respectively, hence
considerable rearrangement, with a corresponding increase inB(about 1
and 3.5mm^2 , respectively). For rennet gels made at 30 8 C,Bwas smaller
(0.25mm^2 ) withnp&8. However, if renneting takes place at a lower pH, the
permeability tends to be higher: see Figure 17.16a.
Long-Term Rearrangement. This concerns changes after the gel
has formed. Figure 17.16a shows that such changes occur in rennet gels,
since theBvalue increases with time after gel formation. This can go along