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(1993) showed that the strength of inter-micellar attractions can be calculated
from the measured yield stress.
15.8.5.3.
Phenomenological Description of Time-Dependent Behaviour
Milk concentrates can exhibit two forms of time-dependent rheological
behaviour: thixotropy (the decrease in viscosity with time at constant shear
rate) and age thickening (the increase in viscosity with storage time). These
can be directly related: age thickening is caused by gradual structure devel-
opment which at a certain point starts to result in thixotropic behaviour, the
time-dependent breakdown of developed structure when the age-thickened
concentrate is sheared.
When concentrates age thicken, the Herschel-Bulkley equation per se or
the Bingham equation has been found to describe adequately instantaneous flow
curves (Bienvenue et al., 2003a, b; Binh Trinh et al., 2007a, b). Bienvenue et al.
(2003a, b) found that the Bingham equation described the flow behaviour of 45
%TS evaporated skim milk concentrates containing different levels of soluble
minerals or different genetic variants of -lactoglobulin, while Binh Trinh et al.
(2007a, b) successfully applied the Herschel-Bulkley equation to reconstituted
whole milks of 40 %TS (the rheological properties of which they had demon-
strated to be essentially the same as those of fresh concentrates).
The rate of viscosity increase during age thickening can be quantified in
terms of the rate of evolution with time of the flow equation constants, or the
rate of increase with time in apparent viscosity, which at a given time is a
function of these constants (V´lez-Ruiz and Barbosa-C´ novas, 1997; Bienvenue
et al., 2003a, b; Binh Trinh et al., 2007a).
Binh Trinh et al. (2007a) developed a novel way of analysing the so-
called hysteresis loop area (the area between the increasing shear rate curve
and the subsequent decreasing shear rate curve on a plot of shear stress versus
shear rate, obtained using the shear sweep function on a controlled shear
stress rheometer). This enabled the evolution of thixotropy with time in
reconstituted whole milks during age thickening to be quantitatively mod-
elled in a way that was independent of experimental limitations.
15.8.6.
Rheometry
Rheological properties can be measured with a wide range of proprie-
tary viscometers and rheometers, varying in sophistication and versatility
(McCarthy, 2006). Many instruments are equipped with computerized con-
trol, data acquisition and data analysis, allowing rapid and accurate measure-
ment of rheological properties.
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