Colloidal gels from proteins and peptides - Physical Gels from Biological and Synthetic Polymers - page 268

9.3.3 Syneresis and permeability

Fractal analysis has been applied to confocal scanning laser microscopic (CSLM) images
and permeation results of casein gels, and the fractal dimensional df, f , lower cut-off length
r 0 (see Equation ( 2.37 )) and apparent pore size of the linear scaling regime calculated
from microscopy data. Values of df f and apparent pore size were also calculated from
permeability data (Mellema et al., 2000 ). During ageing of the gels, a coarsening of the
structure was observed; the pore size increased and the clusters became more compact.
This was re ected in the fractal parameters, since both r 0 and pore size increased during

gel ageing, although values were generally higher than those obtained by computer
simulation. The df f value was also high (~2.2

2.6), which was thought to be an indication
of slow aggregation or rearrangements during aggregation. From these results, it was
concluded that rearrangements such as particle fusion and strand fracture occurred during
gel ageing, and were accelerated by increasing temperature and, even more pronoun-
cedly, by decreasing pH.
Fractal aggregation theories have been applied to the

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flocculation of casein particles by
Bremer et al.( 1993 ). Because fractals ought to be scale invariant, such a gel should also be
scale invariant. In other words, a gel formed from a system with a high volume fraction
(concentration) of particles will resemble a gel with a low particle concentration, when
examined at the appropriate shorter distance scale. Measurements of the permeability of
gels of varying particle concentration can yield information about the effective fractal
dimensionality. For example, the effective fractal dimensionality of one gel was estimated
as 2.39 but by allowing time for the addition of rennet, the permeability was found to
increase, an effect attributed to microsyneresis or rearrangement of the network (Dejimek
and Walstra, 2004 ). The relative rate of change of permeability with time was found to
depend on the casein concentration. At higher concentrations the permeability was found
to change faster than at lower concentration, so Bremer et al.( 1989 )re-estimatedthe
effective fractal dimensionality of the gel before signi cant microsyneresis as 2.23.

9.3.4 Elastic modulus

The enthalpic contribution to the elastic modulus for casein gels was discussed by van
Vliet and Walstra ( 1985 ) and later by Roefs and van Vliet ( 1990 ). The simple power-law
exponent in the concentration dependence of the storage modulus of acid casein gels is
reported to be 2.6, from which Roefs et al.( 1990 ) concluded that the network is very
heterogeneous. Roefs and van Vliet ( 1990 ) examined the magnitude of the dynamic
moduli G 0 and G 00 of acid casein gels as a function of ageing time and temperature,
measuring temperature, pH, ionic strength and composition, casein concentration and the
time scale of the measurement.
By combining these with permeability results, Roefs and co-workers (Roefs and van
Vliet, 1990 ;Roefset al., 1990 ) described acid casein gels as a collection of fractal clusters,
but with different levels. At the first level, protein particles probably do not have a homoge-

neous structure with respect to the distribution of the different casein molecules throughout
the particles. At the second level, the strands and small conglomerates are inhomogeneous,